Proceedings of the
26th international
free electron laser conference& 11 th fel users workshop

Rene bakker
luca giannessi
marino marsi
richard walker
editors

FEL2004
Proceedings of the
26th International Free Electron Laser Conference and11th FEL Users Workshop
August 29 to September 3, 2004
Stazione Marittima, Trieste, Italy

René Bakker
Luca Giannessi
Marino Marsi
Richard Walker
Editors

Published by
Comitato Conferenze Elettra
S.S. 14 – km 163.5 in Area Science Park
I-34012 Trieste
Italy

PROCEEDINGS OF THE
26TH INTERNATIONAL FREE ELECTRON LASER CONFERENCE AND
11TH FEL USERS WORKSHOP

ISBN: 88-87992-02-9

Printed in Italy by Graphart ts

Foreword
The 26th International Free Electron Laser Conference and 11th FEL Users Workshop were held between
August 29th and September 3rd , 2004 at the beautiful seafront location of the Stazione Marittima congress
centre in Trieste, Italy. The Conference and Workshop, known as FEL2004, was organised by Sincrotrone
Trieste, home of the third generation synchrotron light source ELETTRA, the EU funded storage ring freeelectron laser (EUFELE), and the VUV single-pass FEL project FERMI. A total of 287 participants from 18
different countries attended the conference, making this one of the biggest ever conferences. A total of 62 talks
and 158 posters were presented and 184 papers were accepted for publication in these proceedings.
FEL2004 marks the 25th Anniversary of the International FEL Conference, and incidentally 20 years since
the first FEL conference held in Italy, in Castelgandolfo. This marked an appropriate moment look back on theachievements since then, and to consider the future prospects for the field as well as the FEL conference itself.
At the time of the first international FEL meeting held at Stanford in 1979, later classified as the first of
the International FEL Conference series, only one FEL had actually operated, namely the Stanford oscillator,
which first lased in 1977. Since then remarkable progress has been made in the power and spectral range of
operating FELs as well as in their scientific applications. The programme of FEL2004 reflected the very active
nature of the field, and we thank the members of the International Programme Committee for putting together abalanced program highlighting both the current activity and the exciting prospects ahead. We also thank Mike
Poole for a lively personal summary of the FEL field over the last 25 years in the concluding session.
The social programme of the conference included an excursion to the Roman ruins and the magnificent
11th Century basilica with its impressive floor mosaics in Aquileia, and to the town of Grado with its sandy
beaches, its old historic centre, and picturesque harbour. The excursion was followed by a banquet in the
Savoia Excelsior Hotel opposite the conference centre. Following tradition, the FEL Prize was awarded during
the banquet and this years recipients were Hiroyuki Hama and Vladimir Litvinenko for their fundamental andpioneering contributions in Storage Ring Free Electron Lasers (SRFELs).
We would like to express our sincere gratitude to Sincrotrone Trieste for hosting the Conference and tothe members of the Local Organising Committee, and in particular the Local Organising Coordinator Carlo
Bocchetta, for their hard work in taking care of the many organisational aspects of the conference. Special
thanks are due also to Ivan Andrian of Sincrotrone Trieste and his team for organising the abstract and paper
submission as well as the new electronic proceedings.
On behalf of the International Executive Committee (IEC) and local organising committee we would also
like to express our thanks for the generous financial support received from the following institutions: Area
Science Park, Italy, the Council for the Central Laboratory of the Research Councils (CCLRC), UK, Consiglio
Nazionale delle Ricerche (CNR), Italy, Deutsches Elektronen-Synchrotron (DESY), Germany, Ente per leNuove Tecnologie, l’Energia e l’Ambiente (ENEA), Italy, the Istituto Nazionale di Fisica Nucleare (INFN),
Italy, the Regione Autonoma Fiuli Venezia Giulia. The conference also benefited from the financial supportof the 12 industrial exhibitors, listed elsewhere. All of this helped to balance the conference budget as well as
to provide financial support for 10 young researchers who would not otherwise have been able to attend theconference.
This year sees an end to a 20 year old tradition to publish the Conference Proceedings in the journal Nuclear
Instruments and Methods in Physics Research. This decision was reached after an intense debate over several
months amongst the members of the IEC, taking into account the opinion of the FEL community who had
responded in November 2003 to a questionnaire on publication policy with a 2:1 vote in favour of changing
to electronic publication on the Joint Accelerator Conference Website (JACoW). The organisers of FEL2004iii

hope that the rapid publication and the benefits of being included in the JACoW group of conferences willserve the FEL community well in future years.
In keeping with the usual policy, only those papers presented at the conference, either orally or as a poster,
are included in these Proceedings. The change in publication policy has also implied a significant change
in the refereeing of the papers. Since the proceedings do not have refereed status, the decision has beentaken to only perform a light refereeing by members of the International Program Committee to ensure thatminimum standards of readability and content are met. At the same time, authors have been encouraged tosubmit extended articles to the online refereed journal Physical Review Special Topics Accelerators and Beams(PRST-AB), which has agreed to publish a Special Edition of FEL Conference related papers.
Another issue that causes continuing debate amongst the FEL community, which surfaced also at this years
conference, was the question of whether to maintain annual conferences or change to conferences in alternate
years. This year the IEC debated the issue at length and found itself closely divided. To resolve the issue, apoll of the conference attendees was organized in the form of a show of hands. This indicated an approximate
2:1 majority in favour of the status quo, which subsequently swayed the IEC to vote in favour of retaining
annual conferences. Having received and considered bids for FEL2007, the decision was then taken to award
the organisation of FEL2007 to the Budker Institute of Nuclear Physics in Novosibirsk, Russia.
On its 25th anniversary, this years International FEL Conference therefore marks a significant change in theway its proceedings are published. Other important aspects of the conference remain the same for some timeat least: for example, the traditional annual conference, a testimony to the fact that there is no lack of interestin hosting or attending FEL conferences and of the exciting times ahead for the FEL field.
René Bakker
Luca Giannessi
Marino Marsi
Richard P. Walker

iv

FEL Prize
The International Free Electron Laser Prize is awarded each year to recognize individual researchers fortheir outstanding contribution to the field. At the 26th International Free Electron Laser Conference the prize
for 2004 was awarded to Hiroyuki Hama (Tohoku University) and Vladimir Litvinenko (Brookhaven National
Laboratory), in recognition of their fundamental and pioneering contributions to Storage Ring Free Electron
Lasers (SRFELs).

Hiroyuki Hama (left) and Vladimir Litvinenko (right) receiving the 2004 FEL Prize
from the FEL Prize Committee Chairman, Stephen Benson (centre)

Vladimir Litvinenko and Hiroyuki Hama have performed fundamental and pioneering contributions in
Storage Ring Free Electron Lasers (SRFELs). Thanks to their deep understanding of the FEL and to theirachievements, they have promoted the use of SRFELs in a broad scientific community, from synchrotron
radiation to nuclear physics.
They have both worked innovatively at the frontiers of SRFELs. V. Litvinenko installed the electromagnetic
optical klystron OK4 on the by-pass of VEPP3 at Akadiemgorodok (Russia) in 1988, and H. Hama installed
the first optical klystron with adjustable planar-to-helical field in 1996 on UVSOR in Okazaki (Japan). These
improvements produced new short wavelength records for FELs: 240 nm for VEPP3 SRFEL in 1988, 238 nm
for the UVSOR SRFEL in 1996. Then, after a move by Litvinenko to Duke University, 226 nm in 1998, andto 193 nm in 1999.
They have both been very active in advancing the understanding of storage ring FEL dynamics, H. Hama
performed very early systematic sophisticated experimental analysis of the FEL micro-pulse temporal andspectral distribution versus time for different operating conditions starting in 1994. He also carried out detailed studies on FEL performances for different momentum compaction factors. V. Litvinenko developed acomplete theoretical model of giant and super pulses whose findings are in good agreement with measurements
performed on the DUKE FEL, and used super pulses to produce strong coherent harmonics.
They have developed technological improvements to SRFELs that improve the device for users. Hamadeveloped a feedback system to maintain the FEL pulse at perfect synchronism, leading successful pumpprobe two-color experiments in gas phase using FEL light and synchrotron radiation for the first time. A
transverse feedback system was developed in Duke FEL to stabilize beam operation.
A very important contribution of their work has been the production of monochromatic gamma-rays byCompton Back-Scattering with SRFELs. Hama performed the first experimental demonstration at UVSORv

in 1996 in the MeV range. At Duke University, Litvinenko developed a high intensity gamma ray user facility (HIGS), leading to new discoveries in Nuclear Resonant Fluorescence and near-threshold break-up of
Deuterium. This has broadened the use of FELs into the field of nuclear physics.
Besides their leading role in FELs, they continue to make important contributions to the field of physics
as a whole. They have trained many graduate students and have assisted in the commissioning of numerous
synchrotron light sources. Both operated FEL user facilities providing hundreds of hours of FEL light to users
each year. Litvinenko is now working on electron-ion colliders. Hama is involved in the design of the next
generation of storage rings in Japan.
The FEL Prize Committee

Previous FEL Prize Winners
2004 (Trieste) Vladimir Litvinenko and Hiroyuki Hama
2003 (Tsukuba) Li-Hua Yu
2002 (Argonne) H. Alan Schwettman and Alexander F.G. van der Meer
2001 (Darmstadt) Michel Billardon, Marie-Emmanuelle Couprie, and Jean-Michel Ortega
2000 (Durham) Stephen V. Benson, Eisuke J. Minehara, and George R. Neil1999 (Hamburg) Claudio Pellegrini
1998 (Williamsburg) John Walsh
1997 (Beijing) Kwang-Je Kim
1996 (Rome) Charles Brau
1995 (New York) Richard Pantell and George Bekefi
1994 (Stanford) Alberto Renieri and Giuseppe Dattoli
1993 (The Hague) Roger Warren
1992 (Kobe) Robert Phillips
1991 (Santa Fe) Phillip Sprangle and Nikolai Vinokurov
1990 (Paris) Todd Smith and Luis Elias
1989 (Naples, FL) William Colson
1988 (Jerusalem) John Madeyvi

A Tribute to Professor Emeritus
Haruo Kuroda

Professor H. Kuroda will be remembered by the free-electron laser (FEL) community for his enthusiastic
building of the mid-infrared (MIR) wavelength region FEL users facility as one of the most advanced andleading in the world at Noda campus, Science University of Tokyo in 1999 - 2003. He designed and prepared
many users experimental laboratories dedicated to FEL applications in chemistry, physics, material and medical
science and so on, and he started the experimental programs and proposals. After he started routine operationof the mid-infrared region free-electron laser, another FEL in the far-infrared (FIR) wavelength region was justready to start up, and many experiments were planned using both of the MIR and FIR free-electron lasers.
It has been extremely regrettable that Professor H. Kuroda and his followers did not have the possibility
to add their new and fruitful findings using the FELs to his famous, pioneering work in the early history ofsynchrotron radiation sciences because he passed away so suddenly, after contracting interstitial pneumonia,
on the 4th May, 2004. On behalf of the FEL community in Japan, I would like to ask you, all of his friends andhis acquaintances in the world, that now we would share the deep sense of loss and pray for the soul of the lateProfessor H.Kuroda.
After his Buddhist funeral ceremony in the 7th May 2004, the Japanese Government decided to confer adecoration from His Majesty the Japanese Emperor for his great academic contributions. His conferment isnamed The Order of the Sacred Treasure, Gold Rays with Neck Ribbon.
Professor H.Kuroda’s biographical outline is briefly described below. As one of the heartful tributes given
by his old friends in the synchrotron radiation community records (The Independent, England, 27th May 2004)“Haruo Kuroda was one of the world’s foremost experts on the design and application of synchrotron radiation
to the elucidation of a wide range of scientific problems. Haruo Kuorda was a humble, almost self-effacing
individual, short in physical stature, but towering in his intellectual energy and authority”. He will be sadly
missed by all who knew him.

Eisuke John Mineharavii

Haruo Kuroda, Chemist, biographical outline• Born in Tokyo, 28 June1931;• Research Associate, Department of Chemistry, University of Tokyo 1960-1968,• Associate Professor, University of Tokyo 1968-1971,• Professor, University of Tokyo 1971-1977,• Department Chairman, University of Tokyo 1977-1979,• Chairman of the Library Council, University of Tokyo 1988-1991;• Chairman of the Advisory Council, Photon Factory, KEK, Japan 1980-2003;• Chairman of the Library Council, National University of Japan 1988-1991;• Professor, Science University of Tokyo 1992-2003,• And Director of Infrared Free-Electron Laser Center 1999-2003;• Married 1958 to Hiroko Fujimoto (two sons);• Died in Tokyo, 4 May 2004.

viii

CONFERENCE ORGANISATION
Organised by
Sincrotrone Trieste, Italy

Conference Chairs
René Bakker (Sincrotrone Trieste)
Richard Walker (DLS)

Programme Committee Chairs

Users Workshop Chair

René Bakker (Sincrotrone Trieste)
Luca Giannessi (ENEA)

Marino Marsi (Sincrotrone Trieste)

Local Organizing Coordinator

Conference Treasurer

Carlo Bocchetta (Sincrotrone Trieste)

Francesco Antonangeli (Sincrotrone Trieste)

International Executive Committee
I. Ben-Zvi (BNL)
W.B. Colson (NPGS)
M.-E. Couprie (LURE)
A. Gover (Tel Aviv University)
H. Hama (Tohoku University)
K.-J. Kim (ANL & University of Chicago)
Y. Li (IHEP)
V.N. Litvinenko (BNL & Duke University)
G.R. Neil (TJNAF)

C. Pellegrini (UCLA)
M.W. Poole (Daresbury)
A. Renieri (ENEA)
C.W. Roberson (ONR)
J. Rossbach (Hamburg University)
T. Smith (Stanford University)
A.F.G. van der Meer (FOM)
N.A. Vinokurov (BINP)
R.P. Walker (DLS)International Programme Committee
S. Biedron (ANL and MAX-Laboratory)
J. Clarke (ASTeC, Daresbury Laboratory)
M.E. Couprie (CEA)
J. Dai (BFEL)
G. Edwards (Duke U.)
J. Feldhaus (DESY)
M. Ferrario (INFN)
J. Galayda (SLAC)
R. Hajima (JAERI)
H. Hama (Tohoku U.)
T. Hara (RIKEN)
D. Krämer (BESSY)
I. Lindau (SLAC)
A. Lumpkin (APS/ANL)
P. Michel (FZ Rossendorf)

D. Nölle (DESY)
J.S. Oh (PAL)
Y. Pinhasi (The College of Judea and Samaria)
R. Prazeres (LURE)
S. Reiche (UCLA)
M. Shinn (JLAB)
T. Tanaka (RIKEN)
X. Shu (IAPCM)
T. Smith (Stanford U.)
N. Tolk (Vanderbilt U.)
N. Vinokurov (BINP)
Y. Wu (Duke U.)
T. Yamazaki (Kyoto U.)
L.H. Yu (BNL)ix

Local Organising Committee
C. Fiandra
C. Grubissa
P. Michelini
M. Nadalin
G. Risicato
E. Save
R. Skabar
M. Trovò

A. Accettulli
I. Andrian
L. Biecker
C.J. Bocchetta
D. Bulfone
G. D’Auria
G. De Ninno
S. Deiuri
B. Diviacco

Organising Secretariat
the office
via San Nicolò 14, 34121 Trieste, Italye-mail: theoffice@ theoffice.it
web: http:// www.theoffice.it

EDITORIAL TEAM
Paper Reception Desk
C. Grubissa
M. Nadalin
E. Save

M. Antonetti
R. Duimich
C. Garettini

Proceedings Office
I. Andrian
M. Bressan
P. Craievich
S. Deiuri
R. De MonteV. Forchı̀

R. PassuelloG. Penco
C. Roberti
M. Trovò
L. Zambon

Posters

Presentations

S. Di Mitri
G. Risicato
M. Trovò

M. Folla
I. Gregori

Information Technology
C. Allocchio
I. Andrian
A. Cipolat

E. Cocolo
S. Deiuri
M. Stolfa

xINSTITUTIONAL SPONSORS
Area Science Park
Consiglio Nazionale delle Ricerche (CNR)
Council for the Central Laboratory of the Research Councils (CCLRC)
Deutsches Elektronen Synchrotron in der Helmholtz Gemeinschaft (DESY)
Ente per le Nuove tecnologie, l’Energia e l’Ambiente (ENEA)
Istituto Nazionale di Fisica Nucleare (INFN)
Regione Autonoma Friuli Venezia Giulia
Sincrotrone Trieste (ELETTRA)

INDUSTRIAL SPONSORS AND EXHIBITORS
Accel Instruments
Advanced Energy Systems
C.A.E.N. – Costruzioni Apparecchiature Elettroniche Nucleari
CINEL – Strumenti Scientifici
Cinquepascal
CPI – Communications & Power Industries International Inc.
Danfysik
Instrumentation Technologies
LecroyMBE – Mediterranean Broadcasting Equipment
Micos Italia
RMP – Meccanica Progettazione Prototipi
Thales Electron Devices

xi

xii

Contents

Preface
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
FEL Prize . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
A Tribute to Professor Emeritus Haruo Kuroda . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii
Conference Organisation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Sponsors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

FEL Prize Talk and New Lasing
R&D Experiments at BNL to Address the Associated Issues in the Cascading HGHG Scheme
L.H. Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
First Lasing at the ELBE mid-IR FEL
P. Michel, R.W. Dekorsy, P. Evtushenko, F.G. Gabriel, E.G. Grosse, M.H. Helm, M.K. Krenz, U. Lehnert,
W. Seidel, D.W. Wohlfarth, A.W. Wolf, R.W. Wuensch . . . . . . . . . . . . . . . . . . . . . . . .

1

8

FEL Theory
Backward Wave Excitation and Generation of Oscillations in Distributed Gain Media and FreeElectron Lasers in the Absence of Feedback
Y. Pinhasi, Yu. Lurie, G. A. Pinhasi, A. Yahalom . . . . . . . . . . . . . . . . . . . . . . . . . . .
CSRtrack: Faster Calculation of 3-D CSR Effects
M.D. Dohlus, T.L. Limberg . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
A 3D Self-Consistent, Analytical Model for Longitudinal Plasma Oscillation in a Relativistic Electron Beam
G. A. Geloni, E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . .
Benchmark of ASTRA with Analytical Solution for the Longitudinal Plasma Oscillation Problem
G. A. Geloni, E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . .
Off-Axis Orbits in Realistic Helical Wigglers: Fixed Points and Time Averaged Dynamical Variables
J. T. Donohue, J. L. Rullier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Analytic Electron Trajectories in an Extremely Relativistic Helical Wiggler: an Application to the
Proposed SLAC E166 Experiment.
J. T. Donohue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Harmonic Generation and Linewidth Narrowing in Seeded FELs
L. Giannessi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

14
18

22
26
30

34
37

Analytical Solution of Phase Space Evolution of Electrons in a SASE FEL
N. Nishimori . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Behaviour of Electron Beam in Combined a Self-Generated Field and a Reversed Guide Field in the
Helical Wiggler
S.-K. Nam, . Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Evolution of Electron Beam in the Tapered Planar Wiggler
S.-K. Nam, . Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Effect of Liner Induced Phase Fluctuations on the Gain of a Cerenkov FEL
M.I. de la Fuente, K.-J. Boller, P.J.M. van der Slot . . . . . . . . . . . . . . . . . . . . . . . . . .
Simulation Investigation of the Detuning Curve
XJ. Shu, YH. Dou, YZ. Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Harmonic Amplifier Free Electron Laser
J. Jia . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Parameter Analysis For A High-Gain Harmonic Generation FEL By Numerical Calculation Based
On 1D Theory
LiYuhui. Li, J. Jia, Zhang Shancai. Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Improving Selectivity of 1D Bragg Resonator Using Coupling of Propagating and Trapped Waves
N.S. Ginzburg, A.V. Elzhov, A.K. Kaminsky, A.M. Malkin, N.Yu. Peskov, S.N. Sedykh, A.S. Sergeev,
A.P. Sergeev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Analytic Model of Harmonic Generation in the Low-Gain FEL Regime
G. Penn, M. Reinsch, J. Wurtele . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Short Rayleigh Length Free Electron Laser Simulations in Expanding Coordinates
R. L. Armstead, J. Blau, W. B. Colson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Optical Mode Distortion in a Short Rayleigh Length Free Electron Laser
J. Blau, W. B. Colson, R. P. Mansfield, S. P. Niles, B. W. Williams . . . . . . . . . . . . . . . . . .
Wiggler Effects on the Growth Rate of a Raman Free-electron Laser with Axial Magnetic Field or
Ion-Channel Guiding
B. Maraghechi, H. Aghahosseini, A. Kordbacheh . . . . . . . . . . . . . . . . . . . . . . . . . .

41

45
49
53
57
60

64

68
71
75
78

82

Single-Pass FELs
The European X-ray Free Electron Laser Project at DESY
S. Schwarz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Overview of Single Pass FEL Designs Technical Suggestions for Stability Improvement
T. Shintake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Scheme for Generation of Single 100 GW 300-as Pulse in the X-ray SASE FEL with the Use of a
Few Cycles Optical Pulse from Ti:sapphire Laser System
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
An Experimental Study of the Beam-Steering Effect on the FEL Gain at LEUTL’s Segmented Undulators
Y.-C. Chae, M. Erdmann, J.W. Lewellen, A. H. Lumpkin, S.V. Milton . . . . . . . . . . . . . . . . . 100
Start-To-End Injector and Linac Tolerance Studies for the BESSY FEL
M. Abo-Bakr, M.v. Hartrott, J. Knobloch, B. Kuske, A.M. Meseck . . . . . . . . . . . . . . . . . . 104
A Multistage HGHG-Scheme for the BESSY Soft X-ray FEL Multiuser Facility
D. Krämer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Impact Studies of bunch parameter variations on the performance of the BESSY HGHG FEL
B. Kuske, M. Abo-Bakr, A.M. Meseck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
The Influence of the Seed Pulse Shape on the Output Performance of the BESSY Multi-stage HGHGFEL
A.M. Meseck, M. Abo-Bakr, B. Kuske . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
xiv

Velocity Bunching Simulation for the DESY VUV FEL
J.-P. Carneiro, B. Faatz, K. Floettmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
The Potential for the Development of the X-ray Free Electron Laser: Generation of SASE Radiation
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
Attosecond X-ray Source for Light-Triggered Time-Resolved Experiments Associated with the Xray SASE FEL
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
The Potential for the Development of the X-ray Free Electron Laser: Multi-User Photon Distribution
System for XFEL Laboratory
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Sub-Terawatt Mode of Operation of X-ray SASE FEL
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Design Formulas for VUV and X-Ray FELs
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
The Free Electron Laser Klystron Amplifier Concept
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
The Potential for Extending the Spectral Range Accessible to the European X-ray Free Electron
Laser in the Direction of Longer Wavelengths
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
Start-To-End Simulations for PAL XFEL Project
Y. Kim, M.H. Cho, Y. Kim, I. S. Ko, W. Namkung, J. S. Oh, D. Son . . . . . . . . . . . . . . . . . . 151
Seeding High Gain Harmonic Generation with Laser Harmonics Produced in Gases
G. Lambert, B. Carré, M.-E. Couprie, A. Doria, D. Garzella, L. Giannessi, H. Hara, H. Kitamura,
Y. Mairesse, P. Salières, T. Shintake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

Electron beam simulations for the FERMI project at ELETTRA
S.D.M. Di Mitri, R.J. Bakker, C.J. Bocchetta, P. Craievich, G. D’Auria, gdn. De Ninno, B. Diviacco,
L.T.Z. Tosi, V.V. Verzilov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Status Report on SPARC Project
A. Renieri, D. A. Alesini, F. Alessandria, A. Bacci, M. Bellaveglia, S. Bertolucci, M.E. Biagini, C. Biscari, C.J. Bocchetta, R. Boni, I. Boscolo, M. Boscolo, F. Broggi, M. Carpanese, M. Castellano, L. Catani,
E. Chiadroni, S. Cialdi, A. Cianchi, F. Ciocci, A. Clozza, M.B. Danailov, A. D’Angelo, G.D. Dattoli,
G. D’Auria, C. De Martinis, A. Di Pace, G. Di Pirro, R. Di Salvo, A. Doria, D.H. Dowell, A. Drago,
P. Emma, A. Esposito, A. Fantini, M. Ferianis, M. Ferrario, D. Filippetto, F. Flora, V. Fusco, G.P. Gallerano, A. Gallo, A. Ghigo, L. Giannessi, D. Giove, E. Giovenale, S. Guiducci, M. Incurvati, D. Levi,
C. Ligi, C. Limborg-Deprey, F. Marcellini, C. Maroli, M. Mattioli, G. Medici, G. Messina, L. Mezi,
M. Migliorati, C. Milardi, D. Moricciani, P. M. Musumeci, P.L. Ottaviani, S. Pagnutti, D.T. Palmer,
L. Palumbo, G. Parisi, L. Pellegrino, V. Petrillo, L. Picardi, M. Preger, M.Q. Quattromini, P. Raimondi,
S. Reiche, R. Ricci, M. Romè, G. Ronci, C. Ronsivalle, J.B. Rosenzweig, E. Sabia, C. Sanelli, M. Sassi,
C. Schaerf, L. Serafini, M. Serio, F. Sgamma, B. Spataro, A. Stecchi, A. Stella, S. Tazzari, F. Tazzioli,
G. Travish, C. Vaccarezza, M. Vescovi, C. Vicario, M. Zobov, A. Zucchini . . . . . . . . . . . . . . 163

Analysis of Intensity Fluctuations of SASE using the AR Model
R. Kato, S”.”. Isaka, G.I. Isoyama, S.K. Kashiwagi, C”.”. Okamoto, H. Sakaki, S. Suemine, T. Yamamoto 167
Linac Lattice and Beam Dynamics for X-ray FEL at PAL
E.-S.. Kim, D.E. Kim, S.J. Park, M.H. Yoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
Design Study on 0.3-nm PAL-XFEL
J. S. Oh, Y. Kim, I. S. Ko, W. Namkung . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
Design Study of Low-Emittance Injector for SASE-XFEL at Pohang Accelerator Laboratory
S.J. Park, S.G. Baik, J.Y. Huang, D.E. Kim, E.-S.. Kim, I. S. Ko, S.H. Nam, W. Namkung, J. S. Oh,
J.H. Park, M.H. Yoon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

Optimization of a Soft X-Ray SASE-FEL Parameters at Pohang Accelerator Laboratory
M.H. Yoon, J.E. Han, E.-S.. Kim . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Simulating FEM Amplifiers: Features in Various Regimes
A.V. Elzhov, A.K. Kaminsky, E.A. Perelstein, S.N. Sedykh, A.P. Sergeev . . . . . . . . . . . . . . . 187
xv

Design considerations for the coherent radiator, FEL, in the MAX IV proposall. Werin, x. Andersson, x. Brandin, x. Eriksson, T.N. Hansen, x. Larsson, x. Lindgren, x. Tarawneh . . . 190

Coherent Radiation Effects in the LCLS Undulator
S. Reiche, Z. Huang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
Spontaneous Radiation Background Calculation for LCLS
S. Reiche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Generation of GW-level, sub-Angstrom Radiation in the LCLS using a Second-Harmonic Radiator
Z. Huang, S. Reiche . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
Emittance and Quantum Efficiency Measurements from a 1.6 cell S-band Photocathode RF Gun with
Mg CathodeJ.F. Schmerge, J.M. Castro, J.E. Clendenin, D.H. Dowell, S.M. Gierman, R.O. Hettel . . . . . . . . . 205
The Upgrade of the DUV-FEL Facility at the BNL
X.J. Wang, H. Loos, J.B. Murphy, G. Rakowsky, J. Rose, B. Sheehy, Y. Shen, J. Skaritka, Z. Wu, L.H. Yu 209
Expected Properties of Radiation from VUV-FEL at DESY (Femtosecond Mode of Operation)
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

FEL Oscillators
Overview of Terahertz Radiation Sources
G.P. Gallerano, S.G. Biedron . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
High Average Power Operation of a Scraper-Outcoupled Free-Electron Laser
M.D. Shinn, C. Behre, S. V. Benson, M. Bevins, D.B. Bullard, J. Coleman, L. Dillon-Townes, T. Elliott,
J. Gubeli, D. Hardy, K. Jordan, R. Lassiter, G. Neil, S. Zhang . . . . . . . . . . . . . . . . . . . . . 222

Status of the Novosibirsk Terahertz FEL
N.A. Vinokurov, V. P. Bolotin, D. A. Kayran, B. A. Knyazev, E. I. Kolobanov, V.V. Kotenkov, V.
V. Kubarev, G. N. Kulipanov, A.N. Matveenko, L. E. Medvedev, S. V. Miginsky, L. A. Mironenko,
A. D. Oreshkov, V. K. Ovchar, V. M. Popik, T. V. Salikova, M. A. Scheglov, S. S. Serednyakov,
O.A. Shevchenko, A. N. Skrinsky . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

High Power Lasing in the IR Upgrade FEL at Jefferson Lab
S. V. Benson, K.B.B. Beard, C. Behre, G. H. Biallas, J. Boyce, D. Douglas, H. F. Dylla, R. Evans,
A. Grippo, J. Gubeli, D. Hardy, C.H.G. Hernandez-Garcia, K. Jordan, L. Merminga, G. Neil, J. Preble,
M.D. Shinn, T. Siggins, H. Toyokawa, R. Walker, G. Williams, B. Yunn, S. Zhang . . . . . . . . . . . 229

VUV Optics Development for the Elettra Storage Ring FEL
St. Guenster, M.B. Danailov, A. Gatto, N. Kaiser, D. Ristau, F. Sarto, M.T. Trovò . . . . . . . . . . . 233
Coherent Harmonic Generation using the ELETTRA Storage Ring Optical Klystron
gdn. De Ninno, M.B. Danailov, B. Diviacco, M. Ferianis, L. Giannessi, M.T. Trovò . . . . . . . . . . 237
Short Rayleigh Length Free Electron Lasers
W. B. Colson, R. L. Armstead, J. Blau, P. P. Crooker . . . . . . . . . . . . . . . . . . . . . . . . . 241
Electron-Beam Stabilization for the European Storage-Ring Free-Electron Laser at Elettra
M.T. Trovò, D. Bulfone, M.B. Danailov, gdn. De Ninno, B. Diviacco, V.F. Forchi‘, L. Giannessi,
M. Lonza . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243

Tunability and Power Characteristics of the LEBRA Infrared FEL
T. Tanaka, K. Hayakawa, Y. Hayakawa, K. Ishiwata, K. Kanno, A. Mori, K. Nakao, K. Nogami, T. Sakai,
I. Sato, K. Yokoyama . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247

Status of Institute of Free Electron Laser, Osaka university
H. Horiike, M.R. Asakawa, K”.”. Awazu, M. Heya, H”.”. Kondo, Y. Naito, S. Suzuki, N”.”. Tsubouchi . 251
Misalingment Tolerance of a Hole-Coupling Optical Resonator for JAERI ERL-FEL
R. Nagai, R. Hajima, N. Kikuzawa, E.J. Minehara, N. Nishimori, M. Sawamura . . . . . . . . . . . . 255
Optimization of the NIJI-IV FEL System for the Coherent Harmonic Generation in a Q-switched
RegimeH. O. Ogawa, N. S. Sei, K. Y. Yamada, M. Y. Yasumoto . . . . . . . . . . . . . . . . . . . . . . . 258

xvi

Preliminary Design of a Synchronized Narrow Bandwidth FEL for Taiwan Light Source
W.K. Lau, C.W. Chen, H.Y. Chen, J.R. Chen, T.C. Fan, F.Z. Hsiao, K.T. Hsu, C.S. Hwang, C.C. Kuo,
G.H. Luo, D.J. Wang, J.P. Wang, M.H. Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262

Numerical Modeling of the Novosibirsk Terahertz FEL and Comparison with Experimental Results
O.A. Shevchenko, A.V. Kuzmin, N.A. Vinokurov . . . . . . . . . . . . . . . . . . . . . . . . . . 266
Start-To-End Simulations of the Energy Recovery Linac Prototype FEL
Ch. Gerth, M.A. Bowler, B. Faatz, B.W.J. McNeil, B.D. Muratori, H.L. Owen, R. Thompson . . . . . . 270
Stability of a Short Rayleigh Range Laser Resonator with Misaligned or Distorted Mirrors
P. P. Crooker, J. Blau, W. B. Colson . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
Gain and Coherent Radiation from a Smith-Purcell Free-Electron Laser
C. A. Brau, H. L. Andrews, C. H. Boulware, J. D. Jarvis . . . . . . . . . . . . . . . . . . . . . . . 278

FEL Experimental Results
Experimental Demostration of Wavelength Tuning in High-Gain Harmonic Generation Free Electron Laser
T. Shaftan, E. D. Johnson, S. Krinsky, H. Loos, J.B. Murphy, G. Rakowsky, J. Rose, B. Sheehy, J. Skaritka, X.J. Wang, Z. Wu, L.H. Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282

Spectral Phase Modulation and chirped pulse amplification in High Gain Harmonic Generation
Z. Wu, E. D. Johnson, S. Krinsky, H. Loos, J.B. Murphy, T. Shaftan, B. Sheehy, Y. Shen, X.J. Wang,
L.H. Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285

Study of Coherence Limits and Chirp Control in Long Pulse FEL Oscillator
A. Gover, M. Einat, A. Eliran, M. Kanter, BY. Kapilevich, B. Litvak, Yu. Lurie, Y. Pinhasi, Y. Socol,
M. Volshonok, A. Yahalom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

Characterization of Laser-Electron Interaction at the BESSY Femtoslicing Facility
S. Khan, K.H. Holldack, T.K. Kachel, R.M. Mitzner, T.Q. Quast, F.S. Senf . . . . . . . . . . . . . . 293
Measurement and Calculation of the ’Electron Efficiency’ on the ‘CLIO’ Free-Electron Laser
R. Prazeres, F. Glotin, J.M. Ortega . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
Recent Results of the JAERI Energy-Recovery Linac FEL
R. Hajima, I. Iijima, N. Kikuzawa, E.J. Minehara, R. Nagai, N. Nishimori, T. Nishitani, M. Sawamura . 301
JAERI 200 kV Electron Gun with an NEA-GaAs PhotocathodeT. Nishitani, R. Hajima, N. Kikuzawa, E.J. Minehara, R. Nagai, N. Nishimori, M. Sawamura, T. Yamauchi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304

Performance of the Optical Klystron ETLOK-III for Developing Infrared Storage Ring Free Electron
LasersN. S. Sei, H. O. Ogawa, K. Y. Yamada, M. Y. Yasumoto . . . . . . . . . . . . . . . . . . . . . . . 307
Improved Performance of the NIJI-IV Compact VUV/IR FEL and its Application to the Surface
Observation
K. Y. Yamada, H. O. Ogawa, N. S. Sei, K.W. Watanabe, M. Y. Yasumoto . . . . . . . . . . . . . . . 311
A mm-Wave, Table Top Cerenkov Free-Electron Laser
M.I. de la Fuente, K.-J. Boller, P.J.M. van der Slot . . . . . . . . . . . . . . . . . . . . . . . . . . 314
Status of 30 GHz Facility for Experimental Investigation of the Copper Cavity Lifetime (Clic Collider Project)
A.K. Kaminsky, A.V. Elzhov, N.S. Ginzburg, E.V. Gorbachev, V.V. Kosukhin, S.V. Kuzikov, E.A. Perelstein, N.Yu. Peskov, M.I. Petelin, N.V. Pilyar, T.V. Rukoyatkina, S.N. Sedykh, A.S. Sergeev, A.P. Sergeev,
A.I. Sidorov, V.V. Tarasov, N.I. Zaitsev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

Characterization of Storage Ring FEL operating in the Giant Pulse Mode
V. Pinayev, K. Chalut, V.N. Litvinenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
xvii

VISA IB: Ultra-High Bandwidth, High Gain SASE FEL
G. Andonian, R.B. Agustsson, M. Babzien, I. Ben-Zvi, I. Boscolo, S. Cialdi, M. Ferrario, A. Flacco,
J.Y. Huang, V.N. Litvinenko, A. Murokh, L. Palumbo, C. Pellegrini, S. Reiche, J.B. Rosenzweig, G. Travish, C. Vicario, V. Yakimenko . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

Preliminary Measurements of the High-Gain FEL Radiation Properties along the Radiator
T. Shaftan, H. Loos, B. Sheehy, L.H. Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329

FEL Technology
Attosecond X-ray Pulses in the LCLS using the Slotted Foil Method
P. Emma, M. Borland, Z. Huang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
Large-Scale Timing Distribution and RF-Synchronization for FEL Facilities
J. Kim, W.S. Graves, F. O. Ilday, F. X. Kaertner, D. E. Moncton, O. D. Muecke, M. H. Perrott, T. Zwart . 339
High Temporal Resolution, Single-Shot Electron Bunch-Length Measurements
G. Berden, W.A. Gillespie, S.P. Jamison, A.M. MacLeod, B. Redlich, A.F.G. van der Meer . . . . . . . 343
Recent Results and Perspectives of the Low Emittance Photo Injector at PITZ
F. Stephan, K. Abrahamyan, W. Ackermann, G. Asova, J. Baehr, I. Bohnet, J.-P. Carneiro, G. Dimitrov,
K. Floettmann, U. Gensch, H.-J. Grabosch, J.H. Han, M.v. Hartrott, E. Jaeschke, D. Krämer, M. Krasilnikov, D. Lipka, P. Michelato, V.V. Miltchev, L. Monaco, W.F.O. Mueller, A. Oppelt, C. Pagani, B. Petrosyan, D. Pose, D. Richter, S. Riemann, J. Rossbach, W. Sandner, S. Schnepp, S. Schreiber, D. Sertore,
S. Setzer, L. Staykov, I. Tsakov, T. Weiland, I. Will . . . . . . . . . . . . . . . . . . . . . . . . . . 347

Emittance Measurement on the CeB6 Electron Gun for the SPring-8 Compact SASE Source
K. Togawa, H. Baba, T. Inagaki, H. Matsumoto, K. Onoe, T. Shintake, T. Tanaka . . . . . . . . . . . 351
Ampere Average Current Photoinjector and Energy Recovery Linac
I. Ben-Zvi, H.P. Bluem, A. Burger, A. Burrill, R. Calaga, P. Cameron, X. Chang, M.D. Cole, J. Delayen, A. Favale, W. Funk, D. Gassner, H. Hahn, A. Hershcovitch, D. Holmes, H.C. Hseuh, P. Johnson,
D. Kayran, J. Kewisch, R. Lambiase, V.N. Litvinenko, G. McIntyre, A. Nicoletti, L. Phillips, J. Preble, J. Rank, J. Rathke, T. Roser, J. Scaduto, T.J. Schultheiss, K.S. Smith, T. Srinivasan-Rao, A. Todd,
K.-C. Wu, A. Zaltsman, Y. Zhao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355

Status of the 3 1/2 Cell Rossendorf Superconducting RF Gun
D. Janssen, H. Buettig, P. Evtushenko, S. Kruchkov, U. Lehnert, P. Michel, O. Myskin, Ch. Schneider,
J. Stephan, J. Teichert, V. Volkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359

Longitudinal Space Charge Effects in the JLAB IR FEL SRF Linac
C.H.G. Hernandez-Garcia, K.B.B. Beard, C. Behre, S. V. Benson, G. H. Biallas, J. Boyce, D. Douglas,
H. F. Dylla, R. Evans, A. Grippo, J. Gubeli, D. Hardy, K. Jordan, L. Merminga, G. Neil, J. Preble,
M.D. Shinn, T. Siggins, R. Walker, G. Williams, B. Yunn, S. Zhang . . . . . . . . . . . . . . . . . . 363

LCLS Undulator Design Development
I.B. Vasserman, R.J. Dejus, . Den Hartog, . Moog, . Sasaki, . Trakhtenberg, M. White. . . . . . . . . 367

Commissioning of the TTF Linac Injector at the DESY VUV-FEL
K. Honkavaara . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
A Novel Diagnostics of Ultrashort Electron Bunches Based on Detection of Coherent Radiation from
Bunched Electron Beam in an Undulator
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
Industrial Production of Superconducting 1.3 GHz Accelerator Modules and components for FEL
application
MP. Pekeler, HV. Vogel, PS. vom Stein . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
Collimation System for the BESSY FEL
T. Kamps . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
xviii

High Power RF Conditioning and Measurement of Longitudinal Emittance at PITZ
J. Baehr, K. Abrahamyan, G. Asova, I. Bohnet, J.-P. Carneiro, G. Dimitrov, K. Floettmann, H.-J. Grabosch, J.H. Han, M. Krasilnikov, D. Lipka, P. Michelato, V.V. Miltchev, L. Monaco, A. Oppelt, B. Petrosyan, D. Pose, D. Richter, S. Riemann, S. Schreiber, D. Sertore, L. Staykov, F. Stephan, M. v. Hartrott. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
An Electromagnetic Undulator for the Far Infrared at ELBE
R.W. Dekorsy, K.F. Fahmy, E.G. Grosse, P. Michel, W. Seidel, A.W. Wolf, R.W. Wuensch . . . . . . . 389
Bunch Length Measurements at the SLS Linac Using Electro Optical Sampling
B. Steffen, S. Casalbuoni, T. Korhonen, T. Schilcher, V. Schlott, P. Schmüser, H. Sigg, S. Simrock,D. Suetterlin, M. Tonutti, A. Winter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392

Longitudinal Bunch Shape Diagnostics with Coherent Radiation and a Transverse Deflecting Cavity
at TTF2
O.G. Grimm, P. Emma, L. Froehlich, K. Klose, D. McCormick, M. Nagl, O. Peters, M. Ross, J. Rossbach,
H.S. Schlarb, T.J. Smith . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395

Transverse Emittance Measurements at the Photo Injector Test Facility at DESY Zeuthen
V.V. Miltchev, K. Abrahamyan, W. Ackermann, G. Asova, J. Baehr, J.-P. Carneiro, G. Dimitrov,
K. Floettmann, H.-J. Grabosch, J.H. Han, M.v. Hartrott, M. Krasilnikov, D. Lipka, P. Michelato,
L. Monaco, A. Oppelt, B. Petrosyan, D. Pose, D. Richter, S. Riemann, S. Schnepp, S. Schreiber,
D. Sertore, S. Setzer, L. Staykov, F. Stephan, I. Tsakov, I. Will . . . . . . . . . . . . . . . . . . . . 399

The Short-Range Wakefields in the BTW Accelerating Structure of the Elettra Linac
P. Craievich, G. D’Auria, T. Weiland, I. Zagorodnov . . . . . . . . . . . . . . . . . . . . . . . . . 403
The SPARX Project : R&D Activity towards X-rays FEL Sources
D. A. Alesini, F. Alessandria, A. Bacci, M. Bellaveglia, S. Bertolucci, M.E. Biagini, R. Boni, I. Boscolo,
M. Boscolo, F. Broggi, M. Castellano, L. Catani, E. Chiadroni, S. Cialdi, A. Cianchi, F. Ciocci, A. Clozza,
G.D. Dattoli, C. De Martinis, S. S. De Silvestri, A. Di Pace, G. Di Pirro, A. Doria, A. Drago, P. Emma,A. Esposito, M. Ferrario, D. Filippetto, F. Flora, V. Fusco, G.P. Gallerano, A. Gallo, A. Ghigo, L. Giannessi, D. Giove, E. Giovenale, S. Guiducci, M. Incurvati, C. Ligi, F. Marcellini, C. Maroli, M. Mattioli,
M. Mauri, G. Messina, L. Mezi, M. Migliorati, A. M. Mostacci, P. M. Musumeci, M. N. Nisoli, P.L. Ottaviani, S. Pagnutti, L. Palumbo, G. Parisi, L. Pellegrino, V. Petrillo, L. Picardi, M. Preger, M.Q. Quattromini, P. Raimondi, S. Reiche, A. Renieri, R. Ricci, M. Romè, C. Ronsivalle, J.B. Rosenzweig, C. Sanelli,
C. Schaerf, L. Serafini, M. Serio, F. Sgamma, B. Spataro, S. S. Stagira, A. Stecchi, A. Stella, F. Tazzioli,
A. T. Torre, C. Vaccarezza, M. Vescovi, C. Vicario, A. Zucchini . . . . . . . . . . . . . . . . . . . . 407

Spectral Analysys of Charge Emission Spatial Inhomogeneities and Emittance Dilution in RF Guns
M.Q. Quattromini, L. Giannessi, C. Ronsivalle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
On-Line Spectral Monitoring of the VUV FEL Beam at DESY
p. Nicolosi, J. Feldhaus, U. Hahn, U. Jastrow, m.g. Pelizzo, e.p. Ploenjes, l. Poletto, K. Tiedtke . . . . . 415
ABCD Matrix Method: a Case Study
Z.F. Seidov, Y. Pinhasi, A. Yahalom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
Spot-to-Beam Procedure
Z.F. Seidov, Y. Pinhasi, A. Yahalom . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
Guiding Optics System for LEBRA FEL User Facility
T. Tanaka, K. Hayakawa, Y. Hayakawa, I. Sato . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
Upgrade of a Photocathode RF Gun at SPring-8
T.T. Taniuchi, T.A. Asaka, H.D. Dewa, H.H. Hanaki, T.K. Kobayashi, A.M. Mizuno, S.S. Suzuki,
H.T. Tomizawa, M. Uesaka, K.Y. Yanagida . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431

FEL Simulation Code for Undulator Performance Estimation
T. Tanaka . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
Electron Beam Simulations on the SCSS Accelerator
H. Hara, H. Kitamura, T. Shintake . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
Reducing Back-Bombardment Effect Using Thermionic Cathode in IAE RF Gun
T. Kii, K. Hayakawa, K. Masuda, M. Murakami, H. Ohgaki, T. Yamazaki, Y. Yoshikawa, Z. Zen . . . . 443
Renewal of KU-FEL Facility
T. Kii, K. Hayakawa, K. Masuda, M. Murakami, H. Ohgaki, T. Yamazaki, Y. Yoshikawa, Z. Zen . . . . 447
xixBeam Property Measurements on the KU-FEL Linac
K. Masuda, K. Hayakawa, T. Kii, M. Murakami, H. Ohgaki, T. Yamazaki, Y. Yoshikawa, Z. Zen . . . . 450

Upgrade Design of KU-FEL Driver Linac Using Photo-Cathode RF-GUN
H. Ohgaki, K. Hayakawa, T. Kii, K. Masuda, M. Murakami, T. Yamazaki, Y. Yoshikawa, Z. Zen . . . . 454

First Model of the Edge-Focusing Wiggler for SASE
S.K. Kashiwagi, G.I. Isoyama, R. Kato, K.K. Kobayashi, T.N. Noda, K.T. Tsuchiya, S.Y. Yamamoto . . 458
Upgrade of the L-Band Linac at ISIR, Osaka University for a Far-Infrared FEL
R. Kato, G.I. Isoyama, S.K. Kashiwagi, S. Suemine, T. Yamamoto . . . . . . . . . . . . . . . . . . 462
Development of Compact Soft X-ray Source Based on Laser Undulator
Dr. Kuroda, Dr. Hayano, K. Hidume, S.K. Kashiwagi, S. Minamiguchi, T. Saito, D. Ueyama,
Prof. Urakawa, Prof. Washio . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466

Repetitive Bunches from RF-Photo Gun Radiate Coherently
C.A.J. van der Geer, M.J. de Loos, D.A. Jaroszynski, S.B. van der Geer . . . . . . . . . . . . . . . . 470

Research on the Undulator Used for PKU-FEL. . . . . . . . . . . . . . . . . . . . . 474
Study on the Planar Undulator Scheme with Focusing Properties for PKU-FEL
Y. T. Ding, J. E. Chen, S.L. Huang, Y.G. Wang, K. Zhao, J.J. Zhuang . . . . . . . . . . . . . . . . . 478
Beam Loading Tests on DC-SC Photoinjector at Peking University
H. H. Lu, w. Chen, J. Dai, y. Li, c. Shi, y. Yang, J.J. Zhuang

S.L. Huang, J. E. Chen, X. Q. Chu, Y. T. Ding, J. K. Hao, F. Jiao, L. Lin, X. Lu, S. W. Quan, G. M. Wang,
L. F. Wang, R. Xiang, B. P. Xiao, D. Xie, L. M. Yang, B. C. Zhang, K. Zhao, Z. Zhu . . . . . . . . . . 481

The Drive Laser System for DC-SC Injector
X. Lu, Lin. Lin, S. W. Quan, Wang. Wang, K. Zhao . . . . . . . . . . . . . . . . . . . . . . . . . 484
Simplified Method for Experimental Spectral Ratio Calculation of CHG-FEL
Chen Nian. Chen, He Duohui. He, Li Ge. Li, LiYuhui. Li, Zhang Pengfei. Zhang, Zhang Shancai. Zhang 487
Multi-Objective Optimization for Pure Permanent-Magnet Undulator Magnets Ordering Using Modified Simulated Annealing
Chen Nian. Chen, He Duohui. He, Li Ge. Li . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
Design of Undulator for the Shanghai DUV-FEL
J. Jia, Y. Cao, Z. Dai, He Duohui. He, S. Lu, Zhang Shancai. Zhang, Z. Zhao, Q. Zhou . . . . . . . . . 494
Study of Control Grid Thermionic Cathode RF Gun
x. Xiao, L. Jie, L. Ming, Y. Xinfan, S. Xumin, C. Yanan, X. Zhou . . . . . . . . . . . . . . . . . . . 498
Superconducting Undulator with Variably Polarized Light
C.S. Hwang, C.H. Chang, T.C. Fan, W.P. Li, P.H. Lin . . . . . . . . . . . . . . . . . . . . . . . . . 501
Commissioning of Strong Tapered Undulator Developed for IFEL Accelerator
S.V. Tolmachev, P. M. Musumeci, C. Pellegrini, J.B. Rosenzweig, A.A. Varfolomeev, A.A. Varfolomeev
Jr., T.V. Yarovoi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504

FEL and Libera both Push Performance into New Frontiers
R. Ursic, B. Solar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
Optical Systems for the Fourth Generation Light Source, 4GLS
M. Quinn, M.A. Bowler, A. MacDonald, D. Roper . . . . . . . . . . . . . . . . . . . . . . . . . . 511
A Concept for z-Dependent Microbunching Measurements with Coherent X-ray Transition Radiation in a SASE FEL
A. H. Lumpkin, W. M. Fawley, D.W. Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
First Direct Comparisons of a COTRI Analytical Model to Data from a SASE FEL at 540, 265, and
157 nmA. H. Lumpkin, R.J. Dejus, D.W. Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
Use of VUV Imaging to Evaluate COTR and Beam-Steering Effects in a SASE FEL at 130 nm
A. H. Lumpkin, Y.-C. Chae, R.J. Dejus, M. Erdmann, J.W. Lewellen, Y. Li . . . . . . . . . . . . . . 523
Test of Horizontal Magnetic Field Measurements in the Presence of a Strong Vertical Field
I.B. Vasserman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
Development and Measurement of Strain Free RF Photoinjector Vacuum Windows
S.G. Biedron, L. Assoufid, M. Babzien, G. Gill, J.W. Lewellen, Y. Li, J. Qian . . . . . . . . . . . . . 530
xx

Comparison of Parmela and MAFIA Simulations of Beam Dynamics in High Current Photoinjector
S.S. Kurennoy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
RF Design for the Linac Coherent Light Source (LCLS) Injector
D.H. Dowell, L.D. Bentson, R.F. Boyce, S.M. Gierman, J.A. Hodgson, Z. Li, C. Limborg-Deprey,
J.F. Schmerge, L. Xiao, N. Yu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538

Optimal RF Systems for Lightly Loaded Superconducting Structures
T. Zwart, D. Cheever, W.S. Graves, D. Wang, A. Zolfaghari . . . . . . . . . . . . . . . . . . . . . . 542
Electron Beam Diagnostics Using Diffraction Radiation
B.F. Feng, S.E. C. Csorna, G.E. G. Gabella, T.R. Sashalmi . . . . . . . . . . . . . . . . . . . . . . 546
Simulations of the Newark FIR FEL Operation
J. Zheng, K. Chin, J.M.J. Madey, E. Szarmes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
Making an Inexpensive Electromagnetic Wiggler Using Sheet Materials for the Coils
G. H. Biallas, S. V. Benson, T. Hiatt, G. Neil, M. Snyder . . . . . . . . . . . . . . . . . . . . . . . 554
Performance and Modeling of the JLab IR FEL Upgrade Injector
C.H.G. Hernandez-Garcia, K.B.B. Beard, S. V. Benson, G. H. Biallas, D.B. Bullard, D. Douglas, H.
F. Dylla, R. Evans, A. Grippo, J. Gubeli, K. Jordan, G. Neil, M.D. Shinn, T. Siggins, R. Walker, B. Yunn,
S. Zhang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558

Short Electron Beam Bunch Characterization Through Measurement of Terahertz Radiation
S. Zhang, S. V. Benson, D. Douglas, M.D. Shinn, G. Williams . . . . . . . . . . . . . . . . . . . . 562
RF Sources for 3rd & 4th Generation Light Sources
S. J. Lenci, A.J.B. Balkcum, H. P. Bohlen, Y.X.L. Li, A.X.M. Mizuhara, R. Tornoe, E.L.W. Wright . . . 566
High Current Energy Recovery Linac at BNL
V.N. Litvinenko, D.S. Barton, D. Beavis, I. Ben-Zvi, M. Blaskiewicz, H.P. Bluem, J.M. Brennan,
A. Burger, A. Burrill, R. Calaga, P. Cameron, X. Chang, M.D. Cole, R. Connolly, J. Delayen, A. Favale,
W. Funk, D. Gassner, H. Hahn, A. Hershcovitch, D. Holmes, H.C. Hseuh, P. Johnson, D. Kayran,
J. Kewisch, R. Lambiase, G. McIntyre, W. Meng, T.C. Nehring, A. Nicoletti, D. Pate, L. Phillips, J. Preble, J. Rank, J. Rathke, T. Roser, T. Russo, J. Scaduto, T.J. Schultheiss, K.S. Smith, T. Srinivasan-Rao,
A. Todd, N.W. Williams, K.-C. Wu, V. Yakimenko, K. Yip, A. Zaltsman, Y. Zhao . . . . . . . . . . . 570

Thermal and Field Enhanced Photoemission: Comparison of Theory to Experiment
K. L. Jensen, D. L. Demske, D. W. Feldman, N. Moody, P.G. O’Shea . . . . . . . . . . . . . . . . . 574
A Mode Locked UV-FEL
P. Parvin, A.B. Basam, G.R.D. Davoud-Abadi, F.E. Ebadpoor, B. Jaleh, S.B. Sajad, Z. Zamanipour . . . 578

New Concepts
Current-Enhanced SASE Using an Optical Laser and its Application to the LCLS
A.A. Zholents, P. Emma, W. M. Fawley, Z. Huang, S. Reiche, G. Stupakov . . . . . . . . . . . . . . 582
Generation of Terahertz Radiation by Modulating the Electron Beam at the CathodeJ.G. Neumann, G.L. Carr, R.F. Fiorito, H.F. Freund, H. Loos, P.G. O’Shea, T. Shaftan, B. Sheehy, Y. Shen,
Z. Wu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586

Suppression of Multipass, Multibunch Beam Breakup in Two Pass Recirculating Accelerators
C. Tennant, D. Douglas, K. Jordan, L. Merminga, E. Pozdeyev, T.I. Smith . . . . . . . . . . . . . . . 590
Potential Use of eRHIC’s ERL for FELs and Light Sources
V.N. Litvinenko, I. Ben-Zvi . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594
The Harmonically Coupled 2-Beam FEL
B.W.J. McNeil, M.W. Poole, G.R.M. Robb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598
Low Emittance Gun Project based on Field Emission
R.G. Ganter, A.C. Candel, M.D. Dehler, J.G. Gobrecht, C.G. Gough, G.I. Ingold, S.L. Leemann,
K.L. Li, M.P. Paraliev, M.P. Pedrozzi, J.-Y.R. Raguin, R.L. Rivkin, V. Schlott, h”.”. Sehr, A.S. Streun,
A.W. Wrulich, S”.”. Zelenika . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602

xxi

Field Emitter Arrays for a Free Electron Laser Application
K.L. Li, M.D. Dehler, R.G. Ganter, J.G. Gobrecht, J.-Y.R. Raguin, R.L. Rivkin, A.W. Wrulich . . . . . 606

Undulators for the BESSY Soft-X-Ray FEL
j.b. Bahrdt, W.F. Frentrup, A.G. Gaupp, B. Kuske, A.M. Meseck, M.S. Scheer . . . . . . . . . . . . . 610
Proposal of Laser-Driven Acceleration with Bessel Beam
D. Li, K. Imasaki . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
Amplification of Short-Pulse Radiation from the Electron Undergoing Half-Cyclotron Rotation
M.R. Asakawa, K. Imasaki, H. Marusaki, N. Ohigashi, Y. Tsunawaki . . . . . . . . . . . . . . . . . 618
Reasearches of Thomson Scattering X-Ray Source at Tsinghua University
w.h. Huang, H.B. Chen, C. Cheng, Y. Cheng, Q. Du, t.b. Du, Y.Ch. Du, Y.Ch. Ge, X.Z. He, J.F. Hua,
G. Huang, Y.Zh. Lin, Ch.X. Tang, B. Xia, M.J. Xu, X.D. Yuan, Sh.X. Zheng . . . . . . . . . . . . . 622

The Coherent Synchrotron Radiation Influence on the Storage Ring Longitudinal Beam Dynamics
E.G. Bessonov, R.M. Feshchenko, V.I. Shvedunov . . . . . . . . . . . . . . . . . . . . . . . . . . 625
Isochronous Bend for a High Gain Ring FEL
A.N. Matveenko, O.A. Shevchenko, N.A. Vinokurov . . . . . . . . . . . . . . . . . . . . . . . . . 629
The Two-Beam Free Electron Laser Oscillator
R. Thompson, B.W.J. McNeil . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
Harmonic Cascade FEL Designs for LUX, a Facilty for Ultrafast X-ray Science
J. John, W. M. Fawley, G. Penn, M. Reinsch, W. Wan, J. Wurtele, A.A. Zholents . . . . . . . . . . . . 637
Novel Method for Phase-Space Tomography of Rapidly Evolving E-beams
K. Chalut, V.N. Litvinenko, V. Pinayev . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
Acceleration of Electrons in a Diffraction Dominated IFEL
P. M. Musumeci, S. Boucher, A. Doyuran, R.J. England, C. Joshi, C. Pellegrini, J. Ralph, J.B. Rosenzweig, C. Sung, Ya. Tochitsky, S.V. Tolmachev, G. Travish, A.A. Varfolomeev, A.A. Varfolomeev Jr.,
T.V. Yarovoi, R. Yoder . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644

FEL Users Workshop
Advances in the Physical Understanding of Laser Surgery at 6.45 microns
M.S.H. Hutson, G. Edwards . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648
Proposals for Pump-Probe Experiments in the Gas Phase using the TTF2-FEL
M.M. Meyer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654
Picked FEL Micro Pulse for Nano-Second Interaction with Bio-Molecule
S. Suzuki, K”.”. Awazu, K. Ishii, T. Kanai, Y. Naito . . . . . . . . . . . . . . . . . . . . . . . . . 657
Coherent Protein Dynamics Explored at FELIX
r.h.a. Austin, B. Redlich, A.F.G. van der Meer, a.x. Xie . . . . . . . . . . . . . . . . . . . . . . . . 661
Preparation Femtosecond Laser Prevention for the Cold-Worked Stress Corrosion Crackings on Reactor Grade Low Carbon Stainless Steel
E.J. Minehara, A. Nisimura, T. Tsukada . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
THz Imaging by a Wide-band Compact FEL
Y. U. Jeong, H. J. Cha, G. M. Kazakevitch, B. C. Lee, S. H. Park . . . . . . . . . . . . . . . . . . . 667
The Present Applications of IR FEL at Peking University
L. M. Yang, J. E. Chen, Y. Su, M.K. Wang, J. Wu, Y. Xu, K. Zhao . . . . . . . . . . . . . . . . . . 671
Interaction of Intense Ultrashort XUV Pulses with Different Solids - Results from the Tesla Test
Facility FEL Phase I
J. Krzywinski, A.A. Andrejczuk, M”.”. Bittner, D.C. Chvostova, L.J. Juha, M.J. Jurek, A.K. Kauch,
D.K. Klinger, V.L. Letal, J.P. Pelka, H.R. Reniewicz, E.L. Saldin, E.A. Schneidmiller, M.S. Sikora,
R.S. Sobierajski, B.S. Steeg, R. Treusch, V”.”. Vorlicek, A.W. Wawro, M.V. Yurkov . . . . . . . . . . 675

Exploring the Spatial Resolution of the Photothermal Beam Deflection Technique in the Infrared
RegionW. Seidel, H. Foerstendorf, F. Glotin, J.M. Ortega, R. Prazeres . . . . . . . . . . . . . . . . . . . . 679
xxii

Experiments on the Synchronization of an Ultrafast Cr:LiSAF Laser with the ELETTRA Storage
Ring and FEL Pulses
M. Ferianis, G.E. Afifi, M. Coreno, M.B. Danailov, gdn. De Ninno, B. Diviacco, M.T. Trovò . . . . . . 681
Laser Compton Scattering Gamma Ray Induced Photo-Trasmutation
D. Li, S. Amano, K. Imasaki, S. Miyamoyo, T. Mochizuki . . . . . . . . . . . . . . . . . . . . . . 685
Development of a Pump-Probe System using a Non-Coated ZnSe Beam Splitter Cube for an MIRFEL
M. Heya, K”.”. Awazu, H. Horiike, K. Ishii, S. Suzuki . . . . . . . . . . . . . . . . . . . . . . . . 689
Medical Application of Free Electron Laser Trasmittance using Hollow Optical Fiber
S. Suzuki, K”.”. Awazu, K. Ishii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692
Modification of Hydroxyapatite Crystal Using IR Laser
a”S.”. Satoh, A. Danjyo, M. Goto, W. Guan, N. Hayashi, S. Ihara, C. Yamabe, Y. Yamaguchi . . . . . . 695
Vibrational Excitation of Ammonia Molecules by FEL-SUT
Y. Ogi, K. Tsukiyama . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
Photo-Acoustic Spectroscopy with Infrared FEL
M. Y. Yasumoto, H. O. Ogawa, N. S. Sei, K. Y. Yamada . . . . . . . . . . . . . . . . . . . . . . . 703

Tables of Operating and Proposed FELs
Free Electron Lasers in 2004
W. B. Colson, B. W. Williams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706

Indexes
Author Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711
Index of Paper ID’s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721
Producing the Conference Proceedings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725

xxiii

xxiv

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L.H. Yu / Proceedings of the 2004 FEL Conference, 1-7

R&D EXPERIMENTS AT BNL TO ADDRESS THE ASSOCIATED ISSUESIN THE CASCADING HGHG SCHEME
Li Hua Yu, 725C, BNL, Upton , NY11973, USA
Several experiments that can be carried out at BNL's
DUVFEL are discussed to address issues associated withcascaded HGHG FELs. These include: Chirped Pulse
Amplification (CPA), HGHG with seed shorter thanelectron bunch length, 8th harmonic HGHG (from 800 nm
to 100 nm), regenerative synchronization of seed pulse
and electron bunch, tuning of HGHG without changing
seed, and cascading from 400 nm to 100 nm to 50 nm
using NISUS and VISA undulators. These experiments
may have important impact on the development of multistage cascaded HGHG FELs.

INTRODUCTION
The proof-of-principle HGHG experiment at 5 µm [1,2]and recent HGHG experiment at the DUVFEL [3] havegenerated significant interests in the FEL community. The
more relaxed requirement on electron beam current andemittance to generate coherent deep UV output with muchnarrower bandwidth and high pulse energy stability, as
exhibited by the recent experiment, and its potential to begeneralized to soft-x-ray FEL, have attracted muchattention. Several labs[4], including BESSY [5],ELETRRA [6], LBL [7], MIT [8], and SSRF [9] proposed
the development of UVFEL based on HGHG principle orsoft-x-ray FEL based on the cascaded HGHG principle[10,11,12]. Among them SSRF has already started theconstruction of an FEL system based on the HGHG
principle. Hence it would be a contribution to be able tocarry out a first proof-of principle experiment of cascaded
HGHG at the DUVFEL. In this paper, we discuss thisexperiment and several associated experiments that can be
carried out at BNL before this experiment and may also
have important impact on the development of multi-stage
cascaded HGHG FELs.
400nm
2MW

100nm
20MW

MINI NISUS
L=6m

50nm
180MW

NISUS VISA
0.8 m 3m

Figure 1: Cascading HGHG using Fresh Bunches under
the present e-beam conditions, see Table 1, and a seedpulse with a duration of 200 fs.
THE CASCADED HGHG DEMONSTRATIONEXPERIMENT AT DUVFELThe analysis of recent experiment at DUVFEL showsthat it is possible to realize a proof-of-principle cascaded
HGHG experiment with existing system parameters andwith reasonable cost, as we shall show in the following.
This suggested experiment is a cascaded HGHG with two

Available online at http://www.JACoW.org

stages. In the future it is possible to generalize it toseveral stages by other labs. We will also show that eventhough the DUVFEL is a small facility, with present
electron beam parameters and without significant
increment of hardware, we can carry out experiments toaddress several important issues associated with thecascaded HGHG FEL.
Table 1: Present electron beam conditions.
Peak current
Bunch duration
Beam energy
Energy spread
Norm. emittance

I

σt
E

σγ/γ
εn,xy

300
1
288
1×10-4
2.7

A
ps
MeV
π mm mrad

910

output power [W]Abstract

8

10

7

10

6

10

0

1

2
3
wiggler length [m]4Figure 2: TDA simulation of the last stage of a cascading
HGHG from 400 nm, to 100 nm, to 40 nm for a beam
current of 500 A and a seeding at 100 nm of 20 MW.
A cascaded HGHG FEL with two stages isschematically shown in Figure 1. More detailed
description of the principle of the cascaded HGHG isgiven in [10]. In this experiment we propose to use thefirst 6 meters of the existing NISUS undulator to achieve
output at 100 nm using a 400 nm seed into the existing
MINI undulator. When compared with the recent
published PRL paper [3], it is easy to see that theparameters in the proposed experiment, electron beam
current (300 A), energy spread (1×10-4), pulse length(1ps), and emittance (2.7 µm) are the same as we havealready established by the recent results [3]. The electron
beam energy is to be increased from the present 200 MeV
to 288MeV. Simulation shows that when seeded with a 2MW 400-nm 200-fs laser-pulse, the 100 nm stage willreach beyond 20MW with this set of parameters in 6 m(the recent experiment show saturation to 100MW in 5 m,
at 266 nm), but we can always control the output at thedesired 20MW level, for example by tuning the dispersion

FEL Prize Talk and New Lasing

2

L.H. Yu / Proceedings of the 2004 FEL Conference, 1-7

intensity I (A) dE (keV) Energy (keV)

25

100

0

0

-25

-100

-50
20
0
-20

-200
100
0
-100
400

50
0
-5 -2.5

0

2.5

5

0.1
0

0
-1 -0.5

0

0.5

0

4

1

0.1
-8 -4

0

4

Time (ps)

8

0

400

100 nm ! 50nm
400 nm ! 100nm

200
0

-1

-0.5

0
0.5
Time (ps)1

Figure 4: Illustration on double use of an electron bunchin a cascaded HGHG setup.
It is also clear that the space needed by this experimentis available because we only need 6 meters NISUS for the
first HGHG stage. The present NISUS is 10 m long,hence leaving 4 meters room for the second stage. In
addition, the most important hard ware, the VISA parts, isalready in our possession. So the main works for the
implementation of this experiment is the removal of the 4m NISUS and assembly and installation of the 2-m VISA.
Hence the total cost is significantly reduced.
Not only the success of the cascaded HGHG
experiment
providesa
first
proof-of-principle
demonstration, the output of the cascaded HGHG at 50
nm with 180 MW peak power also provides anunprecedented high intensity coherent new light source atthis wavelength.
SEVERAL EXPERIMENTS ADDRESSING THE
ISSUES ASSOCIATED WITH THE CASCADED
HGHG SCHEME
In addition to the cascaded HGHG proof-of-principle
experiment, there is also a series of FEL experiments
closely associated with it, but in smaller scale, hence canbe carried out at DUVFEL earlier. These experiments will
significantly improve and advance the multi-staged
cascaded scheme. In the following, we shall discuss theseexperiments: their significances, and their present status.

Chirped Pulse Amplification (CPA)-8 -4Time (ps)8

Figure 3 Tomography of the electron bunch distribution
for a uncompressed (left) and compressed (right) bunch[13].
Another important issue in the cascading scheme is thetime jitter between the electron bunch and the seed laser.
It is important that the jitter should be much less than theelectron bunch length. As a recent experiment using
electro-optical method [13] showed, the jitter is about 300
fs FWHM. To see the relation between the cascaded FEL
laser pulse and the electron pulse, we plot them in Figure
4 against the background of the current profile obtainedby the tomography in Figure 3. This figure shows thatwith the jitter about 300 fs, it is still possible to arrange
the seed pulse and the cascaded pulse so that the first
HGHG operates at about 200 A while the second HGHG
stage uses the peak of more than 400 A. Therefore our

MOAIS03analysis shows clearly the feasibility of this experiment,
which is based on the existing system parameters.

Current (A)magnet before the NISUS away from maximum
bunching, or use a part of the electron bunch with lesscurrent than 300 A. Following the 6 m NISUS is a shifter
chicane (about 0.3-0.4 m long), which will shift the 100
nm output 200 fs pulse to a “fresh” part of the electron
bunch. This is followed by a 0.8 m long NISUS section asa modulator for the next stage of HGHG, and then by adispersion magnet (about 0.3-0.4 m long). The dispersion
magnet will transform the 100 nm energy modulation into
micro-bunching, which will generate coherent radiation at
50 nm and will be exponentially amplified to saturation at
180 MW power in the 3-m long VISA undulator
following this dispersion magnet.
Here we assume 300 A for the beam current, so thesaturation is at 3 m in the VISA undulator. Within 2
meters the output is only about a factor 2 from saturation,
as shown by Figure 2. Recently a tomography [13] at our
DUVFEL has shown that after compression the peakcurrent is more than 400 A, as is shown in Figure 3 (seethe current profile at the right side of the figure). In near
future, we will improve the peak current to more than 500
A, and the saturation can be reached at 2 meters in VISA.
At the present, we have already the parts for a 2-m long
VISA undulator, hence this will significantly lower thecost of the project.
uncompressed
compressed
200
50

CPA in FEL can be used to generate high peak power
short pulse (bellow 10-20 fs), which will have wide
applications in physics and chemistry and also can beused as seed for the multi-staged cascaded HGHG.
Because of the high efficiency and wide bandwidth of
FEL, CPA using FEL can generate unprecedented shortradiation pulses in short wavelength region (bellow 100nm) [14]. After the recent success of the HGHG
experiment at DUVFEL, we have carried out the first step
towards a first demonstration of CPA in FEL at 266 nm[15]. As shown in Figure 5, the green bars in the lower
part of the figure represent chirped seed with the tail atshorter wavelength, while the blue curved bar represent
the electron bunch with three different chirping of energy(with tail at higher beam energy). The three curves in the
top figure are the output spectrum for these three settings.
The middle one (blue curve) has the largest bandwidth. In
the latter setting the electron beam energy chirp matched3

L.H. Yu / Proceedings of the 2004 FEL Conference, 1-7

to the seed with best overlap in the time-energy phasespace. In the other two cases there is less matching, which
results in a narrower bandwidth. Due to RF curvature, thebest overlap occurs at different part of the seed for eachcase, hence the wavelength is also shifted.
t

γ

λ

0.8
0.6
0.4
0.2

1.4
263

264
265
wavelength (nm)

266

267

Figure 5: Several CPA HGHG Spectra (bottom). The top
part illustrates the explanation for the different spectrums
as an effect or the RF curvature. See text for details.
1.0
SASE spectrum
HGHG spectrum no chirp
CPA HGHG ~1 MeV
CPA HGHG ~2 MeV
CPA HGHG ~3 MeV

normalized spectrum

0.8

1/3 BW of seed

1.3
1.0

1.2
1.1
1.0
0.9
0.40

0.6

1.8 nm
1.5 nmSpectrum at∆γ/γ = 0.62 %

0.0
262

FWHM bandwith (nm)normalized spectrum

1.0

essential for later compression to generate short pulses.
Figure 7 shows the measured bandwidth as a functionof the energy chirp of the electron bunch. Since the seedlaser bandwidth is 5.5 nm, we expect the CPA withbandwidth of 1.8 nm in idealized situation (our current
experiment is carried out in 3rd harmonic of the seed at
800 nm with output at 266 nm, hence the bandwidth isdivided by 3 for a perfect CPA condition). The actuallyachieved bandwidth is 1.5 nm, with future potential offurther improved bandwidth more close to 1.8 nm. Basedon this data, the expected compressed CPA output pulse
length would be about 50 fs or larger, depends on thequality of the preservation of the phase linearity in the
HGHG process.

0.45

0.5

0.0
266 267 268 269 270 271
wavelength (nm)

0.50

0.55
∆γ/γ (%)

0.60

0.65

0.70

0.4

Figure 7: Spectral bandwidth vs Chirp. The inset shows
the recorded spectrum at a chirp of 0.62 %.

0.2

The next steps in this direction will be the measurementof the preservation of the phase chirp linearity by amethod called Spectral Interferometry for Direct Electric
Field Reconstruction (SPIDER) [16] and actually carryout the compression as a first demonstration of CPA in
FEL. This is now in advanced stage of preparation.
In Figure 8 we show the basic principle of the SPIDER.
The 266 nm output pulse is split into two temporarily
spaced pulses and mixed with a longer 800 nm chirped
pulse and creates two 400 nm pulses. Since the 800 nm
pulse is chirped, these two 400 nm pulses not only arespatially separated, but also have their wavelength shifted
relative to each other. Hence, when they are sent to a

0.0
262

264

266
268
wavelength (nm)

270

272

Figure 6: Chirped and unchirped HGHG spectra.
In Figure 6 we plot the 3 spectra with the spectrum of
SASE and HGHG without chirp (the pink curve withminimum bandwidth has nearly fourier transform limited
bandwidth). It clearly shows the significant increase of the
bandwidth for CPA, and the smooth profile of the CPA
spectra, compared with the SASE spectrum indicate thewell preserved coherence for the CPA output, which is
delay
line

τ

BBO
frequency doubler
800 nm 400 nm

two sheared
replicasτtime-seperated
266 nm beam
beam
replicas
HGHG splitter combiner

spectro
meter

2π/τ

t
ω

800 nmchirped laser-pulseωω0ω0 + ΩΩ

Figure 8: Principle of the SPIDER (Spectral Interferometry for Direct Electric-Field Reconstruction) setup [10].

FEL Prize Talk and New Lasing

4

L.H. Yu / Proceedings of the 2004 FEL Conference, 1-7

spectrometer, their spectrum form a interference pattern asshow in the upper right corner of the figure. The fringes
give information about the relation between the phase andfrequency, thus can be used to reconstruct the electricfield of the 266 nm pulse.
A first SPIDER measurement result for an unchirped
HGHG pulse is shown in Figure 9. It is clear the phasechange within the bandwidth is negligible. The
measurement on chirped pulse is still under way.
In the future works, it would be challenging andexciting to develop CPA bellow 200 nm, which would be
an unprecedented achievement, in particular below 100
nm once our electron beam energy is upgraded to
300MeV.
A first SPIDER measurement result for an unchirped
HGHG pulse is shown in Figure 9. It is clear the phasechange within the bandwidth is negligible. The
measurement on chirped pulse is still under way, somepreliminary results are presented in the reference in theseproceedings [16].
In the future works, it would be challenging andexciting to develop CPA bellow 200 nm, which would be
an unprecedented achievement, in particular below 100
nm once our electron beam energy is upgraded to
300MeV.
amplitude
phase

30

100 nm instead of the present 266 nm, as shown in theschematic of Figure 10. The output reaches saturation to
100MW at about 8 m in NISUS, as shown in Figure 11.
There will be non-linear harmonic output at 33 nm of
about 1 MW, which will have significant applications inchemistry too.
As we mentioned before, the local energy spread isfound to be less than 1×10-4 during the recent experiment.
Actually there are indications that this can be as small as
0.3×10-4. Theory of HGHG predicts that the highest
harmonic number is determined by the local energy
spread. Hence it means it is possible to reach even higher
than 8 for the harmonic number in the future (ours will belimited to 8 by the 300 MeV electron beam energy weplan to upgrade to).
The significance of higher harmonic number in HGHG
is that for a cascaded HGHG scheme it means we need
fewer stages of HGHG to achieve shorter wavelength.
Hence the demonstration of 8th harmonic HGHG will
have important impact on future development.
The proposed 8th harmonic HGHG requires only the
reduction of vacuum chamber of the present MINI
undulator (the 0.8 m modulator before the NISUS) fromthe present about 4 cm to 2.1 cm, and a minor
modification of the corresponding supporting mechanicalstructure of the undulator. Hence the cost associated withthis advance is very low, the required man-power is also
very limited.
9

10

10
0

-10

-0.02

-0.01

0

ω - ω (PHz)

0.01

0.02

output power [W]radians

20

8

10

7

10

0

Figure 9: First SPIDER measurement of an unchirped
HGHG pulse.
800nm

Dispersive
Section
MINI

100nm

NISUS

33nm

Figure 10: Experimental setup for lasing at the 8th
harmonic.
th

8 harmonic HGHG at DUVFEL
Our present HGHG is in 3rd harmonic, as we havementioned before. The design was based on data from 10
years ago, and was a conservative one: it was based on theassumption of local energy spread of 1.5×10-3, while ourrecent experiment showed it is bellow 1×10-4. Based on
our new data obtained during the HGHG experiment, we
propose to carry out new 8th harmonic HGHG experimentwith seed still at 800 nm, but output directly shorten to

MOAIS03

6

10

0

2.5

5
7.5
wiggler length [m]10

Figure 11: TDA simulation of the power vs distance for
100 nm in HGHG from 800 nm.

Short pulse HGHG
In the present HGHG experiment the electron bunch
length is 1 ps, while the seed laser pulse length is 9 ps, as
described in the PRL paper [3]. In a cascaded HGHG
experiment the pulse length should be much shorter thanthe electron bunch length. In the proposed cascaded
HGHG experiment, we shall use a seed length of 200 fs
long. Hence as a first step towards the cascaded HGHG
experiment, we shall test one stage of HGHG with 200 fs
seed pulse. When the time jitter between the seed and theelectron bunch is negligible compared with the electron
bunch length, the measurement of the HGHG output

5

L.H. Yu / Proceedings of the 2004 FEL Conference, 1-7

HGHG output 266 nm, 1ps

266 nm, 6 psstretchercompressordelay
266 nm, 0.2ps

Figure 12: Regenerative synchronization of a seed pulse and electron bunches [ref].
power as a function of the relative delay between the seed
and the electron bunch can be used to characterize theelectron beam parameters as a function of time within theelectron bunch length. This information is very important
for the understanding of the properties of the electron
beam.
However, there is a time jitter of about 300 fs FWHM,
as we have mentioned before. This will give an error bar
about the current profile obtained by the scanning of theshort pulse HGHG. Hence a statistical analysis of themeasured scanning data should be carried out to comparewith theory to see if this error bar profile is consistent
with the 300 fs jitter, measured by the electro-opticalmethod.
This experiment does not need new hardware, and has
already been in an early stage of study. The success of
this experiment will confirm the feasibility of the
proposed cascaded HGHG experiment. In particular, it
will confirm the theoretical prediction of the relation
between the output pulse energy fluctuation and the time
jitter.

Regenerative synchronization of a seed laser
with the electron bunch
As we mentioned before, it is important that the time
jitter between the seed laser pulse and the electron bunchshould be much smaller than the electron bunch length.
This condition is roughly satisfied in our proposedcascaded HGHG experiment: the jitter is 300 fs FWHM
while the electron bunch is 1ps. However, further
reduction of this jitter is desirable: it will reduce thefluctuation caused by the time jitter. Furthermore, in the
future possible multi-staged cascaded HGHG FEL, we
may need to use more than two “fresh” parts of theelectron bunch, and to achieve much shorter wavelength,
we may need higher current so the electron bunch should
be further compressed, thus the electron bunch length may
be shorter (e.g., 400 fs bunch length for a 750 A current
with the same electron bunch charge of 300 pC for ourcase to achieve 2 nm soft-x-ray FEL). Both of these will
require the time jitter to be further reduced.
Our recent analysis provides a new scheme to reduce
the time jitter from 300 fs to below 50 fs [17]. In thisscheme, as shown in Figure 12, the HGHG output at 266
nm is sent back to the photo-cathode of the RF gun to

generate a second electron bunch. In the mean time, abeam splitter will divert a small fraction of the HGHG
output to seed the next HGHG stage. In the specificexample as described in detail in the reference [17], using
the present DUVFEL as a demonstration of the basic
principle of this regenerative synchronization scheme, the1 ps output of the HGHG pulse will be stretched by apulse stacking method to the desired photo-cathode pulse
length of 8 ps, while the split seed pulse for the next
HGHG stage is compressed to 200 fs or less. The firstcathode drive laser pulse may have a time jitter relative to
the RF phase of the order of 300 fs, however, since thefirst seed pulse is a few ps long, and the electron bunch is
1ps long, the jitter will not cause any significant
fluctuation in the first HGHG output.
Since the first HGHG output pulse length is completely
determined by the 1ps electron bunch length, it is exactly
synchronized with the electron bunch. The electron bunchat the exit of the RF gun has a time jitter of about 300 fs,
i.e., the same as the time jitter of the photo-cathode laser,which is exactly synchronized with the seed laser pulse.
However, since the electron bunch is compressed from 6
ps to 1 ps, the time jitter of the electron bunch after thecompressor is also reduced by the compression ratio of 6,i.e., reduced from 300 fs to 50 fs. Hence, the jitter of the
HGHG output is also reduced to 50 fs relative to the RF
system. Thus the second electron bunch at the exit of the
RF gun jitters also less than 50 fs.
Much more detailed and lengthy analysis as given byreference [17] shows that the time jitter between thesecond seed pulse and the second electron bunch is
reduced by the compression ratio when compared with thejitter between the first electron bunch and the externallaser, i.e., it is reduced from 300 fs to 50 fs. As a byproduct, the electron beam energy fluctuation of thesecond electron bunch is also reduced by the same
compression ratio, which in our DUVFEL case is about 5
to 6. Due to the high stability of HGHG process, theoperation condition of HGHG can be arranged to fully
explore the slow varying nature of the peak of the Bessel
function in the micro-bunching process [18] so that if theseed intensity is higher then the output of HGHG will beslightly lower and vise versa. Like negative feedback, thisfurther reduces the intensity fluctuation HGHG output.

FEL Prize Talk and New Lasing

6

L.H. Yu / Proceedings of the 2004 FEL Conference, 1-7

As we can see from this brief discussion and as
described in detail in reference [17], the required
hardware for this synchronization experiment mainly
consists of an optical transport line, an opticalcompressor, and a pulse stretcher, all the rest is theexisting DUVFEL system. Hence the cost is also verylow.
Once this synchronization is achieved, a detailed studyof the temporal structure of the electron bunch in the time
resolution of about 50 fs can be realized, and a much
more stable output in the cascaded HGHG output can be
expected, making it much easier to generalize thecascaded scheme to more stages and reach much shorter
wavelength. This would be a significant advance in thefield.

Figure 13: Scheme to tune the HGHG output wavelength
without changing the seed wavelength [19]Tunable HGHG without changing seed wavelength
A new practical scheme to tune the HGHG output
wavelength without changing the seed wavelength has
been proposed recently [19]. The scheme uses the factthat the dispersion section slightly compresses theelectron bunch if it is energy chirped. As shown in Figure
13, after passing the modulator the electron bunch is
chirped by a first RF cavity (“XRF”), and then, after
passing through the dispersion section “DS” the chirp isremoved by the second RF cavity. The energy modulation
impressed upon the electron beam in the modulator isconverted into micro-bunching in the dispersion section as
in the usual HGHG process. However, the electron bunchis slightly compressed too, resulting also the slightcompression of wavelength (if the chirp is positive, i.e.,
the tail of the bunch has higher energy). If the chirp is
negative, it is obvious that the wavelength will become
longer.

Figure 14: The spectrum of several HGHG output withdifferent chirp but for a fixed seed wavelength.

MOAIS03

Recent experiment at DUVFEL has used the chirp
generated in the last section of the accelerator to confirm a
1% tuning. The spectrum of several HGHG output withdifferent chirp but for a fixed seed wavelength are shownin Figure 14. With increased dispersion section we canverify larger tuning range. An analysis shows that it ispossible to tune 20% wavelength when the two RF
cavities shown in Figure 14 are used. It is obvious that
this will greatly simplify the tuning of the HGHG process,and will have wide applications.

Summary
Based on the previous analysis, and the impact andscale of the several experiments, we can summarize theseexperiments in the order of a suggest time sequence asfollows:• Chirped Pulse Amplification• HGHG with seed shorter than electron bunch length• 8th harmonic HGHG (800nm!100nm)• Regenerative synchronization of seed pulse andelectron bunch• Tuning of HGHG without changing seed
• Cascading using NISUS + VISA: 400nm!100nm!50nm.
It is seen that the cascading experiment requires theremoval of the last 4 meters of NISUS and the installationof the VISA section, which will be a significant
interruption of the DUVFEL schedule. Also the assemblyand measurement of the VISA system will take time.
Therefore, even though the cascading will have the mostimportant impact, it is suggested to be implemented after
the completion of the first five experiments. We
emphasize that, as we have explained, this cascading
experiment design is based on the existing beam
parameters and existing parts, the experiment is not only
very important, it is also rather realistic and cost effective.

REFEREENCES[1] L.-H. Yu, M. Babzien, I. Ben-Zvi, L. F. DiMauro, A.
Doyuran, W. Graves, E. Johnson, S. Krinsky, R.
Malone, I. Pogorelsky, J. Skaritka, G. Rakowsky, L.
Solomon, X.J. Wang, M. Woodle, V. Yakimenko,
S.G. Biedron, J.N. Galayda, E. Gluskin, J. Jagger, V.
Sajaev, I. Vasserman, Science, 289 (2000) 932[2] A. Doyuran, M. Babzien, T. Shaftan , S.G. Biedron,L. H. Yu, I. Ben-Zvi, L.F. DiMauro, W. Graves , E.
Johnson, S. Krinsky, R. Malone, I. Pogorelsky, J.
Skaritka, G. Rakowsky, X.J. Wang, M. Woodle, V.
Yakimenko, J. Jagger, V. Sajaev, I. Vasserman ,Phys. Rev. Lett. 86, 5902 (2001)[3] L.H. Yu, A . Doyuran, L. DiMauro, W. S. Graves, E.
D. Johnson, R. Heese, S. Krinsky, H. Loos, J.B.
Murphy, G. Rakowsky, J. Rose, T. Shaftan, B.
Sheehy, J. Skaritka, X.J. Wang, Z. Wu, PRL, 91, 7,074801 (2003)[4] Workshop on the Physics of Seeded FELs ,MIT
http://mitbates.mit.edu/xfel/conference.htm. (6/2004)

L.H. Yu / Proceedings of the 2004 FEL Conference, 1-7[5] D. Krämer, “A Multistage HGHG-Scheme for the
BESSY Soft X-ray Multi User FEL Facility”, theseproceedings (2004).
[6] S. Di Mitri, R.J. Bakker, P. Craievich, G. D'Auria, G.
De Ninno, B. Diviacco, L. Tosi, V. Verzilov, “Startto-end simulations for the FERMI project at
ELETTRA”, these proceedings.
[7] J. Corlett, W. Fawley, G. Penn, W. Wan, and A.
Zholents, M. Reinsch and J. Wurtele, contribution
THPOS51, in these Proceedings[8] http://mitbates.mit.edu/xfel/[9] Zhao Zhentang, private communication (2004)[10] Juhao Wu, and Li Hua Yu, Nucl. Instru. Meth.,
A475, (2001) 104[11] S.G. Biedron, S.V. Milton, H.P. Freund, Nuclear
Instruments and Methods in Physics Research, A475
(2001) 401[12] F. Ciocci, G. Dattoli, A. De Angelis, B. Faatz, F.
Garosi, L. Giannessi, P. L. Ottaviani, A. Torre, IEEE
J. of Quant. Electron., 31-7 (1995), 1242
[13] H. Loos, A. Doyuran, J. B. Murphy, J. Rose, T.
Shaftan, B. Sheehy,Y. Shen, J. Skaritka, X.J. Wang,
Z. Wu, L.H. Yu, PAC 2003

7[14] L.H.Yu, E.Johnson, D.Li, D.Umstadter, Phys. Rev.
E, Phys. Rev. E, 49, 4480 (1994)[15] A. Doyuran, L. Di Mauro, R. Heese, E.D. Johnson, S.
Krinsky, H. Loos,, J.B. Murphy, G. Rakowsky, J.
Rose, T. Shaftan, B. Sheehy, Y. Shen, J. Skaritka, X.
Wang, Z. Wu, L.H. Yu, Proceedings of FEL2003,
Tuskuba , Japan (2003)[16] Z. Wu, E. Johnson, S. Krinsky, H. Loos, J. Murphy,
T. Shaftan, B. Sheehy, Y. Shen, X. Wang, L.H. Yu,“Spectral Phase Modulation and chirped pulse
amplification in HGHG”, these proceedings[17] L.H.Yu, Proceedings of FEL2003, Tuskuba , Japan(2003) BNL-71194-2003-IR[18] Juhao Wu, L. H. Yu, BNL report 67732, (2000)[19] T. Shaftan, S. Krinsky, H. Loos, J. Murphy, J. Rose,
B. Sheehy, J. Skaritka, X. Wang, Z. Wu, L.H. Yu,“Experiments on the HGHG Wavelength Tuning at
the DUV FEL”, these proceedings (2004)

FEL Prize Talk and New Lasing

8

P. Michel et al. / Proceedings of the 2004 FEL Conference, 8-13

FIRST LASING OF THE ELBE MID-IR FEL
P. Michel, F. Gabriel, E. Grosse, P. Evtushenko, T. Dekorsy, M. Krenz, M. Helm,
U. Lehnert, W. Seidel, R. Wünsch, D. Wohlfarth, A. Wolf
Forschungszentrum Rossendorf, Germany
Abstract
First lasing of the mid-infrared free-electron laser at
ELBE was achieved on May 7, 2004. The Radiation Source
ELBE at the Forschungszentrum Rossendorf in Dresden iscurrently under transition from commissioning to regularuser operation. Presently the electron linac produces an
up to 18 MeV, 1 mA (cw) electron beam which is alotted to generate various kinds of secondary radiation. Afterthe successful commissioning of the bremsstrahlung andchanneling-X-ray facilities during 2003 stable lasing has
now been observed in the IR range (15 to 22 µm). The oscillator FEL is equipped with two planar undulator units,
both consisting of 34 hybrid permanent magnets with a period of 27.3 mm (Krms = 0.3 . . . 0.8). The distance between the two parts is variable and the gaps can be adjusted
and tapered independently. At 19.6 µm an optical power of
3 W was outcoupled in a macro pulse of 0.6 ms duration
using an electron beam energy of 16.1 MeV and an energy spread of less than 100 keV. The micropulse charge
was 50 pC and its width slightly above 1 ps. With the installation of a second acceleration module for additional
20 MeV shorter wavelengths will become available in thenear future.

INTRODUCTION
At Forschungszentrum Rossendorf a superconducting
Electron Linac with high Brilliance and low Emittance(ELBE) has been constructed which can deliver a 1 mA
cw beam at 40 MeV [1]. The electron beam is used togenerate infrared light (Free Electron Lasers), X-rays (electron channelling), MeV-Bremsstrahlung, fast neutrons andpositrons. Table 1 gives an overview of the secondary
beams at the ELBE facility and the associated fields of science.

OVERVIEW OF THE ELBE FEL
The ELBE accelerator is fed by a grid-pulsed thermionicgun operating at 250 keV. The gun can deliver 450 ps longpulses and bunch charges up to 77 pC at 13 MHz or 4 pC
at 260 MHz. A macro pulser chops the electron beam withadjustable duty cycle and allows to generate a very flexible
time structure. By means of two RF buncher cavities operating at 260 MHz and 1.3 GHz the pulses are compressed
down to 10 ps upon injection into the first accelerator module.
The Linac uses standing wave RF cavities (1.3 GHz) designed for the TESLA test facility at DESY [2]. Two 9-cell

MOAIS04

Table 1: Secondary radiation sources at ELBE and theirscientific application
0. . . 20 MeV-nuclear physics
γ-radiation-astrophysics
10. . . 100 keV X-rays-radiation damage of cells-study of phase transitions inliquid metals

5. . . 150 µm
infrared FEL-semiconductor physics-radiochemical and biological experiments

0. . . 30 MeV neutrons-materials studies for fusion
reactors

0. . . 30 keV positrons-defect studies in solids

superconducting niobium cavities are contained in a cryomodule cooled with superfluid helium at about 2 K. Eachcavity has its own RF coupler and is driven by a 10 kW
CPI klystron amplifier. The standard accelerating gradientamounts to 10 MeV/m and the beam energy after acceleration is 20 MeV. Downstream the first cryomodule a magnetic chicane is used for bunch length variation. After the
installation of the second LINAC module in near future thefull energy of ELBE of 40 MeV will be available.
Infrared radiation in the 5–25 µm range will be produced
at ELBE in the undulator U27 [3]. It consists of two 34pole sections with a length of 0.98 m each. The undulator structure has a period of λu =27.3 mm and consists of
NdFeB permanent magnets and poles of decarburized iron(hybride type; the units were test modules for the TTFFacility at DESY [4] and are modified for use as a “passive” undulator). The sections are mounted on carriages(delivered by DANFYSIK) such that the distance between
the two sections is adjustable for phase-matching. The
gaps (minimum=13.8 mm, corresponding to Krms =0.70)
of both sections can be varied independently. For high-gain
lasing it is possible to introduce a taper of the field. Bothsections were scanned and adjusted using a calibrated Hall
probe setup at DESY. After installation at ELBE the field
distribution was checked using the pulsed wire method [5].
The inner dimension of 10 x 34 mm2 of the stainless steel
vacuum chamber in the undulator required a well designed
resonator. The cavity requirements are summarized in thefollowing Table 2.
To optimize the extraction ratio over the whole wavelength range we use 5 mirrors with different hole sizes in

Available online at http://www.JACoW.org

9

P. Michel et al. / Proceedings of the 2004 FEL Conference, 8-13

IR Laboratories
Neutrons

Free Electron Laser (IR)Neutron TOF
Experiments
Positron
Production

Accelerator Hall
chicaneRF-generators
Accelerator
Electronics

Bremsstrahlung

X-rays

X-raysExperimentControl

Positrons

10 m

Figure 1: Layout of the radiation source ELBE.
outcoupling mirror

Table 2: Design parameters of the U27 resonatorresonator typestable, near concentric, symmetriccavity length11.53 m, stabilized < 0.5 µm
tilt stability< 6 µradRayleigh range
1m
mirror diameter
7.5 cmradii of curvature
5.94 mg2
0.88
diameter of the 1.5, 2.0, 3.0 and 4.5 mm
outcoupling holes

the upstream mirror chamber. The Au-coated Cu-mirrors
are mounted on a revolvable holder (wheel), which is fixed
to a high-precision rotational stage. Angular adjustmentof the mirror wheel is performed using piezoelectric inchworm UHV motors, which provide both coarse and fineadjustments. A similar construction with 3 mirrors of different curvature is used in the downstream chamber. Here,the angular as well as longitudinal adjustment are designedwith micrometers and a flexible bar for fine tuning driven
by DC-motors outside the vacuum. The translation stage ofthis mirror will be used to adjust the cavity length to <5 µm
accuracy.
To ensure the stability of the resonator at wavelengths
down to 3 µm we require the mirror angular adjustment tohave a resolution and stability in the order of 6 µrad. For
the initial alignment of the mirror angles an accuracy in theorder of 20 µrad is required. To achieve this accuracy webuilt an alignment system consisting of two collinear HeNe lasers using insertable adjustment apertures inside thecavity.

mirrorundulator

DC-Mot.

70%
30%
splitterPC
laser

setting D L à cavity detuning
stabilization d (L + D L) < " 0.5 m m

Figure 2: Schematic view of the resonator length control
system. Its time constant is one Hz and hence fast in comparison to the thermal time constant of the resonator.

A Hewlett-Packard interferometer system is used tomonitor and stabilize the resonator length (see Fig. 2).
The interferometer beam is split into two beams (70% and30%). The low-intensity beam monitors the position of the
upstream mirror using one of five retro reflectors installedadjacent to each outcoupling mirror. The high intensity
beam passes through the same resonator chamber as themain laser and the electron beam. However, constraints
on the width of the vacuum chamber do not leave enoughspace in the cavity for a separate parallel interferometer
beam. Therefore, the latter will pass diagonally from one
side of the upstream cavity mirror to a retro reflector on theother side of the downstream mirror. The control electronics for the two interferometer arms include a servo system
to control and stabilize the relative distance between thetwo cavity mirrors using the motorized micrometer driveon the translation stage of the downstream chamber. Thereis no active tilt stabilization.
Estimating the maximum intracavity laser power, up to
15 W (cw regime) can be absorbed in the mirrors despite

FEL Prize Talk and New Lasing

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P. Michel et al. / Proceedings of the 2004 FEL Conference, 8-13

their high reflectivity of more than 99% . To stabilize themirror wheel temperature we installed a heater in the centerof the wheel. Independently of whether the laser is working
or not all components are at the same equilibrium temperature slightly above the expected saturation temperature.
The mirror wheel is made of Cu to reduce mechanical tension between the mirrors and the surrounding material but
thermally isolated from the high-precision rotational stage.
The heat is dissipated directly to the outside of the vacuum
chamber (Peltier element or air cooling).
Behind the out coupling hole the divergent IR beam
passes through a CVD diamond vacuum window (thickness 320 µm; useable aperture 8 mm) mounted at Brewster
angle. The adjacent optical transport system [6] guides thebeam to the diagnostic station using 4 (3 toroidal and 1flat) gold plated copper mirrors. The optics of the system
was aligned by monitoring the spatial intensity profiles of a
He-Ne guide laser which in turn is aligned to the resonatoraxis. The same laser will be used for indicating the positionof the IR beam in each user laboratory with an accuracy
better than 200 µm. Therefore, all optical components ofthe transport system have to be transparent for IR radiationand for 632 nm as well. Spot size and position of the waist
at the diagnostic table are independent of the wavelength.
Linear polarization is conserved. The transport system andthe diagnostic station [7] both are purged with dry nitrogento avoid absorption in air. From the main beam, approximately 10. . . 40 percent of the total power are extracted bydifferent beam splitters for wavelength measurement andpower monitoring.

FEL COMMISSIONING
Electron beam parameters measurements and diagnostics
One of the first steps in the FEL commissioning was theelectron beam characterization done at a beam energy of
16 MeV. The transverse emittance was measured in the injector with the multislit method, while the emittance of theaccelerated beam was measured with the quadrupole scan.
At the maximum design bunch charge of 77 pC the emittance is measured to be 8 mm mrad. The gain reduction
factor due to the finite emittance was 0.97 at first lasing,i.e., is almost negligible.
Since the FEL gain is linearly proportional to the beam
peak current it is highly desirable to minimise the electron
bunch length in the vicinity of the undulator. Previously,
the bunch length was measured to 1.5 ps (rms) immediately
at the accelerator exit using a Martin-Puplett interferometer(MPI). At the undulator with the beam tuned for lasing thisvalue is however different. One can groupe the beam line
elements, which influence the bunch length, between theaccelerator exit and the undulator in three groups. These
are the magnetic chicane, the “S”–shaped part of the beamline and drift spaces. The chicane can be used to adjust theR56 of the FEL beam line. For the FEL commissioning

MOAIS04

Figure 3: Electron beam parameters dependence on thesecond cavity phase (dots show the cavity gradient needed
for constant energy, squares the energy spread and the line
the bunchlength signal).

the MPI was installed right downstream of the undulator.
Additionally a single Golay cell detectors was installed upstream of the “S” shaped part of the beam line to measure
the total power of the coherent transition radiation, whichis in the first approximation inversely proportional to thebunch length. Note that the two Golay cells installed at
the interferometer can be used in the same way for thebunch length minimisation without scanning the interferometer. One of the key elements to tune the longitudinal
phase space is the second accelerator cavity. Adjusting thecavity phase one changes the electron beam energy spreadand the bunch length in the undulator vicinity because of
the non-zero R56 of the beam line. For that reason the energy spread and the Golay cell signals were measured as afunction of the second cavity phase. Fig. 3 shows results ofthe measurements. The bunch length at its minimum canbe measured with the help of the interferometer. Here the
FWHM of the interferogram is about of 2.5 ps.
The most important observation to note is the following: adjusting the cavity phase to have minimum energy
spread drastically increases the bunch length in the undulator . In fact at the energy spread minimum the bunch length
is so long that it cannot be measured with the MPI. It turnes
out, however, that for lasing at the used (rather long) wavelength it is more critical to minimize the energy spread of
the beam than to minimize the bunchlength.
The electron beam profile and position in the undulator
are measured with the help of OTR view screens. They
are made of beryllium and have a prism shape. The prism
has a 1 mm diameter hole with is precisely aligned to themagnetic axis of the undulator. The view screens are used
for the optical cavity alignment as well, which is important
to ensure the overlap between the electron beam and theoptical mode. It is noteworthy that the view screens are extremely long-term reproducible and reliable, which meansthat every time an inserted view screen takes the same po-

11

P. Michel et al. / Proceedings of the 2004 FEL Conference, 8-13

sition with a 10 µm accuracy.
ELBE is equipped with a strip-line beam position monitor (BPM) system. The resolution of the system is about
10 µm. There are two phenomena, which make this system very useful during the FEL operation. First, there isan energy drift observed for the first 2–3 hours every time
the linac is switched on. A BPM located in a dispersive
region is used to monitor the electron beam energy and tocompensate the drift. The second phenomenon is the dependence of the R56 of the “S” shaped beam line on theelectron beam path through it. Both phenomena are to beinvestigated more detailed in the future.

Observation of the spontaneous radiation
The general idea for the first FEL turn–on was to observe
the spontaneous undulator radiation and to maximize it bysystematic adjustment of the optical cavity and the electron beam parameters. First, the spontaneous radiation wasobserved downstream of the undulator so that the opticalcavity was not incorporated in the measurements. For that
purpose a mirror was inserted in to the beam line behindthe last dipole deflecting the beam to the dump. The spontaneous radiation was outcoupled off the beam line througha KRS–5 window and focused by a parabolic mirror on aliquid nitrogen cooled MCT detector. An accurate alignment of the setup was essential for the spontaneous radiation measurements. For the first observation of the spontaneous radiation we had to use an extremely strong averaging of the data, however, that was an important step for thecommissioning, since once the spontaneous radiation wasobserved we could optimize the machine using it as a tune
signal.

Setting the optical cavity length
The adjustment of the FEL cavity to the correct lengthis an important prerequisite for the achievement of lasing.
The cavity length of the FEL has been determined by employing an external frequency stabilized fs mode-locked
Ti:sapphire laser (Femtolasers, Austria) [8]. The fs laser
is operated at 78.0 MHz, i.e. the 6th harmonic of the FEL.
A 390 MHz reference signal is derived from the RF electronics of the gun, which is used for stabilizing the repetition rate of the fs laser with a phase-lock loop at its 5th
harmonic. This synchronization scheme reduces the timing
jitter of the fs laser to 500 fs. The pulse train of the fs laser
operating at 800 nm with 15 fs pulse duration is directed
through the outcoupling hole into the FEL cavity. The lightre-emitted through the outcoupling hole is detected via abeam splitter and a fast photodiode. When perfect synchronism of the fs laser and the FEL cavity is achieved,
the detected optical pulse is enhanced due to constructive
superposition of pulses circulating in the cavity. This results in an increase of the detected pulse intensity by a factor of five. The correct cavity length is determined by thismethod with an accuracy of some µm, i.e. a relative accuracy of 10−7 . Since the expected FEL operation covers a

Figure 4: FEL spectra measured at different optical cavity
detuning.
cavity detuning range of several 10 µm, this accuracy was
sufficient to start lasing at the preset cavity length.

FIRST RESULTSFirst lasing of the mid-infrared free-electron laser at
ELBE was achieved on May 7, 2004. At 19.6 µm an optical power of 3 W was outcoupled using an macro-pulsed
electron beam with anenergy of 16.1 MeV and an energy
spread of less than 100 keV. The bunch charge charge was
50 pC.

The optical spectrum of the FEL
The FEL spectra were measured with a Czerny-Turnertype spectrometer (SpectraPro-300i from ARC) which contains a turret with three different gratings (75 l/mm, blazed
at 8 µm; 60 l/mm, blazed at 15 µm; 30 l/mm, blazed at
30 µm). For these measurements we used the side exit slit
equipped with a single MCT detector. Fig. 4 shows how
the spectral width decreases with the detuning of the cavity
length.

Detuning curves
Up to now we operate the FEL in a pulsed mode only using an MCT detector to measure the FEL power as a function of time. In that mode the small signal gain is measured
by fitting an exponential function to the rising slope of the
MCT signal in its very beginning. The amplitude of the
MCT detector close to the macropulse end is associatedwith the saturated power. The saturation power as well as
the small signal gain are measured as a function of the optical cavity detuning. Typical results of such measurements
are shown in Fig. 5.
Such measurements are made in the beginning of every
FEL run, since the active cavity length stabilization is not
yet commissioned and the cavity length may change between the runs. The measured detuning curve appears in

FEL Prize Talk and New Lasing

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P. Michel et al. / Proceedings of the 2004 FEL Conference, 8-13

Figure 5: The saturation power (line) and the FEL net gain
(dots) vs. optical cavity detuning.

Figure 6: Optical cavity losses.

correspondence with the shape predicted by theory. It isalso clearly observed that the detuning which optimizes the
FEL gain differs from the detuning that optimizes the saturated power, which is also expected according to the theory.

FEL off

Optical cavity loss measurements

Electron beam energy spectrum
After the electron beam passes the undulator it is deflected to the beam dump by a dipole. There is a quadrupole
doublet between the dipole and the dump, which is normally adjusted to have maximum transmission of the electron beam to the dump. However, it can also be also adjusted to image the electron beam energy spectrum on aview screen. Fig. 7 shows both the electron beam energy
spectra when the FEL is off and when the FEL turns on.
An increase of the energy spread is observed as predicted
by Madey’s second theorem. The change of the electron

MOAIS04

FEL on1.0
0.8

Intensity, a.u.

The optical cavity losses can be measured similar to thesmall signal gain. At the end of the macropulse the electron
beam is turned off instantaneously. Then, the characteristic
decay time of the MCT signal carries the information on
the cavity losses, which includes diffraction losses at theundulator vacuum chamber as well as the losses on the mirrors and the outcoupled beam. Thus, the total cavity losses
were measured as a function of the FEL wavelength. The
losses were also calculated using numerical code GLAD.
The measurements are in reasonable agreement with thecalculations. However, one has to note that the calculations
are also limited in accuracy, probably of the same order ofmagnitude as the measurement accuracy. In the code there
is no element like a tube which could simulate the vacuum
chamber. For that reason a set of apertures was used to that
purpose, which also causes some systematic error. Moredetailed numerical calculations of the cavity losses are in
progress. Results of both the measurements and the calculations are shown in Fig. 6.

0.6
0.4
0.2
0.0
0

5

10

15

20

25

X, mm

Figure 7: Electron beam spectrum change when the FELturns on.
beam mean energy is measured as well, which allows one
to estimate the amount of energy transferred from the electron beam to the optical beam.

Autocorrelation IR pulse length measurements
To characterize the ultrashort pulses generated by the
FEL we built a non-collinear background-free autocorrelator. As SHG medium we use a CdTe crystal [9]. CdTe istransparent for a wide wavelength range in the FIR, thus, agood candidate for SHG of the FEL radiation.
In Fig. 8 we present the autocorrelation function measured at the maximum-power point of the detuning curve.
From the measured autocorrelation we calculate a pulse
duration of 2.1 ps, assuming a Gaussian temporal pulse
shape. The FWHM of the spectrum is approx. 220 nm.
The calculated time-bandwidth product is 0.46 which indicates Fourier-transform limited operation.

13

P. Michel et al. / Proceedings of the 2004 FEL Conference, 8-13

accuracy better than a ps. Two laboratories are intended
to provide users with utmost flexibility for their own experiments, also in scientific areas not covered by in-housegroups (e.g., surface physics, molecular physics).
Instructions for beamtime applications will be available
on the FELBE website (www.fz-rossendof.de/FELBE) by
the end of 2004.

ACKNOWLEDGEMENTS
Figure 8: Power spectrum (left) and corresponding SHG
autocorrelation (right) at the maximum power point of thecavity detuning curve shown in the insert (left).

FURTHER DEVELOPMENT
The ELBE far-IR FEL
To produce IR radiation in the THz region (up to
150 µm) an electromagnetic undulator with an undulator
period of 12 cm is envisaged. In this region the FEL constitutes a unique radiation source. Radiation quanta with thisenergy are appropriate for the spectroscopy of low-energy
elementary and collective excitations in solid-state quantum structures and in complex biomolecules as well (e.g.
in DNA molecules).
Restricting the electron beam of ELBE to energies above
20 MeV, where the energy spread is better than at lower energies, an undulator with 50 periods guarantees a laser gainof 30%. This undulator should be supplied with a rectangular waveguide which is 10 mm high and extends fromthe undulator entrance to the downstream resonator mirror. Appropriate mirror curvatures minimize the resonatorlosses to values below 10%.

The ELBE FEL as a user facility

The authors would like to thank the colleagues from
HEPL Stanford University, DESY Hamburg, Jlab Newport News and FELIX Nieuwegein for strong help anduseful discussions. Special thanks to Prof. Todd Smith,
A.F.G. van der Meer and Kevin Jordan.

REFERENCES[1] F. Gabriel et al., NIM B 161–163 (2000), 1143–1147[2] TESLA Test Facility Linac – Design Report (Ed. D.A. Edwards), DESY print TESLA 95–01[3] P. Gippner et al., Contribution to the 23rd Int. Free Electron Laser Conf. Darmstadt, Germany, 2001, Nucl. Instr. andMeth. A483 (2002) II–55[4] B. Faatz, J. Pflüger and Y.M. Nikitina, Nucl. Instr. Meth. A
375 (1996) 618[5] P. Evtushenko et al., Contribution to the 25th Int. Free Electron Laser Conf. Tzukuba, Japan, 2003
[6] Th. Dekorsy et al., Contribution to the 24th Int. Free Electron Laser Conf. Argonne, USA, 2002, Nucl. Instr. and Meth.
A507 (2003) II–35[7] W. Seidel et al., Annual Report 2001, FZR–341 (2002) 34[8] K.W. Berryman, P. Haar, and B.A. Richman, Nucl. Inst.
Meth. A 358 (1995) 260–263[9] J. Xu, G.M.H. Knippels, D. Oepts, and A.F.G. van der Meer,
Opt. Comm. 197 (2001) 379–383

It is the intention that by the year 2005, the FEL operates as a user facility, being open to users worldwide, provided their scientific proposals have been favorably evaluated by the panel responsible for distribution of beamtime.
Under the name “FELBE” the facility is member of the
EC funded “Integrating Activity on Synchrotron and Free
Electron Laser Science (IA-SFS)”, which comprises mostsynchrotron and FEL facilities in Europe and provides financial support to users from EC and associated states.
The relevant user facilities at FELBE comprise 6 laboratories. Some of these are also used by in-house groups,
mainly in the areas of semiconductor physics, biophysics,
and radiochemistry, and experiments there will require acertain level of collaboration with the in-house researchers.
In particular noteworthy is the fact that a number of otheroptical sources from the visible to the THz frequency range
are available, e.g. for two-color pump-probe experiments.
These sources (Ti:sapphire laser and amplifer, OPO, OPA,
broad-band THz generator) are all based on Ti:sapphireoscillators which are synchronized with the FEL with an

FEL Prize Talk and New Lasing

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Y. Pinhasi et al. / Proceedings of the 2004 FEL Conference, 14-17

BACKWARD WAVE EXCITATION AND GENERATION OF
OSCILLATIONS IN DISTRIBUTED GAIN MEDIA AND
FREE-ELECTRON LASERS IN THE ABSENCE OF FEEDBACK
Yosef Pinhasi, Asher Yahalom, Yuri Lurie, Gad A. Pinhasi
Faculty of Engineering
The College of Judea and Samaria
P.O. Box 3, Ariel 44837, Israel

Abstract
Quantum and free-electron lasers (FELs) are based on
distributed interactions between electromagnetic radiationand gain media. In an amplifier configuration, a forward wave is amplified while propagating in a polarized
medium. Formulating a coupled mode theory for excitation of both forward and backward waves, we identify conditions for phase matching, leading to efficient excitation of
backward wave without any mechanism of feedback or resonator assembly. The excitations of incident and reflected
waves are described by a set of coupled differential equations expressed in the frequency domain. The induced polarization is given in terms of an electronic susceptibility
tensor. In quantum lasers the interaction is described by
two first order differential equations, while in high-gain
free-electron lasers, the differential equations are of thethird order each. Analytical solutions of reflectance andtransmittance for both quantum lasers and FELs are presented. It is found that when the solutions become infinite,
the device operates as an oscillator, producing radiation at
the output with no field at its input, entirely without any
localized or distributed feedback.

INTRODUCTION
Conventional (quantum) lasers, microwave tubes andfree-electron lasers (FELs) are based on distributed interactions between electromagnetic radiation and gain media.
When such devices are operating in an amplifier configuration, a forward wave is amplified while propagating in apolarized medium, in a stimulated emission process [1].
In an oscillator configuration a resonator [2]-[4] or a distributed feedback [5] are employed to circulate the radiation, which is excited and amplified by the gain medium. If
the single-pass gain is higher than the total losses, the radiation intensity inside the cavity increases and becomes more
coherent. After several round trips, the radiation is built up
until arriving at the nonlinear regime and saturation.
In this paper we suggest a mechanism of generationof laser oscillations, without any feedback means. It isshown that under conditions of phase-matching, both forward and backward waves can be excited in a distributed

MOCOS03

Figure 1: Schematic illustration of incident and reflected
waves in a distributed gain medium.
gain medium as illustrated schematically in Figure 1. The
excitation of incident and reflected waves is described bya set of two differential equations coupled by the induced
polarization of the gain media. The coupling coefficient isgiven in terms of the electronic susceptibility tensor.
Two cases are discussed: In quantum lasers, which arecharacterized by isotropic, homogeneous gain media, theinteraction is described by two first order differential equations. In high-gain free-electron lasers, where the susceptibility is space dependent, the set includes two differential
equations of the third order each. The coupled equations
sets are solved analytically for both cases. Oscillation conditions are identified from the derived reflectance and transmittance coefficients.

EXCITATION OF FORWARD AND
BACKWARD MODES
The total electromagnetic field is given by the time harmonic wave vector:


−jωt

(1)
E(r, t) =  E(r)e
where E(r)is the phasor of the wave oscillating at an angular frequency ω. The vector r stands for the (x, y, z) coordinates, where (x, y) are the transverse coordinates andAvailable online at http://www.JACoW.org

15

Y. Pinhasi et al. / Proceedings of the 2004 FEL Conference, 14-17

z is the axis of propagation. In the case of excitation of
forward and backward modes, the phasor can be written as
the sum [6]: y) (2)E(r)= C+ (z) e+jkz z + C− (z) e−jkz z E(x,C+ (z) and C− (z) are scalar amplitudes of forward and y) and axbackward modes respectively, with profile E(x,ial wavenumber kz . The evolution of the amplitudes of theexcited modes is described by a set of two coupled differential equations: d1 ∓jkz z
 · E∗ (x, y) dx dy (3)C± (z) = ∓
e
J(r)
dz
2N

QUANTUM LASERWe relate first to gain media, where the electronic susceptibility does not change along the axis of propagation z.
This situation occurs in quantum lasers, where the atomic
susceptibility of the gain medium is uniform [1]. In thatcase the coupling parameter is not yet space (z) dependentand can be presented in the form κ(ω) = γ(ω) + jβ(ω),
where γ(ω) is the field gain factor. Consequently, the set(8) can be written as two coupled first order linear differential equations:ddz

The normalization of the mode amplitudes is made via thecomplex Poynting vector power:   ∗ (x, y) · ẑ dx dyE⊥ (x, y) × H
(4)
N =
⊥
The total power carried by the forward and backward(propagating) modes is:
  

1
 ∗ (r) · ẑ dx dy


E(r)
×H
P (z) =
2

1
=
(5)
|C+ (z)|2 − |C− (z)|2 ·  {N }2When the interaction takes place in a polarized gain
medium, the driving current density J(r)is given in termsof the induced polarization (dipole moment per unit volume) P(r).
In the time domain, the current density is thetime derivative of the induced polarization. Thus, the phasor representation of the driving current density is given
by:



(6)
J(r)
= −jω P(r)= −jωε0 χ(r, ω) · E(r)where χ(r, ω) is the electronic susceptibility tensor at thefrequency ω (in a homogeneous isotropic medium it is ascalar). Using (6) in (3) results in:C− (z)
C+ (0)(10)−κ sinh [S(L − z)]e+jkz z(κ + jkz ) sinh(SL) − S cosh(SL)=(κ + jkz )2 − κ2 is a complex parameter.
where S ≡The evolution of incident and reflected wave amplitudes
along the gain medium are shown in Fig. 2. It is assumed
that the interaction takes place in the vicinity of the resonance frequency, where κ(ω0 ) is real.
12

(a)

K L=1

2

10
8
6
4
2
0
10

(b)

kzL=1
kzL=2
kzL=3
kzL=4

8

C+ (z)C− (z)

2+κ(z)e−j2kz z−κ(z)C+ (z)C− (z)

(11)

=

+κ(z)
−κ(z)e+j2kz z+κe−j2kz z−κC+ (z)=
C+ (0)(κ + jkz ) sinh [S(L − z)] − S cosh [S(L − z)] −jkz ze(κ + jkz ) sinh(SL) − S cosh(SL)(8)

The coupling parameter:κ(z, ω) ≡ ωε0 y) · χ(r, ω) · E∗ (x, y) dx dy
j
E(x,
2N

|C−(z)/C+(0)|C+ (z)C− (z)=

Analytical solution of the coupled set (10) for a given forward mode amplitude C+ (0) at the input z = 0, while
the backward mode amplitude at the exit of the interaction
region (z = L) is C− (L) = 0, leads to the solution ofincident and reflected wave amplitudes:(7)

Substitution of the field expansion (2) in the excitation
equations (7), the mode amplitudes C± (z) are describedby a set of two coupled differential equations, that can bepresented in a matrix form:ddz+κ−κe+j2kz z|C+(z)/C+(0)|dC± (z) =dz ωε0 ∓jkz z

±j
e
E(r)
· χ(r, ω) · E∗ (x, y) dx dy
2NC+ (z)C− (z)

6
4
2
0

(9)

is in general a complex, space-frequency dependent quantity.

0

0.1

0.2

0.3

0.4

0.5
z/L

0.6

0.7

0.8

0.9

1

Figure 2: The evolution of (a) incident and (b) reflectedwave amplitudes along the gain medium.

FEL Theory

16

Y. Pinhasi et al. / Proceedings of the 2004 FEL Conference, 14-17

The transmission gain is defined by:high gain limit the amplitudes of the forward and backward
waves is described by two coupled third order linear differential equations:

C+ (L)=
C+ (0)−SLe−jkz L(κ + jkz )L sinh(SL) − SL cosh(SL)

(12)

d3
dz 3

+κ
−κe+j2kz z

Respectively, the reflection gain is:C− (0)−κL sinh(SL)=C+ (0)(κ + jkz )L sinh(SL) − SL cosh(SL)(13)

Contour plots of the transmission and reflection power gainin the (kz L, κL) plane are shown in Figure 3. An infinite
gain singularities are inspected when the denominator of
the gain dispersion relations given in (12) and (13) vanishes. This happens when:SLκL + jkz Ltanh(SL) =C+ (z)C− (z)(14)

In that case the forward and backward modes will be excited in the absence of an input signal, resulting in excitation and buildup of oscillations. Equation (14) expresses
the oscillation condition, determining the threshold gain
factor required for excitation of oscillations and their resultant frequencies at steady-state.

=+κe−j2kz z−κC+ (z)C− (z)(15)

where the coupling parameter:0 ζq ωp2
= j
2 (kz + kw )4N vz0 
 w · E∗ (x, y) dx dy×f (x, y) Epm (x, y) V
⊥
⊥

κ

(16)

where Eqpm (x, y) is the pondermotive field, f (x, y) is thetransverse profile of the e-beam and ωp is the plasma frequency of a relativistic beam with average axial electron
velocity vz0 .
We solved the coupled set (15) analytically. The amplitude of the forward wave can be written as:
C+ (z) = e−jkz z

6

ci eλi kz z

(17)

i=1

HIGH GAIN FREE-ELECTRON LASER

and the backward wave’s amplitude is:In free-electron lasers, the accelerated electrons serve asa gain medium and the interaction with the electromagnetic
field takes place along the e-beam axis. Coupled mode
theory for multi transverse mode excitation was developed
previously, deriving an expression for the gain-dispersion
relation in the linear regime of the FEL operation [7].
Set of equations (3) for the different modes were solved
together with the small-signal moment equations describing the evolution in the driving current modulation. In the
5

(a)

2

|C+(L)/C+(0)|

1

4

1

10

1

10

1

2

10

100
10

1

100

KL

3

0

100

10

10

10

0
5

10

(b)

2

|C−(0)/C+(0)|

10

4

100

3
KL

10

2
10

100

1

100

10

1

10

0
10

1

1

10

15

1
0

0

5
kz L

Figure 3: (a) Transmission and (b) reflection contours inthe (kz L, κL) plane for atomic laser.

MOCOS03C− (z) = e+jkz z

6(j − λi )3 λi kz z
ci e
(j + λi )3
i=1

(18)

where the six eigenvalues λi appear in the above solutions
are found from a characteristic equation of the sixth order.
Fortunately it can be written in a third order form:
γ 3 + 3γ 2 + 3γ(1 − jw) + 1 + jw = 0(19)

in which γ = λ2 and w = 2κkz3 , enabling analytical solution of λi . The properties of the eigenvalues λi are discussed in the Appendix. The constants ci are determinedby the boundary conditions. Assuming that there is no prebunching in the electron beam, an initial amplitude C+ (0)is assumed for the forward mode at z = 0 and all the other(0) = C+(0) = C− (0) =boundary conditions are C+
C− (0) = C− (0) = 0 (here denotes first order derivativeddz ). The analytical results were verified using a numericalalgorithm solving the boundary condition problem. Figure 4 presents contour plots of the transmission and reflection power gain in the (kz L, κL3 ) plane. Oscillations are
expected where an infinite gain is obtained.

ACKNOWLEDGMENTS
The research was supported by the Israel Science Foundation.

17

Y. Pinhasi et al. / Proceedings of the 2004 FEL Conference, 14-1750+

Equation (19) can be readily solved and the solutions are:

10

10

(a)

|C (L)/C (0)|2
40

+

1
1

00

100

10

10

KL

100

3

30

0

10

100

10

10

10
0
50

γ2

=

γ3

=

10

(b)

10

2

|C−(0)/C+(0)|= −1 + ba −

10

10

20

a2
b
√
√
√
1
[−γ1 (1 + 3j) − 3 − 3j + 2 3jab]
2
√
√
√
1
[−γ1 (1 − 3j) − 3 + 3j − 2 3jab](23)2γ1where:

00

10

100

40
30
KL

3

100

100

1000

10

1

a = (−jw) 3

10

10

1

1

1

We see that:0

4 − jw) 3

γ3 (w) = γ2∗ (−w)

101b = (2 +

(24)

10

100

10

20

5

10

15

kz L

Figure 4: (a) Transmission and (b) reflection contours inthe (kz L, κL3 ) plane for free-electron laser.

REFERENCES[1] A. Yariv, Nucl. Optical Electronics, Holt Rinehart and Winston (1991)[2] A. L. Schawlow and C. H. Towens, em Phys. Rev. 112, 1940
(1958)[3] V. L. Bratman, N. S. Ginzburg and M. I. Petelin, Optics.
Comm. 30, 409 (1979)[4] T. M. Antonsen and B. Levush, Phys. Fluids B 1, 1097 (1989)

Hence one can deduce the behavior of the roots for negative
w values from their behavior for positive values.
In the case w → 0 we obtain limw→0 γi = −1 fori ∈ [1, 2, 3]. This is obviously a degenerate case in which
the solution is not of an exponential type. Inserting the condition w → 0 into equation (15) one is left with the trivial
C+ (z)
d3= 0 with the solution:
equation dz
3
C− (z)
C+ (z)=C− (z)=

lim γ1=

lim γ2=

lim γ3=w→∞[6] Y. Pinhasi, Yu. Lurie, A. Yahalom, A. Abramovich, Nucl. Instr. Methods Phys. Res. A 483, 510 (2002)w→∞[7] Y. Pinhasi and A. Gover, Phys. Rev. E. 51, 2472 (1995)w→∞

The six eigenvalues calculated from equation (19) come√in positive-negative pairs λ = ± γ. Taking complex conjugate of equation (19) (assuming that w is real):γ ∗3 + 3γ ∗2 + 3γ ∗ (1 + jw) + 1 − jw = 0(20)

reveals that the solutions satisfy the relation:∗(−w) = γn (w)
γm

√

5

1

1

1

3e 4 πj w 2
3e 4 πj w 2(27)

lim λ3lim λ41
1∼= 3 4 (0.383 − 0.924j)w 4

lim λ51
1∼= 3 4 (0.924 + 0.383j)w 4

lim λ61
1∼= 3 4 (−0.924 − 0.383j)w 4

lim λ2w→∞(21)

in which m, n are the solution indices. However, since wehave a total of three roots to equation (19) , at least one of
the roots, say γ1 , satisfies the relation:w→∞that is its real part is even with respect to w and its imaginary part is odd.

1
3
√

1
√
3
1
= −√
3
1
1
∼
= 3 4 (−0.383 + 0.924j)w 4

lim λ1

w→∞

w→∞

(22)

(26)

Since non of those are negative real numbers this meansthat we have three growing exponents and three decaying
exponents in the case of large w those are:w→∞

γ1∗ (−w) = γ1 (w)

1 2 (2)(1)(0)
z c+ + zc+ + c+2
1 2 (2)(1)(0)
z c− + zc− + c−
2

In the opposite limit in which w → ∞ we obtain the following results:[5] H. Kogelnik and C. V. Shank, em J. Appl. Phys. 43, 2328
(1972)

APPENDIX

(25)

w→∞

=

(28)

For large w, λ5 is clearly the most dominant exponent. Although λ1 & λ2 asymptotically approach a finite number,the other eigenvalues continue to grow without limit.

FEL Theory

18

M.D. Dohlus et al. / Proceedings of the 2004 FEL Conference, 18-21

CSRtrack: FASTER CALCULATION OF 3-D CSR EFFECTS
M. Dohlus, T. Limberg, DESY, Hamburg, Germany
Abstract
CSRtrack is a new code for the simulation of Coherent
Synchrotron Radiation effects on the beam dynamics oflinear accelerators. It incorporates the physics of ourprevious code, TraFiC4 [1], and adds new algorithms forthe calculation of the CSR fields. A one-dimensional
projected method allows quick estimates and a greens
function method allows 3-D calculations about hundred
times faster than with the ‘direct’ method for large
particle numbers.
The tracking code is written in standard FORTRAN77
and has its own parser for comfortable input of
calculation parameters and geometry. Phase space input
and the analysis of the traced particle distribution is donewith MATLAB interface programs.

INTRODUCTION
In usual optics and tracking codes for accelerator
development the bunch self fields due to synchrotron
radiation and changes of the bunch shape are neglected.
Therefore special CSR tracking codes have beendeveloped (e.g., TraFiC4 [1], CSRtrack, R.Li’s code [2])and existing codes have been expanded (e.g., Elegant[3,5], TREDI [4]). Essentially two types of approaches
are presently used for the self-consistent calculation ofparticle distributions on curved trajectories. Both areavailable in CSRtrack.
The 1-D approach uses a simplified model for the
calculation of longitudinal forces [6]. It neglects
transverse forces as well as transverse beam dimensions
and assumes that the longitudinal distribution isunchanged at retarded times. A ‘renormalized’ Coulomb
term is used to extract the field singularity in the 1-D
beam.
The sub-bunch approach uses a set of 3-D charge
distributions*, e.g., time-independent Gaussian, toapproximate the source distribution. The physical modelof the sub-bunch method is complete, but the resolutionof phase space modelling is severely limited by thenumerical effort for the field calculation of all point topoint interactions. Even with parallel computing particle
numbers above 103 are difficult to handle (CPU time on acluster is many days).
TraFiC4 and CSRtrack ease that problem by using a
convolution method [8] to reduce the field calculation of
3-D sources to 1-D integrations (for each interaction),
gaining about a factor of ten in manageable particle
numbers.
Further improvement is possible with a pseudo Green’s
function approach; it uses the discretized field of one
reference sub-bunch to calculate all interactions. Thismethod is implemented in CSRtrack and allows tracking
calculations with 104 particles on one CPU in a few hours,
up to 4⋅104 particles have been tracked on 20 CPUs.

MOCOS05

For the tracking of even bigger numbers of particles, thedisadvantage that the effort scales quadratic with thenumber of particles could be avoided by calculating theelectromagnetic fields on a mesh. With a combination ofmesh field calculation and pseudo Green’s function
method, >105 particles in less then one day (using 20
CPUs in parallel) seem to be in reach.

NUMERICAL ASPECTS OF DIFFERENTCSR FIELD CALCULATION METHODSIn the following we discuss different algorithms and theirrelative computation time consumption, which aresummarized in Fig. 2.
A word of warning: if the initial bunch density is
modulated, for instance to study CSR induced instability,
the computation time depends quadratically on the ratioof the bunch length to its fine structure – in any approach.
We will discuss that further in a paper to come.

One Dimensional Approach – Projected Method
The particle distribution is projected to the reference
trajectory and a smooth one dimensional charge density
λ(s) is calculated by binning or filtering. The smoothingis crucial for the stability and accuracy of the simulation
because the micro bunch instability is sensitive to highfrequency components in the charge density.
The longitudinal field E(λ) can be calculated by one
dimensional integration

E ( λ ) ( s0 , t0 ) = ∫ λ ′(u + s0 − vt0 ) K ( s0 , u )du ,with the kernel function K(s0,u) that depends on thegeometry of the trajectory. This integral is a convolution
in time. It can be solved efficiently by FFT methods if E(λ)
is required for a time interval.
The longitudinal field is calculated on a mesh andinterpolated to the projected particle positions. The
particle tracking takes into account external fields and thelongitudinal self field. The effort for the field calculation
depends linearly on the number of particles.

Sub-Bunch Approach
The distribution of source particles is described by a setof sub-bunches with well defined shape. The individual
trajectory of each sub-bunch has to be known in absolutecoordinates back in time. This defines the 3-D source
distribution ρ(r,t) so that potentials and electromagnetic
fields can be calculated by an integration of retarded
sources.
A disadvantage of the sub-bunch approach is the large
numerical effort. For M test particles and N source
distributions (sub-bunches) M×N three-dimensional
integrations have to be performed for every time step.
___________________________________________* 2-D sub-bunches in R.Li’s code

Available online at http://www.JACoW.org

19

M.D. Dohlus et al. / Proceedings of the 2004 FEL Conference, 18-21

Source Distributions and Test Particles

Pseudo Green’s Function Approach

For self consistent tracking the trajectory of eachsource is defined by the motion of an associated test
particle. Therefore M=N+Mt test particles are needed,with Mt the number of additional particles that can beused for more detailed explorations e.g. of the transverse
phase space. The effort for self consistent tracking is atleast proportional to N2. Additional test particles need thecomputation of N×Mt interactions.
If the bunch shape is weakly deformed due to self
forces a perturbation approach can be used. The self
forces to the test particles are calculated for unperturbed
motion of source distributions and test particles. These
forces are used in a second step to calculate the perturbed
motion. The initial condition of test particles can be set as
required (e.g. to investigate an individual slice) but atleast some test particles should be used to verify the
perturbation approach.

The fields E(0)(r,t0), B(0)(r,t0) of a reference sub-bunch(charge q0) that travels along a reference trajectory r0(t)are used to approximate the fields of other sub-bunches(charge qν, trajectory rν(t)). This approach neglectsvertical forces. At the observation time t0 the trajectory of
sub-bunch ν is approximated byrν (t ) ≈ rν (t0 ) + R ⋅ (r0 (t ) − r0 (t0 ) ) .

3-D Sub-Bunches, Convolution Method
Since the field of each source sub-bunch has to be
calculated for every test position by a 3-D integration ofretarded sources, the full field computations is quite time
consuming. For spherical Gaussian sub-bunches thisintegration can be reduced to a 1-D integral [7].
The codes TraFiC4 and CSRtrack adopt a calculation
method that was developed in [8]. A certain type of 3-D
distribution can be represented by the convolution of alongitudinal 1-D profile λ(s,t) with a transverse 2-D
density function η(x,y).
1d distribution

2d distribution

λ ( s, t )η ( x, y )⊗3d distribution

ρ (r )→

Fig 1: Schematic of the Convolution Method
Then the 3-D electromagnetic fields can also calculated
by a convolution of fields E(λ), B(λ) caused by the 1-D
source with the 2-D density function. E(λ) and B(λ) aresplit into singular parts E(λ,s) and B(λ,s), which are
dominated by local effects, and non-singular parts E(λ,ns)
and B(λ,ns). The asymptotic behaviour of the singular partis analytically known so that its convolution with certaintransverse density functions can be computed efficiently.
As the non singular parts depend mainly on long range
interactions, their transverse dependency is weak and theconvolutions E(λ,ns)⊗η, B(λ,ns)⊗η can be approximated byE(λ,ns), B(λ,ns) for sufficiently small transverse dimensions( << 3 R0σ λ2 , with R0 the curvature radius and σλ thebunch length). Therefore the numerical effort Ec isdetermined by the 1-D integration for the non singularparts. The total effort for all source to test-pointinteractions is M×N×Ec.

This shift-rotation-transformation (with rotation
operator R) is used to calculateqΕ(ν ) (r, t0 ) ≈ ν R ⋅ Ε( 0 ) (r0 (t0 ) + R −1 (r − rν (t0 )), t0 )q0(ν)
and B (r,t0) in the same way. The pseudo Green’s
functions E(0)(r,t0), B(0)(r,t0) are calculated once for every
time step on a 2-D mesh in the horizontal plane with Mg
points:Ε( 0) (r, t0 ) = E x ( x, y )u x + E y ( x, y )u y

B ( 0) (r, t0 ) = Bz ( x, y )u z
The numerical effort for the calculation of all self
forces is Mg×Ec+M×N×Ei,g with Ei,g the effort for theinterpolation on the mesh. The approach is effective for
N×M > Mg. Simulations with many particles (>104) are
not limited by the effort for the field calculation (Mg×Ec)
but by the effort for the interpolation (M×N×Ei,g).

Meshed EM Fields
If the density of particles is large compared to the finestructure of the particle distribution (and the self-fields) it
is more efficient to calculate electromagnetic fields on amesh with Mem points and to interpolate them to the test
points. The numerical effort is Mem×N×Ec+M×Ei,em with
Ei,em the effort for the interpolation on the field mesh. The
total effort is not longer proportional to the squared number of particles (M×N with M ≥ N for self consistent
tracking)!
Reasonable EM meshes need at least Mem > 104 points
and therefore the method gets efficient for M, N > 104.
The effort for such particle numbers is still too large(even with parallel computing) for routine investigations.
This is different if the meshed fields approach is
combined with the pseudo Green’s function approach:the total effort is Mg×Ec+Mem×N×Ei,g+ M×Ei,em. Thismethod is still in preparation.
e ffo rt
a .u

10 4

p

10 2

EM

-m

EM

10 3

p

Gr

esh

10 0

10 2

to

10 4

ee

n‘

s

sh
-m e

10 5

+ G

re e

n ‘s

N = M
10 6

Fig. 2: Numerical effort of different CSR fieldcalculation methods vs. # of tracked particles

FEL Theory

20

M.D. Dohlus et al. / Proceedings of the 2004 FEL Conference, 18-21

Iterative Tracking

Shielding

For tracking, self-forces have to be calculated for particles on phase space coordinates that depend on the unknown forces. If the track step is sufficiently small theforces can be approximated for phase space positions calculated without self contributions. To avoid the numericaleffort for very many small steps iterative tracking withmedium step size is used: estimated self forces are calculated for estimated particle positions and are used to improve the position estimation. The iteration is repeateduntil an error criterion is fulfilled.
The numerical integration of the equation of motion in
CSRtrack uses sub-steps that are (much) smaller than thesteps of the iterative force calculation. The forces at substeps are linearly interpolated between the force at thestart point of an iterative step and at its end point. The
error due to this linear interpolation and due to too big
iterative steps is not reduced by iterative tracking.
CSRtrack provides two possibilities to determine thesize of iterative steps: by a recursive algorithm that isbased on the bunch length and curvature radius of the
trajectory and by external definition. Like in all self-field
applying tracking codes, the result has to some extent to
be interpreted and justified by the user (e.g. convergencetests or the inspection of the forces observed by someselected test particles).

CSRtrack provides shielding as of now with parallel
ideal conducting plates with constant distance to thebeam. The user has to specify the maximum distance tothe beam up to which mirror charges will be taken into
account.

CSRtrack 1.0

Particles Definition
Position, momentum and charge of each particle of the
distribution are defined in an absolute Cartesian coordinate system with the horizontal plane as xy-plane. Particles with nonzero charge are source particles that create
self-fields that affect the motion of test particles. In thepresent versions all particles have the source and test
property.

Parallel Computing
CSRtrack is available as a parallel processing codeusing the MPI protocol with the MPICH package. Only
the sub-bunch methods are calculating parallel.
# ofparticles

calc.
steps

MethodCPU

Runningtime

10000~200 Point to point 20x1GHz ~ 10 d
10000~200 Greens funct.
1x1GHz ~0.5 d
41000~200 Greens funct. 20x1GHz ~0.5 d
Table 1: CPU time consumption of CSRtrack runs for
TTF2 and XFEL magnet chicanes

COMPARING RESULTS FOR DIFFERENTMETHODS
CSRtrack is well suited to explore the applicability ofdifferent CSR calculation methods. An example is acalculation for the European XFEL bunch compression
system (see Fig. 4).
The beam is tracked from the gun into the linac up to
about the 100 MeV point with a space charge code
(ASTRA). For the remaining injector linac up to the twomagnetic chicanes for bunch compression a linac tracking
code (elegant) is used. In the chicanes, where the beam
dynamics is dominated by CSR effects, we need to
employ CSRtrack.

Lattice
CSRtrack supports magnetic dipole- and multipolefields that are defined in Cartesian coordinates. The rangeof the fields of one element is limited by two fieldboundaries perpendicular to the horizontal plane. The
dipole field between two field boundaries is constant andparallel to the vertical z-axis. Together with the dipoles areference trajectory is defined that consists of arcs andlines.
To take into account vertical edge focussing at the hardedges of dipoles the tracking algorithm applies discrete
kicks proportional to the vertical offset. The magnetic
multipole field is defined in a local coordinate system(longitudinal, horizontal, vertical) with its origin in theintersection point of the reference trajectory and the fieldboundary.
The magnetic multipole field between field boundaries
depends only on transverse coordinates. It is characterized
by its strength, azimuthal order, transverse offset andskew angle.

MOCOS05

ASTRA(space charge)

ELEGANT(geom. Wakes, CSR)

CSR -Track
1

2 3

4

Fig. 4: Start-to-end calculation for the European XFELIn Fig. 5 the longitudinal phase space at the end of thebeam line is shown; calculated with the 1-D and a 3-D
method of CSRtrack. The RMS bunch length is about
20 µm, the peak current 5 kA.
The longitudinal tails of the initial distribution havebeen over-compressed back towards the center of the
distribution. They have to be excluded from any
meaningful evaluation of beam parameters vs.
longitudinal bunch position such as transverse slice
emittance or, as shown here, slice energy spread. In thegraphs, these particles are color coded.
The 1-D model underestimates the growth in slice
energy spread in the center of the bunch due to CSR
effects by a factor of 5-10.

21

M.D. Dohlus et al. / Proceedings of the 2004 FEL Conference, 18-21

dE/E

dE/E

0.04

0.04

0.02

0.02

0.0

0.0

-0.02

-0.02

-0.04

(dE-dE(0))/E

-0.04

-500

-480

-460

-440

s[µm] (dE-dE(0))/E

0.0

0.0

-0.002-0.002-0.004-0.004-500

RMS((dE-dE(0))/E)

-480

-460

-440

s[µm]

8*10 -4

8*10 -4
6*10 -4

4*10 -4

4*10 -4

2*10 -4

2*10 -4

-500

-480

-460

-440 s[µm]

-480

-460

-440

s[µm]

-500

-480

-460

-440

s[µm]

-500

-480

-460

RMS((dE-dE(0))/E)

6*10 -4

-520

-500

-520

-440

Fig. 5: Longitudinal Phase
Space at the end of thebunch compression system
calculated with the 3-D
Greens function method(left) and the projected 1-D
method (right).
The lower graphs show
the difference in particle
energies due to compression
and the RMS of that value
vs.
longitudinalbunchposition.
The particles in theenergy distribution tails areshown in blue and green.

s[µm]

POSTPROCESSING
We use MATLAB tools on a XP PC to administrate
and manipulate the data files and to run the tracking codeson both the local (XP) computer and a Linux PC cluster,in single CPU or parallel processing mode (see Fig. 6).

Input and output phase space data files can beinspected, changed and plotted.
User options are made invisible if they do not makesense; for example the option to display beam current (I)on the vertical axis disappears if something else than thelongitudinal coordinate is chosen for the horizontal axis.
File formats are checked and detected automatically to
avoid mistakes. Saving data in files works via thestandard XP ‘save as’ window, also the file formats (e.g.,
elegant or ASTRA) can be chosen with the familiar pulldown menu.

FURTHER PLANS, CONCLUSION
Soon a web page will be ready to download a CSRtrack
executable and a user’s guide with input examples. The
program has to be developed further to incorporate themesh option described above.

REFERENCES

Fig.6: MATLAB operating and post-processing GUIs

[1] T.Limberg, A.Kabel, M.Dohlus: Numerical Calculation of
CSR Effects Using TraFiC4. Nucl. Instrum.Meth. A455
(2000) 185-189.
[2] R.Li: Self-Consistent Simulation of the CSR Effect.
EPAC1998, Stockholm, Sweden June 1998.
[3] M.Borland: Simple Method for Particle Tracking with
Coherent Synchrotron radiation. Phys.Rev. ST AB
4(070701), July 2001.
[4] L.Giannessi, P.Musumeci, M.Quattromini: TREDI. NIM A
436, pp. 443-444, Nov. 1999.
[5] P.Emma: private communication[6] E. Saldin, E.Schneidmiller, M.Yurkov: Radiative Interactionof Electrons in a Bunch Moving in an Undulator. NIM
A417 (1998) 158-168.
[7] M. Dohlus: Two Methods for the Calculation of CSR Fields.
TESLA-FEL-2003-05.
[8] M. Dohlus, A. Kabel, T. Limberg: Efficient Field Calculation of 3-D Bunches on General Trajectories. NIM A445
(2000) 338-342.

FEL Theory

22

G. A. Geloni et al. / Proceedings of the 2004 FEL Conference, 22-25

A 3D SELF-CONSISTENT, ANALYTICAL MODEL FOR LONGITUDINALPLASMA OSCILLATION IN A RELATIVISTIC ELECTRON BEAM
Gianluca Geloni, Evgeni Saldin, Evgeni Schneidmiller and Mikhail Yurkov
Deutsches Elektronen-Synchrotron (DESY), Notkestrasse 85,
22607 Hamburg, Germany
Abstract
Longitudinal plasma oscillations are becoming a subjectof great interest for XFEL physics in connection with LSC
microbunching instability 1 and certain pump-probe synchronization schemes 2 . In the present paper we developed the first exact analytical treatment for longitudinal oscillations within an axis-symmetric, (relativistic) electron
beam, which can be used as a primary standard for benchmarking space-charge simulation codes. Also, this result
is per se of obvious theoretical relevance as it constitutes
one of the few exact solutions for the evolution of charged
particles under the action of self-interactions.

INTRODUCTION
Longitudinal space-charge oscillations have beentreated, so far, only from an electrodynamical viewpoint,
or using limited one-dimensional models: in this paper wereport a fully self-consistent solution to the initial value
problem for the evolution of a relativistic electron beam
under the action of its own fields in the (longitudinal) direction of motion. In our derivation the beam is accounted
for any given radial dependence of the particle distributionfunction. For a more detailed description of our work andreferences see [1].
An initial condition is set so that the beam, which is assumed infinitely long in the longitudinal direction, is modulated in energy and density at a given wavelength. Whenthe amplitude of the modulation is small enough the evolution equation can be linearized. An exact solution can befound in terms of an expansion in (self-reproducing) propagating eigenmodes.
Our findings are, in first instance, of theoretical importance since they constitute one of the few exact solutions
known up to date to the problem of particles evolving under the action of their own fields.
Yet, particle accelerator and FEL physics make large
use of simulation codes in order to obtain the influence of
space-charge fields on the beam behavior and these codes
are benchmarked against exact solutions of Poisson equation only; recently partial attempts have been made tobenchmark them against some analytical model accounting for the system evolution. However, such attempts are
based on one-dimensional theory which can only give some
1 E. Saldin et al. Longitudinal Spacs Charge Driven Michrobunching
instability in TTF linac, TESLA-FEL-2003-02, May 2003
2 J. Feldhaus et al.
Two-color FEL amplifier for femtosecondresolution pump-probe experiments with GW-scale X-ray and opticalpulses DESY 03-091, July 2003

MOPOS08

incomplete result. On the contrary, we claim that our findings can be used as a standard benchmark for any spacecharge code from now on.
Our results are of relevance to an entire class of practical problems arising in state-of-the-art FEL technology
when (optically) modulated electron beams are feed into an
FEL. For instance, optical seeding is a common techniquefor harmonic generation. Moreover, two-color pump-probe
schemes have been proposed which rely on the passageof an optically modulated electron beam through an X-ray
FEL and an optically tuned FEL: given the parameters of
the system, plasma oscillations turn out to be a relevant
effect to be accounted for. It is also important to mention, here, the relevance of plasma oscillation theory in theunderstanding of practical issues like longitudinal spacecharge instabilities in high-brightness linear accelerators
which may lead to beam microbunching and break up.

THEORYWe are interested in developing a theory to describe longitudinal plasma waves in a relativistic electron beam. We
do this assuming that transverse coordinates enter purely as
parameters in the description of the fields and of the particle distribution. Our beam is initially modulated at somewavelength λm , in density and energy. It is natural to define the phase ψ = ωm (z/vz (E0 ) − t), where vz (E0 ) ∼ cis the longitudinal electron velocity at the nominal beam
kinetic energy E0 = (γ − 1)mc2 , ωm = 2πvz /λm , t is thetime and z the longitudinal abscissa. It is then appropriate
to operate in energy-phase variables (P, ψ), P being thedeviation from the nominal energy.
Under the assumption of a small energy deviation P , theequations of motion for our system can be interpreted as
Hamilton canonical equations
corresponding to the Hamil
tonian H(ψ, P, z) = e dψEz + ωm P 2 /(2cγz2 E0 ). The
bunch density distribution will be then represented by thedensity f = f (ψ, P, z; r⊥ ). Linearization of the evolution equation for f is possible when f (ψ, P, z; r⊥ )|z=0 =f0 (P ; r⊥ ) + f1 (ψ, P, z; r⊥ )|z=0 , f0 being the unperturbed
solution of the evolution equation with f1  f0 for
any value of dynamical variables or parameters. Moreover we assume f0 (P ; r⊥ ) = n0 (r⊥ )F (P ), where thelocal energy spread function F (P ) is considered normalized to unity. The initial modulation can be written as a sum of density and energy modulation terms:
f1 (ψ, P, z; r⊥ )|z=0 = f1d (ψ, P ; r⊥ ) + f1e (ψ, P ; r⊥ )where f1d (ψ, P, z; r⊥ ) = a1d (r⊥ )F (P ) cos(ψ) andf1e (ψ, P, z; r⊥ ) = a1e (r⊥ )dF/dP cos(ψ + ψ0 ). Here

Available online at http://www.JACoW.org

23

G. A. Geloni et al. / Proceedings of the 2004 FEL Conference, 22-25

ψ0 is an initial (relative) phase between density and energy modulation. Finally it is convenient to define complex
quantities f˜1d = a1d F , and f˜1e = a1e (dF /dP )eiψ0 sothat f1| z=0 = (f˜1d + f˜1e )eiψ + CC. Further definition ofẼz = Ẽz (z; r⊥ ) in such a way that Ez = Ẽz eiψ + Ẽz∗ e−iψallows one to write the Vlasov equation linearized in f˜1 :
∂ f˜1
∂f0
ωm P
+ i 2 f˜1 − eẼz=0.
∂zcγz E0
∂P

iq 2
2π

ĵ1 =

(2)

The next step is to present the equation for the electric fieldẼz which, coupled with Eq. (2), will describe the systemevolution in a self-consistent way.
Starting with the inhomogeneous Maxwell equation for
the z-component of the electric field, passing to complex
quantities and assuming that the envelope of fields and currents vary slowly enough over the z coordinate (this simply
means that we can neglect retardation effects) we have∇2⊥ Ẽz −

2
Ẽz
ωm
4πiωm
= 2 2 j̃1 ,γz2 c2
γz c

+

iq 2
S0
2π

 ẑ



(4)

Definitions of naturally normalized quantities in Eq. (4)are as follows: r̂ = r⊥ /r0 , Êz = Ẽz /E0 , q =km r0 /γz , P̂ = P/(ρE0 ), â1d = −eca1d /J0 , â1e =−eceiψ0 a1e /(J0 ρE0 ), ẑ = ΛP z; F̂ (P̂ ) is normalized tounity and S0 , the transverse profile function of the beam,obeys S0 (0) = 1. Parameters are the typical transverse−1size of the beam r0 , J0 = I0 S(r⊥ /r0 )dr⊥
, E0 =
4πJ0 /ωm (where I0 is the beam current), the plasma wave
1/2
number ΛP = 4I/(IA r02 γγz2 )(IA = mc3 /e being the2
Alfven current), ρ = Λp γz /km . Moreover the rms energy
spread (∆E)2  can be measured by the dimensionless parameter Λ̂2T = (∆E)2 /ρ2 E02 and the dimensionless current densities can be written as ĵ0 = j0 /J0 ≡ S0 (r⊥ /r0 )and ĵ1 = j̃1 /J0 .
An equivalent description of the evolution of our systemin terms of ĵ1 can be obtained using the following result:

(5)

−∞

dẑ 



0


â1d F̂ + â1e

dF̂
dP̂

e−iP̂ ẑ(s)(s)
dr̂⊥ ĵ1 K0 q | r̂⊥ − r̂ ⊥ | ∞dF̂ iP̂ (ẑ −ẑ)
e
dP̂
×
.
dP̂
−∞

(6)

The description in terms of the fields is particularly suitable for analytical manipulations, while the description interms of currents is advisable in case of a numerical approach.

MAIN RESULT
After introduction of the Laplace transform of Êz ,Ē(p, r̂⊥ ), with Re(p) > 0, it follows from Eq. (4) thatLĒ = fwith :(7)ˆ 2⊥ + ĝ(r̂⊥ , p) ,
L=∇


dF̂
dP̂ â1d F̂ + â1ee−iP̂ ẑ
dP̂
−∞
 ẑ
 ∞
dF̂ iP̂ (ẑ −ẑ)e−iq 2 S0dẑ  Êz
dP̂
.
dP̂
0
−∞
 ∞


dP̂

(8)

(3)

which forms, together with Eq. (2), a self-consistent description for our system.
Combining Eq. (2) with Eq. (3) and using properly normalized quantities we obtain an integro-differential equation for the field evolution:
ˆ 2⊥ Êz − q 2 Êz = iq 2
∇


(s)
(s)
dr̂⊥ ĵ1 K0 q | r̂⊥ − r̂ ⊥ | ,

 ∞




−i ωm P z
dF iψ0dP a1d F + a1eej̃1 = −ec
e cγz2 E0
dP
  ∞

−∞
z
ωm P
(z  −z)dF i cγ−ej0dz ẼzdPe z2 E0
.
dP
0
−∞



where K0 indicates the modified Bessel function of thesecond kind. Then, substitution in Eq. (2) yields (using
dimensionless quantities):(1)

Let us now introduce the longitudinal current densityjz (z; r⊥ ) = −j0 (r⊥ ) + j̃1 eiψ + j̃1∗ e−iψ , where j0 (r⊥ ) ∞
ecn0 (r⊥ ) and j̃1  −ec −∞ dP f˜1 . From Eq. (1) follows
 ∞Êz = −f (r̂⊥ , p) = iq 2 D̂0 â1d + D̂â1e


,

(9)

ĝ(r̂⊥ , p) = −q 2 (1 − iD̂S0 ) ,
D̂0 =

 ∞
dP̂
−∞

F̂
, D̂ =
p + iP̂

 ∞
dP̂
−∞

(10)

dF̂ /dP̂
p + iP̂(11)

with the boundary conditions Ē −→ 0 for |r̂⊥ | −→ ∞and ∂ Ē/∂ r̂⊥ −→ 0 for |r̂⊥ | −→ ∞. Solution is found if
we can find the inverse of the operator L, namely a Greenfunction Ḡ obeying the given
conditions; in this boundaryḠ(r̂⊥ , r̂⊥)f (r̂⊥).
case we simply have Ē = dr̂⊥Assuming, without prove, completeness and discreteness of the spectrum of L (we ascribe to alternative theoretical approaches and numerical techniques the assessmentof the validity region of this assumption) we can expand Ḡ
using the eigenfunction of L defined by LΨj = Λj Ψj thus
gettingĒ = Ψj (r̂⊥ ) 
j

Λj




Ψj (r̂⊥)f (r̂⊥
).
dr̂⊥

(12)

To find Êz we use the inverse Laplace transformation andwe perform the integration analytically with the help of Jordan lemma. Although we write results in a general form,
this method is straightforward only in the case of a cold
beam F̂ = δ(P̂ ) that will be the only one considered here.
Then our final result is written as follows:Êz (ẑ, r̂⊥ ) =uj Φj (r̂⊥ )eλj ẑ ,

(13)

j

FEL Theory

24

G. A. Geloni et al. / Proceedings of the 2004 FEL Conference, 22-25


uj =



)f (r̂⊥, λj )
dr̂  Φj (r̂⊥
 ⊥
 
.
∂g

2
dr̂⊥ ∂p Ψj

(14)

p=λj

0,4

The modes Φj are not orthogonal. Appropriate initial conditions can be chosen to obtain a single propagating mode.
In order to excite a single mode at fixed values of j one
must impose:

0,2

^
E

0,0

-0,2

â1e
= −iλj ,â1dˆ 2⊥ − q 2 )Φj .
â1d = (∇

(15)

2,0

-0,40
2

1,5

4

From now on we will deal with case of an axis-symmetricbeam described with a cylindrical (normalized) coordinate
system (r̂, φ, ẑ), with obvious meaning of symbols. It isconvenient to discuss azimuthal harmonics of ĵ1 , Êz and(n)(n)
f which will be indicated with ĵ1 (z, r̂), Êz (ẑ; r̂) and(n)f (r̂, p). Our results Eq. (13) and Eq. (14) take the simpler form:Êz(n) (ẑ, r̂) =(n)unj Φnj (r̂)eλj

ẑ

,

6
8

unj (r̂) =(16)
Ψnj (r̂) =

(17)

p=λj

(18)

1
Kn (q) 0 dξJn (αj ξ)ξf (n) (ξ)

dJn (αj ) dp
[αJn+1 (α)Kn (q) − qKn+1 (q)Jn (α)]p=λ(n)j(20)

Parabolic profile - In this case S0 (r̂) = 1 − k12 r̂2 forr̂ < 1/k1 and S0 = 0 for r̂ ≥ 1/k1 . Solution for the homogeneous problem defined by L can be found in literature(see [1] for references). We can use that solution in order tosolve our eigenvalue problem, and to write the expressions
for the eigenfunctions Ψnj to be inserted in Eq. (13). Let(n)us introduce the following notations: µ2 = iD̂q 2 − Λj ,2(n)
= iD̂K12 , d2 = Λj ,2

δ= (n + 1)/2 − µ /(4δ). Aftersome calculation we find:

MOPOS08(22),

ALGORITHM FOR NUMERICALCALCULATIONS(19)

where αj2 = −q 2 (1 + 1/p2 ).

. (21)

Multilayer method approach - An arbitrary gradient axisymmetric profile can be approximated by means of agiven number of stepped profiles, or layers, superimposed
one to the other. Results for the stepped profile case can bethen used to construct an algorithm to deal with any profile(see [1] for more details).

(n)
It turns out that λj are imaginary and such that −1 <(n)Im(λj ) < 1. The solution for the evolution equation is:

unj =r̂ < 1r̂ ≥ 1

δKn (d) 2(n + 1)−1 1 F1 ( + 1, n + 2, δ)− 1 F1 (, n + 1, δ)] + dKn+1 (d) 1 F1 (, n + 1, δ) = 0 .

Stepped profile - In this case S0 = 1 for r̂ < 1 and S0 =(n) 20 for r̂ ≥ 1. Putting αj2 = −q 2 (1 + 1/λj ) we obtain
the eigenvalue equation:  u J (α r̂)eλj(n) ẑ
r̂ < 1jj nj n(n)  unj Jn (αj ) Kn (qr̂)eλj ẑ r̂ ≥ 1j
Kn (q)

2r̂n e−δr̂ /2 1 F1 (, n + 1, δr̂2 )n (dr̂)e−δ/2 1 F1 (, n + 1, δ) KK
ndwhere 1 F1 is the confluent hypergeometric function, andthe eigenvalue equation analogous of Eq. (18) is now

We give here some explicit calculations for several profile
cases.

Êz(n) (ẑ, r̂) =0,0

Figure 1: Ê = Re(Êz ) vs. ẑ and r̂. q = 1, n = 0; gaussiantransverse profile case with σ = 2.0.



αj Jn+1 (αj )Kn (q) − qKn+1 (q)Jn (αj ) = 0 .

^r

12
14

(n)

dr̂ r̂ Φnj f (n) (r̂ , λj )
0


.
∞
Ψ2nj
dr̂ r̂ ∂g
(n)
∂p
0

0,5

10

^z

j

∞

1,0

,

The linear regime assumption is not too restrictive but
it would be interesting to provide a solution for the fullproblem. As a first step towards this goal we present here anumerical solution of the evolution equation in the case ofan axis-symmetric beam, that we will cross-check with our
main result, Eq. (13). In order to build a numerical solution
it turns out convenient to make use of Eq. (6).
After some manipulations Eq. (6) yields:(n)d2 ĵ1dẑ 2= −q 2 S0

where
G(n) (r̂, r̂ ) =



 1
0

(n)

dr̂ r̂ G(n) ĵ1

In (qr̂)Kn (qr̂ )In (qr̂ )Kn (qr̂),

r̂ < r̂r̂ > r̂

(23)

,

(24)

25

G. A. Geloni et al. / Proceedings of the 2004 FEL Conference, 22-25

Multilayer
Analytical
N ume rical

^
E
0, 4

^
E
0, 4
0, 2

^z= 120, 2Final res ult
1s t Mode
2nd Mode
3r d Mode
4th Mode
5th Modez^ = 0

^ 0
z=
0, 0

^z= 3
0, 0

-0, 2

^z= 9

-0, 4

^z= 6

-0, 2

-0, 6
-0, 4

-0, 8
0, 0

0 ,5

1 ,0

1 ,5

2 ,0

-1, 0
0, 0

r^

Figure 2: Analytical (solid), 15 layers (dotted) and numerical (circles) method. Ê = Re(Êz ) is plotted vs. r̂. q = 1,n = 0; parabolic transverse profile with k1 = 1.0.

Eq. (23) is to be considered together with proper initialconditions for ĵ1 and its z-derivative at z = 0. The interval (0, 1) can be then divided into an arbitrary numberof parts so that Eq. (23) is transformed in a system of thesame number of 2nd order coupled differential equations
to be solved numerically. This gave us the solution of theevolution problem in terms of the beam current. Then we
calculated back Êz and we compared obtained results with
Eq. (13) for different choices of transverse profiles. The
real field Ez should be recovered but all relevant information is included in Re(Êz ). In Fig. 1 we present Re(Êz )as a function of ẑ and r̂ in the case of stepped, profile. The
initial conditions are proportional to the transverse distribution function (stepped), and n = 0; moreover â1e = 0.
Consistency with the perturbation theory approach requiresâ1d  1 but using â1d = ρ will simply multiply our resultsby an inessential factor ρ so, for simplicity, we chose ρ = 1.
Comparison with the Runge-Kutta integration program areshown for example in 2 for the parabolic case. Finally we
may actually select a single mode by fixing appropriate initial conditions as described in Eq. (15). For instance, if we
fix â1e = 0 and we excite only the j = 2 mode for theazimuthal harmonic n = 0, then, in the case S0 = 1 andq = 1 we obtain the results presented in Fig. 3 at ẑ = 0
and in Fig. 4 at ẑ = 10. As it can be seen by inspection
only the third mode is excited and evolves, as it should.

CONCLUSIONSIn this paper paper we presented one of the few selfconsistent analytical solutions for a system of charged particles under the action of their own electromagnetic fields.
Namely, we considered a relativistic electron beam under
the action of space-charge at given initial conditions forenergy and density modulation and we developed a fully
analytical, three-dimensional theory of plasma oscillationsin the direction of the beam motion in the linear regime.

0 ,2

0 ,4

0 ,6

0 ,8

1 ,0

1 ,2

r^

Figure 3: Selective excitation of the third mode. Here n =0. ẑ = 0^E

Final result
1s t Mode
2nd Mode
3r d Mode
4th Mode
5th Modez^ = 10

0, 4
0, 2
0, 0
-0, 2
-0, 4
-0, 6
-0, 8
-1, 0
0, 0

0 ,2

0 ,4

0 ,6

0 ,8

1 ,0

1 ,2

r^

Figure 4: Selective excitation of the third mode. Here n =0. ẑ = 10

We specialized the general method to the important casesof stepped and parabolic transverse profiles, which areamong the few analytically solvable situations. In particular, the stepped profile case could be used to develop asemi-analytical technique to solve the evolution problem
for the field using an arbitrary transverse shape. We also
developed an algorithm able to solve the evolution problem
in terms of the beam currents. Numerical and analyticalor semi-analytical solutions for the fields were then compared and gave a perfect agreement. Finally we showed
how to build up initial conditions in such a way that a single mode is excited and propagates through and we checked
our prescription by setting up particular initial conditions
and looking at the propagation of various eigenmodes.

REFERENCES[1] G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov,
DESY 04-112, see http://xxx.lanl.gov/abs/physics/0407024

FEL Theory

26

G. A. Geloni et al. / Proceedings of the 2004 FEL Conference, 26-29

BENCHMARK OF ASTRA WITH ANALYTICAL SOLUTION FOR THE
LONGITUDINAL PLASMA OSCILLATION PROBLEM
Gianluca Geloni, Evgeni Saldin, Evgeni Schneidmiller and Mikhail Yurkov
Deutsches Elektronen-Synchrotron (DESY), Notkestrasse 85,
22607 Hamburg, Germany
Abstract
During the design of X-FELs, space-charge codes are required to simulate the evolution of longitudinal plasma oscillation within an electron beam in connection with LSC
microbunching instability [1] and certain pump-probe synchronization schemes [2]. In the paper [3] we presented ananalytical solution to the initial value problem for longitudinal plasma oscillation in an electron beam. Such a result,besides its theoretical importance, allows one to benchmark
space-charge simulation programs against a self-consistentsolution of the evolution problem. In this paper we present
a comparison between our results [3] and the outcomes ofthe simulation code ASTRA.

INTRODUCTION
Start-to-end simulations of X-FEL systems require theuse of several codes, able to deal with different parts ofthe setup. In particular, at low energies, simulations mustaccount for space-charge interactions. These codes arealso used in connection with LSC microbunching instability problems [1] and certain pump-probe synchronization
schemes [2]: benchmarking them correctly is of critical importance since it is the only way to build up confidence intheir outcomes.
In this paper we present first results of an ongoing benchmark of the space-charge code ASTRA. Our work takes
advantage of the first three-dimensional, analytical modelfor the description of plasma oscillations within a relativistic electron beam, which has been described in [3] and [4].
This is the first time that such an analytical, self-consistentmodel is used to benchmark space-charge codes, which areusually compared with solutions of the Poisson equation
for specific charge distributions. We claim that our methodshould be considered as a standard for benchmarking thesecodes from now on. In the following we describe how thesimulation is set up, how it is compared with analytical results and we report the outcomes of this comparison as regards the estimation of a typical evolution parameter.

ANALYTICAL STUDY
We consider a radially uniform electron beam with transverse dimension r0 = 1.0 mm and length lb = 2.2 cm
propagating with kinetic energy Ek = 6.0 MeV and current I = 44.97 A. Longitudinal and transverse beam emittances are set to zero. A ρ = 5% density modulation isconsidered at a wavelength λm = 1 mm in the longitudi-

MOPOS090,06

ρ

R elative currentm odulation
Sinusoidalfit

0,04

0,02

0,00

-0,02

-0,04

-0,06
0

1

2

3

4

5

6

7

z

Figure 1: Relative current modulation level as a functionof position inside the beam line (in m) and sinusoidal fit analytical results. Parameters are given in the text.

nal direction. This modulation is uniform in the transverse
direction.
Our analytical theory [4] deals with the longitudinal dynamics of the system, so it is applicable, roughly speaking, when the beam does not evolve, transversely, during
the characteristic plasma oscillation length λp . This can be
implemented in a simulation by focusing the beam using
as we did, for instance, a longitudinal magnetic field Bz(compare with the next Section).
In our theory we describe the system evolution equivalently in terms of fields or currents. The former description is suitable, as has been remarked in [4] for numerical manipulations, while the latter gives us back a fully
analytical model: the results out of these descriptions, ofcourse, coincide. Our theory provides the longitudinal fieldEz (z, r) and current density Jz (z, r) as a function of thelongitudinal z and radial position r. As a first investigation, nevertheless, we were interested in how these quantities, averaged over the transverse beam distribution, compare with the analogous ones from ASTRA. Averaging Jzover the transverse distributionof the beam we get backr
the beam current I(z) = 0 0 Jz rdr, while integrating Ez
over z and averagingas for Jz we get back the momentumrz
pz (z) = −2e/(cr02 ) 0 ( 0 Ez dz  )rdr.
In our theory the fields are presented as a superposition of propagating eigenmodes. The parameters describedabove correspond to a region where the one-dimensional
asymptotic treatment of plasma oscillation is not applicable, and care was taken to choose them such that the

Available online at http://www.JACoW.org

G. A. Geloni et al. / Proceedings of the 2004 FEL Conference, 26-29

pz

7242 V/m, me being the electron mass in eV.
The maximum field on axis, multiplied by ez/c = 0.1 e
m/c is the maximum momentum modulation at z = 10 cm,
which may be compared with ASTRA results. Indeed, we
preferred to average Ez (z, r) at z = 10 cm over the transverse beam distribution and compare with the analogous
averaged value of pz from ASTRA.

M om entum m odulation
Sinusoidalfit

8000

27

6000
4000
2000
0
-2000
-4000

ASTRA SIMULATION

-6000
-8000
0

1

2

3

4

5

6

7

z

Figure 2: Momentum modulation (in eV/c) as a functionof position inside the beam line (in m) and sinusoidal fit analytical results. Parameters are given in the text.

first eigenmode is dominant with respect to the others. In
this case the beam current and the longitudinal momentum, considered as functions of z, are nearly sinusoidal andtherefore can be easily fitted 1 giving back, in both cases,
the same estimation for the wavelength of plasma oscillations, λp = 7.34 m. In Fig. 1 we present the modulationlevel as a function of z, while in Fig. 2 we plot pz (z) asfrom our theory. Both figures also include sinusoidal fits.
An alternative estimation of the plasma wavelength can beobtained, in the approximation when only the first eigenfunction is important, using the following equation (compare with [4]):1/2/Λ0  7.31m .
λp = 4I/(IA r02 γγz2 )(1)3Here IA = mc /e is the Alfven current, γ = γz = 12.7417
corresponds to a kinetic energy of 6 MeV and the first
eigenvalue Λ0 = 0.3804 is obtained from our analyticalmethod: note that Λ0 is sensibly different from unity, which
is a clear signature of the fact that the one-dimensional theory cannot be applied.
Together with the benchmark for the full program, one
can obtain, as a sort of by-product, a separate benchmark
for the electromagnetic solver of ASTRA alone. In fact, ata short distance z  λp the beam has not yet appreciably
evolved so that Ez is the solution to the electrostatic problem of the initial charge distribution. Our analytical technique gives, at z = 0.1 m, an electric field on axis (r = 0)Ez = 7235 V/m. We checked that one can recover roughly
the same value (with an accuracy of order 10−3 ) from thewell-known expression for the impedance per unit lengthof drift:



km r0
km r0
4
K1
1−
Z=
,
(2)
km r02γγ
where km = 2π/λm and K1 is the modified Bessel function of the second kind of order 1. In fact (I/IA )Zme =1 For this purpose we used the program ORIGIN.

For our purposes we used a modified version of ASTRA[5] using dynamic memory allocation, which allowed us to
set the number of macroparticles Nptc = 12 · 106 and weused the customary Generator program to produce a uniform, cold beam with no modulation. No particular option
for noise reduction was used. A 5% modulation was thensubsequently introduced by rearranging the z positions of
the particles using a short code written ad hoc: this allowed
to overcome numerical noise problems in the z direction,
related with the Generator program, but not with ASTRA
itself. A solenoidal field Bz = 7 T has been used to decouple the longitudinal from the transverse dynamics. The
question obviously arises if the transverse particle motion
is truly negligible. Because of Bz , particles undergo small
circular trajectories in the transverse plane with Larmor
frequency ωL = qBz /(γme ), q being the macroparticle
charge. The radius of these circles are related to the transverse velocities of the particles which are altered though,during the beam evolution, by the transverse space charge
force. A quick estimation shows that the particle-tracker
maximal integration step (which was set to 10 ps, corresponding to about 3 mm) is too long to sample the Larmor
motion correctly. Yet, if the effect of Larmor motion is negligible at any point in the z direction, this fact is not of concern. We checked that this is the case analyzing the transverse rms angular spread as a function of the z-position,and the maximal transverse momentum also as a functionof the z-position. We set the beam line length L = 7 m,which is about one full plasma oscillation length, according to our analytical estimations. A simple and conservative estimate shows that, at z = L = 7 m, every particle
moved, transversely, 6.5 · 10−5 m at most. This distanceshould be compared with the smaller transverse dimension
typical of our system. ASTRA divides the beam in several
radial slices for the calculation of the space-charge interactions. In our simulations we used 10 radial rings, with adifference of a factor 2 in thickness between the outer andthe inner ring. Given the beam dimension r0 = 1.0 mm wehave that throughout all the evolution a particle can move,at most, the dimension of the thinner ring. Moreover, one
should account for the fact that the transverse motion of
the particles introduce a small change in the longitudinal
projected motion of order (p⊥ /pz )2 ; however this can be
estimated to be less than 10−10 or, on a length of 7 m, lessthan 1 nm, which is completely negligible.
The previous discussion allows us to consider the transverse particle motion negligible and to compare ASTRAFEL Theory

28

G. A. Geloni et al. / Proceedings of the 2004 FEL Conference, 26-29

pz

pz

4000
150000100000

2000

50000

0
0

-2000
-50000

-4000

-6000
-0,002-100000-150000-0,001

0,000

0,001

0,002

-0,015

ζ-0,010-0,005

0,000

0,005

0,010

0,015

ζ

Position along the beam line z = 3 m

Figure 3: Particle longitudinal momenta pz (in eV/c) as afunction of the position inside the beam (in m) at 3 m inside
the beam line. The solid line represents the momentum
averaged over r. Nbin = 400.

Figure 4: Average particle longitudinal momentum pz (ineV/c) as a function of the position inside the beam (in m)
at 3 m inside the beam line. Nbin = 400.

N ptc
26000

results with our analytical results.
In order to calculate the space-charge fields, ASTRA divides the beam also in a number Nbin of longitudinal slices,or bins: this is a critical parameter which should be studied
to obtain correct results. A right estimation of the fields
will occur only when a sufficiently large number of bins
is chosen: considering a modulation wavelength λm , anintuitive guideline is that the number of bins per radiantshould be larger than unity. At the same time, the number of particles in each bin should be large. We ran several
ASTRA simulations with different longitudinal bins. The
maximum number of bins was Nbin = 800, for a 2.2 cmlong bunch modulated at λm = 1 mm, which means that,when Nptc = 12 · 106 , about 103 particles can be expected,
roughly, to be present in each longitudinal slice for eachradial ring.
The ASTRA output file consists of several information,
among which the phase-space state of every particle. To
give an example, in Fig. 3 we plot the particles longitudinal
momentum pz as a function of the longitudinal coordinate
inside the bunch at 3 m down the beam line for Nbin = 400
2. We wrote a short code to get the average pz and position(see the solid line in Fig. 3) of particles as a function of thelongitudinal coordinate from ASTRA output: this program
divides the bunch length (2.2 cm) in 500 parts, then the raw
data from the simulation is read by the code and the average momentum and position is calculated for each slice.
Results for the same example case in Fig. 3 are shown in
Fig. 4 and Fig. 5.
The data in Fig. 4 and Fig. 5 and their analogous for every simulation run at any position down the beam line havebeen subsequently fit. The particle momenta have been fit
with a tilted sinusoidal function A + B sin(2πz/λm ) + Cz,
where the tilting is due to the fact that the tail of the bunch
2 actually only one particle in 500 was selected for the plot, in order tomake the figure file more easily manageable.

MOPOS09

24000

22000

20000

18000

16000

14000

12000
-0,015-0,010-0,005

0,000

0,005

0,010

0,015

ζ

Figure 5: Particle density distribution normalized to Nptc
as a function of the position inside the beam (in m) at 3 m
inside the beam line. Nbin = 400.

is decelerated, while the head is accelerated by the spacecharge fields. The particle density distribution, instead, hasbeen fitted using A + B sin(2πz/λm + π/2), B/A giving the relative modulation level. Only the inner 10 periods have been used in the fits (nearer the bunch center, inthe longitudinal direction) since, as the bunch progresses
through the beam line, spurious edge effects get more andmore important.
For every ASTRA run (with a fixed number of longitudinal slices Nbin ) we could plot the current modulation level
and the absolute energy modulation and fit them, as before,
using a sinusoidal function.
The results in the case of Nbin = 400 are shown in Fig.
6 and Fig. 7, from which we have two estimation for theplasma wavelength, λp = 7.32 m and λp = 7.44 m respectively, which differ of about 1.6%.
As said before several ASTRA runs were performed
with different numbers of longitudinal slices Nbin . This
allowed us to plot the plasma wavelength as a function of

29

G. A. Geloni et al. / Proceedings of the 2004 FEL Conference, 26-29

λpρ

Analysis -Fields
Analysis -C urrents
ASTR A -C urrents
ASTR A -M om entum

10,5

0,06
10,0

0,04
9,5
9,0

0,02

8,5

0,00
8,0

-0,02
7,5

-0,04

7,0
6,5

-0,06
0

1

2

3

4

5

6

7

0

5

10

15

20

25

30

35

z

Figure 6: Averaged relative current modulation level as afunction of the position in the beam line (in m) and sinusoidal fit. Nbin = 400.

pz

N bins/λm

Figure 8: Benchmark of ASTRA - self-consistent problem:comparison between λp (in m) as a function of Nbin /λm
calculated by ASTRA and with our analytical method.

Ez

8000

7000

6000

6500

4000

40

ASTR AAN ALYSIS

6000

2000
5500

0
5000

-2000
4500

-4000
4000

-6000
3500

-8000
0

1

2

3

4

5

6

7

z

3000
0

5

10

15

20

25

30

Position along the beam line z = 10 cm

Figure 7: Average momentum modulation (in eV/c) as afunction of the position in the beam line (in m) and sinusoidal fit. Nbin = 400.

the number of bins per modulation wavelength and to compare the results with analytical estimations. This result ispresented in Fig. 8. As one can see at least 20 bins per
wavelength are required in order to obtain acceptable results. Finally, to benchmark separately ASTRA electromagnetic solver, we plotted the electromagnetic fields estimated from the average momenta at z = 10 cm, as afunction number of bins per wavelength and we comparedthese data with our analytical expectations. The result isshown in Fig. 9. It can be seen that results in Fig. 8 andFig. 9 are in agreement: as the number of bins decreases,
the fields are underestimated and the plasma wavelength isthen badly overestimated.

CONCLUSIONS

35

40

N bin/λm

Figure 9: Benchmark of ASTRA - electromagnetic problem: comparison between the fields at 10 cm down the
beam line (in V/m) as a function of Nbin /λm calculated
by ASTRA and with our analytical method.

tween analysis and simulations, provided that critical parameters like the number of longitudinal bins for spacecharge calculations are chosen correctly.

REFERENCES[1] E. Saldin et al., TESLA-FEL-2003-02[2] J. Feldhaus et al., DESY 03-091[3] G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov, MOPOS08, this conference[4] G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov,
DESY 04-112, see http://xxx.lanl.gov/abs/physics/0407024[5] http://www.desy.de/ mpyflo/

We benchmarked ASTRA simulation by means of ananalytical, self-consistent three-dimensional model developed by us in [4]. Results show a very good agreement be-

FEL Theory

30

J. T. Donohue et al. / Proceedings of the 2004 FEL Conference, 30-33

OFF-AXIS ORBITS IN REALISTIC HELICAL WIGGLERS: FIXED POINTSAND TIME AVERAGED DYNAMICAL VARIABLES
J.T. Donohue, Centre d'Etudes Nucléaires de Bordeaux-Gradignan, BP 120, 33175 Gradignan,
FranceJ. L. Rullier, CEA CESTA, BP 2, F-33114 Le Barp, FranceωP ( y ) = ωP ( 0) + KP y + ⋅ ⋅ ⋅Abstract2

Many years ago Fajans, Kirkpatrick and Bekefi (FKB)
studied off-axis orbits in a realistic helical wiggler, bothexperimentally and theoretically. They found that as the
distance from the axis of symmetry to the guiding center
increased, both the mean axial velocity and the precession
frequency of the guiding center varied. They proposed aclever semi-empirical model which yielded an excellent
description of both these variations. We point out that aapproximate model proposed by us several years ago canbe made to predict these delicate effects correctly,
provided we extend our truncated quadratic Hamiltonian
to include appropriate cubic and quartic terms. We
develop an argument similar to the virial theorem tocompare time averaged and fixed-point values ofdynamical variables. Illustrative comparisons of ourmodel with numerical calculation are presented.

INTRODUCTION
In 1985 Fajans, Kirkpatrick and Bekefi performed anexperiment with a low-energy free electron laser (FEL)
operating in the amplifier mode in the microwave
region[1]. The wiggler was helical, and a uniform axial
field was present. The electron beam was furnished by apulse-line diode in single shot operation. Among otherstudies, they investigated what happened when the beam
was injected off axis, simply by displacing their wiggler
in the transverse direction. Both beam and FEL
measurements were carried out. In general, they foundthat for small displacements, the FEL operation remained
satisfactory. Two properties of the beam were measured
quantitatively as a function of the off-axis injection
distance. The mean axial velocity was observed to satisfy
a simple quadratic law

β z ( y ) = β z ( 0) + Kβ y + ⋅ ⋅ ⋅2where Kβ is a number which depends on the FEL
parameters, and y denotes the displacement of the beam
centroid from the wiggler axis at injection. The symbol
denotes the time average of the corresponding
dynamical quantity Throughout this paper we shall use
only dimensionless quantities with mc as the unit ofmomentum, 1/kw the unit of length and ckw the unit of
frequency. A second important property was theprecession of the displaced quasi-circular FEL orbits.
Again, for small displacements, a simple quadratic
behavior was found for the precession frequency ωP.

MOPOS22

where KP denotes another constant. Since the quantities
β z ( 0 ) and ω P ( 0 ) are just the values on the ideal orbit,
they may be considered as known. The real task is tocompute the quantities Kβ and KP .
The authors analyzed the wiggler magnetic field in
detail, and proposed two formulas to describe themodification of the mean axial velocity and theprecession frequency. The former is described byβ⊥ =β z Ωw I 0 ( kw yg ) ( I 0 ( λ ) − I 2 ( λ ) )γ β z − Ω 0 − 2Ω w I 0 ( k w y g ) I 1 ( λ )1subject to γ =1 + βz22+ β⊥where γ is the dimensionless energy. The quantities Ω0and Ωw are eB0 / mc k w and eBw / mc k w , respectively,
22

yg denotes the off-axis injection distance, and λ is ± k w ρ ,where ρ is the radius of the FEL motion. A somewhat
simpler expression had been proposed by Freund andGanguly [2],β⊥ =β z Ωw I 0 ( kw yg )subject toγ β z − Ω0γ1=
1 + βz2+ β⊥

2For the precession, FKB proposed the formulaω p = ck w

β ⊥ Ω w ( I 0 ( kw yg ) − I 2 ( kw yg ) )Ω 0 − 2Ω w I 0 ( k w y g ) I 1 ( λ ).

In the three cases investigated by FKB, their formulawere remarkably successful. That of Freund and Ganguly
for the diminution of the mean axial speed was somewhat
less precise, but adequate.
Given the success of these formulas at describing thedata, one might well consider the problem solved.
However, having proposed an analytic (but approximate)method of calculating the trajectories in a helical wiggler
with axial guide field [3], we felt challenged to show that
our model could be used to generate equally successful

Available online at http://www.JACoW.org

31

J. T. Donohue et al. / Proceedings of the 2004 FEL Conference, 30-33

expressions, perhaps in a more systematic way. We don’tknow the details of the adiabatic magnetic field used by
FKB to inject into the wiggler, so we address a related but
slightly different problem. Suppose that an electron is on
the ideal axially centered helical trajectory, and thendisplace the electron by a small amount in a transverse
direction, leaving its velocity vector unchanged. We
remind the reader that the ideal orbit satisfies two
conditions: 0 Group II 
ψ =φ −z =, π Group I 

 1
+ 1  cos ψ ,2ργβ z = Ω 0 − 2Ω w I1 ( ρ ) where ρ denotes the constant radius of the helix. The
notation Group I corresponds to γβ z > Ω 0 and Group II
toγβ z < Ω 0 .

There is also the reversed field

configuration, studied by Conde and Bekefi [4], where theaxial velocity is anti-parallel to the axial field, or
γβ z Ω 0 < 0 . If one chooses the z-direction such thatΩ 0 > 0 , then the reversed field is a special case of GroupII, typically with a very small radius. The effect of asmall displacement is then calculated by linearizing theequations of motion around the ideal helix. This
procedure is described in detail in the monograph of
Freund and Antonsen [5]. The electron then has two
independent normal modes of oscillation, whose
frequencies are well-known. It turns out that one of these
two frequencies is numerically close to the unperturbed
constant axial velocity βz.
In our approach to calculating the trajectories, the keyrole is played by the Helical Invariant, Pz, a conserved
quantity which is a consequence of the screw symmetryof the wiggler field [6]. We find the fixed point of the
Hamiltonian (where the first derivatives with respect toour chosen dynamical variables vanish), expand to second
order in our variables, and then find the normal modes ofoscillation of the resulting quadratic system. If we denotethe complex normal mode amplitudes in our modelby A+ and A− , with the Poisson brackets { Aα , Aβ } = iδ αβ ,*our Hamiltonian may be written as
2

( ).

2

H = H fp + Ω + A+ + Ω − A− + O A

3Neglecting the cubic and higher order terms, we find thesimple dynamics,
Aα ( t ) = Aα ( 0 ) ei Ωα t.

With our rather complicated choice of dynamicalvariables the transformation to normal modes wasstraightforward, and we obtained a quantitatively accurate
description of the transverse motion as a Ptolemaic
superposition of three independent circular motions. One

is the projection of the standard FEL helix, the second,
driven mainly by the mismatch in transverse velocity,
occurs at a frequency near the relativistic cyclotron fieldΩ / γ , while the third is a very slow motion, whose0effective frequency is

β z − Ω β , where Ωβdenotesthat oscillation frequency which is close to β z . It is thisslow motion that is the precession seen by FKB.
In terms of our model, the calculation of the effects
observed by FKB is straightforward. Displacing theelectron from the ideal helical orbit produces a change inthe Helical Invariant that is second order in thedisplacement. The resulting changes in the axial velocity
and frequency are readily computed, and can be compared
to experiment. Proceeding in this way, we find extremely
poor agreement between our calculations and experiment.

TIME AVERAGES AND FIXED POINTS
The difficulty encountered in attempting to calculate
the mean axial velocity was traced to the source, the factthat the time average of a dynamical variable in theneighborhood of a fixed point is not its value at the fixed
point. The time averages of our normal modes ofoscillation, which we had assumed to be zero, were in fact
different from zero. If our quadratic approximation to the
Hamiltonian were exact, this would not occur. However,the cubic terms in the Hamiltonian generate such nonzero time average values. While the inclusion of the
cubic terms into our model makes it non-soluble, it ispossible by using a perturbation approach to obtain thelowest order corrections by calculating third derivatives at
the fixed point. The required labor is greatly facilitated byusing symbolic manipulators such as MAPLE or
Mathematica. If one is interested in calculating thedependence of the precession frequency on thedisplacement, some fourth derivatives at the fixed point
are also needed. We present below a sketch of our
method.
The essential tool in our approach is a proposition
similar to the virial theorem in classical mechanics.
Given a general Hamiltonian, and a complex dynamicalvariable A(t) of the sort we use, we consider the time
average of the following quantityd( A ( t ) e ) = lim
dt

A (T ) e

iω t

iω T

− Q ( 0)=0T
provided the variable is A(t) bounded. But by Hamilton’s
equationsd∂H  iω tiω t.
A(t ) e= i ω A(t ) + *  e
dt
∂A 

For technical reasons, it is more convenient to computethe higher order terms using the squared Hamiltonian, andwe arrive the following result

(

T →∞

)

FEL Theory

32

J. T. Donohue et al. / Proceedings of the 2004 FEL Conference, 30-33(ω + Ω ) A ( t ) e
α

iω t

α

=−

( )

1

∂ H

2H

∂Aα

2

cubic

*

e

βz =

iω t

where represents the cubic and higher order terms in themulti-variable Taylor series expansion of the squared
Hamiltonian at the fixed point. For our purposes, we
keep only the cubic terms, and find non-vanishing
contributions only for the nine following values of thearbitrary frequency ω,ω j = {0, ± 2Ω + ± 2Ω − , ( Ω + ± Ω − ) , − ( Ω + ± Ω − )} .
This means we may write, correct to second order in thedisplacement,
A+ ( t ) = A+ ( 0 ) e

9+ ∑ a j+eiΩ + t

+

j

j+

( )

∂ H

2H

∂Aα

2

cubic

*

e

iω j tA( t ) = A( 0 ) eiΩt

In order to compute the quantities a j + , we need the
cubic part of the squared Hamiltonian, which we write as
+

2

+

− iS

( A − cc ) − iL A ( A − cc ) − iR ( A − cc )
2

+

+

3

−

+

+

+

+

2

−

+

+

*

2

p

2
2
1 + pρ + Aρ (ρ ,ψ ) +  ψ + Aφ (ρ ,ψ ) + Pz − pψ
 ρ


(

)

The complex dynamical variables A+ and A- are linearly
related to the usual variables,()

A± = a± p ρ + ib± ( ρ − ρ f ) + ic± pψ − ( pψ ) f + d ± (ψ − ψ f )pψ = ( pψ ) f + id + ( A+ − cc ) + id − ( A− − cc )

−

A− )

H

(

−i 2 K + A+ + L+ A−
2

2)

2Ω + HA− .

In these expressions the

In order to calculate the slope of the FKB precession
frequency, we must calculate the change in the time
average of the oscillation frequencies caused by thehigher order terms in the Hamiltonian. The relevant
equation isd ℑ ln A+

Ω+ =

H

2

= M

quartic

=

dt

1

∂H 2

4H

A+ ∂A+ *+ cc .

+ A+

4

+ M

+

where ρf, ψf and ( pψ ) f denote the values of the variablesat the fixed point. The time averaged axial velocity is then

− A−

4

+ N A

+

2

A

−

2

+⋅⋅⋅

The details of the explicit calculation are too long to begiven in this paper, and we give only the final result:Ω+= Ω + + C + + A+

C+ + =−))

A+ + dCHANGES IN TIME AVERAGEDFREQUENCIES

H ρ ,ψ , z , pρ , pψ , Pz =

(

+

z

−

where cc denotes complex conjugate. The ten quantities
K+ etc. may be computed most easily if we write thesquared Hamiltonian in cylindrical coordinates, as in ref.
[7],

(

(

2i d

amplitudes are linear in the displacement y, and we thus
can calculate the coefficient of y2 in β , Kβ .

+( A A − cc ) − iT ( A A − cc ) + ( + ↔ − )2−fThis receives contributions from both the cubic part andfrom three of the many quartic contributions. These may
be written as

HIGHER ORDER TERMS

2ψand similarly forwhere on the right-hand-side only the first approximation
to the variables is to be used.

H cubic = − iK A

Pz − ( p )A+ =with a similar expression for A− ( t ) . Here the quantities

−1

ψ

H
Explicit calculation yields

j =1(ω + Ω ) a =pH=− iω j t

a j + are second order in the displacement. We findPz −C+ − =−

2+ C+− A

2

−

,

M+
H
T+
 3 ( K + + R+ ) + L− + S +
,
−


2 
2Ω + + Ω −2Ω + − Ω − 
Ω+
Ω−
2H
2

1

N
2H

−

2

2

2

2

 K + L+ + K − L − 


2
Ω+
Ω− 
H 
1

T+
S−
T−
 S+
,
+
+
+


2  2Ω + Ω
2Ω + − Ω −2Ω − + Ω +2Ω − − Ω + 
+
−
H
1

2

For the quantity

2

2

2

Ω − a similar expression holds

provided one makes the substitution + ↔ − throughout.
Note that C+ − = C−+ .

COMPARISON WITH NUMERICALSIMULATIONSAt this point we can calculate Kβ and KP. However, inorder to verify this analysis, we carried out numericalcalculations of the trajectories using solvers of differential

MOPOS22

J. T. Donohue et al. / Proceedings of the 2004 FEL Conference, 30-33

equations available on MAPLE and Mathematica. Our
approach is simple. We start with an electron on the ideal
trajectory suited to its energy. We then displace theposition of the electron tangentially through a distance y,keeping the velocity unchanged. We then calculate thetrajectory of the electron for long times, typically 100
periods, in order to obtain reliable numerical estimationsof the time averaged axial velocity and the precession
frequency. We performed this calculation for the threecases studied by FKB. In each of these, the frequency
concerned by the precession was Ω+ so we added two
more, for which the relevant frequency was Ω-. These
include a Group II configuration with a large axial field,
which we label low-ρ, and a reversed field configuration,of the sort investigated by Conde and Belkefi. The results
are summarized in the Table, which indicates various
properties of the trajectory, the frequencies, theprecession frequency intercept ωP(0) (in the FKB units of
108s-1). The last eight lines show comparisons of ourtheory (denoted by T) with the simulations (S). The
agreement between these is quite good.
FKB b
FKB c
low ρ,
group II group II Group II
1.312
0.4
1.8
0.05833 0.025
0.063
1.2264 0.16863 0.750
3
3.30
3.18
2.094
1.904
1.97584
3.4
1.33
2.467710.31543 0.21602 0.06073
0.911498 0.644436 0.912532
000π0.65416 0.90481 0.640016 1.25171-0.23792 0.19576 0.286011 0.91155-6.217
4.199
2.523
0.5812-0.00110 -0.00304 -0.00230 -0.0991-0.11976 -0.38085 -0.16418 0.00047-1.580-3.290-2.793-13.46

FKB agroup I
0.16
B0 (T)
0.025
Bw (T)V (MeV) 0.16863
λw (cm) 3.30
kw (cm-1) 1.904
1.33
γ0.22461ρf
0.64327(βz) f0.16863

ψf

Ω+
Ω−
ωP(0)
d+
d−
ℑA+
T
y2

reversedβz B0 < 0
1
0.147
0.750
3.18
1.97584
2.467710.08433-0.911002.10919-0.90526-3.389-0.1018-0.0008-7.133-1.575ℑA+
S
2y-3.292-2.795-13.15-7.128-1.085ℑA−
T
2
y-1.246-1.525-20.68-10.69-1.085-1.247-1.524-20.88-10.76-0.00952 -0.0165-0.0095 -0.0165-2.4868 1.3272
-2.56
1.31

-0.0076-0.0076
0.89201
0.88-0.00094-0.00094
0.21120.20

0.00170.00170.07146
0.072

ℑA−
S
y2
Kβ T
Kβ S
KP T
KP S

33

CONCLUSION
We may thus conclude that our approach of calculating
the contributions of the higher perturbatively is
successful. However, one word of caution is necessary.
The generally small values we find for KP, especially incolumns 5 and 6, are the result of cancellations of muchgreater changes in the separate pieces. Indeed, the change
in the fixed point frequency due to the displacement isalmost exactly cancelled by the contribution of the higher
order cubic and quartic terms. This suggests that in a yet
more sophisticated approach such cancellations could be
avoided.

REFERENCES
1 J. Fajans, D.A. Kirkpatrick, and G. Bekefi, Phys. Rev.
A 32 (1985) 3488.
2 H. P. Freund, A. K. Ganguly, IEEE J. Quantum
Electron., QE-21 (1985) 1073
3 J. T. Donohue, J.L. Rullier, Phys. Rev. E 49 (1994) 766.
4 M. E. Conde, G. Bekefi, Phys. Rev. Lett. 67, (1991)
3082.
5 H. P. Freund and T. M. Antonsen, Jr., Principles of
Free-electron Lasers, 2nd Edition, Chapman and Hall,
London .
6 R. D. Jones, Phys. Fluids 24 (1981) 564.
7 J. T. Donohue, J. L. Rullier, Nucl. Instr. And Meth. A
507 (2003) 56.

TABLE
Comparison of theoretical (T) and simulation (S) values
for various quantities. Five different configuration werestudied FKB a, b and c, low ρ Group II, and reversed
field.

FEL Theory

34

J. T. Donohue / Proceedings of the 2004 FEL Conference, 34-36

ANALYTIC ELECTRON TRAJECTORIES IN AN EXTREMELYRELATIVISTIC HELICAL WIGGLER: AN APPLICATION TO THE
PROPOSED SLAC E166 EXPERIMENT
J. T. Donohue, Centre d'Etudes Nucléaires de Bordeaux-Gradignan, BP 120, 33175 Gradignan,
FranceAbstract
The proposed experiment SLAC E166 intends togenerate circularly polarized gamma rays of energy 10
MeV by passing a 50 GeV electron beam through a meterlong wiggler with approximately 400 periods. Using ananalytic model formulated by Rullier and me, I present
calculations of electron trajectories. At this extremely
high energy the trajectories are described quite well by
the model, and an extremely simple picture emerges, evenfor trajectories that that fail to encircle the axis of the
wiggler. The calculations are successfully compared withstandard numerical integration of the Lorentz force
equations of motion. In addition, the calculation of thespectrum and angular distribution of the radiated photons
is easily carried out.

PROPOSED EXPERIMENT AND ITSRELATION TO FELS
The experiment E-166 at SLAC proposes to produce
circularly polarized photons of energy 10 MeV bysending a beam of electrons of energy 50 GeV through ahelical undulator one meter long [1,2]. The wiggler
period is 2.4 mm. The aim is to convert the polarized
photons into longitudinally polarized positrons by pair
production on a Ti target. Polarized leptons enable one toperform high precision tests of the Standard Model of
weak and electromagnetic interactions, and theexperiment is intended as a demonstration of principle. A
key feature of the experiment is the helical wiggler Its
properties, along with some beam properties are
summarized in Table 1. Much information can be isfound in the detailed report of Mikhailichenko [3], who
designed the wiggler.
Table 1: Beam and Wiggler and Specifications
Energy50 GeV
Ne/bunch
1×1010σx , σx40 µm
γεx= γεx
3×10-5 m radType
HelicalPeriod0.24 cm
Length1m
Field on axis
0.76 T
Inner diameter
0.89 mm0.1704Ωw
kw
26.18 cm-1

MOPOS23

Although the wiggler is too short for any substantial
bunching to occur, and consequently the system can't beclassed as a Free Electron Laser (FEL), it does resemble
many FELs that operated at much lower energy. . It also
will be the highest energy photon source available, andmay be seen as a test –bed for ultra high energy FELs. In
particular, the FEL experiments performed at the
CEA_CESTA facility [4] used helical wigglers and low
energy (a few MeV) electron beams. Rullier and I
developed a model to simulate the trajectories of theelectrons in those experiments [5]. Our much earlier
work on the analytic but approximate calculation of
trajectories had been successful in describing trajectories
in helical wigglers with an axial guide field [6], but was
inapplicable in the absence of an axial field. A key
advantage of our older approach is its ability to describe
trajectories which don't encircle the axis of the wiggler.
Our second approach is also capable of describing suchtrajectories. Now the radius of the SLAC E-166 beam (40µm) is much greater than the radius of the ideal helicaltrajectory (0.665 nm), which implies that most electrons
will be following trajectories that do not encircle the axis.
While there is no major problem in calculating suchtrajectories by numerical integration of the Lorentz force
equations of motion (I use both the NDSolve procedure in
Mathematica, and the dsolve procedure in MAPLE), it isof interest to see what our model predicts. In fact, theconditions of the experiment are favorable, since the highenergy limit of our model is quite simple. One can write
simple closed form expressions for the position andvelocity variables as functions of time.
An important experimental issue is the emission patternof the radiation generated by the electrons during theirpassage through the wiggler. For the ideal helicaltrajectory, one may compute this most easily in the comoving Lorentz frame, where the electron has onlytransverse motion. The resulting relative velocity is only
0.17, which means that the radiation is mainly at thefundamental frequency, with a small admixture of thesecond harmonic. Standard formula may be found, forexample, in Jackson’s book [7], where the problem 14.8
addresses the question (and provides the answer). A
simple generalization furnishes the amplitudes for
positive and negative helicity radiation. A straightforward
Lorentz transformation then produces the angular
distribution of the radiation in the laboratory frame. As
might be expected the emission occurs mainly in a coneof half angle 1/γz, where γz denotes the quantity

Available online at http://www.JACoW.org

35

J. T. Donohue / Proceedings of the 2004 FEL Conference, 34-36

γ z = (1 − β z 2 )−1/ 2

where βz is the axial velocity of theelectron in the laboratory. Both the photon energy and thepolarization are highly correlated with the laboratory (lab)emission angle. The relations among the lab frequency ω,
co-moving fundamental frequency ω! 0 , on-axis wiggler
fieldΩ w = eBw / mc k w ,2labemission

angle

θ,

longitudinal rapidity y, and circular polarization P are:

ω=

cos 2

ω! 0 =

θ

ω! 0 e y+ e 2 y sin 22
ck wγβ z

1 + ( k w ργβ z )

2

θ
2
≅

ckwγβ z1 + Ωw2eBwΩw =≅ 0.934 Bwλw
mc 2 k w

β z = tanh yP≅

1 − e 2 y tan 2
1 + e tan
2y

2

−


 ( Ω− + Ω+ ) t  2
 ( Ω− + Ω+ ) t  ( u + iv )0 cos  + Ω ( k + iq)0 sin 

2
2

 w



where

( u + iv )0 ≡ u ( 0 ) + iv ( 0 )= x ( 0 ) + iy ( 0 ) + ρ f ≅ x ( 0 ) + iy ( 0 )Similarly,( k + iq )0 ≡ k ( 0 ) + iq ( 0 )()≅ γ β x ( 0 ) + i β y ( 0 ) + iΩ w

Since the quantity (Ω− + Ω+ ) t/ 2 " ρ f z /2 is always

small in a one-meter-long wiggler, one may replace thecosine by 1, and the sine by its argument. I find to a good
approximationx ( t ) + iy ( t ) ≅ − ρ f eiz ( t ) + x ( 0 ) + iy ( 0 ) + z 

2

θ

2

)

γβ z = 2Ω w I1 ( k w ρ ) 1/ ( k w ρ ) + 1 ≅ Ω w / k w ρ2In order to obtain both high photon polarization andenergy, the emitted photons must make an angle of lessthan 5 µ radians with the axis. The conversion target isplaced 10 m downstream from the wiggler, which meansthat its diameter must be about 100 µm .

The model presented in ref. 5 is based on finding the
fixed point of the Hamiltonian, making a series expansion
keeping only quadratic terms, and then a transformation
to two normal modes. The dynamics is simply that of two
uncoupled harmonic oscillators. The squared frequenciesof the oscillations were known from much earlier work;
they may be found in the monograph of Freund andAntonen [8]. According to our model, the frequency ofgreater magnitude is positive, while, for zero axial field,that of lesser magnitude is negative. In fact, for small
radius (In the remainder of this paper we shall use only
dimensionless quantities with mc as the unit ofmomentum, 1/kw the unit of length and ckw the unit of
frequency), one findsΩ ± ≅ ± ( β z ) f 1 ± 12 ρ f − 12 ρ f 2

This espression shows that the transverse position is asuperposition of the FEL helix, with the period of the
wiggler, an initial constant displacement, and a drift atconstant velocity . The time derivative of this expression
yields the transverse velocity,
β x ( t ) + i β y ( t ) ≅ −i β z ρ f eiz ( t ) + β x ( 0 ) + i β y ( 0 ) + iΩ w / γ
The resulting transverse motion is quite simple, consisting
only of the ideal FEL helix and a constant drift. Whatturns out to be essential is matching the initial velocity as
closely as possible to the ideal value,

β x = 0,

THE MODEL(+

 γ ( β x ( 0 ) + i β y ( 0 ) ) + iΩ w 


γβ z



θ

The relation between the radius of the ideal helix and theaxial momentum is(

conjugate coordinate and momentum pairs called (u,q)
and (v,k). The key equation needed is the following,
which is valid in the high energy limit:i z t − Ω −Ω ) t / 2 )x ( t ) + iy ( t ) = − ρ f eiz ( t ) + e ( ( ) (×

β y = −Ω w / γ

It will be essential to the success of the experiment thatthese conditions be realized as closely as possible.

COMPARISON WITH SIMULATION
In order to verify that the simple motion found above is
indeed correct, we have calculated numerically sometrajectories using the NDSolve package in Mathematica.
The trajectories were calculated with high precision, anda typical 400 period trajectory took about 90 seconds on aPC.

)

where ρf denotes the radius and (βz )f the axial velocity at
the fixed point. The dynamical variables are two

FEL Theory

36

J. T. Donohue / Proceedings of the 2004 FEL Conference, 34-36
xH tL H red L , yHtL H blue L − model
1× 10 - 1 0

5× 10

vs t, 400 periods

-11

500

1000

1500

2000

2500

-5 × 10 - 1 1-1 × 10 - 1 0

Figure 1. Difference between numerical solution andmodel keeping sine and cosine. Red is for x(t), blue y(t).
In figure 1 I show the differences between anumerically calculated trajectory and the model in which
the sine and cosine are retained. The x-difference isshown in red, the y difference in blue. For this trajectoryx ( 0 ) = −1.7415 × 10−6 ,y ( 0 ) = 0.005,

β x ( 0 ) = 1.7415 × 10 , β z ( 0 ) = −1.7414 × 10−6 ,−8β z ( 0 ) = 1 − 1.02 × 10−10 ,EFFECT ON RADIATION EMISSION
Without going into detail, one sees that for electrons
that are injected with the ideal velocity, the resulting
motion is basically the standard helix, except that it is notcentered on the axis. For such trajectories, the radiation
pattern is the same as the ideal one, except that the axis of
the cone must be taken over the true axis of the helix.
This necessarily leads to some “smearing” of the radiation
pattern. A more serious problem occurs for thoseelectrons whose injection velocity is not ideal. If thetransverse drift is sufficiently large, the radiation patternmight be strongly affected. Further study is needed tosettle this.

CONCLUSION
While we have not considered all the possible
trajectories that are likely to occur in the proposed
experiment, we are confident that the major part of themwill be correctly described by our analytic approach. The
even simpler approximation appears to be adequate formost purposes.

z=0

For comparison the ideal injection would have y (0) = 0

REFERENCES

and β x (0) = 0 . The initial y value is about 2 µm fromthe axis. In general the agreement between the model andthe numerical calculation is excellent.
In Figure 2 I show the difference between the same
numerical calculation and the simplified version of themodel, in which the cosine is replaced by 1, and the sineby its argument.
x H t L H red L , y H t L H blue L − linear-5 × 10-9-1 × 10-8-1.5 × 10-8-2 × 10-8-2.5 × 10

-8

500

1000

1500

model

2000

vs t,

2500

Figure 2. Difference between numerical solution and thesimplified model with sine replaced by its argument andcosine by 1. Red is for x(t), blue y(t). Note change of scalecompared to Figure 1.
Here the agreement remains surprisingly good for the xcoordinate, and slightly less so for the y-coordinate.
However, the true value of they-coordinate isapproximately 0.005 throughout the trajectory, so therelative error remains small.

MOPOS23

1 http://www.slac.stanford.edu/exp/e166/
2 G. Moortgat-Pick, Eur. Phys. J. C 33 s1047 (2004).
3 A. A. Mikhailichenko, Report CBN 02-10, (2002).
Available at site indicated in ref. [1].
4 T. Lefevre et al, Phys Rev. Lett. 1188 (2004).
5 J. T. Donohue, J. L. Rullier, Nucl. Instr. And Meth. A
507 (2003) 56.
6 J. T. Donohue, J. L. Rullier, Phys Rev. E 49 766(1994).
7 J. D. Jackson Classical Electrodynamics, 2nd Edition,
John Wiley & Sons, Inc. 1975.
8 H. P. Freund and T. M. Antonsen, Jr., Principles of
Free-electron Lasers, 2nd Edition, Chapman andHall, London .

37

L. Giannessi / Proceedings of the 2004 FEL Conference, 37-40

HARMONIC GENERATION AND LINEWIDTH NARROWINGIN SEEDED FELS
L. Giannessi, ENEA Via E. Fermi 45, 00044, Frascati, Italy
Abstract
The process of harmonic generation in a seeded, single
pass, Free Electron Laser, are studied in thetime/frequency domain following the evolution of theharmonics within a self consistent time dependent model.
The first and second order correlation functions of thefundamental and of the higher order harmonics fields arestudied as a function of the input seed amplitude.

exp(ζ i ) = 1

INTRODUCTION
Single pass Free Electron Lasers (FEL) operated in Self
Amplified Spontaneous Emission (SASE) configuration
are amplifiers of the natural shot noise of the driving
electron beam. The spectral properties of the output
radiation are the result of the amplification of the wide
bandwidth noise arising from the stochastic distribution of
the electron beam current, in the narrow bandwidth FEL
amplifier. The properties of the output radiation, in termsof temporal coherence and intensity stability, have been
extensively studied in literature [1][2][3] and reflect thestochastic nature of the electron beam shot noise. In a
recent experiment at BNL[4] it has been shown thatseeding a single pass FEL with an external laser allows toimprove the spectral properties and the temporal stabilityof the laser source. In the same experiment it has been
demonstrated that these properties are transferred to thehigher order harmonics generated by the FEL. There is a
widespread interest in this process, because emission onhigh order harmonics represents a significant resource toextend the wavelength tunability of an FEL and several
recent proposals of FEL facilities rely on schemes basedon seeding an harmonic generation[5]. The input seed, inorder to be effective, must be characterized by enoughintensity to overcome the intensity associated to the beam
shot noise. The equivalent input intensity associated to abunched beam is given by [6],I 0 = exp(ζ i )2

period λu (with ku = 2π λu ) and strength K, and to an~
optical field E ( z , t ) = E ( z , t ) exp(i (ωt − kz ) ) , being~E ( z , t ) the slowly varying field component. In thespecific case of randomly distributed electrons, theaverage exp(ζ i ) is the normalized sum of ne
independent phasors, i.e.,

ρPe

ne

(3)

We estimate the number of interfering electrons ne withthe following naïve procedure. We define as
n1,e = I peak λ0 e0 c

(4)the number of electrons contained in a single resonant
wavelength. Interference effects between electronscontained in contiguous wavelengths must be estimated.
The field generated in a given longitudinal “slice” slips
along the bunch and is amplified while the bunch travels
along the undulator. This amplification must be
considered in evaluating the interference between thefields emitted by electrons from different slices. The fieldevolution in presence of gain is given by [6],
z
 i
 z
  i  z

−i

−1 

E0   3 +1  2 L~
3L
 3  2L
 (5)
+e
+e
E (z ) =
e

3 


g

(

g

)

where Lg = λu 4π 3 ρ is the FEL gain length. We canuse eq. (5) as a function of the longitudinal coordinate, toweight the electron number in each slice. Adding up theweighted number of electrons contained in all the slices,in a portion of the bunch of length Lλ0 λu , we getL~ne = n1,e ∫ E0 E (z ) dz = f (L ) I peak Lg λ0 λu e0 c
0

(1)

Σb

where Σ b is the electron beam cross section and

Pe = I peak m0 c 2γ e0 is the e-beam peak power. The
parameter

1  [λ K ( J 0 (ξ ) − J 1 (ξ ))] I 
ρ =  u2γ 4πΣ b
I A 
2

(

[(

(2)

)]

is the Pierce parameter, with ξ = K 2 4 1 + K 2 2 , andζ i = (k + ku )zi − ωt + ϕ 0,i are the electron phases in the
ponderomotive potential associated to an undulator of

Available online at http://www.JACoW.org(6)

The dimensionless function f (L ) grows linearly with L
for the first gain lengths, then converges rapidly to theconstant ∼ 4.3. Assuming ne ≈ 4.3 I peak Lg λ0 λu e0 c as thetotal number of interfering electrons, we get from eq.(1)I 0 ≈ λu e0 c 4.3I peak Lg λ0

1
3

g

) ρΣP

e

(7)

b

The equivalent input seed intensity I0 can be estimatedmore accurately by considering the gain length
corrections associated to diffraction/inhomogeneous
effects [8][9]. In this paper we will study with a timedependent numerical model, the coherence properties of

FEL Theory

38

L. Giannessi / Proceedings of the 2004 FEL Conference, 37-40

TEST CASES AND NUMERICAL MODELDESCRIPTION
The analysis of longitudinal coherence in a single pass
FEL amplifier has been developed by implementing a 1Dtime dependent model of an FEL amplifier in PERSEO[10]. PERSEO is a library of FEL dedicated functions
available in the Mathcad environment. The basic elementof PERSEO is a FEL pendulum-like equation solver forthe particle dynamics, coupled with the field equations inthe slowly varying envelope approximation (SVEA). The
integrator includes self consistently the higher orderharmonics. Transverse effects, as inhomogeneous
broadening due to emittances, are accounted for by
introducing an equivalent energy spread. In order toinclude time dependency, both the slowly varying field
distribution and the electron phase space distributions are
sampled longitudinally. At each time step the longitudinalslippage of radiation over the electron beam is applied
shifting the radiation parameters array over the electron
parameter arrays by an interpolation procedure. The
implementation is capable of simulating the FEL
interaction process for any profile of the input field/ebeam current, satisfying the SVEA approximation. In thecases studied, a continuous current distribution/input seed
distribution, with a periodic boundary condition in thesimulation window, has been considered. This choice
allowed to minimize the number of parameters affecting
the results. In table 1 the main simulation parameters areshown.
Table 1: Main simulation parameters.
Case label

A

B

C

λ0 (nm)50

15

5

Undulator K (peak)

2.2

2.2

2.2

Energy (MeV)

500

900

1550

En. spread (MeV)

0.4

0.4

0.4

Ipeak(A)

500

800

1500

N. emitt.(mm-mrad)

1

1

1

Σb (mm2)

3.2×10-2

1.8×10-2

1.04×10-2

Pierce parameter ρ

2.86×10-3

2.26×10-3

1.94×10-3

I0, eq.(1) (W/cm2)

4.4×104

2.9×105

1.9×106

Sim. window (µm)

250

200

200

Sampl. period (µm)

0.625

0.5

0.5

Sim. bandwidth

4%

1.5%

0.52%

We have selected three configurations with theoperating wavelength in the VUV. This choice is driven
by the general interest in seeding FELs with very high

MOPOS26

order harmonics of the Ti-Sa laser, generated in gases[11].
These sources span the VUV region of the spectrum witha considerable level of peak power and constituteinteresting candidates for seeding FEL amplifiers[5].
From the numerical representation point of view, at thesewavelengths diffraction effects in the FEL dynamics areless severe. This mitigates the lack of accuracy due to theone dimensional FEL model implemented in PERSEO.

RESULTS
The statistics of radiation and its coherence properties
are studied with the first and second order correlation
functions. In the time domain, the first order classicalcorrelation function is defined by [12]~ ~E (t )E * (t + τ )g1 (τ ) =~ 2
E (t )(8)2~
E (t + τ )An estimation of the coherence length can be obtainedby the relation [12]2z c = c ∫ g1 (τ ) dτ
+∞

(9)

−∞

In the hypothesis of a SASE FEL operating in the
exponential growth regime, the coherence length (9) is amonotonic growing function of the longitudinalcoordinate z in the undulator, and reads [3],

zc =

1 λ0
6 ρ

z
2πLg

(10)

In fig.1, the coherence length evaluated according toeq.(10) has been compared with the values calculated
from the simulation data,
4

Coherence Length (µm)

an FEL amplifier seeded with an input seed of amplitude
varying across the “threshold” eq. (7).

3

2

1

0

Theory, eq. (10)Numerical, eq. (9)
0

5

10

15

Z (m)

Fig. 1. Coherence length as given by eq. (10) (dashedline) and as calculated from the simulation data,according to eq.(9) (continuous line)
The plot in fig. 1 has been obtained simulating theconfiguration in column A of table 1, starting from thenatural shot noise (no input seed). The beam energy
spread has been set to zero in order to preserve thehomogeneous conditions in which eq.(10) has been

39

L. Giannessi / Proceedings of the 2004 FEL Conference, 37-40

derived. The agreement is reasonable until saturation,
which is occurring at z∼10m, is reached.
In fig. 2 the growth of the laser intensity as a functionof the longitudinal coordinate is shown. The parameters
are those of tab.1, col. A, with an input seed represented
by a perfectly uniform classical wave of intensity
Is=3.1x105 W/cm2.
7

10

600

(c)

(b)

(a)

I0

Coherence length (µm)

510

Av. Intensity (W/cm2)

those of table 1, column A. At 500µm the coherence
length saturates because of the limited extension of thesimulation window (250µm). The value of the intensity
calculated according to eq.(1) is shown as a verticaldashed line. In figs. 5 and 6 are shown the equivalentplots obtained with the parameters listed in columns B
and C of table 1 respectively.

1st harm.
3

10

10

50 nm
400

200

3rd harm.
10

0

1

10

th

5 harm.
0

5

Z (m)

10

15

Fig. 2. Laser intensity vs. the longitudinal coordinate forthe first three odd harmonics. The regions of exponential
growth (a), harmonics generation (b) and saturation (c)have been indicated in the figure.
In fig. 2 we can distinguish the region, labeled with (b),where the growth of the third/fifth harmonic intensity isdriven by the beam bunching due to the ponderomotive
potential relevant to the first harmonic field.
The typical spectra for the third harmonic field, as
calculated in regions (a) and (b) are shown in figs. 3.a,brespectively. In fig. 3.a the third harmonic field is not yet
locked in phase to the bunching induced by thefundamental. The situation changes in fig. 3.b, where thephase of the third harmonic field is determined by thebunching on the fundamental and the coherence
properties of the seed are transferred to the third
harmonic. A similar behaviour is observed for the fifth
harmonic.
Spectrum (a.u)

(a)

16.6

16.7

(b)

16.8 16.5

Wavelength (nm)

16.6

16.7

Wavelength (nm)16.8

Fig.3. Third harmonic spectrum in the region (a) (atz∼4.7m) and in the region (b) (at z∼7.2m). The relative
r.m.s. linewidth is ∼0.174 % in (a) and ∼0.076 % in (b).
In fig.4 it is shown the behaviour of the maximum
coherence length reached along the undulator, as afunction of the input seed intensity. The parameters are

3

10

4

10

5

10

6

10

Intensity (W/cm2)

7

10

8

Fig. 4. Maximum coherence length reached along theundulator, as a function of the input seed intensity in thetest case A. The dashed line indicates the thresholdintensity I0 evaluated according to eq. (7).
500
I0

15 nm
Coherence length (µm)

3

250

1st
3rd
5th
0
3
10

4

10

5

6

10

10

7

10

Intensity (W/cm2)

8

9

10

10

Fig. 5. As in fig.4 with the parameters of tab.1, col. B.
500
I0

5 nm
Coherence length (µm)

10

16.5

1st
3rd
5th

250

1st
3rd
5th
0
4
10

5

10

6

10

7

10

Intensity (W/cm2)

8

10

9

10

Fig. 6. As in fig.4 with the parameters of tab.1, col.C
As expected the power level required to ensure
coherence on the higher order harmonics grows with theharmonic order. Comparing figs. 4, 5 and 6 it appears thatthe equivalent seed I0 obtained according to eq.(7),FEL Theory

40

L. Giannessi / Proceedings of the 2004 FEL Conference, 37-40~~
E (t ) E (t + τ )2

g 2 (τ ) =~ 2
E (t )

[

(11)

2
~
E (t + τ )

]

(12)

RMS

In figs.7, 8 and 9 it is shown the minimum along theundulator of the r.m.s. intensity (12), as a function of theseed intensity, in the cases A, B and C respectively. The
averages in (12) are taken over the temporal extension ofsimulation window.

sqrt(g2(0)-1)

I0

1st
3rd
5th

0.5

I0

0.6

1st
3rd
5th

0.4
0.2

5 nm

0 4
10

5

10

6

10

7

10

2

8

10

9

10

Intensity (W/cm )Fig. 9. As in figs. 7,8 with the parameters of tab.1, col. C

Fluctuations of the higher order harmonics are larger
than fluctuations on the fundamental. The amplitude of
the seed required for suppressing the fluctuations exceedsby orders of magnitude the intensity provided by eq.(7).

CONCLUSIONS
We have analysed the coherence properties of a seeded
FEL amplifier as a function of the seed amplitude. The
equivalent intensity associated to the beam shot noise,eq.(7), has been compared to the transition to coherence
induced by the presence of a seed. The results obtained so
far constitute a preliminary analysis which gives anindication about the power requirements of the input seed,in order to be effective in improving the coherence
properties of a single pass FEL.

REFERENCES
50 nm
0 3
10

4

10

5

6

10

7

10

Intensity (W/cm2)

8

10

10

Fig. 7. Standard deviation of the intensity fluctuations vs.
the seed intensity with the parameters of tab.1, col. A
0.8
I0sqrt(g2(0)-1)

0.8

2

as a function of the longitudinal coordinate along theundulator. From the definition (11), and assuming~ 2
I (t ) ∝ E (t ) , it follows thatg 2 (0) −1 = I I

transition is smoother than the one observed inestablishing the temporal coherence (figs. 4,5 and 6).

sqrt(g2(0)-1)

slightly overestimates the intensity required to establish
coherence on the fundamental harmonic, as the
wavelength decreases (parameters of col. C, fig.6). It
must be stressed that the intensity of eq.(1) still matches
quite well the intensity that can be obtained byextrapolating the laser intensity at z=0 from thesimulation data.
The intensity fluctuations have been studied calculating
the second order correlation function g 2 (τ ) [12]:

0.6

1st
3rd
5th

0.4
0.2
0 3
10

15 nm
4

10

5

10

6

10

7

10

2

Intensity (W/cm )

8

10

9

10

Fig. 8 As in fig. 7, with the parameters of tab.1, col. B
In a SASE FEL in the exponential growth regime, wehave g 2 (0) − 1 = 1 [3]. As expected the effect of the seedis that of suppressing the intensity fluctuations but thisMOPOS26[1] R. Bonifacio, L. De Salvo, P. Pierini, N. Piovella, C.
Pellegrini, Phys. Rev. Lett. 73 (1994) 70 andreferences therein.
[2] P. Pierini, W. M. Fawley, Nucl. Instrum. & Meth. A
375 (1996) 332-335[3] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov,
Optics Communications 148, (1998) 383–403[4] L. H. Yu et al., Phys. Rev. Lett. 91 (2003) 74801[5] Workshop on the Physics of Seeded Free Electron
Lasers, 17-19 June 2004, MIT campus, Cambridge,
MA http://mitbates.mit.edu/xfel/conference.htm[6] G. Dattoli, P.L. Ottavini, Journal of Appl. Phys. 86(1999) 5331
[7] See e.g. G. Dattoli, A. Renieri, A. Torre, Lectures on
the Free Electon Laser Theory, World Scientific ed.
(1993) p. 493[8] M. Xie, in Proceedings of the Particle Accelerator
Conference, Dallas, TX, 1995 (IEEE, Piscataway, NJ,
1996), p. 183. Sect. A 483, 101 (2002).
[9] G. Dattoli, L. Giannessi, P.L. Ottaviani, C.
Ronsivalle, Journal of Appl. Phys. 95 (2004) 3206
[10] http://www.enea.perseo.it[11] P. Salières et al., Science 292 (2001) 902[12] See e.g. R. Loudon, Quantum Theory of Light,
Oxford Univ. Press (2000), chapter 3.

41

N. Nishimori / Proceedings of the 2004 FEL Conference, 41-44

ANALYTICAL SOLUTION OF PHASE SPACE EVOLUTION OF
ELECTRONS IN A SASE FEL
N. Nishimori∗ , JAERI, Ibaraki, Japan
Abstract
I present an analytical solution for the phase space evolution of electrons in a self-amplified spontaneous emission
Free Electron Laser (FEL) operating in the linear regime
before saturation, by solving the one dimensional FEL
equation together with the solution of the cubic equation,
which represents the evolution of the FEL power. The analytical solutions for the phase space evolution are complementary to the solution for the optical evolution and holduntil the optical amplitude grows greater than one-tenth of
the amplitude in saturation. The amplitude in saturation
obtained from a time dependent numerical calculation inwhich the analytical solutions are used as the initial values
is shown to be equal to that obtained in the conventional
theories.

INTRODUCTION
A self-amplified spontaneous emission (SASE) freeelectron laser (FEL) has been developed worldwide as anintense coherent x-ray radiation source [1, 2, 3]. The development has been supported by extensive theoretical studies[4, 5, 6], which can account for various types of experimental results such as the exponential increase of SASE powerwith the undulator length [1]. However, those studies havemainly focused on the property of the radiation field, andthe phase space evolution of electrons of a SASE FEL has
been studied only in numerical simulations so far [6].
In this paper, I present an analytical solution for thephase space evolution of electrons in a SASE FEL operating in the linear regime before saturation, by solving
the one dimensional (1D) equations of electron motion together with the solution of the cubic equation, which represents the evolution of SASE power. The solutions forthe energy and phase changes of electrons are respectively
represented by sum of three independent terms similarly tothe solution of the cubic equation; an exponentially growing term, an exponentially decaying term and an oscillatingterm. The 1D Maxwell equation results in the same field
gain as the solution of the cubic equation, when the solution for the electron phase is substituted into the Maxwell
equation. The solutions for the phase space evolution arethus complementary to the solution for the optical evolution. The present solutions hold until the optical amplitude grows greater than one-tenth of the amplitude in saturation. The field in non-linear regime near saturation is
obtained from a numerical calculation which uses the analytical solutions as the initial values and solves the 1D FELequations. The peak amplitude in saturation obtained in the∗ nisi@milford.tokai.jaeri.go.jp

Available online at http://www.JACoW.org

calculation agrees well with those obtained in conventional
theories [5, 6].

1D FEL EQUATIONS
The present study starts with the Colson’s dimensionless FEL equations under the slowly varying envelope approximation (SVEA) [7]. Some of the variables used in thepresent study are however defined differently from those of
Colson’s variables, as described later in this section. The
simplest situation is considered in the present study where
the electron pulse has a rectangular shape with density ofne and an initial energy of γ0 mc2 with no energy spread.
The electron pulse length is assumed to be longer than theslippage distance Nw λ. Here Nw is the number of undulator periods, λ = λw (1 + a2w )/(2γ02 ) is the resonant wavelength, λw = 2π/kw is the period of the undulator and aw
is the undulator parameter. The fundamental FEL parameter in MKSA units is given byρ=
1[eaw F ne /(0 m)/(4ckw )]2/3 ,γ0(1)

where F is unity for a helical undulator or Bessel function [JJ] for a planar undulator [5]. The dimensionlesstime is defined by τ = ct/λw , so that δτ = 1 corresponds
to the transit time of light through the undulator period.
The longitudinal position of the ith electron is defined by
ζi (τ ) = [zi (t) − ct]/λ, so that δζ = 1 corresponds to λ.
The dimensionless field envelope is defined bya(ζ, τ ) =2πeaw λw FE(ζ, τ ) exp[iφ(ζ, τ )],γ0 2 mc2(2)

with phase φ(ζ, τ ), which is equivalent to the Colson’s
dimensionless field envelope [8] divided by 2Nw2 and to
the Bonifacio’s envelope [5] multiplied by (4πρ)2 . HereE(ζ, τ ) is the rms optical field strength. The dimensionless energy and phase of the ith electron are respectively
defined by µi (τ ) = 4π[γi (t) − γ0 ]/γ0 and ψi (τ ) = (kw +k)zi (t) − ωt, where k = 2π/λ is the wave number of theresonant wavelength λ.
In the present definition, evolutions of a(ζ, τ ), µi (τ ) andψi (τ ) are respectively given by [8]dµi (τ )dτdψi (τ )dτ∂a(ζ, τ )∂τ

= a[ζi (τ ), τ ] exp[iψi (τ )] + c.c.,(3)= µi (τ ),(4)= −(4πρ)3 exp[−iψi (τ )]ζi (τ )=ζ . (5)The angular bracket indicates the average of all the electrons in the volume V around ζ.

FEL Theory

42

N. Nishimori / Proceedings of the 2004 FEL Conference, 41-44

PHASE SPACE EVOLUTION
The lasing process in FELs starts with formation of a
uniform field in time and space. This process is known as
the spectrum narrowing in the frequency domain [4] or as
the longitudinal phase mixing in the time domain [9]. The
evolution of the uniform field before saturation is represented by three complex roots of the cubic equation [5, 8].
The field in τ for the steady-state region where ζ < −τ isgiven byEquation (10) has the exponentially growing term, the exponentially decaying term and the oscillating term, similarly to Eq. (8). Equations (8) and (10) are the analyticalexpressions for the phase space evolution in a SASE FEL
operating in the linear regime; only numerical solutions for
those have been obtained previously [6].
3

2

1

=

|a(0)|e[exp(4πρτ eiπ/6 ) +3exp(−4πρτ e−iπ/6 ) + exp(4πρτ e−iπ/2 )].(6)The ith electron interacts with the field in the steadystate region due to the slippage, and the energy modulation at τ  during δτ  is given from Eq. (3) by δµi (τ  ) =[a(τ  )eiψi (τ ) + c.c.]δτ  . Here the linear regime before saturation is defined as the regime where the electron phaseremains almost unchanged due to the weak FEL field, i.e.,ψi (τ  ) ≈ ψi (0). The energy modulation in the linear
regime is expressed by δµi (τ  ) ≈ [a(τ  )eiψi (0) + c.c.]δτ  .
The energy change of the ith electron at time τ , µi (τ ), is
given by the sum of those modulations during τ : τµi (τ ) ={a(τ  ) exp[iψi (0)] + c.c.}dτ  .
(7)0

The integration of Eq. (7) after substitution of Eq. (6)yieldsµi (τ )

2|a(0)|×3(4πρ)=√{e2π 3ρτ cos[ψi (0) + φ(0) + 2πρτ − π/6]√

−e−2π 3ρτ cos[ψi (0) + φ(0) + 2πρτ + π/6]
+ cos[ψi (0) + φ(0) − 4πρτ + π/2]}.

(8)

The first term in the right hand side of Eq. (8) is the exponentially growing term, the second is the exponentiallydecaying term, and the third is the oscillating term.
The phase modulation at τ  during δτ  is given from Eq.
(4) by δψi (τ  ) = µi (τ  )δτ  . The phase change of the ithelectron at time τ is given by the sum of those modulations
during τ : τ∆ψi (τ ) = ψi (τ ) − ψi (0) =µi (τ  )dτ  .
(9)0

The integration of Eq. (9) after substitution of Eq. (8)yields∆ψi (τ )=2|a(0)|×3(4πρ)2√{e2π 3ρτ cos[ψi (0) + φ(0) + 2πρτ − π/3]√

+e−2π 3ρτ cos[ψi (0) + φ(0) + 2πρτ + π/3]
+ cos[ψi (0) + φ(0) − 4πρτ + π]}.
(10)

MOPOS29

0

Y

a(τ )

iφ(0)

4πρτ=2
=3
=4
=6
=10

-1

-2

-3
-3

-2

-1

0

1

2

3

X

Figure 1: Electron distributions in√ a phase plane of
X = ∆ψi (τ )(4πρ)2 /[|a(0)|√ exp(2π 3ρτ )/3] and Y =µi (τ )(4πρ)/[|a(0)| exp(2π 3ρτ )/3] derived from Eqs.
(8) and (10) for 4πρτ = 2, 3, 4, 6, 10. The center of theelectron microbunch is located at (X, Y ) = (0, −1) when
4πρτ ≥ 4.
Using Eqs. (8) and (10), one can study the distribution ofelectrons in a longitudinal phase space. The electrons contained in the resonant wavelength at τ = 0 are numberedfrom the front to back along the propagating direction in
the present study. The relative position between two adjacent electrons is represented by ζi (0) − ζi+1 (0) > 0, andthe relative phase between two adjacent electrons is givenby ψi (0) > ψi+1 (0), since ψi (τ ) = 2πζi (τ ) + kw zi (t)by definition. One can calculate the values of Eqs. (8) and(10) for each i and plot the point in a phase space of ∆ψi (τ )and µi (τ ). The point rotates counterclockwise in the phasespace, as i increases. The distribution of the electrons attime instant τ in a longitudinal phase space of∆ψi (τ )X=Y= µi (τ )3(4πρ)2√|a(0)|e2π 3ρτ

(11)

and
3(4πρ)√|a(0)|e2π 3ρτ(12)

is elliptical as shown in Fig. 1. The shape of the distribution gradually changes when 4πρτ < 4 and remains almost
constant when 4πρτ ≥ 4.
The gain of the steady state field in the linear regime
before saturation where |∆ψi (τ )|  1 is obtained by substitution of Eq. (10) into Eq. (5) as follows:∂a(τ )∂τ=

4πρ|a(0)|eiφ(0)[exp(4πρτ eiπ/6 + iπ/6)
3− exp(−4πρτ e−iπ/6 − iπ/6)+ exp(4πρτ e−iπ/2 − iπ/2)].
(13)

43

N. Nishimori / Proceedings of the 2004 FEL Conference, 41-44

Equation (13) is the same as ∂a(τ )/∂τ obtained from differentiation of Eq. (6). This means that Eqs. (8) and (10)are complementary to Eq. (6). The magnitudes of the gain
and phase shift are almost constant when 4πρτ ≥ 4.

EVOLUTION IN HIGH GAIN REGIME
In this section, the field and electron phase space evolutions are studied in the high gain regime, which is definedby 4πρτ ≥ 4 where the exponentially growing terms only
survive in Eqs. (6), (8) and (10). In this case, the field isgiven by|a(0)| 2π√3ρτ iφ(τ )a(τ ) ∼
e
e
,
(14)
3
where φ(τ ) = 2πρτ + φ(0), and the energy and phasechanges of the ith electron are respectively given by√
2|a(0)|e2π 3ρτπµi (τ ) ∼cos ψi (0) + φ(τ ) − , (15)3(4πρ)
6√


2|a(0)|e2π 3ρτπ∆ψi (τ ) ∼cos ψi (0) + φ(τ ) − . (16)3(4πρ)2
3
The shape of the distribution in a longitudinal phase spaceof X and Y is simply represented by the ellipse X 2 + Y 2 −√3XY = 1. The ellipse rotates clockwise as φ(τ ) increases linearly with τ . The electrons are lined along theellipse counterclockwise as the identification number i increases. The electron at the microbunch center satisfies thecondition of ∆ψi (τ ) = 0. The electron just in front of
the electron at the microbunch center satisfies the condition of ∆ψi−1 (τ ) < 0 for the bunch to be formed. Thus
the microbunch center in the high gain regime is located at(X, Y ) = (0, −1) in Fig. 1 and the electrons inside the microbunch are concentrated around ψi (0) + φ(τ ) − π/3 =π/2 when 4πρτ ≥ 4.
0.01

µi(τ)

0.005

0
π/2
π
3π/2

|a(τ )|∂ (4πρ)2∂(4πρτ )∂φ(τ )∂(4πρτ )|a(τ )|×(4πρ)2cos[ψi (0) + φ(τ ) − π/3]}ζi (τ )=ζ , (17)= −cos{ψi (0) + φ(τ ) + 2=(4πρ)2|a(τ )|
sin{ψi (0) + φ(τ ) + 2
×|a(τ )|(4πρ)2cos[ψi (0) + φ(τ ) − π/3]}ζi (τ )=ζ . (18)

One can calculate the values of the right hand sides of Eqs.
(17) and (18) as a function of the value of |a(τ )|/(4πρ)2
and find that Eq. (13) begins to deviate from Eqs. (17) and(18) around |a(τ )|/(4πρ)2 = 0.15. In the calculation thevalue of ψi (0) + φ(τ ) is uniform over 2π.

SATURATION

04πρτ=10-0.005-0.01-0.22, where ρ = 0.00447 and |a(0)| = 7.1 × 10−5 ρ3/2 areused. Those values are typical parameters in JAERI FEL[10]. The crosses are the distribution when 4πρτ = 10,
the open squares when 4πρτ = 11 and the open circles
when 4πρτ = 12. The figure also shows the time evolutionof four different electron particles, initial phases of whichare ψi (0) (solid line), ψi (0) + π/2 (dotted line), ψi (0) + π(dash-dotted line) and ψi (0) + 3π/2 (dashed line). One
can find that the ellipse expands exponentially in size dueto the exponential increase of |a(τ )| and rotates clockwise
due to the linear increase of φ(τ ). The intersection of theellipse and the line ∆ψi (τ ) = 0 where µi (τ ) < 0 is the location of the microbunch center. The exponential decreaseof the energy of the microbunch center corresponds to the
exponential decrease of the energy of the microbunch as awhole. The energy radiated by the microbunch is used forthe field amplification.
The field gain in the linear regime where |∆ψi (τ )| 
1 is given by Eq. (13). However, the gain deviates from
Eq. (13) in the non-linear regime near saturation where
the amplitude grows and |∆ψi (τ )|  1 does not hold any
more for some electrons. The threshold amplitude for the
non-linear regime can be roughly estimated from Eq. (5) inwhich Eqs. (14) and (16) are substituted as follows:

=11
=12

-0.1

0
∆ψi(τ)

0.1

0.2

Figure 2: Electron distributions in a phase plane of ∆ψi (τ )and µi (τ ) derived from Eqs. (8) and (10) when 4πρτ = 10
(crosses), 11 (open squares), 12 (open circles). The time
evolution of four different electrons, initial phases of whichare ψi (0) (solid line), ψi (0) + π/2 (dotted line), ψi (0) + π(dash-dotted line) and ψi (0) + 3π/2 (dashed line), are also
shown. The FEL parameter ρ = 0.00447 and |a(0)| =7.1 × 10−5 ρ3/2 are used.
The evolution of the electron distribution in a longitudinal phase space of ∆ψi (τ ) and µi (τ ) is shown in Fig.

One can calculate the efficiency and amplitude in the
non-linear regime near saturation by solving the time dependent 1D FEL equations together with the initial values
given by Eqs. (14), (15) and (16). In the high gain and linear regime, where 4πρτx ≥ 4 and |a(τx )|/(4πρ)2 = x forx ≤ 0.15, Eq. (14) is rewritten bya(τx )|a(0)| 2π√3ρτx iφ(τx )∼ee= xeiφ(τx ) .
2(4πρ)
3(4πρ)2(19)

The energy and phase of the ith electron at τx are derived
from substitution of Eq. (19) into Eqs. (15) and (16) andare respectively given byµi (τx )π∼ 2x cos{ψi (0) + φ(τx ) − },4πρ6π
ψi (τx ) ∼ ψi (0) + 2x cos{ψi (0) + φ(τx ) − }.
3

(20)
(21)

FEL Theory

44

N. Nishimori / Proceedings of the 2004 FEL Conference, 41-44|a(τ)|/(4πρ)

2

1

1

0

0

τ=τp

-1

0

2

4
6
4πρ(τ-τ 0.1 )

8

-1
10

Figure 3: The amplitude gain ∂[|a(τ )|/(4πρ)2 ]/∂(4πρτ )(solid line) and phase shift ∂φ(τ )/∂(4πρτ ) (dotted line)
calculated numerically from the 1D FEL equations given
by Eqs. (22), (23), (24) and (25) as a function of 4πρ(τ −τ0.1 ). The initial values for the calculation are derived from
Eqs. (19), (20) and (21).

Solving the 1D FEL equations numerically with the initial values given by Eqs. (19), (20) and (21), one can calculate the phase space evolution of electrons and the fieldevolution. The equations for τ ≥ τx are written as follows:i (τ )
d µ4πρ

d(4πρτ )dψi (τ )d(4πρτ )|a(τ )|∂ (4πρ)2∂(4πρτ )∂φ(τ )∂(4πρτ )|a(τ )|= 2cos[ψi (τ ) + φ(τ )],(4πρ)2µi (τ )
=
,
4πρ

(22)
(23)

|∆ψi (τ )|  1 has been solved analytically from the 1D
FEL equation. The evolutions of ∆ψi (τ ) and µi (τ ) arerepresented by sum of three independent analytical solutions similarly to the evolution of the SASE field; an exponentially growing term, an exponentially decaying term
and an oscillating term. The distribution in a longitudinal
phase space of ∆ψi (τ ) and µi (τ ) expands exponentiallywith time in size, rotating clockwise linearly in the highgain regime where 4πρτ ≥ 4. These expansion in sizeand clockwise rotation corresponds to the exponential increase of the amplitude and linear increase of the phaseof the radiation field, respectively. The microbunch center is located where ∆ψi (τ ) = 0 and µi (τ ) < 0, and theenergy of the microbunch center decreases exponentially,
which corresponds to the exponential increase of the SASE
power. The analytical solutions hold until the optical amplitude grows greater than one-tenth of the amplitude in saturation. A numerical calculation which solves the 1D FELequations together with initial values given by the present
analytical solutions results in the peak amplitude in saturation |a(τp )| = 1.18(4πρ)2 , which agrees well with theconventional theories.

ACKNOWLEDGEMENTS
The author would like to acknowledge valuable discussions with S. Hiramatsu at KEK, H. Hama at Tohoku univand E. Minehara at JAERI.

REFERENCES= −cos[ψi (τ ) + φ(τ )]ζi =ζ ,
=

(24)

2

(4πρ)
sin[ψi (τ ) + φ(τ )]ζi =ζ . (25)|a(τ )|[1] V. Ayvazyan et al., PRL 88, 104802 (2002).
[2] C. Limborg, NIM A 507, 378 (2003).
[3] T. Shintake et al., NIM A 507, 382 (2003).

Figure 3 shows ∂[|a(τ )|/(4πρ)2 ]/∂(4πρτ ) and∂φ(τ )/∂(4πρτ ) as a function of 4πρ(τ − τx ) whenx = 0.1. It is found that ∂[|a(τ )|/(4πρ)2 ]/∂(4πρτ )decreases down to 0 when 4πρ(τp − τ0.1 ) = 3.7. Here τp
is the time when the efficiency and amplitude reach theirpeaks and the amplitude gain turns to negative.
Integration of ∂|a(τ )|/∂(4πρτ ) from 4πρτ0.1 to 4πρτpyields 4πρτp∂|a(τ )|d(4πρτ ) = 1.08(4πρ)2 .
∂(4πρτ
)4πρτ0.1[4] Kwang-Je Kim, PRL 57, 1871 (1986); NIM A 250, 396(1986); Kwang-Je Kim and Ming Xie, NIM A 331, 359(1993).

The peak amplitude is thus given by[9] N. Nishimori, R. Hajima, R. Nagai and E.J. Minehara, NIM
A 507, 79 (2003).

|a(τp )| = 1.18(4πρ)2 ,(26)

which agrees well with the peak amplitude of the SASE in
the steady-state regime obtained in a numerical calculation[5]. Equation (26) does not depend on x.

CONCLUSION
The phase space evolution of electrons in a SASE FEL
operating in the linear regime before saturation where

MOPOS29[5] R. Bonifacio et al., Riv. Nuovo Cimento 13, 9 (1990).
[6] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, in The
Physics of Free Electron Lasers, (Springer, Berlin, 2000),
pp. 48–54.
[7] W.B. Colson and S.K. Ride, Phys. Lett. 76A, 379 (1980).
[8] W.B. Colson, in Laser Handbook, edited by W.B. Colson,
C. Pellegrini, and A. Renieri (North Holland, Amsterdam,
1990), Vol.6, pp. 115–193.

[10] N. Nishimori, R. Hajima, R. Nagai, and E.J. Minehara, PRL
86, 5707 (2001); NIM A 483, 134 (2002).

45

S.-K. Nam et al. / Proceedings of the 2004 FEL Conference, 45-48

BEHAVIOUR OF ELECTRON BEAM IN COMBINEDA SELF-GENERATED FIELD AND A REVERSED GUIDE FIELD
IN THE HELICAL WIGGLER
Soon-Kwon Nam ∗ and Ki-Bum Kim
Department of Physics, Kangwon National University, Chunchon 200-701, Republic of Korea
Abstract
We have studied behaviour of electron beam in combined a self-generated field and a reversed axial-guide fieldin the tapered helical wiggler. The divergence of electron
beam is caused by three-dimensional effects on the electron beam loss, we employ a tapered and reversed axialguide field magnetic field. Evolution of energy spread andemittance of electron beam are investigated using three dimensional simulation. Beam cross-section, transverse momentum variation and cross-section view of electron beam
are also calculated along z axis. The electron beam loss
is reduced by optimizing the magnetic field strength andtapering parameter of reversed axial guide field.

symmetric about the z-axis. Therefore the density and velocity profiles can be written as only function of r, that is,nb (r, θ, z) = nb (r), vb (r, θ, z) = vb,θ (r)êθ + vb,z (r)êz
The self-generated electric field Er (r) induced by the spacecharge, azimuthal self-magnetic field induced by the axial
current Jz (r), and axial self-magnetic field induced by theazimuthal current Jθ (r). One can find the self-generated
field from the steady state Maxwell equations.
Within above assumptions, the equilibrium selfgenerated field components areE(r, θ, z) = Er (r)êr(2)

Bs (r, θ, z) = Bθ (r)êθ + Bz (r)êz

INTRODUCTIONIn free-electron laser(FEL), the gain increases when the
beam current and the wiggler field amplitude are increased.
When the free-electron laser experiments operate at thehigh-current regime and the intense wiggler field regime
to get the sufficiently large gain, the axial-guide field makeus to steer the electron beam in the axial direction [1–4]
and the electron motion can be altered by the axial-guidefield and self-field effects [5–11] .
In this work, we study the behaviour of electron beam in
combined a self-generated field and a reversed axial-guidefield in the tapered helical wiggler. Cross-section, profileand density of electron beam are investigated using three
dimensional simulation.

THE SELF-GENERATED FIELD AND
EXTERNAL FIELD
The space charge and current of electron beam generate
the self-electric and self-magnetic fields. The Maxwell’sequations in steady state are∇ · E = 4πρ0 , ∇ × B =

4π
J
c

(1)

We assume that equilibrium properties (electron densityand velocity) are uniform in the z-direction with ∂nb /∂z =0 and ∂vb /∂z = 0. There is no equilibrium electric fieldparallel to z-direction with E · êz = 0. Where nb is electron density and vb is mean velocity of electron. The radial
density and velocity profiles are assumed to be azimuthally∗ snam@kangwon.ac.kr; Tel:+82-33-250-8463; fax:+82-33-257-9689

Available online at http://www.JACoW.org

Therefore the self-generated fields are determined from thesteady-state Maxwell’s equations1 ∂ 
rEr (r) = 4πρ0 (r)r ∂r
1 ∂Bθ (r)∂Bz (r)êθ +êz∇ × B(r) = −
∂r
r ∂r

4π 
Jθ (r)êθ + Jz (r)êz=c∇ · E(r) =(3)where ρ0 (r) = −efb (r) is charge density, Jz (r) =−fb (r)evz is axial current density, Jθ (r) = −fb (r)evθ isazimuthal current density and fb (r) is electron beam profile function. The axial velocity and azimuthal velocity ofelectron beam are vz = βb c and vθ = rωr , where βb = vb c
is the normalized axial velocity, ωr is the angular velocity.
The self-generated field amplitude depends on the electron beam profile. We consider Gaussian shape electron
beam. The profile function fb (r) for the Gaussian density
is


cn nb
r2
exp
−
fb (r) = 
(4)
2rb2
2πrb2
where cn = πrb2 is the normalized factor and the self electric and magnetic field are
»
„
«–
2αrb2
r2
1 − exp − 2
êr
r
2rb
»
„
«–
2αβb rb2
r2(5)
Bsθ (r) = −1 − exp − 2
êθ
r
2rb
»
„
«
„
«–
2
2
2
2αωr rbrr
Bsz (r) = −exp − 2 − exp − w2
êz
c
2rb
2rb
Esr (r) = −FEL Theory

46

S.-K. Nam et al. / Proceedings of the 2004 FEL Conference, 45-48

y(cm)

1

(a)

1

(c)

(b)

1

0

0

0

-1

-1

-1

-1

0

1

-1

0

x(cm)

1

-1

0

1

x(cm)

x(cm)

2

ks=0.01ks=1
ks=2.5

0.6

0.4

0.2

0.0

80

60

40

20
0

200

400

600

800

0

z [cm]

where α = πenb , ωp = (4πnb e2 /me )1/2 is plasma frequency of electron beam, ωr = kw cβ is the angular velocity, rb is the electron beam radius and rw is the cylindricalwaveguide radius.
The scalar potential and vector potential of the selfgenerated field which satisfies Es = −∇Φs and Bs =∇ × As are 2 
rr2
Φs = αrb2 Γ − Ei − 2 − log
2rb
2r2bAsθ = Φs βb êzαωr rb2r2
Asz =2rb exp − 2
cr
2rb

2
+(r2 + 2rb2 − rw
) exp

2

4

6

8

z [m]

Figure 2: The electron beam cross section along z-axis of
the wiggler for various self-field parameters.

(6)


r2
− w2
2rb


êθ

 x −uwhere Ei(x) = −∞ e u du is exponential integrate func m 1
tion, and Γ = limm→∞
k=1 k − log m ≈ 0.577 is

MOPOS32

ag=0
ag=-1
ag=-2
ag=-3

100

Number of electron (%)

Electron beam cross section (cm )Figure 1: Cross section views of electrons at (a) the entrance of wiggler and (b) the end of wiggler for κs = 2, ag =0 and(c) κs = 2, ag =-2, t =0. Dotted(solid) line indicate r = rb (2rb ).

Figure 3: Number of electron along z-axis of the wiggler
in rb for various reversed axial guide field strength.
Euler-Mascheroni constant.
The vector potential of helical wiggler magnetic field in
Cylindrical coordinate system is defined asBw 
I0 (kw r) + I2 (kw r) cos(kw z − θ) êr
kw
(7)

Bw 
I0 (kw r) − I2 (kw r) sin(kw z − θ) êθ
+
kw

Aw =

and vector potential of axial-guide field Bg = Bg êz whichsteer the electron to axial direction is Ag = 12 Bg rêθ .

HAMILTONIAN FORMALISM AND THE
TAPERING PROFILE OF GUIDEMAGNETIC FIELD
The Hamiltonian of relativistic test electron is
H = (cP + eA)2 + m2e c4 − eΦs ≡ γme c2 − eΦs (8)47

S.-K. Nam et al. / Proceedings of the 2004 FEL Conference, 45-48

(b)

(a)

0.2

0.0

x'

0

2

Ptran

y[c m ]

1

1

-1

(c)

-0.2
0
-1

0

1

30

40

x [cm]

50

Pz

-1

0

1

x [cm]

Figure 4: Electron beam profiles at the exit of the wiggler for aw = 3, κs = 2, ag = −2, t = 0.6. Dotted(solid) line
indicate r = rb (2rb ).

100

Number of electron (%)

H̄ =
80

q
q
1 + (P̄ + Ā)2 − Φ̄s = 1 + Σh2i − Φ̄sh1 = P̄r + aw (I0 (r̄) − I2 (r̄)) cos(z̄ − θ)
P̄θ
ag r̄
+
+ Āsθ + aw (I0 (r̄) + I2 (r̄)) sin(z̄ − θ)r̄2h3 = P̄z + Āsz

60

40

where ag = eBg /me c2 kw is a dimensionless axial-guidefield strength, aw = eBw /me c2 kw is a dimensionless wiggler field amplitude, and r̄ = kw r, z̄ = kw z.
The tapered guide magnetic field ag (z) = ag (0)ft (z),where ft (z) is the tapering profile function.

εt=0

εt=0.3εt=0.6

20

εt=1
0

2

4

6

8

z [m]

ft (z) =Figure 5: Number of electron along the z-axis of wiggler
in rb for various tapering parameters.

where P is the canonial momentum, p = P + eA/c is
1 + (p/me c)2 is thethe mechanial momentum, γ =relativistic mass factor, me is the electron rest mass, e
is the electron charge and total vector potential is A =Aw + Ag + Asθ + Asz .
Conveniently, we introduce the dimensionless potentials,
canonical momentum, and Hamiltonian defined by

Ā =

(10)

h2 =

eA
eΦs
P
H
, Φ̄s =, P̄ =, H̄ =
me c2 kw
me c2 kw
me c
me c 2(9)

In the dimensionless scalar and vector potential of self2
field, the constant α becomes α = κs kw/4, where κs =2is the dimensionless strength of the self-field.
ωp2 /c2 kw
Therefore the dimensionless Hamiltonian is1
for 0 ≤ z < zt
1 + cn t (z − zt ) for z > zt

(11)

where zt is the starting position of the tapering, t is tapering parameter, and cn is constant which satisfy ft (z =zf , t = 1) = 2. The electron orbits can be calculated fromthe equation of motions which derived from the Hamiltonian of Eq. 10.
We make the incident electron beam using the beam parameters such as electron beam energy Eb = 3 MeV, energy spread Es = 5 %, emittance x,y = 10 πmm · mrad.
Fig. 1(a) shows the cross section view of the incident electron beam which is the initial state of the Gaussian random distribution. Fig. 1(b) shows the cross section viewsat the exit of the wiggler for self-field parameters κs = 2
without axial guide field, and (c) with uniform axial guidefield ag = −2 for aw = 3. Those parameters correspondto the wiggler magnetic field strength Bw = 2.67 kG, theguide magnetic field strength Bw = 1.78 kG and the electron beam current Ib = 368 A for wiggler period λw = 12cm and electron beam radius rb = 0.4 cm.
Fig. 2 shows the electron beam cross section area
along z-axis of the wiggler for various self-field parameter stength. The cross section area is reduced by increasing
self-field parameter. Number of electron in rb along z-axis

FEL Theory

48

S.-K. Nam et al. / Proceedings of the 2004 FEL Conference, 45-48(a)Electron Density

30

20

20

10

10

0
0.0

0.5

1.0

1.5

Electron Density

2.0

(c)

30

0
0.0

20

10

10

0.5

1.0

1.5

0.5

1.0

1.5

2.0

kw r

2.0

(d)

30

20

0
0.0

(b)

30

0
0.0

0.5

1.0

1.5

2.0

kw r

Figure 6: Electron beam density versus kw r; (a) incident electron beam, (b) κs = 2 and ag = 0, (c) κs = 2, ag = −2 andt = 0, (d) κs = 2, ag = −2 and t = 0.6.
of the wiggler for various reversed axial guide field strengthis shown in Fig. 3.
Fig. 4 shows the cross section view, transverse momentum variation and x versus x phase space for κs = 2,ag = −2 and  = 0.6. The number of electron in rb
along z-axis of the wiggler for various tapering parameters is shown in Fig. 5. The electron densities versus kw r
are shown in Fig. 6. The electron density with tapered andreversed axial guide field is increased by about twice correspond to that of without axial guide field case in centerof electron beam.

CONCLUSION
We studied behaviour of electron beam in combined aself-generated field and a reversed axial-guide field in thehelical wiggler. Evolution of energy spread and emittanceof electron beam were investigated by using three dimensional simulation. Beam cross-section, transverse momentum variation and cross-section view of electron beam werealso calculated along z axis. The electron beam loss was
reduced by optimizing the magnetic field strength and tapering parameter of reversed axial guide field.

ACKNOWLEDGEMENTS
This work was supported by a Korea Research Foundation grant.

MOPOS32

REFERENCES[1] L. Friedland, Phys. Fluids. 23 (1980) 2376.
[2] P. Diament, Phys. Rev. A23 (1981) 2537.
[3] H. P. Freund and A. T. Drobot, Phys. Fluids. 25 (1982) 736.
[4] H. P. Freund, Phys. Rev. A27 (1983) 1977.
[5] C. Chen and R. C. Davidson, Phys. Fluids. B2 (1990) 171.
[6] C. Chen and R. C. Davidson, Phys. Rev. A43 (1991) 5541.
[7] L. Michel, A. Bourdier and J. M. Buzzi, Nucl. Instri. andMeth. A304 (1991) 465.
[8] S. Spindler and G. Renz, Nucl. Instri. and Meth. A304
(1991) 492.
[9] L. Michel-Lours, A. Bourdier and J. M. Buzzi, Phys. Fluids.
B5 (1993) 965.
[10] A. Bourdier and L. Michel-Lours, Phys. Rev. E49 (1994)
49.
[11] R. C. Davidson, Physics of Nonneutral Plasmas (Addison
Wesley, 1990).

49

S.-K. Nam et al. / Proceedings of the 2004 FEL Conference, 49-52

EVOLUTION OF ELECTRON BEAM
IN THE TAPERED PLANAR WIGGLER
Soon-Kwon Nam ∗ and Ki-Bum Kim
Department of Physics, Kangwon National University, Chunchon 200-701, Republic of Korea
Abstract
We have investigated the evolution of electron beam in
the tapered planar wiggler field with a self-electric fieldand self-magnetic fields. In order to suppress the divergence of emittance and spread of the electron beam by
the three-dimensional effects on the off-axis electron anda self-generated field effects, the tapered and bent wiggler
field is applied. We calculate the emittance, transverse trajectories and Fourier transformation of electron beam using three dimensional simulation by optimizing the magnetic field strength, a tapering parameter and self-field parameters. This method could be expected to enhance theefficiency compared to those of a untapered wiggler in afree-electron laser.

INTRODUCTION
The free-electron laser which the new electromagnetic
generation source have been active areas of research due totheir attractive properties, such as high efficiency, tunablefrequency from microwave to X-ray, and powerfule output.
The quality of the electron beam plays an important roleand limits the operating wavelength, gain, and efficiency.
Free-electron laser operation often requires sufficiently
large gain, which increase when the beam current is increased. In the high-current regime, the electron motion
can be altered by the self-generated field effects [1, 2, 3, 4,
5, 6, 7].
In this work, we study the evolution of electron beam in
the tapered planar wiggler field with self-electric and selfmagnetic fields. To suppress the divergence of emittanceand spread of the electron beam, we apply the tapered andbent wiggler field.
The emittance, transverse trajectories and Fourier transformation of electron beam are calculated using three dimensional simulation by optimizing the magnetic fieldstrength, a tapering parameter and self-field parameters.

THE SELF-GENERATED FIELD AND
EXTERNAL MAGNETIC FIELD
The scalar potential of planar wiggler magnetic fieldwith bent pole face isφ=−Bw
cosh(kx x) sinh(ky y) cos(kw z)
kw(1)∗ snam@kangwon.ac.kr; Tel:+82-33-250-8463; fax:+82-33-257-9689

Available online at http://www.JACoW.org

and if kx x ≪ 1 and ky y ≪ 1, the wiggler magnetic field isderived from Eq. 1.
¡
Bw = Bw 

1+



2 2
ky y ¢kxxcos(kw z)
2 + 22kx xy cos(kw x)
2

2

(2)

−kw y sin(kw x)

In order to fulfill Maxwell’s equations the scalar potential must be a solution of the Laplace equation ∇2 φ = 0.
2,
Therefore we can find the relation such as kx2 + ky2 = kw√
and we choose the case as kx = ky = kw / 2.
The vector potential of planar wiggler magnetic field
which satisfy Bw = ∇ × Aw defined as

Bw 2
k xy sin(kw x)êx
kw x
ky2 y 2 ¢k 2 x2Bw ¡1+ x +
sin(kw z)êy
+
2
kw
2

Aw = −(3)

The space charge and current of electron beam generate
the self-electric and self-magnetic fields. The Maxwell’sequations in steady state are∇ · E = 4πρ0 , ∇ × B =

4π
J
c

(4)

The self-generated electric field Er (r) induced by the
space charge, azimuthal self-magnetic field induced by theaxial current Jz (r). One can find the self-generated fieldfrom the steady state Maxwell equations.
We assume that equilibrium properties (electron densityand velocity) are uniform in the z-direction with ∂nb /∂z =0 and ∂vb /∂z = 0. And there is no equilibrium electricfield parallel to z-direction with E · êz = 0. Where nb iselectron density and vb is mean velocity of electron. The
radial density and velocity profiles are assumed to be azimuthally symmetric about the z-axis. Therefore the density and velocity profiles can be written as only functionof r, which means nb (r, θ, z) = nb (r) and vb (r, θ, z) =vb,z (r)êz .
There is no equilibrium electric field parallel to zdirection with E · êz = 0.

¢
1 ∂ ¡rEr (r) = 4πρ0 (r)r ∂r4π
1 ∂Bθ (r)Jz (r)êzêz =∇ × B(r) =cr ∂r∇ · E(r) =(5)where ρ0 (r) = −efb (r)is charge density, Jz (r) =−fb (r)evz is axial current density, fb (r) is electron beam

FEL Theory

50

S.-K. Nam et al. / Proceedings of the 2004 FEL Conference, 49-52

1

1

(b)

0

-1

(c)

x
y

FFT

kwx (kwy)

kwy

(a)
0

-1
-1

0

1

0

50

kwx

100

150

0.0

0.5

ω

kwz

Figure 1: Electron trajectories and Fourier transformation aw = 1, Θ = 90◦ and κs = 2.

0.5

1

(a)

(b)

(c)

y

0

x'

Ptran

1
0.0

-1
0
-1

0

1

-0.5
4

x

6

8

Pz

-1

0

1

x

Figure 2: Electron beam profiles at the exit of the wiggler with (a) electron beam cross section, (b) transverse momentum
variation and (c) x versus x′ phase space. Other electron beam parameter are aw = 1, Θ = 90◦ and κs = 2. Dotted(solid)line indicate r = rb (2rb ).
profile function and βb = vb c is the normalized axial velocity of electron.
The self-generated field amplitude depend on the electron beam profile. We consider Gaussian shape electron
beam. The profile function fb (r) for the Gaussian density
is
µ
¶
r2
cn nb
exp
−
fb (r) = p
(6)
2rb2
2πrb2

ity, rb is the electron beam radius and rw is the cylindricalwaveguide radius.
The scalar potential and vector potential of the selfgenerated field which satisfies Es = −∇Φs and Bs =∇ × As are¶µ 2 ¶¸·µrr2
Φs = αrb2 Γ − Ei − 2 − log
2rb
2r2b
(8)
Asθ = Φs βb êzwhere nb is electron density, cn = πrb2 is the normalized
factor and the self electric and magnetic field are
¶¸
·
µ
r2
2αrb2
êr
1 − exp − 2
Esr (r) = −
2rb
r
(7)
¶¸
·
µ
r2
2αβb rb2sêθ
1 − exp − 2Bθ (r) = −2rbr

R x −uwhere Ei(x) = −∞ e u du is exponential integrate func¢¡Pm 1tion, and Γ = limm→∞
k=1 k − log m ≈ 0.577 is
Euler-Mascheroni constant.

where α = πenb , ωp = (4πnb e2 /me )1/2 is plasma frequency of electron beam, ωr = kw cβ is the angular veloc-

MOPOS33

HAMILTONIAN FORMALISM
The Hamiltonian of relativistic test electron isp
H = (cP + eA)2 + m2e c4 − eΦs ≡ γme c2 − eΦs (9)51

S.-K. Nam et al. / Proceedings of the 2004 FEL Conference, 49-52

Nunber of electron in 2rb (%)

100

90

80

untaperd case
Θ=80
Θ=70
Θ=60
70
0

2

4

6

8

z
Figure 3: Number of electron along the z-axis of wiggler
in 2rb for various tapering parameter Θ of wiggler field.
Other parameters are aw = 1 and κs = 2.
where P is the canonial momentum,
p p = P + eA/c is
1 + (p/me c)2 is thethe mechanial momentum, γ =relativistic mass factor, me is the electron rest mass, e
is the electron charge and total vector potential is A =Aw + Asθ + Asz .
Conveniently, we introduce the dimensionless potentials,
canonical momentum, and Hamiltonian defined by
Ā =

H
eA
eΦs
P
(10)
, H̄ =, Φ̄s =, P̄ =me c 2me c
me c2 kw
me c2 kw

In the dimensionless scalar and vector potential of self2/4, where κs =field, the constant α becomes α = κs kw
2is the dimensionless strength of the self-field.
ωp2 /c2 kw
Therefore the dimensionless Hamiltonian isH̄ =q

1 + (P̄ + Ā)2 − Φ̄s =q
1 + Σh2i − Φ̄sh1 = P̄x + kx2 xy sin(kw x)¡
ky2 y 2 ¢k 2 x2h2 = P̄y + 1 + x +sin(kw z)22sh3 = P̄z + Āz(11)where aw = eBw /me c2 kw is a dimensionless wiggler
field amplitude. To correct the electron energy loss in wiggler, the wiggler magengtic field is tapered as aw (z) =aw (0)ft (z), where ft (z) is the tapering profile function
for 0 ≤ z < zt
1
(12)ft (z) = 1 + cn (z − zt ) cos Θ22+ (z − zt ) cos Θ for z > zt
where zt is the starting position of wiggler tapering, Θ istaper parameter, and cn is constant which satisfy ft (z =zf , Θ = 45o ) = 1/2.

The electron orbits can be calculated from the equations of motion which are derived from the Hamiltonianof Eq. 11. Fig. 1 shows the electron trajectories in (a) the(kw x, kw y) plane and (b) (kw x(kw y), kw z) plane, and (c)the Fourier transformation for a single electon and untapered wiggler case. Other parameters are aw = 1 andκs = 2 which correspond to the wiggle magnetic fieldstrength Bw = 1.78 kG and the electron beam current
Ib = 1.47 kA for wiggler period λw = 6 cm and electron
beam radius rb = 0.4 cm. In the planar wiggler with bentpole face, the electrons move periodically not only y direction but x direction.
We made the incident electron beam using the beam parameters such as electron beam energy Eb = 3 MeV, energy spread Es = 5 %, emittance ǫx,y = 10 πmm · mrad.
Fig. 2 shows the electron beam cross section, transevers
momentum variation and x versus x′ phase space at the exitof the wiggler with aw = 1, Θ = 90◦ and κs = 2.
The number of electron along z-axis of the wiggler in 2rb
for the various wiggler parameter Θ is shown in Fig. 3. The
number of electron for the case of the tapered wiggler isincreased about 1.6 % compared to that of untapered case.
The wiggler tapering parameter of Θ = 80◦ was used.

STEADY-STATE SOLUTION
Assume that y component of canonical momentum P̄y =py − eAy /c is exact constant of the motion. Therefore, we
assume that P̄y = 0 (i.e. py = eAy /c) and interest the(x, z) plane only. The Hamiltonian of Eq. 11 become
³
¡¡
¢
¢2
H̄ = 1 + P̄x2 + 1 + kx2 /2 sin(kw z)(13)¢2 ´1/2¡+ P̄z + Āsz
− Φ̄s
We can find the steady-state solution P̄z = 0, kw z =π/2 which satisfy r̄ ′ = ψ ′ = P̄r ′ = P̄ψ ′ = 0 from theequations of motion derived from the Hamiltonian.
³¡¢2 ´1/2
k 2 x2 ¢2 ¡γ = 1+ 1+ x
+ P̄z + Āsz
2

(14)

One can find the kw x0 from Eq. 14.
Fig. 4 shows Poincarè surface of section plot in(kw z, P̄z ) plane at p̄x = 0 for various tapering parameters
and kw x0 . In the strong wiggle field regime, the electron
orbits for tapered wiggler Θ = 80o are more stable thanthose of a untapered wiggler case.

CONCLUSION
We investigated the evolution of electron beam in the tapered planar wiggler field with a self-electric field and selfmagnetic fields. To suppress the divergence of emittanceand spread of the electron beam by the three-dimensional
effects on the off-axis electron and a self-generated field
effects, the tapered and bent wiggler field was applied. We
calculated the emittance, transverse trajectories, Fourier

FEL Theory

52

S.-K. Nam et al. / Proceedings of the 2004 FEL Conference, 49-52

6
(c)

(b)

(a)

Pz

4

2

0
π0

0

kwz

π0

kwz

π

kwz

Figure 4: Poincarè surface of section plot in the (kw z, P̄z ) plane at p̄x = 0 for (a) Θ = 80o and the various kw x0 , (b)Θ = 80o and kw x0 =0.615 and (c) Θ = 90o and kw x0 =0.615. Other parameters are aw = 5, kw rb =0.4 and Eb =3 MeV.
transformation and Poincarè surface of section of electron
beam using three dimensional simulation by optimizing themagnetic field strength and a tapering parameter of axial
guide field. This method could be expected to enhance theefficiency compared to those of a untapered wiggler in afree-electron laser.

ACKNOWLEDGEMENTS
This work was supported by a Korea Research Foundation grant.

REFERENCES[1] C. Chen and R. C. Davidson, Phys. Fluids. B2 (1990) 171.
[2] C. Chen and R. C. Davidson, Phys. Rev. A43 (1991) 5541.
[3] L. Michel, A. Bourdier and J. M. Buzzi, Nucl. Instri. andMeth. A304 (1991) 465.
[4] S. Spindler and G. Renz, Nucl. Instri. and Meth. A304
(1991) 492.
[5] L. Michel-Lours, A. Bourdier and J. M. Buzzi, Phys. Fluids.
B5 (1993) 965.
[6] A. Bourdier and L. Michel-Lours, Phys. Rev. E49 (1994)
49.
[7] R. C. Davidson, Physics of Nonneutral Plasmas (Addison
Wesley, 1990).

MOPOS33

53

M.I. de la Fuente et al. / Proceedings of the 2004 FEL Conference, 53-56

THE EFFECT OF LINER INDUCED PHASE FLUCTUATIONS ON THE
GAIN OF A CERENKOV FELPeter van der Slot, Isabel de la Fuente∗ , Klaus Boller
Laser Physics and Non-Linear Optics Group,
Department of Science and Technology, University of Twente, The Netherlands
Abstract
In a Cerenkov FEL (CFEL), the phase velocity of an EM
wave is determined by geometry (i.e., waveguide radius
and inner liner radius) and by material parameters (i.e., thedielectric constant of the liner). Changes or fluctuations in
any of these parameters induce changes (or fluctuations) inthe phase velocity of the EM wave and thus can degrade
the gain of the CFEL. To investigate the effect of such fluctuations on the gain, a method is developed to describe theeffect of a slowly varying inner liner radius on the EM wave
propagation and consequently on the gain of the CFEL. As
an example, results for a low gain, 800 mA Cerenkov FEL
operating at a frequency of 50 GHz and a maximum beam
voltage of 100 kV are presented.

INTRODUCTION
It is well known that errors in the magnetic field of an
undulator can result in (serious) degradation of the gainof an undulator based Free-Electron Laser (FEL) [1, 2].
These errors couple to the electron motion and manifest
themselves as fluctuations in the phase of the electronwith respect to the ponderomotive potential. As the gain
is based on longitudinal phase-bunching of the electrons,
these phase fluctuations will in general lower the gain of thedevice. The effect of the undulator errors is wavelength dependent and this leads to increasingly stringent toleranceson the undulator to avoid significant reduction in the gainat shorter wavelength [2].
In a Cerenkov FEL (CFEL), an electron beam interacts
with an electromagnetic (EM) field as they co-propagate
through an axial-symmetric, lined cylindrical waveguide.
The longitudinal wavenumber of the EM wave is determined by geometry (waveguide radius and inner liner radius) and by material parameters (dielectric constant of theliner). Coherent amplification of EM waves takes placewhen the phase velocity of the waves approximately equals
the electron beam velocity and the EM-wave has a longitudinal electric field component. Therefore, variations orfluctuations in the dielectric constant or in the geometry of
the liner result in changes of the longitudinal wavenumber
and consequently in the relative phase between the EMwave and the co-propagating electrons. As the EM wave isthe ponderomotive potential in a CFEL, it can be expectedthat these fluctuations will influence the gain of a CFEL as
well. However, here the errors in the liner are coupled to∗ i.delafuentevalentin@utwente.nl

Available online at http://www.JACoW.org

the radiation field whereas in the undulator based FEL theerrors of the undulator are coupled to the electron motion.
To our knowledge, we are the first to investigate liner
induced phase fluctuation in the ponderomotive potential
and their effect on the gain of a Cerenkov FEL. This information is especially important for the design of low gain
Cerenkov FEL devices (see e.g., [4]) as liners made fromcommercial tubes have variations in the inner radius ranging from a few hundred microns down to a few tens of microns (e.g., for precision tubes). Low gain devices are usually designed as an oscillator and have a low net-gain perpass such that any degradation of the gain seriously effects
the performance of the device.
The organization of the remainder of this work is as follows. We will consider an axial-symmetric lined waveguide for which the inner radius of the liner rd (z) varies
slowly with axial distance z and is otherwise constant. We
first discuss, in the limit of no electron beam, the influence of the liner fluctuations on the propagation of an EM
wave in such a waveguide. Then we will use the SVAP approximation to derive the fundamental FEL equations fromMaxwell’s equations. We continue with applying the set of
equations to a low gain CFEL that uses an 800 mA electron
beam with a maximum energy of 100 kV to generate morethan 1 kW in continuous wave mode, to study the effect ofliner irregularities on the performance of the device. By applying a linear change of rd with distance z the formulation
can also be used to model a tapered version of the CFEL.

WAVE PROPAGATION IN AN
IRREGULAR LINED WAVEGUIDE
Consider an axial-symmetric waveguide lined with a dielectric that has a varying inner radius rd (z) and is otherwise constant. Let rg be the radius of the waveguide, whichis also equal to the outer radius of the liner. As for the caseof constant rd , it is sufficient to solve Maxwell’s equations
for the longitudinal field components alone, since they
 =0completely specify the electromagnetic wave. As ∇
within the vacuum and dielectric region separately, and assuming a eiωt dependence for the fields, the wave equation
can be written as



2
2
Ez (r, z) 2⊥ + ∂ + ω∇=0(1)
Bz (r, z)∂z 2c2for each region. Here c = c0 in the vacuum region,c = √c0r in the liner region, and c0 is the speed of lightin vacuum. As observed above, the longitudinal wavenumber is a function of z due to the longitudinal variation of

FEL Theory

54

M.I. de la Fuente et al. / Proceedings of the 2004 FEL Conference, 53-56

rd (z). Assuming that the longitudinal wavenumber, k(z)will be slowly varying with distance z, we will follow the
WKB approximation [3] and make the ansatz that the fields
have a longitudinal variation according to
  z

g(r)



Ez (r, z) =exp ik(z )dz .
(2)
k(z)
0
In agreement with the WKB approximation, we neglect thesecond order derivative in k(z). Substituting (2) into thewave equation (1) gives


ω2
2
2

∇⊥ − k (z) + 2 g(r) = 0,(3)cwhich is Bessel’s equation. However, eq. 3 still has an implicit dependence on the distance z through the longitudinal wavenumber k(z) and this would in general violate theassumption that g(r) is a function of r alone. However, we
assume that the variations in k(z) are slow and small, i.e.,∆k(z) = k(z)−k0 << k(z), where k0 is the wavenumber
corresponding to a constant rd equal to the average liner radius rd0 . Thus, we find, in first approximation, kz ≈ k0 andthe transverse profile of the EM-wave remains unaffectedby the slowly varying inner radius. On the other hand, asmall value of ∆k(z) z may give an appreciable value in thephase factor exp 0 (k0 + ∆k(z  ))dz  . Thus ∆k(z) will
be retained in the phase factor. The phase α(z, t) of theelectromagnetic wave is given by zk(z  )dz  − ωt,(4)α(z, t) =0

where the slowly varying longitudinal wavenumber is given
by
 z
 z
∂k 
∂rd 
∂k
k(z) = k0 +dz≈
k+dz . (5)0
∂rd rd0 0 ∂z 
0 ∂z
It is assumed here that the inner radius of the liner is equal
to the mean radius at z = 0. To summarize, the transverse
mode pattern is not influenced by the slowly varying innerboundary of the liner which only influences the phase of
the propagating EM-wave through kz . Variations in rd (z)are considered slow if they are slow compared to a radiation wavelength, because the SVAP approximation, used
to derive the dynamical FEL equations, includes an average over one ponderomotive wavelength (i.e., a radiation
wavelength).
To find the fields, within these approximations, eq. (3)is solved and the usual boundary conditions are applied.
The solution consists of axial-symmetric, propagating EMwaves that can be divided into two classes. These are
the well known T E0n and T M0n modes with respectively
Ez = 0 and Bz = 0. Only modes with Ez = 0 are ofinterest, as these modes are responsible for the bunchingof the electrons in a Cerenkov FEL. Limiting ourselves tothe interesting case of a phase velocity less then c0 , the expressions for the fields, used to derive the dynamical CFELMOPOS39equations, are as follows. The transverse wavenumbers κnand κn for the vacuum respectively liner region are given
by
κn =

2 −
k0n

ω2
c20

κn =

r

ω2
2 ,
− k0n
c20

(6)

whereas the components for the T M0n are given by 0n (r, t) = ω iI1 (κn r)êr − κn I0 (κn r)êz A0n (z, t)
E
k0n
(7)
and


2
 0n (r, t) = ik0n 1 − κn I1 (κn r)A0n (z, t)êθ (8)B2
k0n
in the vacuum region and by
 0n (r, t) =Eκn= ω i  [an J1 (κn r) + bn Y1 (κn r)] A0n (z, t)êr −
κn

κn
−
[an J0 (κn r) + bn Y0 (κn r)] A0n (z, t)êz
(9)
k0n
and
 0n (r, t) =Bκ2 κn= ik0n 1 + 2n
[an J1 (κn r)+
k0n κn+bn Y1 (κn r)] A0n (z, t)êθ(10)in the liner region. In these equations,
A0n (z, t) = a0n 1kn (z)

eıαn (z,t) .

(11)

DYNAMICAL EQUATIONS FOR CFELIn this section a non-linear formulation is given for a
Cerenkov FEL with an irregular liner. As usual, we startwith expressing the total field as a sum over the T M0n
waves (eqs. (7) to (10)) found for the irregular, axially symmetric, lined waveguide with no electron beam present [5].
The amplitude of each mode is z−dependent such that thewave can be amplified by the electron beam. This total field
is substituted into Maxwell’s equations with the electron
beam as the driving term for the field. Using the orthogonality property of the modes, a single mode amplitude isfiltered out from Maxwell’s equation by multiplying it withthe transverse profile of that mode and integrate Maxwell’sequation over the cross-section of the waveguide. Then theslowly varying amplitude and phase (SVAP) approximation is applied to obtain the final dynamical equation that
describes the amplification of the mode amplitude. The setof equations is closed by complementing it with Lorentz’s
equation that describes the motion of the electrons within
the beam under influence of the electromagnetic fields andM.I. de la Fuente et al. / Proceedings of the 2004 FEL Conference, 53-56

Figure 1: Calculated power as a function of the standard
deviation of the liner irregularities. See the text for moredetails. The lines are for guidance only.
the axial magnetic guide field present. As the derivation isstraightforward and very similar to [5] we only present the
final result for the mode amplitude,κ2 ∂a
2 kn (z)(1 − 2n ) 0n =k0n ∂z rd0
ωp2 βz0βr iαn= −4 2e +
drr iI1 (κn r)
2
c0 An rd0
|β
z|
0
κn
+
I0 (κn r)e−iαn (12)k0nwhere An is a normalization constant, ωp is the plasma freequency and a0n (z) = mc
a0n (z) with a0n (z) the complex
z-dependent amplitude of (11). Here, . . . is an averageover all electrons within one ponderomotive wavelength,
i.e., one radiation wavelength. Note that with the electron
beam present, the phase of the T M0n mode is not solely
given by α0n (z, t) as the dynamical CFEL equation (eq.
(12)) also drives the phase of the complex amplitude a0n .
Therefore the total relative phase of an electron with respect to the ponderomotive potential is given by the sum ofthese two phases.

LINER IRREGULARITIESThe above given formulation is used to investigate theeffect of irregularities in the inner radius of an otherwise
constant liner used in a low gain CFEL operating at a nominal frequency of 50 GHz [4]. The CFEL uses a 800 mA
electron beam with a radius rb of 1mm and a maximum
beam voltage Vb of 100 kV to generate an output power inexcess of 1 kW. Using a liner with the following parameters, r =5.8, rd0 =1.5 mm, length L=0.7 m and thicknessd =1.3 mm, the CFEL requires a beam voltage Vb of 75.1
kV to obtain maximum output power at 50 GHz. The liner55

fluctuations are generated using a uniform random distribution between −δrd and δrd that is filtered with a low-passspatial filter. The filter has a cut-off distance of 0.1 m andremoves fast fluctuations. To estimate the influence on the
maximum power, 20 different realizations of the fluctuations are generated for each maximum amplitude δrd . For
each realization the maximum power Pmax or, if not saturated, the power Pend at the end of the liner, and the standard deviation σr of the fluctuations are calculated. The average of these values are plotted in fig. 1 for a liner lengthof 70 cm. The error bar in Pmax represent the average standard deviation of Pmax (Pend has a similar standard deviation). With no fluctuations, the laser has a saturated powerof Pmax = 1.9 kW at a distance zsat = 67 ± 1 cm. Fromthe simulations it follows that both Pmax and zsat decrease
with increasing σr and at the same time the spread in bothincreases, i.e., zsat = 55 ± 8 cm at σr = 40 µm. It follows
from fig. 1 that a rms fluctuation of approx. 40 µm is already sufficient to lower the maximum power, on average,
by a factor of 2. On the other hand, fig. 1 also shows thata particular realization of the liner fluctuations can also enhance the saturated power and this will be investigated in
the next section.

TAPERED LINERIn the previous section we considered a dielectric linerwith an inner radius that fluctuates slowly but randomly
with distance z and found that even small fluctuations canseriously degrade the gain of a CFEL. If, on the other hand,
we were to apply a linear taper starting at some distance,
we expect to enhance the gain and obtain a higher output
power. The latter is the result of keeping the bunch awayfrom reaching the bottom of the ponderomotive potential
well by changing the phase velocity of the EM wave. As
the average electron velocity decreases, the phase velocityof the EM wave must be reduced as well to avoid saturation. Because dk0n /drd0 is negative, one has to reduce theinner liner radius to avoid trapping. This will reduce thegap between the electron beam and liner and will thus have
limited applicability. However, it is interesting to find out
if a negative taper on rd (z) improves the performance andby how much.
We consider the same CFEL as in the previous section.
The growth of the power as a function of z is shown in fig.
2 where the length of the liner has been extended to L = 3
m to allow for some distance for the taper. As the CFEL
has initially a gap of 0.5 mm between the electron beamand the liner, the length of the taper is limited and the maximum liner length depends on the slope of the taper. Fig. 2
shows the power as a function of z for different, negative,
slopes of a taper that starts at z = 60 cm. If the slope is
not large enough, the laser will not reach saturation within
a liner length of 3 m. The output of the laser increases withincreasing slope of the taper up to the point where the liner
diameter is such that the gap with the electron beam is reduced to zero and electrons start to hit the liner before the

FEL Theory

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M.I. de la Fuente et al. / Proceedings of the 2004 FEL Conference, 53-56

tween electron beam and liner becomes zero. At this point
the laser is not yet saturated, so other methods of tapering
may still further improve the performance.

ACKNOWLEDGEMENT
This research is supported by the EU, contract G5RDCT-2001-00546.

REFERENCES[1] A. Friedman, S. Krinsky, L.H. Yu, FEL gain reduction due towiggler errors. IEEE J. of Quantum Elec, 30, 1295 (1994)[2] R. Tatchyn et.al. Research and development toward a 45 - 1.5
Å linac coherent light source (LCLS) at SLAC. Nucl. Instr.
and Meth. in Phys. Res. A 375, 274 (1996)

Figure 2: Calculated power as a function of distance z for
different slopes of the taper. The taper starts at z=0.6 m.
end is reached. At this point the output power is close to 10
kW (drd /dz = -0.229 mm/m). A still larger slope results ina shorter distance to reach the point of zero gap and a gradual decrease of the maximum power; for a slope of -0.417
mm/m the maximum power is already reduced to 8.7 kW
at z = 1.95 m. For a slope of -0.188 mm/m we extended theliner length and found a maximum power of 10.4 kW at a
distance of 3.65 m where, again, the gap was reduced tozero. It should be pointed out that although the decrease ingap as a result of the negative taper increases the couplingstrength between electrons and EM wave, it is the change
in phase velocity that prevents the laser from reaching saturation. To conclude, for this particular CFEL, it is foundthat a negative taper on rd0 increases the maximum attainable power with a factor of 5 before the gap is reduced tozero. Note that at that point the laser was not saturated.
Therefore, further improvements are to be expected byusing different methods of tapering that avoid reducing thegap. These methods are changing the dielectric constant or
the outer waveguide radius. This is currently under study.

CONCLUSIONS
We have demonstrated that, in first approximation, thetransverse mode profile of a CFEL is not influenced by aslowly varying inner radius of the liner. However the liner
does effect the phase velocity of the propagating wave. We
derived the dynamical CFEL equation and applied it to investigate the influence of liner fluctuations and a taper ofthe inner liner radius on the performance of the CFEL. It
was found that an rms fluctuation that is approximately 3% of rd0 is already sufficient to decrease the maximum
power by a factor of 2, at least for the configuration investigated. Note that this rms fluctuation is comparable to the
manufacturing accuracy of commercially available (quartz)
tubes. By applying a negative taper to rd0 the maximum
power can be increased by a factor of 5 before the gap be-

MOPOS39[3] W. Elmore and M. Heald, Physics of Waves, New York,
Dover (1985)[4] I. de la Fuente, P.J.M. van der Slot, K-J. Boller, A mm-wave,
table top Cerenkov Free-Electron Laser. This proceedings.
[5] H.P. Freund, A.K. Ganguly, Nonlinear Analysis of the
Cerenkov Maser, Physics of Fluids B 2, 2506, (1990)

57

XJ. Shu et al. / Proceedings of the 2004 FEL Conference, 57-59

SIMULATION INVESTIGATION OF THE DETUNING CURVE
Xiaojian Shu, Yuhuan Dou, Yuanzhang Wang, Institute of Applied Physics and Computational
Mathematics, P. O. Box 8009, Beijing 100088, P. R. China
Abstract

INTRODUCTION
An obstacle to the development of a short pulse freeelectron laser (FEL) oscillator is the slippage that occurs
between the electron beam and radiation duo to theirdifferent velocities, which results in lack of overlapping
between the electron and the optical pulses and areduction in gain, and so is called the laser lethargy effect[1]. This effect can be overcome by slightly shortening
the length of the optical cavity from synchronism so tokeep the overlapping between the electron and the opticalpulses [1, 2]. The FEL power as a function of cavity
length, which is named the detuning curve, has beenstudied abundantly both theoretically and experimentally.
The detuning curves are usually calculated by onedimensional (1D) simulations due to the simplicity andlittle consumption of the computer time, which in generalare good agreement with super-mode theory [3] andexperiments. To our knowledge there is almost no
detuning curve calculated from three-dimensional (3D)
simulations. However, recently it is found that the lengthof the detuning curve seems to be shorter than possible
assuming a one-dimensional super-mode theory when thegain is high in the experiments of an infrared FEL
oscillator [4, 5]. On the other hand, the lethargy effects ismore severe in a far-infrared FEL such as the CAEP FIR
FEL [6] because the slippage length which is proportional
to the optical wavelength is large compared to the shortelectron pulse produced by an RF linac. It is of interestingand necessary to obtain more exact detuning curve from
3D simulations to study it more carefully.
In this paper, the detuning curves of the CAEP FIR
FEL [6] and the Jefferson Lab IR Demo FEL [4, 5] arecalculated with the help of our 3D code [6-8], which arecompared with those from 1D simulations and supermode theory, and the experiments. The influence of the
optical guiding and other three-dimensional effects on the
detuning curve is studied. It is found that the length of thedetuning curve from 3D simulations is shorter than thatfrom 1D simulations and super-mode theory.

CAEP FIR FELFirstly, as usual, the detuning curves are calculated byusing our one-dimensional time-dependent code GOFELP[9, 10]. In simulations, the distribution functions of theelectrons and optical pulses are assumed as Gaussian. The
transverse overlap factor between Gaussian mode of TE00
of the optical cavity and the electron beam with aparabolic transverse density profile is considered in thecode [11].
In Fig. 1 we show the output power as a function ofcavity length with the parameters of CAEP FIR FEL [6]as listed in Table 1. In simulations, the current is adjusted
to obtain the same gain as 3D simulations and the loss ofthe cavity is given the result of 3D simulations. The rangeof the detuning curve is from about –70 µm to –360 µm
and the length is about 290 µm.
Table 1: CAEP FIR FEL Parameters
Electron beam
Energy (MeV)
Energy spread (%)
Peak current (A)

6.5
1
8
15

Micro bunch (ps FWHM)
Wiggler
Period (cm)Peak field strength (kG)

Number of periods

3350

Optical
Wavelength (µm)
Cavity length (m)Mirror curvature (m)

110.7
2.536
1.768

1.2
1D
1.0

Power (arb.)

The detuning curves of free-electron laser oscillators
are calculated with the help of our three-dimensional code,
which are compared with those from one-dimensional
simulations and super-mode theory, and the experiments.
The influence of the optical guiding and other threedimensional effects on the detuning curve is studied. It isfound that the length of the detuning curve fromthree-dimensional simulations is shorter than that fromone-dimensional simulations and super-mode theory.

0.8
0.6
0.4
0.2
0.0
-400

-300

-200

-100

0

Cavity length detuning (µm)
Figure 1: Detuning curve of CAEP FIR FEL from 1D
simulations.

Available online at http://www.JACoW.org

FEL Theory

58

XJ. Shu et al. / Proceedings of the 2004 FEL Conference, 57-59

1.2

1D, ∆γ/γ=0

1.0Power (arb.)

Then the detuning curve is calculated by using our 3D
code OSIFEL [6-8]. As shown in Fig. 2, the curve has
almost same shape as Fig. 1 but moves toward zero point,
i.e. synchronism point, which cannot be observed andfixed in experiments. The range of the detuning curve isfrom about –25 µm to –330 µm and the length is about
300 µm, which approach the result of 1D of 290 µm. The
reason is that the gain and loss are almost same in 1D and3D simulations and the net gain is small [6].

0.8
0.6
0.4
0.2

1.2
3D

0.0
-35

0.6

0.2

-300

-200

-100

0

Cavity length detuning (µm)
Figure 2: Detuning curve of CAEP FIR FEL from 3D
simulations.

JLAB IR DEMO FEL
Fig. 3 shows the detuning curve calculated by using our
1D code with Jlab IR Demo FEL parameters [4, 5] listed
in Table 2. In the simulations, the energy spread is zero inorder to cut down on the computer time. The range of thedetuning curve is from about –0.2 µm to –31 µm and thelength is about 30 µm. Note that the curve is very sharp,
which is totally different to Fig. 1 and results fromexperiments [4, 5], due to high small signal gain of more
about 150% in the 1D simulations without energy spread.
Table 2: Jlab Demo FEL Parameters Used in Simulations
Electron beam
47.8
Energy (MeV)
0.5
Energy spread (% FWHM)
8.7
Emittance (mm.mrad rms)
58.8
Peak current (A)1
Micro bunch (ps FWHM)
Wiggler
2.7
Period (cm)5.61
Peak field strength (kG)
40.5
Number of periods
Optical
3.1
Wavelength (µm)
8.0105
Cavity length (m)4.05
Mirror curvature (m)9.63575
Loss (%)

MOPOS40

-25

-20

-15

-10

-5

0

Figure 3: Detuning curve of Jlab IR Demo FEL from 1D
simulations without energy spread.

0.4

0.0
-400

-30

Cavity length detuning (µm)

0.8Fig. 4 shows the detuning curve calculated by using our
3D code. The shape of curve becomes gently, not so sharp,
since the small signal gain is about 100% in the 3D
simulations, which approaches the gain in theexperiments. The range of the detuning curve is fromabout 0 µm to –20 µm and the length is about 20 µm,
which is shorter than 30 µm obtained from the 1D
simulations without energy spread, but little longer than
16µm of that from the experiments [5] and in good
agreement with experiments. The 3D simulations give
better results than the 1D calculations and super-mode
theory.
1.2
3D
1.0

Power (arb.)

Power (arb.)

1.0

0.8
0.6
0.4
0.2
0.0
-25

-20

-15

-10

-5

0

Cavity length detuning (µm)
Figure 4: Detuning curve of Jlab IR Demo FEL from 3D
simulations.
Then the energy spread of the electron beam isconsidered in 1D simulations. Fig. 5 shows the detuning
curve from the 1D simulation with the energy spread of
0.5%. Fig. 4 and 5 are remarkably similar to each other.
The range of the detuning curve is from about 0 µm to–22 µm and the length is about 22 µm, which is little

59

XJ. Shu et al. / Proceedings of the 2004 FEL Conference, 57-59

longer than 20 µm that obtained from the 3D simulations
and in better agreement with the experiments than the 1D
simulations without the energy spread. The small signal
gain is about 80%, which is smaller than that from the 3D
simulations. The optical guiding effects result in an
increase in the gain. Note, however, that the length ofdetuning curve from the 3D simulations and experiments
seems to be shorter than possible assuming a higher gain.
1.2

1D, ∆γ/γ=0.5%

Power (arb.)

1.0
0.8
0.6

ACKNOWLEDGMENTS

0.4

This work is supported by High Power Radiation
Laboratory under National 863 RD Program andNational Laser Technology Committee, China.

0.2
0.0
-25

simulations with TE00 mode and energy spread cangive good results due to the facts that the emittance ofthe electron beam is very small and the optical cavity isa stabile.
The optical guiding effects cause an increase in thegain in the 3D simulations. In general the increase in
the gain results in an increase in the length of thedetuning curve. It is found, however, that the length ofdetuning curve from the 3D simulations andexperiments seems to be shorter than possible with ahigher gain. Does it hint that the optical guiding effects
can shorten a detuning curve even though the gain is
increased in the case of a high gain FEL oscillator? It is
the subject of a future work.

-20

-15

-10

-5

0

Cavity length detuning (µm)
Figure 5: Detuning curve of Jlab IR Demo FEL from 1D
simulations with energy spread.

CONCLUSION AND DISCUSSION
In this paper, the detuning curves of the CAEP FIR
FEL and the Jefferson Lab IR Demo FEL arecalculated with the help of our 3D code, which arecompared with those from 1D simulations and theexperiments. The influence of the optical guiding andother three-dimensional effects on the detuning curveis studied. It is found that the length of the detuning
curve from 3D simulations is shorter than that from 1D
simulations when the gain is high and in better
agreement with experiments. The 3D non steady-state
simulations give better results than the 1D calculations
and super-mode theory. The 1D non steady-state

REFERENCES[1] H. Al-Abawi et al., Optics Comm. 30 (1979) 235.
[2] W.B. Colson and A. Renieri, J. Phys. Colloq. 44(1983) 11.
[3] G. Dattoli et al., Nucl. Instr. and Meth. A 285 (1989)
108.
[4] S. Benson et al., Nucl. Instr. and Meth. A 429 (1999)
27.
[5] G.R. Neil et al., Nucl. Instr. and Meth. A 445 (2000)
192.
[6] Xiaojian Shu and Yuanzhang Wang, Nucl. Instr. andMeth. A 483 (2002) 205.
[7] Wang Taichun and Wang Yuanzhang, High Power
Laser and Particle Beams, 7 (1995) 25, (in Chinese).
[8] Xiaojian Shu et al., Optical Engineering, 39 (2000)
1543.
[9] Xiaojian Shu, Optics Comm. 105 (1994) 188.
[10]Xiaojian Shu et al., J. Appl. Phys. 77 (1995) 426.
[11]D.C. Quimby et al., IEEE J. Quantum Electron.
QE-21 (1985) 979.

FEL Theory

60

J. Jia / Proceedings of the 2004 FEL Conference, 60-63

HARMONIC AMPLIFIER FREE ELECTRON LASER
Jia Qika
National Synchrotron Radiation Laboratory, University of Science and Technology of China
Hefei, Anhui, 230029, China
Abstract
The harmonic optical klystron (HOK) in which thesecond undulator is resonant on the higher harmonic of
the first undulator is analysed as a harmonic amplifier.
The optical field evolution equation of the HOK isderived analytically for both CHG mode (Coherent
Harmonic Generation, the quadratic gain regime) and
HGHG mode (High Gain Harmonic Generation, theexponential gain regime), the effects of energy spread,energy modulation and dispersion in the whole process
are considered.

INTRODUCTION
One way of free electron laser (FEL) developing toward
short wavelength is using harmonic. In the coherent
harmonic generation (CHG) [1,2] scheme an optical
klystron(OK) has been used, an external laser pulse isfocused into the first undulator, the wavelength of thelaser is resonated with the fundamental radiation of the
optical klystron, with optimized system parameters the
harmonic radiation in the second undulator is coherently
enhanced. Analyze shown that if make second undulatorof OK resonant on the higher harmonic, namely the
wavelength of fundamental radiation of the second
undulator matches with nth harmonic optical field in thefirst undulator, it will be more beneficial to the harmonic
generation [3]. To distinguish it from the normal optical
klystron, we temporarily call such optical klystron the"harmonic
opticalklystron"(HOK).
A
similarconfiguration was proposed and used for high gain
harmonic generation (HGHG) [4].the scheme evolved
from many earlier ideals (e.g. ref. [5]). In the HGHG
mode the optical power grows exponentially while in the
CHG mode the optical power grows quadratically, bothmodes are harmonic amplifier. Cascaded optical klystron[6,7] and cascaded harmonic optical klystron [8-9] for Xray FEL are also proposed and discussed.
So far the theory of optical klystron amplifier has all
approximated it as the scheme with separate functions:the energy modulation only be considered in the first
undulator, the dispersive effect only occur in dispersive
section, and the gain section generate radiation. In Ref [4]the HGHG problem is solved for the small energy spread
limit, in the second undulator the electron beam isassumed be mono-energetic and dispersive effect isignored. The amplifying process of optical klystron (andharmonic optical klystron) have been analysed mostly by
calculating the bunching factor at the entrance of thesecond undulator (the techniques developed for
microwave klystron). But such approximation treatments
are not always appropriate. In this paper I derive the

MOPOS41

optical field evolution equation complete analytically for
HOK, the energy spread effect and the dispersive effect inthe whole process will be considered in the derivation.

OPTICAL FIELD EVOLUTIONEQUATIONS
We use the one-dimensional FEL theory and start fromthe paraxial optical field equation and the electron phaseequation:da~se − iφ= λs re auδ p ne
dz
γ

d φ
=−
dz 2
2

2ku k s auδ pγ

2a~ s = a s e i ϕ s(1)

Re(a~s e iφ )
,
2

(2)
2

, as=eEs/(mc ks) and au=eBu/(mc ku)
where
are dimensionless vector potential of the rms radiation
field Es and undulator field Bu, respectively; ks=2π/λs,
ku=2π/λu are the corresponding wave number; ϕs is thephase of radiation field; φ=(ks+ku)z-ωst is thepondermotive phase of electron, re is the classical electron
radius; ne and γ is the density and energy of electrons; theangular bracket represents the average over the electron’s
initial phases and initial phase velocities. δp is thepolarization modify factor: for circularly polarized helicalundulator δp=1; for linearly polarized planar undulator
with even nth harmonic radiation δp =0, and with odd nth
harmonic δp=[J,J]n,n −1[ J , J ] n = ( − 1) 2 [ J n − 1 (
2

na u2
na u2
) − J n +1 ()]
2
2 (1 + a u )2 (1 + a u2 )2

J is integer order Bessel function.
The electron phase in the second undulator is

φ 2 = φ 20 + φ 20 ' z2 + ∆φ 2 .

(3)
The first term of the right hand side of eq.(3) is theelectron phase at the entrance of the second undulator
φ 20 = nφ1 ( z 20 ) + (k u 2 − nk u1 ) z 20 .
(4)
The second part in the right hand side of eq.(4) is aconstant for all electrons. φ1(z20) is the electron phasereferenced to the first undulator valued at the entrance ofthe second undulator and given by
φ1 ( z 20 ) = φ10 + φ10 ' l1 + ∆φ1 + ∆φ d ,(5)where φ10 and φ10’ is the initial phase and phase velocity(detuning parameter), ∆φ1 is the phase change due tointeraction with optical field of the seed laser in the first
undulator and given from eq.(2)Available online at http://www.JACoW.org

61

J. Jia / Proceedings of the 2004 FEL Conference, 60-63

l1∆φ1 = −2k s1 k u1 a u1δ p1 Re ∫ (l1 − z1 )a~s1e iφ10γ2dz1 . (6)

ks1 and as1 are the wave number and the dimensionlessvector potential of the seed laser field (rms) , respectively.
∆φd is phase change in the dispersive sectiond∆φd = ∫ ks (1−
0

k d 1
k
)dz = − s ∫ ( 2 + β⊥2 )dz = − s2 Ld
βII
20 γ
2γ
(7)
1

d
z
e
Ld = d + ( 2 ) 2 ∫ ( ∫ Bd dz ' ) 2 dz
mc
00

is equivalent drift length, d and Bd are the lengths andmagnetic field of the dispersive section, respectively.
Using resonant relation of FEL and the phase velocity
expression φ ' ≅ k u (1 − γ r2 / γ 2 ) , eq.(7) can be written as∆φ d = −Nd =k u Ld γ= N d λu φ1 ' (l1 ) − 2πN d(1 + au2 )γ 2
2
r

(8)

d
z
1
e
[ d + ( 2 ) 2 ∫ ( ∫ Bd dz ' ) 2 dz ] , (9)2
λu (1 + au )mc
00where γr is the resonant energy, Nd is the dispersive
section parameter, it is the scale parameter of optical
klystron itself and independent on the electron beam. The
physical meaning of Nd is that it is number of wavelengthsof the light passing over the resonant electron in thedispersive section. For electrons with different energy Nd
also can be expressed as

Nd =γ δ∆φ d
,
4π δγ

(10)

obviously Nd describe the dispersive strength
The second term of eq.(3) φ20’ is electron phase velocity
at the entrance of the second undulatorkγ r2) = u 2 φ1 ' (l1 )
2
k u1
γ 20
φ1 ' (l1 ) = φ10 '+ ∆φ1 ' ,φ 20 ' = k u 2 (1 −l1

∆φ1 ' = −2k s1ku 2 au1δ p1 Re ∫a~s1eiφ1

γ2

0

(11)

dz1 .

(12)

The third term of eq.(3) is phase variation due to theinteraction with the radiation field in the second undulatorz2∆φ 2 = −2k s 2 k u 2 au 2δ p 2 Re ∫ ( z 2 − z 2 ' )a~s 2 e iφ2

0

γ

2

dz 2 ' (13)Therefore the electron phase in the second undulator (wedrop the constant term) is

φ 2 = nφ10 + φ10 ' [n(l1 + N d λu1 ) + z 2 λu1 / λu 2 ] −l1− 2k u1 k s1 au1δ p1 Re ∫ [n(l1 − z1 + N d λu1 ) + z 20

λu1 a~s1e iφdz1]
λu 2 γ 2
1

+ ∆φ2
(14)

The harmonic generation problem of HOK including
the electron beam quality effects and dispersive effects forwhole process from beginning to saturation can be
numerically solved by substituting above expression into
eq.(1).

SUPERRADIANCE REGIME(CHG MODE)
Owing to the short length of first section undulator(modulator) the optical field in the modulator isapproximately constant. The third term of the right handside of eq.(14) is phase variation due to the interaction
with the seeding optical field. The integral function in theterm varied approximately linearly with z1, so taking its
median in the integral is a reasonable approximationl
2k u1 k s1 a u1δ p1 a s1
λ u1 z 2−∫0 [l1 − z1 + N d λu1 + nλu 2 ] cos(φ10 + φ10 ' z1 )dz1
γ2l
≈ n∆ξ cos(φ10 + φ10 ' 1 )
2
(15)
where
1

∆γ
N1
z
+ Nd + 2 ) m
nλu 2 γ2au1δ p1a s1∆γ m= 4πN1γ(1 + au21 ) .

∆ξ = 4π (

(16)

(17)

∆γm /γ is the maximum energy modulation induced in thefirst section undulator.
In coherent harmonic generation (CHG) mode, theelectron beam current is low and the length of the gain
section of HOK (or OK) is short, while the Nd may bevery large. It have L2< 3Lg (Lg: the power gain length)
and Nd+N1/2>>N2/n ≥ z2/nλu2. Therefore the z2 in ∆ξ canbe approximated with its median:∆ξ = 4π (N1N ∆γ+ Nd + 2 ) m ,22n γ

and the phase variation due to interaction with theradiation field (the last term of the right hand side ofeq.(14)) can be neglected. Thus the optical field in CHG
mode for HOK isre λ s 2 au 2δ p 2 nea~s 2 = −J n (n∆ξ )

γ

× i e
n

−iφ10 'λu 1 [ n (N1N+ N d ) + 2 )]22

l 2 sin c(18)

φ02 ' l 2
2

For a Gaussian initial energy distribution of theelectron beam the corresponding radiation intensity isre λ s 2 au 2δ p 2 ne l 2 2 2
a~s22 = () J n (n∆ξ ) f γ2

γ

(19)

N + N2 / n σ γ 21) ]}f γ = exp{− [4πn( N d + 1
22γ

FEL Theory

62

J. Jia / Proceedings of the 2004 FEL Conference, 60-63

where δp2=[J,J]1. For given energy spread and energy
modulation (i.e. given seed laser) we can give the optimal
dispersive parameter

Nd

opt.

=

N + N2 / n
1
n
n +1
min[
,
]− 1
4πn
σ γ / γ ∆γ m / γ
2

The third term contributes small and can be neglected formany cases.
For mono-energetic electron beam and weakmodulation we can obtain [10]If we do following substitution in eq.(19)au2→au, δp2→δp=[J,J]n, N2/n→N2,
then we have the nth harmonic radiation intensity for OK
configuration. The advantage of HOK over OK for CHG
is obvious: the energy spread effect is reduced, theradiation is also enhanced by proper selecting undulator
parameters to make (au2[J,J]1)2 >>(au[J,J]n) 2 [6].
Moreover besides the odd harmonic the HOK also canoperated at the even harmonic of the seed laser.

EXPONENTIAL GAIN REGIME (HGHG
MODE)
For the HGHG mode, the electron beam current isrelatively high, the length of the second undulator must be
sufficiently long to reach the exponential gain regime:
L2>3Lg. Therefore the condition Nd+N1/2>>N2/n may not
be satisfied. Substituting eq.(14) into eq.(1) andlinearizing it, after averaging over a uniform initial phase
distribution of electrons, the optical field evolution
equation in linear region for HOK is given by

where ∆ξ * = ∆ξ ( z 2 *) , Z *: 0<Z *<l2− ( 2k u 2 ρ 2 ) 3∂

z2∫ J 0 ( 2k u 2 ( z 2 − z 2 ' )∆γ m∂φ02 ' 0+ (2k u 2 ρ 2 ) ie

l2

0

0

DISCUSSION
From eq.(18) and eq.(23) the division of the CHG modeand HGHG mode for mono-energetic electron beam canbe estimated: z2≈3.73Lg, therefore the length of the second
undulator for HGHG mode should be at least four time
longer than the power gain length: N2>4Ng. Figure 1 is anumerical result of equation (21) compared with the result
given by numerically solving the equation (1) and eq.(14).
It shows that the linear approximation is valid from start
up to near saturation (linear region). It also shows that thequadratic gain regime (the CHG mode) is for z2<4Lg.
1E-6

γ

(a)
(b)

1E-8
HGHG
2

as

)

1E-9
CHG

1E-10
1E-11

(21)

1E-12

z
l
−i 2 nφ10 '( 1 + N d λu 1 ) 2
2

0∫ (z − z ')2

where ρ is Pierce parameter, φ02’ is the electron phasevelocities (referenced to the second undulator) at theentrance of the first undulator (note it is different withφ20’):

ku 2
γ2
φ10 ' = k u 2 (1 − r2 )
k u1
γ0 .

2

4

6

8

10

z/Lg

2

× J 2 n (n(∆ξ + ∆ξ ' ))a~s 2 e −iφ02 '( z2 + z2 ') dz 2 '(22)
In the right hand side of equation (21), the first term
correspond to the coherent enhancement process, we cansee that the dispersion effect (∆ξ) and energy-spread
effect (the exponential factor) include the contribution not
only from dispersive section, the modulation section, butalso from gain section. The formula (18) can be obtained
from this term. The second term corresponds to the usual
gain process, it gives usual gain results when the seedlaser is off, the Bessel function in it indicates the effect of
the additional energy spread due to energy modulation.

MOPOS412− iφ ' z− iφ ' z∫ J n (n∆ξ ( z 2 ))e 02 2 dz 2 = J n (n∆ξ ( z 2 *))∫ e 02 2 dz 2

1E-7

0

φ 02 ' =(23)l× a s 2 e −iφ02 '( z2 − z2 ') dz 2 '
3

2

l2

−i[ nφ10 '( 1 + N d λu 1 ) +φ02 ' z 2 ]da~s 2 8k u22γ 2 ρ 2
2=ei n J n (n∆ξ )k s 2 a u 2δ p 2
dz 2
3

4k u 2γ 2 ρ 2
J n (n∆ξ *)e 3ku 2 ρ 2 z2
3k s 2 au 2δ p 2
2

as2 (z2 ) ≈(20)

Figure 1, (a) the linear approximation (equation (21))(b) the result given by numerically solving theequation (1) and (14)

1E-12

as

2

1E-13

b
a

1E-14

0.0

0.2

0.4

0.6

0.8

z(m)

Figure 2, CHG (a) a result of analysis formula (eq. (19))(b) the result of the linear theory (eq.((21))
Figure2 is a result of analytical formula (equation(19)) compared with the result of the linear theory (theJ. Jia / Proceedings of the 2004 FEL Conference, 60-63

equation (21) for the CHG. It can be seen that theagreement between them is very well.
From eq.(21) we noted that for the linear region the
additional energy spread due to energy modulation only
affects usual gain term but not the coherent enhancement
term. Therefore, for CHG scheme, in which the coherent
enhancement term is dominant, one should chose seedinglaser filed as1 and despersive field Nd to make n∆ξ ≅ n+1
so that Jn=Jn max, and at the same time a large as1(strong
modulation) and a small Nd (weak dispersion, to reduce
the effect of energy spread) are preferred. For HGHG
scheme, the additional energy spread effect due to energy
modulation must be considered, this gives the up limit forseeding laser filed as1:
2
∆γm /γ < ρ, a s1 < ( 2 + K 1 ) ρ
4πN 1 K 1δ p1(24)

For high harmonic, the optimal ∆ξ=(n+1)/n notchanged much so does the energy modulation ∆γm/γ andthe seeding optical filed (as1). But as harmonic number
increase, the energy spread effect factor and the Bessel
function term Jn decrease, both them make the gain
degradation. The energy spread factor is more importantby comparison. To reduce the energy spread effect we canreduce the dispersive field strength (Nd), but that Jn(∆ξ)
may also be decreased. The best way is reducing theenergy spread itself, this can be achieved by adopting the
local (slice) energy spread of electron bunch, namely
adopting ultra-short pulse of seeding laser.
In summary we have derived optical field evolution
equations complete analytically for harmonic optical
klystron. By numerically solving the equation (1) and (14)the harmonic generation problem including the effects ofenergy spread, energy modulation and the dispersion inwhole process can be easily described. Both CHG modeand HGHG mode are analysed as harmonic amplifier. The
linear theory is given and analysed for HGHG mode. For
CHG mode the analytical formula is given and theadvantages of HOK over OK were demonstrated. The

63

optimal parameters for harmonic amplifier are discussed
briefly.

REFERENCES[1] R.Coisson and F. De martini, “Free-electron coherent
relativistic scatter for UV generation”, Physics ofQuantum Electronics(Addison-Welsley,1982)
Vol.9,p939[2] J.M.Ortega, et al., “Ultraviolet Coherent Generationfrom an Optical Klystron”, IEEE QE-21, pp909919,1985[3] Q.K. Jia, “Coherent harmonic generation using thenon-symmetric optical klystron”, High Power Laserand Particle Beams,Vol.6, No.3, pp450-454,1994.(InChinese); “Optimization of optical klystron for
coherent harmonic generation FEL”, Nucl. Instr.
Meth. A407, pp246-250, 1998
[4] L.H.Yu, "Generation of intense uv radiation bysubharmonically seeded single-pass free-electron
laser", Phys.Rev.A44,pp5178-5193,1991[5] R.Bonofacio, et.al, “Generation of XUV light byresonant frequency tripling in a two-wiggler FEL
amplifier”, .Nucl.Instr. & Meth. A296, pp787790,1990[6] V.N.Litvinenko, “High gain distributed optical
klystron”, Nucl.Instr. & Meth. A304, pp463-464,1991[7] G.R.Neil,H.P.Freund, "Dispersively enhanced
bunching in high-gain free-electron lasers",
Nucl.Instr. & Meth. A475,pp381-384,2001[8] J.Wu, L.H.Yu, “Coherent hard X-ray production bycascading stages of High Gain Harmonic Generation",
Nucl.Instr. & Meth. A475,pp104-111,2001[9] E.L.Saldin et.al., “Study of a noise degradation of
amplification process in a multistage HGHG FEL”,
Optics Comm.202, pp169-187,2002[10] Jia Qika,,“One-dimensional theory of high gain
harmonic generation free electron laser” Nucl.Instr. &Meth. A519,pp489-492,2004

FEL Theory

64

LiYuhui. Li et al. / Proceedings of the 2004 FEL Conference, 64-67

PARAMETER ANALYSIS FOR A HIGH-GAIN HARMONIC GENERATIONFEL BY NUMERICAL CALCULATION BASED ON 1D THEORY
Li Yuhui,
Jia Qika,
Zhang Shancai
National Synchrotron Radiation Laboratory University of Science and Technology of China
Hefei, Anhui, 230029, China
Abstract
High-gain harmonic generation (HGHG) free-electron
laser (FEL) is an important candidate for fourthgeneration light source. Lots of research works about it
have been done all along. Recently a further 1D theory
about HGHG FEL has been developed. It considers theeffects of different parameters for the whole process. An
initial program based on this theory has been made. In
this paper, a brief compare of the results from this 1D
program and from TDA (3D code) is discussed and it also
analyses the parameters for Shanghai deep ultra violate
free electron laser source (SDUV-FEL), including
electron beam energy spread, seed laser power, strengthof dispersion section etc.

to the harmonic wavelength of seed laser, to achievecoherent radiation at this higher. The pondermotive phaseof electron in the second undulator can be calculated by
the equation below[1]:φ2 = nφ10 + φ10'[n(l1 + Ndλu1) + z2λu1 / λu2 ]l1
a~ eiφ1－2ku1ks1au1δ p1 Re∫[n(l1 − z1 + Ndλu1) + z2λu1 / λu2 ] s1 2 dz1 + ∆φ2γ0---------------- (3)where φ10 and φ10’ is the initial phase and phase velocity;
ks1 and as1 are the wave number and the dimensionlessvector potential of the seed laser field (rms) , respectively;
z1 , z2 are the coordinate in the two section undulator; ∆Φ2is phase variation due to the interaction with the radiation
field (as2) in the radiator:z2∆φ 2 = −2 k s 2 k u 2 au 2δ p 2 Re ∫ ( z 2 − z 2 )INTRODUCTION
The high-gain harmonic generation (HGHG) scheme
is one of leading candidates for VUV to X-ray FELs.
Ordinarily, a modified TDA3D code, which takes into
account the effect of dispersive section, is used tosimulate the process of HGHG-FEL.
Recently, a 1D theory about HGHG-FEL has beendeveloped [1]. Different from the previous theories, it
accounts for the energy modulation and density
modulation (bunching) for a whole process. In this paper,
we present some analysis about the choice of seed laser
power and dispersive strength based on it.

The 1D paraxial optical field equation and theelection phase equation are:e − iφda~s= λ s re au δ p ne
γ
dz

(1)

2 k u k s au δ p
d 2φRe( a~s e iφ )
=−
2
dz
γ2

(2)

The symbols in the equations express the common
meaning. Especially, δp is the polarization modify factor:
for circularly polarized helical undulator δp=1; forlinearly polarized planar undulator with even nthharmonic radiation δp =0，and with odd nth harmonic
δp=[J,J]n.
As well known, the process of HGHG-FEL is thethree steps: the electron beam first pass an undulator(modulator) with a resonant seed laser for energy
modulation. Next, the beam travels through a dispersive
section, to form spatial bunch. Finally the beam enters asecond undulator (radiator), which is tuned in resonance

MOPOS42a~s 2 e iφ2

γ2

0

dz 2

'

(4)

From equations (1)-(4), the optical field evolution
equation for linear region can be given by:−i[ nφ10 '( 1 + N d λu 1 ) +φ02 ' z 2 ]da~s 2 8k u22γ 2 ρ 2
2=ei n J n (n∆ξ )dz 2
k s 2 a u 2δ p 2
3− ( 2k u 2 ρ 2 ) 3

l

∂

z2

0

02

× as 2 e∆γ m

J ( 2k ( z − z ' ))γ∂φ ' ∫−iφ02 '( z 2 − z 2 ')

u2

2

2

0

(5)

dz 2 '+ (2k u 2 ρ 2 ) 3 ie

BRIEF REVIEW OF THE 1D THEORY'zl−i 2 nφ10 '( 1 + N d λu 1 ) 2
2∫ (z − z ')2

2

0

× J 2 n (n(∆ξ + ∆ξ ' ))a~s 2 e −iφ02 '( z2 + z2 ') dz 2 'Where∆ξ = 4π (∆γ
N1z+ Nd + 2 ) m
nλu 2 γ2

(6)∆γm/γ is the energy modulation induced by interactingwith the seed laser:

∆γ m

γ

= 4πN1

au1δ p1a s1
2(1 + au1 )(7)

The radiation power in the radiator can be describedby eqs (1)-(4). But from the equations, analytical results
are difficult to get without various approximations andsimplifications. Therefore, a program is written to give us
a numerical calculation.
The angular bracket in eq (1) represents the averageover the electron’s initial phase (Φ0) and initial phasevelocities (Φ0’). The program calculates it by means of
numerical integration. We assume Φ0 has a uniform

Available online at http://www.JACoW.org

65

LiYuhui. Li et al. / Proceedings of the 2004 FEL Conference, 64-67

distribution and Φ0’ has a Gauss distribution (Gaussianbeam). The integrate region of Φ0’ is set between -6σ ～6σ , σ is the standard deviation. The seed laser is assumed
to be a Gaussian wave.

Table 1: Parameters for SDUVElectron beam parameters for HGHG:
γ:538.117 Peak current : 400A
Energy spread : 0.05％
Seed laser beam parameters:
Wavelength: 266nm
Input seed power: 16MW
Rayleigh range: 0.8m
Magnet parameters:
Modulative section
Length : 0.98m
Undulator period: 3.5cm
Number of periods: 28
Peak magnetic field: 0.8T
Dispersive section
Induced dispersion : 0.75 (dψ/dγ)
Radiative section
Undulator Period: 2.5cm
Peak magnetic: 0.62T

Power(W)First, to check the program, we make a comparison
between the results from the program and from thesimulation code TDA3D. Three set of parameters are usedin this comparison, including the Shanghai deep
ultraviolet FEL source (SDUV) [2], the Accelerator Test
Facility at BNL [3] and the Sincrotrone Trieste(ELETTRA) [4].
To simplify the program, we directly use a numericalintegration for the process of average Φ0 and Φ0’. Theenergy spread is taken into account but the emittance isignored to save computation time. To compare the results
under same condition, we set the emittance a very smallvalue for TDA3D.
From Figs1-3, the computation by our program gives
a good agreement with the simulation by the code
TDA3D.

10M

1M

100k

TDA3D
1D theory

10k

1k

100
0

1

2

3

4

5

6

7

Z(m)

Fig1 Results of the program and TDA3D for SDUV

Table 2: Parameters for the BNL FEL
Electron beam parameters for HGHG:
γ82
Peak current
110A
Energy spread
0.043％
Seed laser beam parameters:
Wavelength
10.6µmInput seed power
0.7MW
Rayleigh range
0.76m
Magnet parameters:
Modulative section
Length
0.684mUndulator period
7.2cm
Number of periods
9Peak magnetic field
0.202T
Dispersive section
Induced dispersion
1.5(dψ/dγ)
Radiative section
Undulator Period
3.3cm
Peak magnetic
0.494T

10M

1M

Power(W)RESULT COMPARE WITH TDA3D

100M

TDA3D
1D theroy

100k

10k

1k

100

0

1

2

3

4

5

z(m)

Fig2 Results of the program and TDA3D for the BNLFELFEL Theory

66

LiYuhui. Li et al. / Proceedings of the 2004 FEL Conference, 64-67

Table 3: Parameters from ELETTRA
Strength of dispersive section:

12

Saturation Length(m)Electron beam parameters for HGHG:
γ1956.947
Peak current
600A
Energy spread
0.05％
Seed laser beam parameters:
Wavelength
200nm
Input seed power
150MW
Rayleigh range
3m
Magnet parameters:
Modulative section
Length
2.964mUndulator period
5.7cm
Number of periods
52
Peak magnetic field
1.35T
Dispersive section
Induced dispersion
0.4(dψ/dγ)
Radiative section
Undulator Period
4cm
Peak magnetic
0.977T

Nd=5
Nd=20

10

Nd=40
Nd=60

8

Nd=60
Nd=5

6

Nd=20
Nd=40

4

0

10

20

30

40

50

Pseed(MW)Fig4 Saturation length as function of seed laser power fordifferent Nd

Saturation Power(MW)

300.0

1G
100M

Power(W)

10M
1M
100k

TDA3D
1D theory

250.0

Nd=5

200.0

Nd=20

dispersive section strength:
Nd=5
Nd=20
Nd=40
Nd=60

150.0

100.0

Nd=40
Nd=60

10k

0
1k

10

20

30

40

50

Pseed(MW)

100

0

5

10

15

20

25

Z(m)

Fig5 Saturation energy as function of seed laser power fordifferent Nd

Fig3 Results of the program and TDA3D for ELETTRAPARAMETER OPTIMIZING FOR SDUVThe HGHG-FEL experiment involves lots ofparameters, which are relevant to the magnet field, theelectron beam and the seed laser. Among them only few
ones are tuneable during the experiment. The seed laser
power and the strength of dispersive section are mostimportant of all.
Energy modulation term ∆γm /γ is relevant to the seedlaser power, it represents an additional energy spread andshould be less than the Piece parameter. This gives anupper limit for the seed laser power. For the caseconsidered here, it is about 50MW.
Using the parameters listed in Table 1, we calculate
the variation of the saturation length and the saturation
power with seed laser for different Nd. The results are
given in Fig4 and Fig5.

MOPOS42

From Fig 4, with increase of the input power, thesaturation length drops dramatically initially for low input
power and then the descending speed slows down. For agiven input power, the saturation length also drops off
with increase of Nd. But when Nd becomes sufficiently
large, the saturation length ascends instead of dropping.
For Nd = 60, saturation length has minimum value when
the seed laser power is about 20MW.
Fig5 shows, as seed laser power increases, thesaturation power decreases. For a given laser power lessthan 15MW, the saturation power has little difference fordifferent Nd.
Therefore, we choose 15MW seed laser power anddispersive strength Nd=40 for SDUV. To illustrate thischoice clearly, we give the power development alongradiator with seed laser to be 15MW for different Nd(Fig6) and the power development with Nd=40 fordifferent seed laser power (Fig7) respectively:

67

LiYuhui. Li et al. / Proceedings of the 2004 FEL Conference, 64-67

Pseed = 15MW

Nd = 5250.0

Output Power (MW)modulator, the dispersive section, as well as the radiator.
So it is function of radiator distance z2. Because thecoherent enhancement process is dominant in the first
four gain length of the radiator [5], z2 in ∆ξ isapproximated with its median over 4Lg i.e.2 Lg .

200.0

Nd = 5
Nd = 20150.0

Nd = 20

Nd = 40

100.0

2

4

6

8

10

12

14

16

Z/Lg (Lg = 0.5297m)

Fig6 Power development along radiator for different Nd(Pseed =15MW)

0.3
8

0.2

Saturation LengthJn(n∆ξ)

0.0

-0.1

-0.2

4
0

Output Power (MW)

300.0

15MW

200.0

100.0

Pseed:
5MW
15MW
25MW

20

30

40

50

Fig8 Saturation length and Jn(n∆ξ) as function ofdifferent seed laser power.
From Fig8, we can see that when seed laser power isabout 20MW, where the saturation length has theminimum value, the Bessel function Jn(n∆ξ) just reaches
its maximum value. The coincidence verifies our analysis
above.

250.0

150.0

10

Pseed(MW)5MW

Nd = 400.1

6Jn(n∆ξ)

0.0
0

0.5

0.4

Nd = 40

50.0

Nd=60

10

Saturation Length (m)

300.0

25MW

50.0

SUMMARIZING

0.0
0

2

4

6

8

10

12

14

Z/Lg (Lg = 0.5297m)

Fig7 Power development along radiator for different seedlaser power (Nd=40)
As mentioned above, for Nd = 60, the saturation
length reaches a minimum value when laser power isabout 20MW (Fig4), Here we make some analysis for thephenomena.
In the right hand side of linear approximate equation(5), the first term denotes the coherent enhancement
process, the Bessel function Jn(n∆ξ) is important to it; thesecond term denotes the usual exponential gain process
and the energy modulation ∆γm /γ affects it greatly; thecontribution of the third term is small, can be neglect.
Therefore, Jn(n∆ξ) and ∆γm /γ should be emphasized tothis problem.
It has been mentioned that we constrain the seed laser
less than 50MW to guarantee the energy modulation ∆γm/γ less than the Piece parameter (ρ=0.217%). Therefore
the additional energy spread induced by energy
modulation is relatively small (at 20MW seed laser, ∆γm /γ=0.14%) that it shouldn’t be the leading reason for theincrease of saturation length. Thus the Bessel functionJn(n∆ξ) should be dominant for this phenomena. We
calculate the variation of Bessel function Jn(n∆ξ) withseed laser power for Nd = 60. ∆ξ denotes the total
dispersion that consists of the contribution from the

A program based on a 1D HGHG theory is
introduced. First, the program is checked with modified
code TDA3D. Then the seed laser power and thedispersive strength are optimized for SDUV. Finally theaffect of the seed laser power and the dispersive strength
to the saturation length and saturation power are analyzed
and discussed. For a further work, we can add in theeffect of emittance as an equivalent energy spread. And
use a Monte Carlo process for the numerical integration tosave the computation time.

REFERENCES[1] Jia Qika,,“One-dimensional theory of high gain
harmonic generation free electron laser” Nucl.Instr.
& Meth. A519,pp489-492,2004[2] Z.T.Zhao et.al, “The Shanghai High Gain Harmonic
Generation DUV Free Electron Laser” Nucl.Instr. &Meth.A528, p591-594, 2004
[3] S.G.Biedron, H.P.Freund, L.-H. Yu, “Parameter
analysis for a high-gain harmonic generation FEL
using a recently developed 3D polychriomatic code”
Nucl.Instr.&Meth. A445. pp95-100,2000[4] Li Hua Yu, Juhao Wu, “Simulations for the
FERMI@ELETTRA proposal to generate 40- and10-nm coherent radiation using the HGHG scheme”
Nucl.Instr.&Meth. A507. pp455-458,2003[5] Jia Qika,“harmonic amplifer free electron laser” ,thisproceeding

FEL Theory

68

N.S. Ginzburg et al. / Proceedings of the 2004 FEL Conference, 68-70

IMPROVING SELECTIVITY OF 1D BRAGG RESONATOR USINGCOUPLING OF PROPAGATING AND TRAPPED WAVES
N.S.Ginzburg #, A.M.Malkin, N.Yu.Peskov, A.S.Sergeev, IAP RAS, Nizhny Novgorod, Russia
A.V.Elzhov, A.K.Kaminsky, A.P.Sergeev, S.N.Sedykh, JINR, Dubna, Russia
Abstract
In the paper FEM oscillator operation based oncoupling of quasi cut-off mode with propagating wave,
which is amplified by the electron, is considered. The
coupling is realized by periodical corrugation of sidewallof microwave system. The cut-off mode provides the
feedback while the efficiency in steady-state regime ofgeneration is almost completely determined by the
propagating mode, synchronous to the beam. The main
advantage of a discussed scheme is provision of higher
selectivity over transverse index than traditional schemeof FEM with a Bragg resonator. The novel feedback
scheme should be tested on a JINR- IAP FEM as amethod of increasing operating frequency.

INTRODUCTION
A number of oscillator schemes based on theinteraction between propagating and locked waves are
known in microwave electronics. One of them is ascheme of a gyrotron with an electron beam that excites aquasi cut-off mode while the output of radiation isprovided by the propagating wave coupled with thelocked one via corrugation of the waveguide side walls.
Another example is a scheme [1] of CARM or FEM in
which the electron beam interacts both with a propagating
wave (at the first harmonic) and a quasi-cutoff wave (atthe second harmonic). In this case direct coupling of the
waves is absent and the waves interact by modulating thebeam.
In this paper we discuss one more variant of such a
device that uses a beam of electrons interacting only witha propagating wave, and the latter is coupled with a quasi
cut-off trapped mode. This coupling is realized by either
helical or azimuthally symmetric corrugation. The quasi
cut-off mode provides the feedback in the system leading
to the self-excitation of the whole system while theefficiency in steady-state regime of generation isdetermined by the propagating wave, synchronous to theelectrons. The main advantage of above scheme isprovision of higher selectivity over transverse index than
traditional scheme of FEM with Bragg resonators. The
novel feedback scheme should be tested at a JINR-IAP
FEM as a method of increasing operating frequency for
fixed transverse size of interaction space.

(rr
E = Re (B( t )E ( r ) f ( z )err
E = Re A+ ( t , z )E A ( r⊥ )e −ihz − im Aϕ e iωc t
and a trapped feedback modeB⊥

−im B ϕ iωc t

e

)

(1a)

)

(1b)

Here ωc is a carrier frequency, which is chosen equalrto the eigenfrequency of the cut-off mode, E A, B (r⊥ )functions specify the transverse structure of the modes.
Assuming that the Q-factor of the cut-off mode is high,one can consider its longitudinal structure f (z ) fixed, as
the longitudinal structure of the propagating mode A(z )is changed under influence of the electron beam.
Helical corrugationr = r0 + r1 cos(h z + m ϕ )(2)( r0 is a mean radius of the waveguide, h = 2π d , dand r1 are the period and the depth of the corrugation
correspondingly) under the Bragg conditionsh ≈ h , m = m1 − m2
(3)
provides the coupling of the propagating and trappedmodes. Dispersion diagrams, showing the coupling ofpartial waves are presented in Fig.1.

ω
ωc

h

0

h

FIGURE 1
Operating frequency is close to eigenfrequency of the

MODEL AND BASIC EQUATIONS
Let us consider a model of a FEM oscillator based oncoupling of a synchronous wave propagating forward to
the direction of the electron beam motion

trapped mode ωc =cν B
, hence we obtain a relation on
r0

the geometrical parameters___________________________________________#

ginzburg@appl.sci-nnov.ru

MOPOS49

Available online at http://www.JACoW.org

69

N.S. Ginzburg et al. / Proceedings of the 2004 FEL Conference, 68-70

ν B2 − ν A2
2π
≈
d
r0

(4)

where ν A,B are the roots of Bessel functions (or theirderivatives) corresponding to the modes of a regular
waveguide.
Forward wave A(z ) is synchronous to the electron
beam moving in the + z direction. Corresponding
synchronism condition can be represented as(5)ω − hv|| = Ω ,where Ω is the frequency of oscillations of particles in a
spatially periodic wiggler field or in homogenous guiding
magnetic field. A system of equations describing both theprocess of amplification of synchronous wave and its
scattering to the trapped mode under assumption that thetime Q/ ωc of the changing of the amplitude of the cutoff mode is substantially exceeds the electron transit time
can be presented in the form:))∂A= iαBf ( Z )e iδz + J∂Z)L)∂B 1 )+
B = −iα∫ A+ ( Z )e − iδZ f * ( Z )dZ∂τ 2Q0where J =

(6a)

(6b)

1
e −iθ ( Z ) dθ 0 is an amplitude of RF∫
2π 0current, which is determined by the electron motion
equations

(

)

(7)

In Eqs. (6), (7) we have used the following dimensionlessvariablesandparameters:

Z = zCh ,τ = ωt ,θ = ω t − hz − ∫ Ωdt is electron phase in the field of)
A± = eκµA± mcωγ 0 C 2 ,the synchronous wave,

)
A

Z =0

= 0 , Bˆ

τ =0

= Bˆ 0 ,θ Z =0 = θ 0 ∈ [0,2π ) ,∂θ=∆∂Z Z =0(8)

where L is the normalized length of the resonator and ∆is initial detuning of synchronism between the electrons
and the wave at the carrier frequency.
Obviously, when the coupling between modes isabsent ( α = 0 ) Eqs. (6), (7) describe the convective
mechanism of instability, and self-excitation of theoscillations is impossible. Thus, the self-excitation of thesystem is provided by the coupling with the cut-off mode(α ≠ 0) . To obtain starting conditions we linearize theequations of motion. In the assumption that the length of
the interaction space is large ( L >> 1 ) the main
contribution to excitation factor in the right hand of Eq.
(6a) related with exponentially growing wave having for∆ = 0 the longitudinal wavenumber g = −

1 i 3
.
−
2
2

As a result for amplitude of trapped wave we get

2π

∂ 2θ
= Re Aˆ + ( Z )e iθ∂Z 2

detuning of the Bragg frequency ω = h c from the cutoff frequency.
Initial and boundary conditions of the equations(6), (7) are given by:)
B = eκµB N A mcγ 0 C 2 ωN B ,3L

1
α2 B 2∂B+B=−eϕ(δ , L )
3
∂τ 2Q

(9)
2



 − iL2 − iδL
1
1
 e
−
δ − g +π L δ − g −π L 

ϕ (δ , L ) = The self-excitation condition can be presented in a
form:
3L

1
α2 2
<−
e
Re ϕ(δ , L )
2Q
3

(10)

Self-excitation of the generator is possible if thefunction Re ϕ (δ , L ) presented in Fig.2 is negative.

13

 eI cλ2 K 2 µ 
C =  03
2
 mc 4π γ 0 N A 
is a Pierce parameter, I 0 is an unperturbed beam current,µ is a parameter of inertial bunching, K is a parameterof the coupling between the wave and electrons
proportional to the amplitude of the electrons transverse
oscillation, α is the coupling coefficient of waves on the
Bragg grating which is proportional to the depth of thegrating r1 , N A,B are the norms of the propagating andthe trapped modes correspondingly, Q is the Q-factor of

the trapped mode, δ = (ω − ω c ) / Cω is the normalized

FIGURE 2

FEL Theory

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N.S. Ginzburg et al. / Proceedings of the 2004 FEL Conference, 68-70

RESULTS OF THE SIMULATIONS
Establishment of a stationary regime of generation
found from numerical simulation of the nonlinear
equations (6), (7) are shown in Fig.3. Efficiency is rather)
high η ~ 3 . It is important to note that in optimal
conditions the main part of the energy extracted fromelectron beam transforms into the radiation of the
propagating mode A but not dissipated with the trappedwave B.
According to estimations based on above feedback
mechanism it is possible to decrease effective coupling
parameter sufficient for an oscillator self-excitation incomparison with traditional Bragg FEM schemes, where afeedback wave possesses rather high group velocity [2].
Correspondingly in oversized microwave system where
Bragg conditions are satisfied for a large number ofcouples of modes with different transverse indices it ispossible to provide selective excitation of a single couple
consisting of a cut-off mode and operating wave which is
amplified by the electron beam. Above method of mode
control should be tested in JINR-IAP FEM at Ka bandand then used as a method of increasing operating
frequency for fixed transverse size.

MOPOS49

L = 4,

δ ≈ 1.7 ,∆ ≈ −1.5

FIGURE 3

REFERENCES[1] Savilov, A.V. et al., Phys. Rev. E58, 1002 (1998).
[2] Bratman V.L., Denisov G.G., Ginzburg N.S., Petelin
M.I., IEEE J. Quant. Electr. QE-19, 282 (1983).

71

G. Penn et al. / Proceedings of the 2004 FEL Conference, 71-74

ANALYTIC MODEL OF HARMONIC GENERATION
IN THE LOW-GAIN FEL REGIME∗
G. Penn, M. Reinsch, J.S. Wurtele† , LBNL, Berkeley, CA 94720, USA
Abstract

ANALYTIC MODEL

Harmonic generation using free electron lasers (FELs)
requires two undulators: the first uses a seed laser to modulate the energy of the electron beam; the second undulator
uses the subsequently bunched beam to radiate at a higher
harmonic. These processes are currently evaluated using
extensive calculations or simulation codes which can be
slow to evaluate and difficult to set up. We describe a simple algorithm to predict the output of a harmonic generation
beamline in the low-gain regime based on trial functions
for the output radiation. Full three-dimensional effects areincluded. This method has been implemented as a Mathematica script which runs rapidly and can be generalized
to include effects such as asymmetric beams and misalignments. This method is compared with simulation results
using the FEL code GENESIS, both for single stages ofharmonic generation and for the LUX project, a design concept for an ultrafast X-ray facility, where multiple stages
upshift the input laser frequency by factors of up to 200.

INTRODUCTION
There is growing interest in using seeded electron beams
to drive a free electron laser (FEL), rather than relying on
amplification of noise. This allows for controlled timing
and pulse structure. The seed can be a laser field which isthen amplified by the FEL instability, or it can be an initial current variation (bunching) in the electron beam. The
second method allows for harmonic generation, where theoutput wavelength can be at a harmonic of the initial perturbation [1]. The possible use of multiple stages of suchharmonic generation is an area of active study, for example
in the LUX [2] project, which is an R&D project in ultrafast X-ray production. Here, an analytic model for predicting and optimizing the FEL output from an idealized, prebunched electron beam is presented, with emphasis on harmonic generation. While previous examinations of seeded
electron beams either assume the laser field structure in advance [3, 4], or rely on summations over single-particle radiation fields [5], this formalism uses a trial-function approach to obtain simple analytic prescriptions for determining the output laser field. These expressions only apply to FELs in the low-gain regime, but include the full
3-dimensional dynamics. A set of scripts implemented in
Mathematica allows for rapid calculation of the dominantmode produced by a seeded electron beam, as well as ameans to rapidly optimize FEL and beam parameters.
∗ Work supported by the Director, Office of Science, U.S. Dept.

Energy under Contract DE-AC03-76SF0098.
† also at UC Berkeley, Berkeley, CA 94720, USA

Available online at http://www.JACoW.org

of

The output from the radiating undulator, or radiator, ishere approximated as a simple Gaussian mode, but is otherwise kept arbitrary:
Ey = e E0 eiΦ0 G(x, y, s) exp(iks − iωt),

(1)

where


ZR
1 k(x2 + y 2 )exp −ZR + i(s − s0 )2 ZR + i(s − s0 )(2)characterizes the structure of the mode. The laser wavelength is λ = 2π/k, the frequency ω = ck, and ZR is theRayleigh length. The longitudinal coordinate s represents
the position along the undulator, and at s = s0 the laser is
at its waist with spot size (ZR /2k)1/2 . It is possible to generalize this to include higher-order transverse modes. Notethat this field only characterizes the output from the radiator, and so will be described by vacuum field solutions.
The particle motion due to the undulator is√2c
au sin(ku s),
vu 
(3)
γ
G(x, y, s) ≡where the undulator period is λu = 2π/ku , the normalized field strength is au = eB0 /mcku , and B0 is the RMS
dipole field on axis from the √undulator. The dipole field on
axis is taken to be Bx = − 2 B0 cos(ku s). For a single
particle, the forward motion satisfies
t = t(s = 0) +a2us−sin(2ku s),vz
4cku γ 2(4)where vz is the average forward velocity, and the last termarises from the motion in a planar undulator.
The change in energy of a particle is given by
dγ
ds

= −


e Ey v u
mc2 vz(5)√− e kaL G(x, y, s)ei(ks−ωt)

2 ausin(ku s),γ

where the normalized (complex-valued) laser field isaL =eE0 iΦ0
e .
mc2 k

(6)

Averaging over an undulator period yields
√
dγ
2k
= −m
au aL G(x, y, s)JJ(ξ)eiΨ ,
ds
2γ

(7)

FEL Theory

72

G. Penn et al. / Proceedings of the 2004 FEL Conference, 71-74

where JJ(ξ) ≡ J0 (ξ) − J1 (ξ), ξ ≡ ka2u /4ku γ 2 , and theponderomotive phase Ψ ≡ ks − ωt + ku s. To leading orderin 1/γ 2 , this phase evolves according todΨk2= ku + k(1 − c/vz )  ku − (1/γ 2 + v⊥
/c2 ), (8)ds22is also averaged over an undulator period.
where v⊥
The undulator field increases with strength off-axis. For
an undulator with equal focusing in both planes, and taking into account the slight transverse dependence of au in2
Eq. (3), the average of v⊥/c2 over an undulator period isroughly given by

√

2
v⊥
a2
2(Jx + Jy )= u2 +
,
2
c
γ
γβu

(9)

where βu ≡ 2 γ/au ku is the matched beta function for
the undulator, and Jx , Jy are the transverse actions for thisvalue of the beta function: 2 
dx
γ x2
+ βu
,
(10)
Jx ≡
2 βu
ds
and similarly for Jy . If external focusing is used, however,then Jx and Jy will no longer be constants of the motion.
Now we can expand out the equation for Ψ,
dΨ
ds

 δk
γ − γr2au δau ku −+2−kr
γr
1 + a2u√au− 2
ku (Jx + Jy ) ,1 + a2uwhere IA ≡ 4π0 mc3 /e  17 kA. This is the electric field
generated by the net bunching of the electron beam, and wewish to generalize this to include the possibility of having
no seed pulse, but a pre-bunched beam. Using the relationthat d|aL |/ds = e(e−iΦ0 daL /ds), Eq. (14) can be generalized to√daL
I 2 2 au=i
(15)
JJ(ξ) G∗ (x, y, s)e−iΨ .
ds
IA γZR
The above average is a correction to the usual bunchingparameter, b ≡ exp(−iΨ). The generalized bunchingparameter will be defined as
B(s) ≡ G∗ (x, y, s)e−iΨ .

(16)Harmonic generation, for example in the LUX designconcept, uses a seed laser to generate an energy modulationin one undulator, which is then converted into microbunching by means of a chicane. The additional slippage which
results from the chicane is characterized by the parameter
R56 , defined by c∆t = R56 (γ−γ0 )/γ0 . Following this, thebunched beam produces radiation while passing through asecond undulator. Because the bunching includes Fouriercomponents at harmonics of the initial laser seed, this second, radiating undulator can be tuned to a higher harmonicof the laser seed. Here, we consider a simplified case where
the modulator applies an energy modulation which depends
solely on the phase Ψ of the electrons. The energy distribution after modulation then takes the form

(11)f (X̄) ∝ H[(γ−γ0 −κx Jx −κy Jy +γM sin Ψ)/∆γ ]. (17)where we define k = kr +δk, and the resonant wave vector
is
2γr2
ku .
(12)
kr ≡
1 + a2u

We will consider both Gaussian and uniform energy profiles, where ∆γ is equal to the RMS energy spread andmaximum deviation, respectively. This energy distribution
includes the possibility for “beam conditioning”, where
there is a correlation between energy and transverse amplitude. The transverse component of the distribution function is exp(−Jx /x − Jy /y ), where x is the normalized
emittance in the x-plane. The wave vector in the following
radiator will be a harmonic, n, of the resonant wave vector
in the modulator. Thus, we will want to look at the quantityexp(−inΨ) instead of the bunching at the first harmonic.
After the modulator, the beam passes through a dispersive section with a resulting phase shift ∆Ψ = k0 R56 (γ −γ0 )/γ0 , where k0 is the wave vector corresponding to themodulator. After this dispersive section, the higher harmonic bunching will be given by

The detuning can be expressed equivalently in terms of δkor as a shift in undulator strength δau . Using the resonancecondition, the argument of the Bessel functions in Eq. (7)is ξ = (1/2)a2u /(1 + a2u ).
Finally, there is the expression for the laser field, assuming the power given up by the electron beam goes into asingle mode. For the mode defined by Eq. (2), the power is
PL =

mc3
1
1
ZR
c0 E02 π= kZR|aL |2 ,
2
k
8
re

(13)

where re = e2 /(4π0 mc2 ). By conservation of energy, the change in power is given by dPL /ds =−(I/e)mc2 (dγ/ds), where I is the peak current anddγ/ds ≡ dX̄f (X̄)(dγ/ds). The term X̄ is used asa shorthand to represent the full set of 6D phase space variables, and the distribution function f (X̄) is normalized sothat dX̄f (X̄) = 1. Noting that PL scales as |aL |2 , wehave√
I 2 2 aud|aL |=
JJ(ξ) m eiΦ0 G(x, y, s)eiΨ ,ds
IA γZR(14)

MOPOS57|e−inΨ | = Jn (kR56 γM /γ0 )Fγ (kR56 ∆γ /γ0 ),(18)

where k = nk0 is the wave vector of the higher harmonic.
The function Fγ depends on the form of the energy distribution:Fγ (x) =exp(−x2 /2),
(sin x)/x,

Gaussian
uniform.

(19)

The averages over particle energy and ponderomotive
phase within the radiator yield the same Fγ and Bessel

G. Penn et al. / Proceedings of the 2004 FEL Conference, 71-74

function as above for the initial bunching parameter, butwith kR56 replaced with kR56 + 2ku s. In addition toG∗ (x, y, s), there are extra phase terms which depend on
transverse coordinates which must be considered. Below,
we assume that the beam has the properly matched beta
function for the undulator. The final result for the generalized bunching at the higher harmonic is



δk
γ0 − γr
B(s) = exp iku s
−2
kr

γr
γM
× Jn (kR56 + 2ku s)
γ0 

ZR
∆γ
× Fγ (kR56 + 2ku s)
γ0 ZR − i(s − s0 )× F (x , cx (s), s)F (y , cy (s), s),(20)(1 − ic)−1/2

× 1 − ic +

(21)

where
F (, c, s)=

cx (s) ≡ 2ku s

the laser field can result in a good estimate for the output power. In the configurations being considered, a pure
Gaussian mode is expected to be a reasonable approximation to the FEL output except in the emittance-dominated> λ/(4π). In this paper, only a simpliregime, /γ0 ∼fied FEL configuration is considered, but the trial function
method applies to more general cases as well.
The resulting integrals are simple enough to implement
as a Mathematica script, which allows for rapid optimization. Because the optimization procedure is to maximize
the output power, any additional constraints (undulator
field, R56 , or energy modulation) can be simultaneously
optimized to obtain the largest possible output power. Thus
any optimizations performed on the beamline can occur simultaneously with the trial function optimization for ZR
and s0 , greatly reducing the computational time required.

SIMULATION RESULTS
kr βu /γ0
ZR − i(s − s0 )

−1/2

.

The quantity
√

73

2
au
κx
ku
−
2
1 + a2uγr−κxkR56 (22)γr

is related to the slippage due to transverse emittance, andsimilarly for cy (s). If it is the strength of the undulator
which is being tuned, the detuning term δk/kr can be replaced with 2au δau /(1 + a2u ).
The laser field at the end of the radiator is then given by√ L
I 2 2 auaL = iJJ(ξ)B(s)ds,(23)
IA γZR0
and the laser power is given by Eq. (13).

TRIAL FUNCTIONS
The result is still not fully defined because ZR and s0
are free parameters. In general, after fixing ZR and s0 ,any radiation field can be described using a sum of normal modes, but here we are restricting attention to a single,
Gaussian mode. Because the exact result will include thepower contained within all these modes, the analytic resultis expected to always fall below the correct value. Thissuggests varying the free parameters to maximize the output power, yielding a greatest lower bound to the correct
result.
This method is essentially a trial function approach, andany trial function which is a valid vacuum laser field canbe used. The closer the trial function is to the exact result,the more accurate this estimate for the power will be. Furthermore, the prediction for the laser power is expected to
be second-order accurate compared to the optimized trial
function; in other words, even a poor approximation to

FEL simulations using the GENESIS code [6] have been
compared with this analytic theory. Two cases are considered, the first stage of a cascade which converts 200 nm
wavelength to 50 nm, and the final stage which converts
3.13 nm wavelength to 1.04 nm. All sections are assumed
to use planar undulators.
For a given set of trial functions, the analytic model finds
the closest fit to the actual radiation, and predicts a lower
bound on the total output power. Even if the trial function
does not accurately represent the radiation field producedby the FEL, the prediction for the output power may stillserve as a good estimate.
Table 1: Comparison between analytic model and simulations using GENESIS for two case studies.
Analytic
GENESIS:
Case
Results
Theory M 2 ≡ 1 fit M 2
50 nm
PL (MW)
130.3
134.2
134.2
ZR (m)
1.12
0.94
0.97
s0 (m)
1.20
1.19
1.21
M2
≡1
≡1
1.04
1.04 nm PL (MW)
35.1
39.0
39.0
ZR (m)
52.7
49.0
33.0
s0 (m)
-10.4
-14.6
0.73
M2
≡1
≡1
1.72
The electron beam parameters are: I = 500 A, γ0 =6067, and the normalized emittances are x = y = 2 µm.
Results for the two cases considered are given in Table 1.
The transverse mode structure of the output radiation is described in terms of the M 2 parameter, which is the ratio of
the emittance of the laser to the minimum emittance, λ/4π.
This parameter can also be described as the ratio of the idealized Rayleigh length for the given waist diameter to theobserved Rayleigh length. In terms of power flux, the RMS
width of the laser at the waist is (λM 2 ZR /4π)1/2 . For
the first stage, producing radiation at 50 nm by going to

FEL Theory

74

G. Penn et al. / Proceedings of the 2004 FEL Conference, 71-74

the fourth harmonic, the energy modulation is γM = 2.68,
and the chicane is set to an optimized value of R56 = 92
µm. The radiating undulator has an 8 cm period and is
2.4 m long. The electron beam is taken to be matched tothe undulator, with β = 16.28 m. The resonant undulator
strength is au = 6.709, but optimal performance occurs at
au = 6.686. An analysis of the GENESIS results showthat 7.8 MW of power lies outside the predicted Gaussianmode. The analytic theory underestimates the total powerby 3.9 MW, a relative error of 3%. For the final stage, producing radiation at 1.04 nm by going to the third harmonic,
the energy modulation is γM = 1.10, and the idealized chicane uses R56 = 3.2 µm. The radiating undulator has a 2.8
cm period and is 8.4 m long. The electron beam is taken
to be matched to the undulator, with β = 29.00 m. The
resonant undulator strength is au = 1.3186, but optimal
performance occurs at au = 1.3181. In the simulation results, 2.3 MW of power lies outside the predicted Gaussianmode. The analytic theory underestimates the total powerby 3.9 MW, a relative error of 10%. A generalization totrial functions having two or more transverse modes would
be desirable for more accurate results.

Figure 1: Comparison of analytic theory with simulations
using GENESIS. Results for harmonic generation at 50 nm
and 1.04 nm, as the energy modulation γM is varied.
The dependence of the output radiation on the energy
modulation is shown in Figure 1, and also shows good
agreement between the analytic model and numerical simulations. The value of R56 is re-optimized for each case.
For short wavelengths, FEL performance is more sensitive
to the energy spread, as slippage along the length of theundulator leads to debunching of the electron beam. The
optimal power of 60 MW can only be increased either byusing a different undulator design or by lowering the harmonic number.
The agreement between theory and simulations only falters for the 1.04 nm case, when the magnetic fields are
tuned below the resonant value, as shown in Figure 2.
Far from resonance, there is roughly 5 MW of power in

MOPOS57

Figure 2: Comparison of analytic theory with simulations
using GENESIS. Results for harmonic generation at 1.04
nm, as dipole field strength (au ) is varied.
the form of higher-order transverse modes, with values ofM 2 ∼ 10. This radiation is generated by particles having
large transverse amplitude, which also move forward more
slowly. When the magnetic field is too high these higherorder modes do not appear, because there are no particles
moving fast enough to be in resonance. For earlier stages
which are not emittance-limited, the analytic calculations
are in much closer agreement with numerical simulations.
Other sources of error are the nonlinearity of the interaction, where the FEL instability or trapping may increase
the output power; the neglect of betatron motion and betatron phase mixing, which may decrease the output power;
and an oversimplification of the geometry of each stage ofharmonic generation. In the above examples, the FEL instability is unimportant. For example, in the 1.04 nm case,simulations at low beam current, when the FEL gain lengthis much longer than the total length of the system, would
scale to a total output power of 38.9 MW at 500 A. However, for larger values of the applied energy modulation,
nonlinear effects become important for reducing particle
slippage and maintaining a large bunching parameter.

REFERENCES[1] L.H. Yu et al., Science 289 (2000) 932–934.
[2] W.A. Barry et al., Report LBNL-51766, LBNL (2002).
[3] M. Arbel et al., Nucl. Instr. Methods A 445 (2000) 247–252.
[4] L.H. Yu and J. Wu, Nucl. Instr. Methods A 483 (2002) 493–
498.
[5] V.N. Litvinenko, Nucl. Instr. Methods A 359 (1995) 50–56.
[6] S. Reiche, Nucl. Instr. Methods A 429 (1999) 243–248.

75

R. L. Armstead et al. / Proceedings of the 2004 FEL Conference, 75-77

SHORT RAYLEIGH LENGTH FREE ELECTRON LASER SIMULATIONSIN EXPANDING COORDINATES
R. L. Armstead, W.B. Colson, and J. Blau
Physics Department, Naval Postgraduate School
333 Dyer Road, Monterey, CA 93943
Abstract
For compact short-Rayleigh length free electron lasers(FELs), the area of the optical beam can be thousands oftimes greater at the mirrors than at the beam waist. A fixed
numerical grid of sufficient resolution to represent the narrow mode at the waist and the broad mode at the mirrors
would be prohibitively large. To accommodate this extremechange of scale with no loss of information, we employ acoordinate system that expands with the diffracting opticalmode. The simulation using the new expanding coordinates
has been validated by comparison to analytical cold-cavity
theory, and is now used to simulate short-Rayleigh length
FELs.

INTRODUCTION
A short-Rayleigh length optical cavity may give several advantages for a high-power FEL, including reduced
mirror damage and improved beam quality [1]. However,such a design poses difficult numerical problems. Since
the mode area expands within the cavity many thousandsof times, a very large grid is required to accurately represent the mode at both the waist and the mirrors. For example, assume a Rayleigh length of z0 = 0.1 and a cavity length of S = 30, both normalized to the undulator
length, L. Then the mode radius will expand by a factorof (1 + (S/2)2 /z02 )1/2 = 150. If we assume 100 gridpoints in each dimension are needed to accurately represent
the mode at the waist, then 15000 gridpoints are needed at
the mirrors. A two-dimensional complex, double-precisionarray of that size requires about 4 GB of RAM, beyond
the limits of many computers. Furthermore, the simulation runtime increases as the square of the number of gridpoints. For the typical parameters given above, we estimate it would require about 4 hours for each pass throughthe optical cavity, running a three-dimensional simulationin (x, y, t) on a 2 GHz IBM G5 processor. For some setsof parameters, several hundred passes are needed to reachsteady-state operation, implying that the program would
take many weeks to run. Furthermore, if we wish to include
a 4th dimension in the simulation (z) to study longitudinalmodes and pulse effects, we would need at least 100 slices
in the z direction. In addition, steady-state in 4D requires
thousands of passes. The memory requirements would thengrow to 100’s of GB and the simulation runtime would increase to many years. One solution to this numerical problem is to abandon a fixed Cartesian grid, and instead use acoordinate system that expands with the diffracting optical

Available online at http://www.JACoW.org

mode. This approach [2], [3] is explained below for the
FEL.

PARAXIAL EQUATION
As usual, the equation to be solved for the complex electric field a is the paraxial wave equation expressed in dimensionless coordinates,[∂x2 + ∂y2 − (4/i)∂τ ]a(x, y, τ ) = 0.

(1)

The dimensionless coordinates x, y, and τ are, interms of the dimensioned coordinates X, Y, and Z:
x ≡ X(π/λL)1/2 , y ≡ Y (π/λL)1/2 , and τ ≡ Z/L,where
L is some characteristic length (which in FEL simulations
will be the undulator length), and λ is the optical wavelength. The paraxial equation follows from the usual fourdimensional second-order partial differential wave equation on the assumption that deviations from plane-wave behavior in the longitudinal (Z axis) direction are slow, a reasonable condition for a laser. Eq. 1 has been studied extensively [4], and is solved reliably by the application of an
FFT, except for the numerical difficulty of the expanding
beam due to diffraction.
Adopting the convention that a subscript in x, y, or τ
stands for the derivative with respect to that variable, Eq. 1
becomesaxx + ayy − (4/i)aτ = 0.

(2)

TRANSFORMING THE COORDINATES
In order to see the motivation for a coordinate transformation, consider the exact fundamental-mode solution to
Eq. 2:a(x, y, τ ) = a0 (πz0 /A)1/2 exp(−πr2 /A)eiφ ,(3)where z0 is the dimensionless Rayleigh length Z0 /L, andwhere the dimensionless beam area is
A = πz0 [1 + τ 2 /z02 ],(4)

so that the 1/e beam radius is
w = w0 [1 + τ 2 /(z0 )2 ]1/2 ,where w0 = z0

1/2

(5)

, and

φ(r, τ ) = − arctan(τ /z0 ) + πr2 τ /(Az0 ).

(6)

FEL Theory

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R. L. Armstead et al. / Proceedings of the 2004 FEL Conference, 75-77

Thus, for the case that τ  z0 , A ≈ πτ 2 /z0 and φ ≈−π/2 + r2 /τ, so thatif ττ = z0 /τ 2 . Integrating this first order differential equation for τ  with respect to τ yieldsa(r, τ ) ≈ a0 (z0 /τ ) exp(−r2 z0 /τ 2 ) exp (ir2 /τ )

τ  = z0 [1/τ1 − 1/τ ],(7)

to within a constant phase factor. It is clear from Eq. 7 thatfor large τ the radius of the beam expands linearly with τ ,which suggests that we define the new “expanding” independent variables by
1/2x ≡ z0 x/τ,

(8)

1/2

y  ≡ z0 y/τ,


(9)




and a new dependent variable v(x , y , τ ) such thata(x, y, τ ) = (1/τ )v(x , y  , τ  ) exp(ir2 /τ ),(10)

where r2 ≡ x2 + y 2 .
The phase factor exp(ir2 /τ ) characterizing an expanding spherical wave, as well as the spherical amplitude expansion factor 1/τ, are explicitly factored out from a, so
the remaining function v has to account only for the small
diffraction effects not contained in the solution for theGaussian fundamental mode. In addition, the inverse dependence of x and y  on τ means that the dimensions of theprimed numerical grid decrease with increasing τ , i.e. inprecisely the region where the physical beam (represented
on the unprimed grid x and y) becomes large by diffraction.
Then some algebra, outlined below, shows thatv(x , y  , τ  ) itself does indeed satisfy exactly the same
paraxial wave equation as does a(x, y, τ ).
First, evaluate ax = (vx xx /τ + i2xv/τ 2 ) exp(ir2 /τ ),1/2
by the chain rule applied to Eq. 10. But xx = z0 /τ by
1/2
Eq. 8. So ax = (vx z0 /τ 2 + i2xv/τ 2 ) exp(ir2 /τ ). One
more derivative with respect to x yields
1/2

axx = exp(ir2 /τ )[vx x z0 /τ 3 + i4vx z0 x/τ 3(16)

where the constant of integration is written z0 /τ1 so thatτ  = 0 when τ = τ1 . The well-understood FFT method
may then be applied to Eq. 15, without the numerical difficulty of following a rapidly-expanding wavefront.
The solution for the optical field a in the near field(τ < τ1 ) is calculated in the conventional coordinates x, y,and τ , then connected (using Eq. 10) onto the expandingcoordinate solution in the far field (τ ≥ τ1 ). Rememberthat τ = τ1 corresponds to τ  = 0.
Notice that for the special case of the fundamental modein expanding coordinates,v(r , τ  ) = (a0 z0 ) exp[−(r )2 ],(17)

which is independent of τ  . This trivial outcome will not
apply when the fundamental mode is modified by the presence of electrons in the FEL, but does provide an opportunity to compare a numerical simulation to an exact solution.
In the simulation of an actual FEL, there may be a mixtureof modes rather than just the fundamental mode, but thetransformation can handle the general case as well with nomodification.
The schematic representations in Fig. 1 and Fig. 2 show|a| expanding as a function of τ and |v| as a function of τ 
respectively, to illustrate the effect of the coordinate transformation. In an actual numerical simulation, we calculate|a| in the region τ = 0 to τ = τ1 in (x, y, τ ), then switch
to the primed system (x , y  , τ  ) to calculate |v| for τ > τ1 ,corresponding to τ  > 0. Then we apply the transformation to recover a(τ ) for τ > τ1 . The dashed lines in the
diagrams remind us of the relative size of the integration
steps in the primed and unprimed systems.

(11)+i2v/τ 2 − 4vx2 /τ 3 ].
In the same fashion, we find that
1/2

ayy = exp(ir2 /τ )[vy y z0 /τ 3 + i4vy z0 y/τ 3
2

2

(12)

Figure 1: Contours of constant optical field amplitude |a|as a function of Cartesian coordinates (r, τ ) for free-spacediffraction of a spherical wavefront.

(13)

In terms of the numerical integration using the expanding coordinates, constant time steps ∆τ  , correspond totime steps in the unprimed coordinates which increase
quadratically with τ, so that ∆τ = τ 2 ∆τ  /z0 . This is aconsequence of the Eq. 16, and the effect shows clearly inthe progression of integration “slice” size in Fig. 3.

3+i2v/τ − 4vy /τ ].
Furthermore,aτ = exp(ir2 /τ )[vx xτ /τ + vy yτ /τ + vτ  ττ /τ
−v/τ 2 − ir2 v/τ 3 ].
Substituting Eqs. 11, 12, and 13 into Eq. 2 yields
vx x + vy y = 4τ 2 vτ  ττ /(iz0 ).

(14)This can be written as the paraxial wave equation in theprimed coordinates,

FREE-SPACE DIFFRACTION

vx x + vy y − (4/i)vτ  = 0,

The upper left picture in Fig. 3 shows a cross-section of
the optical field amplitude |a| in terms of the unprimed co-

MOPOS65(15)

R. L. Armstead et al. / Proceedings of the 2004 FEL Conference, 75-77

77

LARGER RANGE

Figure 2: Contours of constant virtual field amplitude |v| asa function of expanding coordinates (r , τ  ) for free-spacediffraction of a spherical wavefront.

ordinates (x, τ ) as τ goes from 0 to 3 with τ1 = 1, forthe propagation of a spherical wavefront in free space. The
color scale, shown in the lower-right, goes from blue (small
amplitude) to yellow (large amplitude). Integration for τ
between 0 and 1 is performed in the conventional coordinate τ in ten steps with ∆τ = 0.1. The interval τ = 1 → 3
corresponds to expanding coordinate τ  = 0 → 0.2. Thisis also integrated in ten equal steps, with ∆τ  = 0.02, andis displayed in the lower picture as the ”virtual” field amplitude |v| in the primed coordinates. In this calculation theRayleigh length z0 = 0.3 corresponds to initial waist size
1/2
w0 = z0 ≈ 0.55. Notice that the virtual field amplitude|v| appears not to change with τ  for the fundamental mode,
which is precisely what Eq. 17 predicts. Also note that,compared to τ, the range of τ  is much diminished by thetransformation Eq. 16. The optical field a for τ ≥ τ1 = 1
is then given in terms of the transformation Eqs. 8, 9, 16,
and 10. The ratio of the beam area at τ = 3 to the beam
area at the waist is 100.
The right-hand pictures in Fig. 3 are both end-on crosssections at τ = 3. The upper is the optical field amplitude |a(x, y)|, and the lower is the virtual field amplitude|v(x , y  )|, also at τ = 3, corresponding to τ  = 0.2.

Another calculation, shown in Fig. 4, spans a muchlarger range, τ = 0 → 30, with z0 = 0.1. Conventional
coordinates are used for for τ = 0 → 1 and primed coordinates for τ = 1 → 30, for which τ  = 0 → 0.1. Ten equal
steps ∆τ  suffice to take the field all the way to τ = 30 andpreserve its Gaussian shape. The ratio of the beam area atτ = 30 to that at its waist is (1 + 302 /0.12 ) = 90, 000,
and is much too large for integration in conventional coordinates. Using the coordinate transformation method, there
are no distortions in the outcome, which is the same as theexact analytical result.

Figure 4: Free-space diffraction of a fundamental Gaussianmode in Cartesian coordinates |a(x, τ )| (top), and expanding coordinates |v(x , τ  )| (bottom) for z0 = 0.1, τ1 = 1,and τ = 0 → 30.
Furthermore, multiple transverse modes have been accurately propagated over this range.

ACKNOWLEDGMENTS
The authors are grateful for the support from NAVSEA,
ONR, and the JTO.

REFERENCES[1] D.W. Small, R.K. Wong, W.B. Colson, R.L. Armstead,“Free electron lasers with short Rayleigh length”, Nuclear
Instruments and Methods in Physics Research A393 (1997)
262.
[2] E.A. Sziklas and A.E.Siegman, “Diffraction calculations using fast Fourier transform methods,”, Proc. IEEE 62, 410(March 1974).

Figure 3: Free-space diffraction of a fundamental Gaussianmode in Cartesian coordinates |a(x, τ )| (top), and expanding coordinates |v(x , τ  )| (bottom) for z0 = 0.3, τ1 = 1,and τ = 0 → 3.

[3] E.A. Sziklas and A.E. Siegman, “Mode calculations inunstable resonator with flowing saturable gain. 2: Fast
Fourier transform method,” Appl. Opt. 14,1873-1889 (August 1975).
[4] W.H. Press et. al., “Numerical Recipes in C”, 2nd Edition,
Cambridge University Press, New York, 1992.

FEL Theory

78

J. Blau et al. / Proceedings of the 2004 FEL Conference, 78-81

OPTICAL MODE DISTORTION IN A SHORT RAYLEIGH LENGTH FREE
ELECTRON LASER
J. Blau, W.B. Colson, B.W. Williams, S.P. Niles and R.P. MansfieldPhysics Department, Naval Postgraduate School
333 Dyer Road, Monterey, CA 93943
Abstract

The dimensionless current density is given by

A short-Rayleigh length free electron laser (FEL) will
operate primarily in the fundamental mode with a Gaussian
profile that is narrow at the waist and broad at the mirrors.
The gain medium will distort the optical wavefront andproduce higher-order modes that will expand more rapidly
than the fundamental. Wavefront propagation simulations
are used to study optical mode distortion, as electron beam,
undulator, and optical cavity parameters are varied.

INTRODUCTION
A proposed design for a high-power free electron laser
calls for a short-Rayleigh length optical cavity [1]. This
design has several advantages. The strongly-focused optical mode is narrow at the waist, enhancing the interaction with the electron beam. The small interaction volume
should improve optical beam quality, encouraging the development of a fundamental Gaussian mode. The rapidlyexpanding mode will reduce the peak intensity on the cavity mirrors, lessening the possibility of mirror damage.
The narrow, high-current electron beam will distort the
optical mode, as new light is created due to spontaneousand stimulated emission along the length of the undulator. Higher-order modes may develop, and propagate to
the cavity mirrors. Some power may be lost outside themirrors, but the portion that remains within the cavity willproduce a combined wavefront that no longer has a simple
Gaussian profile.

SHORT-RAYLEIGH LENGTH FELPARAMETERS
A proposed high-power FEL has electron beam energy
Eb = 80 MeV, bunch charge q = 200 pC and bunch lengthlb = 0.15 mm, yielding a peak current of Iˆ = 400 A. The
normalized emittance is n = 3 mm-mrad, with a beam
radius of rb = 60 µm. The undulator consists of N = 22
periods, each of length λ0 = 2.36 cm, for a total length of
L = 52 cm, with a peak magnetic field B̂ = 0.7 T. The
undulator parameter is K = 1. The optical cavity is S =18 m long, with Rayleigh length Z0 = 6 cm, and quality
factor Qn = 4, corresponding to 25% power transmission
per pass. The optical wavelength is λ = 1 µm.
Our simulations use dimensionless parameters [2]. Longitudinal distances are normalized to the undulator length
L, and transverse distances are normalized to (Lλ/π)1/2 .

MOPOS66j=

8N (eπKL)2 ρe,
γ 3 mc2(1)

where ρe ∝ Iˆ is the electron particle density, γ = Eb /mc2
is the Lorentz factor, e and m are the electron charge andmass, and c is the speed of light. For the above parameters, j = 200. The dimensionless electron beam radius is σ = rb /(Lλ/π)1/2 = 0.15 and the dimensionlessRayleigh length is z0 = Z0 /L = 0.12. The dimensionlesscavity length is τmirr = S/L = 35.

SIMULATION METHOD
Our wavefront propagation program has been described
elsewhere [3]. At each time step, it uses the relativistic
Lorentz force equations to determine the electron motionin the presence of the undulator and optical fields, and theparabolic wave equation to evolve the optical wavefront in(x, y, t). The simulation can follow multiple and arbitrarytransverse optical modes, as they interact with the electron
beam and bounce back and forth in the optical cavity, including mirror transmission and edge losses. We typicallystart the simulation in weak optical fields, and allow it toevolve over many passes through the cavity until the FEL
reaches steady-state.
Recent improvements to our program include a faster
Fourier transform algorithm [4], a more accurate integration method that uses next-nearest neighbors in the propagation of the wavefront matrix, and an expanding coordinate system to follow the rapidly-diffracting optical modewith a reasonable grid size [5].

SIMULATION RESULTS
For each set of simulation runs described below, we startwith the nominal parameters given above. Then we varysome of the parameters to determine the effect on FEL performance and optical beam quality.
Fig. 1 shows the steady-state extraction for many simulations as the current density j is varied while emittance isheld constant. Extraction is defined as the fraction of electron beam power converted to optical power on a single
pass through the undulator. A theoretical curve, discussed
below, is also shown for reference.
Since the weak-field gain is proportional to j, there isa minimum threshold value of j ≈ 20 below which there
is no extraction, because the cavity losses exceed the gain.
For larger values of j, the power will grow over each pass

Available online at http://www.JACoW.org

J. Blau et al. / Proceedings of the 2004 FEL Conference, 78-81

79

4.5

! (%)

Simulation
Theory

3

1.5

0
0

100

200

300

j
Figure 1: Extraction η versus current density j, for a seriesof simulations (solid red line), compared to theory (dashedblue line).

Figure 2: Optical field amplitude |a(x, y)| at the output
mirror for several values of current density j.
until the laser reaches saturation in strong optical fields.
Basic FEL theory [2] predicts that for high gain, j  1,
the extraction should grow asη≈(j/2)1/3.
8N(2)

Eq. 2 is plotted as a dashed blue line in Fig. 1. The similarslope of the two curves confirms the j 1/3 dependence, but
the theory curve is well below the simulation curve. However, Eq. 2 is only an approximation, and doesn’t include
the effects of mode distortion.
Fig. 2 shows the steady-state optical wavefront profile atthe output mirror for several values of j. For low current,
j = 30, the laser appears to be operating close to the fundamental mode. For moderate current, j = 150, the modeis beginning to distort. For high current, j = 270, there
is at least one higher-order Laguerre-Gaussian mode evident. This series clearly shows the effect of the FEL gain
medium on mode distortion.
Fig. 3 shows the results of many simulations as the electron beam radius σ is varied. The beam angular spread isalso varied to keep the emittance constant. For small beamradii, the corresponding large angular spread reduces overlap with the optical beam over the length of the undulator, hence lowering extraction. For large beam radii, manyelectrons are outside the strongly focused optical beam at
the waist, again reducing extraction. The simulations predict that the optimal beam radius is at σ = 0.12.

Figure 3: Simulation results for extraction η versus electron
beam radius σ.

Figure 4: Optical field amplitude |a(x, y)| at the output
mirror for several values of electron beam radius σ.
There is a curious feature in the center of Fig. 3, aroundσ ≈ 0.12, where the extraction appears to briefly rise a bit
higher than the overall trend. This may be due to opticalmode distortion around that value. Fig. 4 shows the output
wavefront for several values of σ.
We also consider varying the electron beam focus pointfrom τβ = 0−1, normalized to the undulator length L. The
simulations give a fairly constant extraction over the entire
range, as shown in Fig. 5, predicting that the short-Rayleighlength FEL should be fairly insensitive to fluctuations in theelectron beam focal point. The optical mode profiles (notshown) do not change much over this range.

Figure 5: Simulation results for extraction η versus electron
beam focus position τβ within the undulator.
Next, we look at the effects of varying the number of

FEL Theory

80

J. Blau et al. / Proceedings of the 2004 FEL Conference, 78-81

Figure 6: Simulation results for extraction η versus numberof undulator periods N .

Figure 8: Simulation results for extraction η versus undulator taper strength δ.

Figure 7: Optical field amplitude |a(x, y)| at the output
mirror for various number of undulator periods N .

Figure 9: Optical field amplitude |a(x, y)| at the output
mirror for several values of undulator taper strength δ.

undulator periods N , keeping the undulator period λ0 constant. The simulation results are plotted in Fig. 6. Notethat changing N affects many other dimensionless parameters; for example, the electron current density j ∝ N 3 .
Consequently, if there are too few periods, the gain will
be below threshold, and the simulation results indeed showthat there is no extraction for N < 10, corresponding to
j < 20. Above that, the extraction increases rapidly, untilN ≈ 14. For larger values of N , even though j continues
to increase, the extraction drops off. The optical wavefronts
in Fig.7 predict the development of higher-order modes as
N increases.
The results for undulator length motivate considerationof tapering the undulator, to extend saturation and enhance
extraction. Fig. 8 shows simulation results as the undulator
taper rate is varied. The taper rate is defined by


∆K
K2
,
(3)
δ ≈ −4πNK
1 + K2The extraction changes very little over this entire range,
confirming that a short-Rayleigh length FEL can maintain
good extraction while reducing optical intensity on the mirrors. Fig. 11 shows the output wavefronts at several valuesof z0 . Note that these are not all drawn to the same scale
since the beam width expands as z0 decreases.
Finally, we vary the cavity length over the range τmirr =S/L = 5 − 35. The mirror curvature is also changed tokeep z0 constant. Again there is little variation in the extraction, as shown in Fig. 12, although the optical mode
profiles, shown in Fig. 13 become increasingly distorted as
the cavity is lengthened. Again, these are not all drawn
to the same scale; the beam width expands dramatically asτmirr increases.

where ∆K/K is the change in the undulator parameter.
The simulations confirm that a positive taper could significantly improve FEL performance. A taper rate of δ = 11π
produced an extraction of 5.9%, compared to the untapered
value of 3.4%. Tapering also seems to improve the beam
quality. Fig. 9 shows the output wavefront for several taper
values; at δ = 11π it is close to the fundamental mode.
Next we show a series of simulations varying theRayleigh length from z0 = 0.05 − 0.85, normalized to theundulator length L. The results are shown in Fig. 10.

MOPOS66

ACKNOWLEDGMENTS
The authors are grateful for the support from NAVSEA,
ONR, and the JTO.

J. Blau et al. / Proceedings of the 2004 FEL Conference, 78-81

81

Figure 10: Simulation results for extraction η versus
Rayleigh length z0 .

Figure 12: Simulation results for extraction η versus cavity
length τmirr .

Figure 11: Optical field amplitude |a(x, y)| at the output
mirror for several values of Rayleigh length z0 .

Figure 13: Optical field amplitude |a(x, y)| at the output
mirror for several values of cavity length τmirr .

REFERENCES[1] W.B. Colson, ”Short Rayleigh length free electron lasers”,
Proc. FEL2004.
[2] W.B. Colson, in: W.B. Colson, C. Pellegrini, A. Renieri(Eds.), Laser Handbook, Vol. 6, North Holland, Amsterdam,
1990.
[3] J. Blau, Ph.D. Dissertation, Naval Postgraduate School,
http://handle.dtic.mil/100.2/ADA401739 (2002).
[4] Frigo, Matteo and Johnson, ”FFTW: An adaptive softwarearchitecture for the FFT”, Proc. 1998 Intl. Conf. Acoustics
Speech and Signal Processing, 1381 (1998).
[5] R.L. Armstead, J. Blau, and W.B. Colson, ”Short Rayleighlength free electron laser simulations in expanding coordinates”, Proc. FEL2004.

FEL Theory

82

B. Maraghechi et al. / Proceedings of the 2004 FEL Conference, 82-84

WIGGLER EFFECTS ON THE GROWTH RATE OF A RAMAN
FREE-ELECTRON LASER WITH AXIAL MAGNETIC FIELD OR
ION-CHANNEL GUIDING⋆

B. Maraghechi,1,2, H. Aghahosseini,1 and A. A. Kordbacheh1,21Department of Physics, Amirkabir University of Technology, Tehran, Iran
2
Institute for Studies in Theoretical Physics and Mathematics (IPM),
P.O. Box 19395-5531, Tehran, Iran∗
Abstract
A relativistic theory for Raman backscatteing in the
beam frame of electrons is used to find the growth rate of afree-electron laser (FEL), in the Raman regime. First, a one
dimensional helical wiggler and an axial magnetic field areconsidered. The wiggler effects on the linear dispersion relations of the space-charge wave and radiation are includedin the analysis. A numerical computation is conducted to
study the the growth rate of the excited waves. It was foundthat the wiggler effects on the growth rate decreases thegrowth rate on both group I and group II orbits. Next, thegrowth rate under an ion-channel guiding, instead of an axial magnetic field, under similar condition is calculated andis studied numerically.

INTRODUCTION
Lab-frame analysis of a FEL with a one dimensional helical wiggler and an axial magnetic field was first presented
by Kwan and Dawson [1] using fluid model. In linearizing
the relativistic factor, they included the energy exchange
between the beam and the space-charge wave but neglected
the exchange of energy between the beam and the radiation. The fully relativistic treatment of this problem, in thelab-frame, was first presented by Bernstein and Friedland[2] but they did not analyze the wiggler effect on the dispersion relations of the growing waves. Mehdian et al. [3]derived a nonlinear dispersion relation, with the wiggler
effects on the dispersion relation of the excited waves included, but they did not find the growth rate. Ion-channel
guiding of the electron beam in a FEL has been proposed
as an alternative to guiding by a solenoid (or quadrupole)magnetic field [4]. This type of guiding involves the formation of a positive ion core by expulsion of electrons from a
preionized plasma channel into which the electron beam is
injected. Jha and Kumar [5] have calculated the growth ratewith the higher order relativistic terms neglected.

BEAM-FRAME ANALYSIS WITH AXIALMAGNETIC FIELD
A relativistic and cold electron beam is passed througha uniform static axial guide magnetic field, and a static∗ Electronic mail: behrouz@aut.ac.ir

MOPOS69

helical (wiggler) magnetic field, which is periodic along
the guide axis. In the beam frame of reference, the wiggler field comprises a propagating electromagnetic (pump)wave, which undergoes stimulated Raman backscattering.
This process is characterized by the parametric decay of thepump wave (ω1 , k1 ) into a forward-scattered space-charge
wave (ω2 , k2 ) and a backscattered electromagnetic wave
(ω3 , k3 ). The transverse and longitudinal components ofthe velocity are treated as relativistic. The unperturbed
state in the beam frame is characterized by n(0) = n0 /γ|| ,andE(0) =

B(0)

=

V(0)

−γ|| v|| Bw(b
x − iby)exp[i(k1 z + ω1 t)] + c.c.,
2c
¡

=

(1)

¢
−iγ|| Bw(bx − iby)exp[i(k1 z + ω1 t)] + c.c.
2(2)+bz B0 ,
iγ|| vw(b
x − iby)exp[i(k1 z + ω1 t)] + c.c.,(3)2vw =ΩwL v||.
(Ω0L − γ0 kw v|| )Perturbation composed of a longitudinal plasma wave
(ω2 , k2 ) and a transverse backscattered electromagnetic
wave (ω3 , k3 ) are considered. The frequencies and wave
numbers satisfy the phase matching conditions, ω3 = ω2 −
ω1 and k3 = k2 − k1 . These waves are assumed to vary as
exp[i(k2 z + ω2 t)], and exp[i(k3 z + ω3 t)]. The amplitudesof the longitudinal space-charge wave are E2 , V2 , and n2
and the x and y components of the radiation are E3 , B3 ,and V3 .
The relativistic momentum equation in the beam framemγdV/dt + mVdγ/dt = −eE − ec−1 V × B,

(4)with dγ/dt = −e/(mc2 )V.E and with the use of the linearized relativistic factor, can be linearized as follows£ ∂V(1) ¡ (0)¢¤+ V .∇V(1) + V(1) .∇V(0)∂t¡ ∂V(0) (0) (1)+mc−2 γ03 γ||−3V .V∂tmγ0 γ||−1

Available online at http://www.JACoW.org

83

B. Maraghechi et al. / Proceedings of the 2004 FEL Conference, 82-84¢¡+V(0) .V(1) V(0) .∇V(0) − ec−2 V(0) V(0) .E(1)¢¡+V(0) E(0) .V(1) + V(0) .E(0) V(1) = −e E(1)¢+c−1 V(0) × B(1) + c−1 V(1) × B(0) .
(5)

0.8

0.4

L

∆ (cm-1)

0.6

After substituting the first order quantities in Eq. (5),and making use of the phase matching-conditions in the
coupling terms, the terms corresponding to (ω2 , k2 ) and(ω3 , k3 ) phases will give equations for the longitudinal
space-charge wave and the transverse wave (radiation), respectively. The fluid-Maxwell equations will be

0.2

mγ0 γ||−1 ω2 V2 = ieE2 − ec−1 γ|| Vw B3 + ec−1 γ|| Bw V3
(6)
0

¡
−1

mγ0 γ||¢

2ω3 V3 − k1 γ|| Vw V2 − mc−2 ω1 γ03 γ||−1¡ 2 2¢
γ|| Vw E3 − c−1 γ||2 V|| Vw Bw V3

×Vw2 V3 − ec−2−1= −2eE3 − 2ec

B0 V3 + eγ|| Bw V2 ,

ω2 n2 + k2 n0 V2 = 0,

(7)

(9)

k3 cE3 = −ω3 B3 ,

(10)

(11)

Equations (6)-(11) form a system of linear homogenious
algebraic equations. The necessary and sufficient condition
for a nontrivial solution is the dispersion relation³´³´
ωp2 ω3+Ψωc + ω32
k2 ω1 ωp2 h k3 ω1ωw
k1 ω3 (1 − a1 ) i³´=−+
ωc + ω3 − a1 a2
2k 2 ω1 − ωc ω1 − ωc

ω22 − ωp2 Φh× 1−

k32 c2 − ω32 +w

k1 ω2 ωca1 a2 i¡¢−.
ωc + ω3
k2 ω1 ωc + ω3

5

10

15

20

25

B0 (KG)
Figure 1: Lab-frame spatial growth rate ∆L as a function of
axial magnetic field B0 . With wiggler effects (solid line);
without wiggler effects (dotted line).

(8)

4πen0 V2 = iω2 E2 ,−k3 cB3 = 4πen0 V3 − 2πeγ|| Vw n2 + ω3 E3 .

0

(12)

The wiggler effects on the linear dispersion relations of thespace-charge wave and radiation are contained in Φ and Ψ,
respectively. For zero wiggler, they reduce to an ordinary
longitudinal plasma oscillations and a transverse electromagnetic wave in a magnetized plasma. If coupling to theradiation is removed Φ becomes unity and the wiggler has
no effect on the space-charge wave. On the other hand, if
coupling to the space-charge wave is removed Ψ becomes
nonzero, which shows the direct effect of wiggler on theradiation.
The real parts of the frequencies and wave numbers satisfy the linear dispersion relations for the space-charge
wave and radiation, respectively, with all of the effects of

the wiggler and guide magnetic fields included. The imaginary parts of the complex frequencies and wave numbersof the growing waves may be expressed in terms of the labframe growth rate ∆L . This will give the lab-frame spatial
growth rate of the space-charge wave and radiation with thelab-frame temporal growth rate taken to be zero;
2
h k ω
ωw
k2 ωp2
k1 ω3 (1 − a1 ) i
3 1
³
´
+
ωc + ω3 − a1 a2
8kγ|| ω1 − ωc ω1 − ωchk1 ω2 ωca1 a2 ih 2
¡
¢−
× 1−
k3 c − v|| ω3
ωk2 ω1 ωc + ω3
c + ω3∆2L =ωp2 v|| ωc (1 − a1 ) a1 a2 k3 c2
a1 a2 ωc ωc v||
+
¡
¢2 −
ω
+
ω
2(ωc + ω3 )2c
32 ωc + ω3
2 2
2 i−1 h¡a1 a2 v|| (k3 c + ω3 )+
ω2 − k12 c2 a1 ωc (ωc2(ωc + ω3 )2¢ (ωc − ω1 − a1 a2 ) i−1
−ω1 )
.
(13)
2ω12 (ω3 + ωc − a1 a2 )2+The wiggler effects, through Φ and Ψ, on ∆L are shownin Fig. 1 (solid lines). Dotted lines show ∆L when the
wiggler effects are neglected. Lab-frame values for theunperturbed electron density, wiggler wavelength(period),and Lorentz factor were taken to be n0 = 1012 cm−3 ,λw = 2 cm, and γ0 = 2.5, respectively. The wiggler isassumed to be Bw = 1500 G. It can be observed that the
wiggler effects on the growth rate decreases the growth rateon both group I and group II orbits.

FEL WITH ION-CHANNEL GUIDING
As an alternative to guiding by an axial magnetic field,
focusing of the electron beam can be accomplished by an

FEL Theory

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B. Maraghechi et al. / Proceedings of the 2004 FEL Conference, 82-84

¡ 2
¢¡
¢
ωi − k12 v||2 ω2 + a1 a2 i−1 h 2×
k3 c − ω3 v||¢2
4¡
2k12 v|| ω32 − a1 a2¢i−1
a1 a2 v|| ¡+.
ω2 + a1 a2
2
2ω3∆ (cm-1)

0.3

0.2

(17)

L

Variation of the growth rate ∆L with the ion-channel
guiding frequency ωi /kw c is shown in Fig. 2 with wiggler
effects on the excited waves included. Growth rate in bothgroup I and group II orbits increase sharply as the resonance is approached.

0.1

REFERENCES
0

0

0.5

1

1.5

ωi /kwc

2[1] T. Kawn and J. M. Dawson, Phys. Fluids 22, 1089 (1979).
[2] I. B. Bernstein and L. Friedland, Phys. Rev. A 23, 816 (1981).

Figure 2: Lab-frame spatial growth rate ∆L as a functionof ion-channel frequency ωi /kw c with wiggler effects included.

[3] H. Mehdian, J. E. Willett, and Y. Aktas, Phys. Plasma 5, 4079
(1998).
[4] K. Takayama and S. Hiramatsu, Phys. Rev. A, 37, 730 (1988).
[5] P. Jha and P. Kumar, Phys. Rev. E, 57, 2256 (1998).

ion-channel. The transverse electrostatic field generated by
the ion-channel is¡¢
xx + byy ,Ei = 2πeni b(14)and the wiggler induced velocity will be given by Eq. (3)with vw given byvw =ΩwL kw v||2
2 v2 )(ωi2 − γkw
||

,

(15)

where ωi2 = 2πni e2 /m is the betatron frequency squared.
With similar procedure as in the axial magnetic field case,the dispersion relation can be found as³´³´
ω 2 − ωp2 Φ k32 c23 − ω32 + ωp2 + Ψ´³
2 2 2 3 h
ω3 (1 − a1 ) ωi2 − k12 v||2 iωw ωp v||
−k2 kw³´= ³´2 k3 v|| −2 v2
k1 v|| ω3 − a1 a2
2 ωi2 − kw
||
h
a1 a2
ω2 ω12 i
× 1−
−
.
(16)
ω3
k1 k2 ω3 v||2

Expressing imaginary parts of the complex frequencies
and wave numbers of the growing waves in terms of thelab-frame growth rate ∆L will give the lab-frame spatial
growth rate of the space-charge wave and radiation
2 2 2 3hωw ωp v||
k2 kw
a1 a2
ω2 ω12 i−³´2 1 −
ω3
k1 k2 ω3 v||22 v2
8γ||2 ω2 ωi2 − kw||³´h
ω3 (1 − a1 ) ωi2 − k12 v||2 ih³´
× k3 v|| −ω2 + a1 ωi2 c2
k1 v|| ω3 − a1 a2∆2L =MOPOS69

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S. Schwarz / Proceedings of the 2004 FEL Conference, 85-89

THE EUROPEAN X-RAY FREE ELECTRON LASER PROJECTAT DESY
A.S.Schwarz, Deutsches Elektronen-Synchrotron, Hamburg, Germany
for the XFEL Group
Abstract

The X-ray Free Electron Laser XFEL is a 4th generationsynchrotron radiation facility based on the SASE FEL
concept and the superconducting TESLA technology forthe linear accelerator. In February, 2003, the German
Federal Ministry of Education and Research decided that
the XFEL, proposed by the International TESLACollaboration, should be realized as a European project
and located at DESY/Hamburg. The ministry alsoannounced that in view of the locational advantage,
Germany is prepared to cover half of the investment andpersonnel costs for the XFEL. In the course of the lastyear work has concentrated on the following areas: setting
up of an organizational structure at DESY for the
preparation of the project, discussions with potential
European partners on several levels, selection of a newsite for the XFEL facility and the preparation of the'project approval procedure'. The present status of thetechnical layout of the Linear Accelerator, the SASE
Undulator and Photon Beam lines and the experimentstations will be presented.

BASIC DESIGN CONSIDERATIONS
The basic idea underlying the XFEL is the extension of
the principle of linear accelerator based Self
Amplification of Spontaneous Emission (SASE) Free
Electron Lasers (FELs) to the hard X-ray (~1Å
wavelength) regime. The ultra-high brilliant laser pulses

100 MeV
Injector

3rd Harmonic

500 MeV
Booster

Bunch
Compressor

with sub-100-fs pulse length and a large degree of
coherence will allow to probe the dynamic state of matterwith atomic resolution in space and time and to study
non-equilibrium states and very fast transitions between
different states of matter [1]. Compared to 3rd generationsynchrotron sources the gain factors for the peakbrilliance for the SASE lines and the spontaneousradiation exceed 109 and 104, respectively. Usingsuperconducting Rf technology for the linear accelerator
allows for a large flexibility in the electron bunch
patterns.

TECHNICAL LAYOUT
The principle layout for the first stage of the XFEL
facility is shown in Fig.1 [2], [3]. The electron beam isaccelerated in a linear accelerator using superconducting
Rf technology to approx. 20GeV and then distributed into
several beam lines, This allows to use the electron beam
for several FELs and spontaneous radiators and facilitatesparallel operation of many experiments, including R&D
on the light generation process and beam line hardware.
The SASE FELs cover the photon energy range
between 200eV and ≤15keV in a continuous way. The
emphasis is on the production of hard X-rays such that 1Å
wavelength can safely be reached with conservative
assumptions on the beam parameters.

20 GeV
Main Linac >100
Modules

Collimator

Switch-yard

Undulators

PhotonBeamlines

Dumps

0m

50m 80m

ca. 150m

ca. 1700m

ca. 270m

ca.2150m

ca. 3300 m

Figure 1: The principle layout of the XFEL facility

The overall length of the facility is 3.3km (2.15km
for the linear accelerator complex including the beamcollimation section and 1.15km for the undulator andphoton beam lines). The length scales are largely
determined by

Available online at http://www.JACoW.org•••

the required electron beam energy and theavailable accelerating gradient of thesuperconducting Rf structures
the requirements of the machine optics inthe beam distribution sections,the saturation length of the undulators

Single-Pass FELs

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S. Schwarz / Proceedings of the 2004 FEL Conference, 85-89••

provisions for spare space for future options(e.g. laser- or self-seeding) andthe photon diagnostics and transport lines.

The XFEL is laid out as a multi-user facility. In its 1ststage, it will have 5 undulator beam lines, 3 of which
are SASE-FELs (two for the Å wavelength regime, one
for softer X-rays), the other two for hard X-ray
spontaneous radiation. Initially, 10 experimental
stations are foreseen. The underground experimental
hall has a floor space of 50×90m2 and more stations
can be added later. The site allows to extend the user
facility for more beam lines in a later stage (see Figure
2).
Table 1: XFEL Design Parameters
Performance Goals for the Electron Beam
Beam Energy

10 - 20 GeVEmittance (norm.)

1.4 mrad × mm

Bunch Charge

1 nC

Bunch Length

80 fs

Energy spread (uncorrel.)<2.5 MeV rms

An overview of the main XFEL parameters is given in
Table 1. The undulator parameters have been optimisedfor one Å wavelength at a beam energy of 17.5 GeV.
This implies that at the nominal maximum beamenergy from the linac of 20GeV at 23MV/m
accelerating gradient, the 57Fe line at 0.08nm, ofinterest for certain experiments, will be accessible.

ELECTRON BEAM DISTRIBUTION
The XFEL linac can accelerate more than 3,000
bunches per RF pulse, serious beam dynamics
problems related to higher order modes in the cavities
are not expected [4]. User requirements regarding
beam time structure will vary over a large range, fromsingle or few bunches to partial or full trains per RF
pulse. Generation of such patterns is possible at thesource, at the end of the linac or by a combination of
both. From the point of view of maximum flexibility asystem using programmable fast kickers appears to be
the optimum solution. Beam loading conditions in the
linac could be quasi static, i.e. the same from pulse topulse, and bunches could be distributed to different
beam lines according to the needs of the respective
experiments.

Main Linac

ca. 1150 m

23 MV/m

Linac Length

approx. 1.5 km

Inst. Accelerator Modules

116

Installed Klystrons

29

Beam Current (max)

5 mABeam Pulse Length

0.65 ms# Bunches p. Pulse (max)3250

Bunch Spacing (min)200 nsRepetition Rate

10 Hz

Max. Avg. Beam Power

650 kW

Performance Goals for SASE FEL Radiation
photon energy

15 – 0.2 keVwavelength

0.08 – 6.4 nm

peak power

24 – 135 GW

average power

66 – 800 W

number photon per pulse

1.1 – 430 × 1012

peak brillance

5.4 – 0.06 ×1033 *average brillance

1.6 – 0.03 ×1025 ** in units of photons / (s mrad2 mm2 0.1% b.w.)

FRBIS01

ca. 90 m

Acc. Gradient @ 20 GeVelectron beamline
photon beamline
SASE 1 – 3Undulator 1 – 2
shafts 1 – 4
beamdump 1 – 2experimental hall
XFEL, 2nd phase

Figure 2: The 1st stage user beam line layout (coloured)and the possible extension.
The required switching devices are demanding,though, regarding jitter tolerances and reliability. In
addition to switching the electron beam, it is also
possible to switch the FEL process on and off by phaseshifters, such that different photon pulse time structures
can be generated in a beam line with a sequence ofseveral undulators [5].
The beam transport lattice from the end of the linac
to the undulators includes sections for diagnostics andcollimation to protect the undulators from potentiallylarge amplitude halo or mis-steered beam. A large
momentum acceptance is foreseen so that energy
modulation with a bunch train by up to 3% is possible.
The lattice layout and the civil construction in the
beam distribution region for the 1st phase of the user
facility will also already take into account thepossibility of later adding more beam lines.

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S. Schwarz / Proceedings of the 2004 FEL Conference, 85-89

PHOTON BEAM LINES
The generic layout for the undulator and photon
beam lines is shown in Fig.3. Following the light
generation in the undulator sections, a gasfilter section
with photon monitoring is added that allows to tune theintensity of the photon beam. This is followed with aphoton diagnostic section. Before entering theexperimental hall, the photons pass through a mirror
system, with e.g. a double crystal monochromator.
After the monochromator, the photon beam is split into
several beams that are transferred to a range ofexperiments in the experimental hall.
The undulator sections have a maximum total lengthof 250m. Variable gap (min. 10mm) type 5m longundulator segments are foreseen, which not only
permits to independently adjust the photon energy
within certain limits, but also facilitates the precise
steering of the electron beam for optimum overlap withthe photon beam [6]. Typical Distances are ~650m
between the exit of the undulator and the opticalelements and ~200m between the optics and theexperiment.

50 m

Control 2

Exp. 2
Experiment 1
15 m

Exp. 3Contr.3

Special X-Ray
OpticsOpt.
Laser

Control 1

Instrument/Probe

Detector

Figure 4: A generic layout of the experimental area atthe end of one of the five photon beam lines of the firststage of the European XFEL facility

PARAMETER FLEXIBILITY
With conservative assumptions for the slice energy
spread of the electron bunch (2.5MeV), the slice
emittance (1.4mm mrad) and the size of the undulator
gap (10mm) a wavelength of 1Å can be reached at abeam energy of 17.5GeV with a saturation length ofapprox. 140m. Improvements in the slice emittance or
the energy spread at a given beam energy would allow
a reduction of the saturation length or a reduction of
the photon wavelength below 1Å at the same undulator
length.
Furthermore, the expected higher performance of thesuperconducting cavities of the linear accelerator will
permit to operate at even shorter wavelength, provided
that the electron beam quality can also be further
improved to guarantee saturation in the SASE FEL
process.
The required klystron power per station is 4.8MW,
well below the maximum power of 10MW of themulti-beam klystrons developed in industry for the
TESLA project. This will not only cover the power
needs for an operation at higher energies, but also
allow to operate the linac at higher repetition rates (andduty cycles) at lower energy (the main limitation thenbeing the average power of the RF system).

Figure 3: The generic layout for the undulator andphoton beam lines
A generic layout of the experimental area at the end ofa given photon beam line is shown in Fig.4. The area
available for experiments is approximately 750 square
meters for each of the five photon beam lines of thefirst stage of the XFEL facility.

In contrast to conventional linacs, with thesuperconducting accelerator technology even a
continuous wave (CW, 100% duty cycle) operation of
the linac is conceivable [3], although only at reduced
energy/accelerating gradient in order to avoid
excessive cryogenic load into the Helium at 2K. Suchan option is not viewed as being part of the initial stageof the facility, but could become attractive if loweremittance, high duty cycle beam sources become
available [7], possibly in combination with advanced
FEL concepts.
The superconducting linac allows for a wide
flexibility in the generation of bunch train patterns. The

Single-Pass FELs

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S. Schwarz / Proceedings of the 2004 FEL Conference, 85-89

nominal beam pulse length is 0.65ms with max. 3250
bunches per pulse at a spacing of min. 200ns.
Depending on the requirements of the user community,
single bunches or few bunches per pulse train are
possible as well as bunch trains with varying bunch
spacing.

PRESENT ACTIVITIES/STATUS
The XFEL was originally proposed as integral part of
the TESLA project together with a 500 – 800 GeV e+eLinear Collider based on superconducting RF (SRF)
technology [8]. In a later update [9], the proposal was
modified such as to build the XFEL with its own,
separate linac for the benefit of flexibility regarding
construction, commissioning and operation of the
facility, maintaining the SRF technology identical tothe collider linac and a common experimental site
16km northwest from the DESY site in Hamburg.
The German government decision in 2003 to go ahead
with the XFEL as a European project and to postpone
the decision on the collider led to a revision of the site.
The new site layout, sketched in Fig.5, has the XFEL
linac starting on the DESY site, permitting to make
optimum use of existing infrastructure, and the user
facility in a rural area about 3km west-northwest fromDESY south of the city of Schenefeld.

Project Approval Procedure
In Germany, the legal procedure necessary to prepare
the civil construction and operation for such a large
scale facility as the XFEL is the ‘Project Approval
Procedure’. The legal basis for such a procedure is atreaty between the Bundesländer Hamburg andSchleswig-Holstein which has been signed by therespective governments in July, 2004.

3.3k
m

Figure 5: Sketch of the XFEL site near DESY
For the Project Approval Procedure a relatively
detailed planning of the various underground andsurface buildings and the construction and operation
phases of the facility has to be performed. After thedecision for the site in October 2003, the planning for

FRBIS01

the Project Approval Procedure has started. It is
foreseen to prepare all necessary material describing
the project by spring 2005. The examination of theplanning information by a public authority will thentake likely until the end of 2005 such that constructionof the European X-Ray Laser Laboratory XFEL canstart in the year 2006.

Towards a European XFELThe project organisation at the European level isongoing. A steering committee and two working
groups, one on scientific-technical (STI) and one on
administrative and financial issues (AFI), have been
established early in 2004, with members from all
European countries which are interested inparticipating in the project. The main task of thesegroups is to prepare the documents required for thetechnical definition and organisational structure of the
project by 2005. The final decision to move into theconstruction phase is expected for 2006. The
construction time until beam operation will be 6 years.
The total project cost is estimated at 684 M€ (year2000 price level), of which Germany will cover 50%.
A Memorandum of Understanding (MoU) regulating
the preparatory phase for the construction of theEuropean XFEL has been prepared by the presently
participating countries and is expected to be signed
before the end of the 2004.

The XFEL Project Group at DESY
In the summer of the year 2003 a project group wasestablished at DESY in order to organise thepreparatory work towards start of construction of the
facility in 2006. The charge of this group thus covers
the present intermediate phase of the project during
which the organisation at the European level is inprogress. The main tasks are the further optimisation of
the overall design of the XFEL, starting from the
supplement [9] of the TESLA Technical Design Report[8], the specification, prototyping, etc. of major
technical components towards industrial production
and the preparation of the site for the facility near the
existing DESY site in Hamburg. While the group has at
the start been formally arranged purely within the
DESY laboratory, it is also thought to serve as anorganisational structure to facilitate and integrate
participation from outside collaborators in thisintermediate phase, for the time being until a European
project group has been established.
The DESY XFEL group is managed by a project
leader, a deputy project leader and an administrative
project coordinator. In order to structure the work, in
total 37 work packages (WPs) have been defined. The
WPs are grouped into 6 main topics as listed in Table2.

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S. Schwarz / Proceedings of the 2004 FEL Conference, 85-89

Table 2: Work Package Groups for the organization of
the preparatory work for the XFEL at DESY
WP groupTopic01
Linear Accelerator
02
Accelerator Sub-systems
03
Photon Beam Lines
04
General Issues
05
Infrastructure
06
Site and Buildings
For each of the 37 WPs a person has been nominated as
the coordinator in charge for this part of the workwithin the DESY laboratory. It is expected that
responsibility for part of or entire WPs will be takenover by persons from outside DESY, once the project
organisation develops from its present stage to theEuropean level.
The project group holds regular weekly meetings.
Participation via video by external groups can be easilyarranged and has occasionally been used. In addition to
the main weekly project meeting, a considerable
number of other sub-group meetings, either on aregular basis or when required, take place (examples:
preparations for the Project Approval Procedure forlegal permission of construction, accelerator module
group, beam dynamics group). A web site has been set
up to serve as information platform among theparticipating groups and institutes [10].

CONCLUSIONThe European X-Ray Free Electron Laser Laboratory
will provide unprecedented opportunities for basic
research with photons in the 1Å regime. The baseline
design offers a conservative approach to reach thiswavelength. It offers a considerable amount offlexibility and allows later incorporation of further
developments in the photon generation scheme. The
preparatory work for the XFEL is well underway at
DESY and on the European level.
With the R&D work progressing towards industrial
production of major components and the preparations
for the site and the legal procedure (project approval
procedure) well under way, the project should be readyto go into the construction phase in ~2 years from now
such that the facility could be commissioned in 2012.

ACKNOWLEDGEMENTS
The author wishes to thank all members of the XFELGroup as well as the TESLA collaboration who haveprovided the basis for this report. Special thanks go to
Reinhard Brinkmann, Thomas Tschentscher and Hans
Weise.

REFERENCES[1] H. Dosch, “Advanced Analysis in Nanospace:
Research with the XFEL”; LINAC04, XXIIInternational Linear Accelerator Conference,
Lübeck, Germany, August 16-20, Paper MO101;
see also http://www.linac2004.de/[2] R. Brinkmann, “Accelerator Layout of the XFEL”,
LINAC04, XXII International Linear Accelerator
Conference, Lübeck, Germany, August 16-20,
Paper MO102; see http://www.linac2004.de/[3] H. Weise, “The TESLA XFEL Project“, 9thEuropean Particle Accelerator Conference,
EPAC'04, July 5-9, Lucerne, Switzerland; see
http://www.epac04.ch/[4] N. Baboi, “Multi-Bunch Beam Dynamics Studies
in the TESLA XFEL”, LINAC04, XXIIInternational Linear Accelerator Conference,
Lübeck, Germany, August 16-20, Paper TUP57;
see also http://www.linac2004.de/[5] E. L. Saldin, E. A. Schneidmiller and M. V.
Yurkov, DESY-TESLA-FEL-2004-02, May 2004.
[6] M. Tischer et al., Nucl. Instr. Meth.
A483(2002)418.
[7] M. Ferrario, J.Sekutowicz and J. Rosenzweig, “An
Ultra-High Brightness, High Duty Factor,
Superconducting RF Photoinjector”, EPAC2004,
Lucerne, MOPKF043.
[8] F. Richard et al. (eds.), “TESLA Technical Design
Report“, DESY 2001-011, March 2001;
http://tesla.desy.de[9] R. Brinkmann et al. (eds.), “Supplement to the
TESLA XFEL TDR“, DESY 2002-167, October
2002; http://xfel.desy.de[10] Information Portal of the XFEL Group for the
preparation of the XFEL project at DESY:
http://xfel.desy.de/Single-Pass FELs

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T. Shintake / Proceedings of the 2004 FEL Conference, 90-95

OVERVIEW OF SINGLE PASS FEL DESIGNSTECHNICAL SUGGESTIONS FOR STABILITY IMPROVEMENT
Tsumoru Shintake, RIKEN/SPring-8, Japan
Abstract
The single pass FEL based SASE is only one realistic
candidate to generate intense coherent radiation at X-ray
wavelength. To achieve high gain amplification of FEL
signal, we need to provide a high density electron beamwith low transverse emittance and maintain its trajectoryin precisely straight line along the fairly long undulator,
typically, 100 m or even longer. To do beam based alignment or simply guide the beam, the machine has to bevery stable, with low pulse-to-pulse jitter and slow drift.
This paper will provide some technical suggestions toimprove today’s linear accelerator to meet the above demand.

INTRODUCTION
The FEL: free electron laser using a high energy electron beam running in an undulator as an active media has
been realized and used for various applications in infrared
wavelength. However, when the requested wavelength
becomes short, the interaction of the electron beam withthe undulator radiation becomes weaker, since the energy
exchange is performed through transverse motion of thebeam along sinusoidal trajectory in the undulator, and its
amplitude is inversely proportional to the beam energy,
thus FEL becomes harder to be realized in shorter wavelength. Additionally, bellow 200 nm wavelength, no efficient mirror material is available as the cavity reflector,
and all mirror material becomes weaker against intenseradiation circulating in the FEL resonator.
To avoid this difficulty, the X-ray free-electron laser(FEL) based on linear accelerator technology using theprinciple of self-amplified spontaneous emission (SASE)
appears to be the most promising approach. SASE does
not require the resonator, instead it amplifies the spontaneous signal associated with the incoming electron beam,
for several decade of magnitude, until it reaches to saturation condition along a fairly long undulator.
To realize this type of new FEL, we have to establish
the following two major technologies.
(1) Generation of high density electron bunch with apeak intensity at a few kA, at the same time thebeam emittance has to be very low, typically 1
π.mm.mrad for transverse, and 10-4 energy spread.
(2) Transport above electron bunch fairly straight trajectory in the long undulator line. The alignment
tolerance is typically 10 to 50 micron-meter foreach Q-magnet in X-ray FELs.
To perform these requirements, in many accelerator
laboratories, new R&D programs for X-ray FEL havebeen started in these years. Up to now, R&D’s are mostly
focused on the development of low-emittance electronsource using photo-cathode RF-gun, or HV gun using

MOBIS01

thermionic cathode. Recently, very promising results arereported from those R&D’s at FEL2004 conference.
To achieve the high peak current in a bunched beam,
we currently believe the magnetic chicane type bunchcompressor will be capable of handling the low emittancebeam without emittance dilutions. There are a large number of studies on this subject, and can be found elsewhere.
However, on the second issue, not many studies havebeen carried out, because this is not a single subject andthe target cannot be clearly specified, since it varies onboundary conditions of each detail designs. The issue is
widely cross-related between, undulator technology, beam
optics, electron beam monitoring, and X-ray beam detection.
In this paper, the author wishes to illuminate machinestability issues behind each of these technical details. To
perform the beam based alignment on undulator beamline, machine has to provide fairly stable beam during
iteration process: measuring beam position carefully withchanging the beam energy. Also on tuning the chicane
magnet, we need careful measurement on bunch length v.s.
energy or CSR noise radiation from the beam line. Everytuning and beam study will request stable beam and quiet
environment (low electro-magnetic radiation from power
supplies).
In this paper, we compare machine stability of the linear accelerators with storage ring and discuss various aspects of machine stability. The author will also try to provide some technical suggestions on improving the machine stability.

STABILITY COMPARISON
Table-1 compares various aspects related to the machine stability of the storage ring and linear accelerator(pulse mode). In the storage ring, machine runs mostly insteady state condition, while the pulse mode linear accelerator runs in transient condition, this cause the majordifference of the machine stabilities in two types.
The electron beam trajectory in a storage ring is a“closed orbit”, which is an eigen vector of the wavefunction (ring optical matrix). Therefore, even with different initial conditions, in practice with beam injection
errors, beam converges to unique closed orbit (eigen vector) after damping. On the other hand, in the linear accelerator, the trajectory is not an eigen vector, it is an open
single-pass trajectory, which varies with initial conditions,in practice, injection error. Therefore, the stability of theelectron source is very important in the linear accelerator.
In the storage ring, there is a synchrotron damping effect, which is a combined effect of synchrotron phasestability phenomena on rf-voltage and radiation damping
effect. Thanks to this effect, the initial condition error orsome temporal error excitations are damped, and the

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T. Shintake / Proceedings of the 2004 FEL Conference, 90-95

beam trajectory approaches to the steady state closedorbit. But, in the linear accelerator, there is no phasestability phenomena, therefore no negative feedback actson the beam in natural, and also there is no synchrotron
radiation damping. Thus, we do not have any helpful phenomena on beam stabilization in the linear accelerator,
and the beam accumulates error during its accelerationfrom the electron source to the undulator, until it isdamped.
According to the beam quality issue, i.e., shape of thebeam distribution function, in the storage ring, beam tails
are cleaned up during many turns by quantum excitation
due to the synchrotron radiation, and by limited rf-bucket
height or collision to the beam aperture, finally it approaches to the Gaussian shape. In the linear accelerator,
there is no such natural beam cleaning effect. Additionally,
we have the dark-current emission from metallic surface
in high-field at the rf-gun and also in the linear accelerating structure. In order to clean up and avoid contamination, we have to prepare beam collimators in proper locations, where we carefully need to study the wakefield
effect associated to non continuous change in beam aperture.
The state of the art achievement on stability has been
made recently in storage rings after introducing the “Topup mode” operation[1]. The beam intensity (or beam current) stability reached to 2 x 10-4 level, and the beam energy stability is in the range of 10-5 to 10-6. for period of aday(the beam energy spread is 10-3). There is no question
to all synchrotron radiation users being satisfied withthese beam stabilities. For example, protein crystallography, can be smoothly performed if the beam energy stability at <10-3 level.
On the other hand, today’s linear accelerator has muchpoorer performance, unfortunately. The charge stability
from electron gun and after acceleration is in the order of
10-2 in single bunch mode. The energy stability is about
10-3, which depends on the power supply stability, especially the line-type pulse modulator power supply stability
is in 10-3 level. The author believes that there is muchrooms of improvement on the machine performance.
The super conducting accelerator technology will solvea part of the jitter problem.

The X-ray FEL based on SASE mode will be used forvery wide applications, among them; unique applications
will be the basic study on high field phenomena in condensed matter, and imaging of single molecular or nanostructure by single shot. In such applications the intensity
stability of 10-2 level and 10-3 energy stability will begood enough. However, the beam trajectory inside theundulator line has to be stable within 10 to 50 micronmeter (depends on design choice) for 100 m long undulator line in X-ray FELs.
Change in energy will cause trajectory deviation withdispersion in focusing system, or bunch compression factor change in chicane magnet. The charge variation willcause energy variation through beam loading effect, andbunching ratio change through space charge repulsive
force, or betatron phase shift through radial space charge
force. Those parameters are closely related in complex
manner, so it is not simple to specify the beam stability
requirement, and not be described further in this paper.
The author instead will try to provide suggestions on improving the machine stability by introducing today’s advancing technology in industries.

JITTER AND DRIFT SOURCES
The possible jitter sources of pulse-to-pulse change in
intensity, energy, timing, etc., and sources of long-term
parameter change are listed below.
(1) AC line voltage and phase fluctuation.
(2) Power supply fluctuation (due to temperature, orother reasons).
(3) Switch-tube pulse-to-pulse jitter. Residual ONvoltage and delay time variation of thyratron tube
in pulse modulator power supply for the highpower klystron.
(4) EM noise interfere from switching power supply of
modulator and inverter type power supply.
(5) AD, DA digitising and quantized resolution noise.
(6) Temperature fluctuation on all hardware components.
(7) Ground motion of natural and human activity.
We need to cure all these sources of fluctuation. In an
ideal machine, thermal noise will define all the residual

Table-1. Stability comparison.

Machine condition

All hardware are in the steady state condition.

Trajectory
Damping

Closed-Trajectory (Eigen-vector)
Synchrotron damping

Beam cleaning

During many turns, synchrotron excitation andbeam tail loss make Gaussian beam.

Noise bandwidth~ 1 kHz
Narrow tune resonance.

Linear Accelerator(Pulse Mode Machine)
Transient condition(less stable)
Open-Trajectory (Not Eigen vector)
No Damping EffectSingle pass. No natural beam cleaning
exists. Dark-current contamination is a
big problem.
~GHz. Bunched electron beam samples
all the noise in wide frequency spectrum.

Energy andintensity stability

10-5 ~ 10-6

10-2 ~ 10-3

Storage Ring Machine

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T. Shintake / Proceedings of the 2004 FEL Conference, 90-95

Fig. 1. UPS as an energy storage and power regulation.
fluctuations, however practical machine is far from such
ideal conditions. From the following section, possible
cure to these fluctuations will be discussed.

AC Line stabilization
AC line provides all the energy to the accelerator, thus
it is one of the most important fluctuation source. Today’s
power generator plants form a network connection andexchange energy to compensate variation of energy consumption in a day or a week, and also regional unbalance
between a city and industrial zone. Therefore, voltage andphase are always changing (AC phase is artificially used
to control power flow in the network).
Also, in spring and summer seasons, lightning in thunderstorm causes short-term power glitches, sags or power
down, resulting in beam loss, or vacuum pump down. On
the other hand, in pulse mode operation of the normal
conducting accelerator, machine runs at 10 to a few hundred pps, in which, after firing each pulse, the power supplies need to be re-charged within a cycle, thus systemcreates pulse power loading to external power grid.
In order to avoid the power down, and also prevent thesystem to sending the pulse loading to external site, theaccelerator should be equipped with UPS (uninterruptible
power supplies). A small UPS system has been used to
backup the computer power in important network servers,
where mostly the small size chemical batteries were used.
For large scale application, such as in a hospital or semiconductor fabrication line, a diesel engine was used, but itruns limited time only after the AC power down, and can
not be used continuously. An advanced system using flywheel energy storage [2] and IGBT switching power controller can be found in large scale applications, such as
semiconductor fabrication line.
UPS system using lead acid battery also used in a large
system, however, it needs frequent maintenance on thebattery with careful treatment of acid. The lead acid battery is also massive.

MOBIS01

In electric car development, a new type of energy storage using “double layer capacitor” appears to be the mostpromising battery [3]. The energy to mass ratio is ten
times higher than the lead acid battery, and does not use
the chemical process to store the electric charge, therefore
the life time is much longer. The USP system capable ofhandling 400 kW using this type of capacitor is already onmarket [4].
Fig. 2 shows a possible UPS power regulation system.
The key points are(1) The double layer capacitor store energy for UPS
function.
(2) The switching inverter converts DC power to AC
power with high regulation and its cycle is locked
to a clock generator in the accelerator.
(3) The AC power from external grid is converted to
DC power through active rectifier on the double
layer capacitor, and regulated.
(4) The DC power is also directly distributed to accelerator, and used for various voltage throughswitching converter. In this scheme, we can simplify each power supply by eliminating AC-DC
converter parts.
(5) Pulse loading effect in the linear accelerator isalmost perfectly compensated by the energy storage in UPS.
Detail information of the double layer capacitor can befound in ref. [3].

EM NOISE
The traditional design of the line type pulse power supply (modulator) generates strong EM noise. The rush current in thyratron switch is usually 1000A or more, thevoltage swing across the switch is 20 to 50 kV, and theswitching speed exceeds order of 10 kV/100 ns. If thecircuit is not properly designed, the switching circuit willradiate EM noise in wide frequency spectrum at DC to a
few tens MHz. Once this radiation spreads out to envi-

T. Shintake / Proceedings of the 2004 FEL Conference, 90-95

93(1) Signal modulation of rf-carrier and de-modulation.
(2) Frequency up and down conversion.
(3) Local frequency generation using PLL.
(4) Level adjustment according to the beam intensity.
All of those functions can be integrated into a chip basedon ASIC technology. We may also realize those circuits
via traditional design like circuit boards in a shielding box.
With ASIC, we may eliminate shielding box, since thechip size is much smaller than the typical wavelength of
signal, thus it is in-sensitive to noise environment. Also it
is easy to utilize the laser trimming technique to adjust
the balance of mixers, or the amplifier gain, thus it isfairly easy to produce repeatable parameter for many
Fig. 2. Klystron pulse modulator for SCSS project. All number of circuit in mass production, which resulting in
HV components are installed in metallic shield tank, and reducing the fabrication cost.
filled with oil.
Additionally, standardization of basic functions listed
above by means of ASCI design will make easier to shareronment of accelerator system, its runs along the power the circuit design between each accelerator design groups,
line or control line, finally cause various effects on the which will enhance the R&D efficiency.
system. Most sensitive part is the beam diagnostics, anduser experiments.
THE MECHANICAL STRUCTURE
In order to cure this noise, we have to design the noise
Mechanicalsupport structure of accelerator component
source not to radiate to outside, or to keep the rush current
within the closed circuit. To do this, the Faraday cage is also important subject for stability issue. Since the Xconcept provides best guideline on hardware design. As FEL requires very small electron beam emittance: 1
shown in Fig. 2, if the switching circuit is perfectly sur- π.mm.mrad, the beam size in the undulator becomesrounded by a closed metallic boundary, no EM field will about 100 micron-meter or smaller. We need to keep overcan leak out. But weed to make holes to provide in and lapping of the electron beam and X-ray radiation throughout power feeds, or control lines. We can stop the noise undulators, therefore, the position stability of focusing
leakage through these holes and wires by properly choos- component has to be very stable.
Traditionally we use a support structure made by steel
ing filter, so called, common-mode choke. Today, suchframework to support Q-magnet, and position of the beamfilters can be easily found in market.
Fig. 3 shows the klystron power supply developed in pipe is about 1 m high from floor. Since the heat capaciSCSS project based on Faraday-cage concept. All of the tance of the steel framework usually not so big, theswitching device and high voltage components of the framework temperature always follows the air temperamodulator are installed into a metallic shield box made by ture. If the room temperature changes 1 deg.C, the steel
stainless panels, and filled with oil to prevent the circuit framework will expand 12 micron-meter, which is alreadyfrom high voltage discharge. The stainless panels are close to the tolerance limit of the alignment.
If the temperature distribution around the steel framestandard components designed for water supply, so it is
not expensive. This design is also desirable to isolate high work is not uniform, it will cause transverse displacement.
voltage circuit from the environmental change, i.e., the If there is forced air flow inside tunnel, or a heat source
located nearby (a lump or cooling water), this type of dishumidity, temperature, or dust contamination.
The same guideline can be applied to all the circuit placement becomes not negligible.
The author would like to suggest the following designcomponents in liner accelerators.
for support structure in X-FEL.
ASIC DEVICE(1) Locate beam height as low as possible. Lower
structure makes vertical and transverse displaceASIC: Application Specific Integrated Circuit is widely
ment due to thermal expansion smaller, and also
used in rf, wireless and optical fiber communications, andprovides higher stiffness.
also electrical test equipments [5]. This technology is(2) Use low thermal expansion material.
based on silicon and germanium integrated circuit, which(3) Use massive volume structure rather than frame
suitable to design frequency up- and down- converting
work. Larger heat capacity makes sensitivity tomixer and amplifier in rf-detector and modulator, or BPM
ambient temperature change smaller. Larger mass
detector. In linear accelerators, rf: radio-frequency power
makes vibration amplitude from external force
is used as the energy source of particle acceleration, or
smaller.
beam monitoring signal. There are basic functions ofSingle-Pass FELs

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T. Shintake / Proceedings of the 2004 FEL Conference, 90-95

Units
ChemicalformulaThermalexpansion
Thermalconductivity
Specific heat
DensityCompressive
strength *Tensilestrength *SteelTable-2. Material Properties for Support Structure
Alumina Granite Concrete AnocastTM

0.24

0.03

0.014

0.24~0.3
2.4

0.23~0.26
2.32

0.35
2.6

0.16
2.2

30~100110-117350

650-1100

-

15.2

25.5

48

10-6 /C

6~15

7

5 ~ 157 ~ 1317

W cm/°C

0.8~2

0.17~0.29

0.02

0.01

Cal/g°C
g/cm3

0.1
7.8
10002000

0.19
3.8

0.2
2.6~2.7

~2000

130

MPa

1800

260-300

Fused Silica

0.45**Al2O3

MPa

Cordierite
2MgO-2Al2O35SiO2
1~0.1 *
1.7 **

Epoxy resin
quartz

Fe(C)

SiO2

* room temperature - **~25ºC through ±1000ºC
Table 2 compares several materials for support structure.
Among them, candidates for the support structure will becordierite ceramic or fused silica. In industrial ceramic
factory, the cordierite has been used as high-voltage bushing operating at high temperature in a dust cleaning
chamber at the power generation plant. Therefore, technology to fabricate meter-size cylinder with cordierite andfixing to metal flange exists in ceramic factory [6]. We
may employ the cordierite ceramic tube as the stable support with reasonable cost. Fig. 3 shows our ceramic support for SCSS project, on which focusing Q-magnet and
BPM will be installed in the undulator line. The outersurface of the ceramic is covered by soft polymer sponge(black color) for protection. Inner volume is filled withsand to damp mechanical vibration. With careful measurement, we found the thermal expansion ratio was
1.9x10-6 (1/C).

The same concept can be applied to large scale magnetic device, such as the undulator. In the undulator, linear
arrays of permanent magnet generate periodic transverse
field. Since the field is fairly uniform in transverse plane,
we do not need precise positioning of the undulator.
However, the field intensity is a strong function of the gap
size of two magnet arrays, we need to precisely maintainthe relative position of the gap, tolerance is order of 1
micron-meter.
In the undulator design, steel structure have been used
to hold the magnetic array. However, as mentioned above,the steel frame work does not have enough heat capacity,
thus it changes the dimension with ambient temperaturechange.
The author would like to suggest the granite table as the
support structure for the magnet array of the undulator.
From the thermal expansion point of view, cordierite will

Fig. 3. Ceramic material is suitable to stable support for accelerator component.

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T. Shintake / Proceedings of the 2004 FEL Conference, 90-95

95

Fig. 4. Granite table as the support structure of the undulator magnet. Massive granite will provide high rigidity against various deformation forces. In-situ field measurement will be performed by movable probe, whose linear guide has to be integrated into the chamber.
be the best choice, but ceramic factory can not handle a
few meter long structure. If we chose granite, we can finda few meter long solid block with reasonable cost. Casted
concrete, with steam heat treatment, may be alternative
candidate, but we need a careful study on slow dimension
change with drying for few years.
Fig. 4 shows illustration of the idea. Massive granite
will provide high rigidity against various deformation
forces. The assembly and field tuning will be made in alaboratory, the we transport the undulator to the tunnel.
During this transport, various external forces will be applied and also internal force due to temperature change
will cause deformation. Therefore, the support structure
has to have high rigidity.
In the X-ray FEL, since the field tolerance is very tight,
while the beam quality will not be good as one in thestorage ring, and also dark-current emission from the linear accelerator cause degradation of magnetic property.

Therefore, in-situ field measurement will be non evitableprocess and scheduled measurement has to be repeatedonce per year, for example. As shown in the figure, in-situ
field measurement will be performed by a movable probe,
whose linear guide will be integrated into the chamber.
When we install the focusing elements and undulators,
the tunnel becomes as Fig. 5. Beam line height will be 1mor lower, the undulator will be accessible from top cover.
The total length of undulator line will be 100m or longer
in X-FEL.

CONCLUSIONThe X-ray FEL based on SASE mode request revolutionary improvement on accelerator performance. The
super conducting accelerator technology will solve a partof the jitter problem, but at the same time it may introduce new type of difficulties. Now, the X-FEL is a big
challenge to the accelerator community. Continuous persevering efforts in each detail will be requested.

REFERENCES

Fig. 5. Accelerator tunnel image. Focusing elements siton the ceramic cylinders, and undulators are on the
granite table.

[1] Hitoshi Tanaka et. al., “Top-up Operation at SPring-8- Towards Maxmizing the Potential of a 3rd Generation Light Source”, EPAC2004.
[2] Active Power Inc.,
http://www.activepower.com/[3] Okamura Laboratory Inc.,
http://www.okamura-lab.com/index.htm[4] Shizuki electric Co.,
http://www.shizuki.co.jp/electric/v_lineup.html[5] for example, Maxim Integrated Products, Inc.,
http://www.maxim-ic.com/asics.cfm[6] for example, Daito Co.,
http://www.daito-otk.co.jp/frame15.htm

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SCHEME FOR GENERATION OF SINGLE 100 GW 300-AS PULSE IN THE
X-RAY SASE FEL WITH THE USE OF A FEW CYCLES OPTICAL PULSEFROM TI:SAPPHIRE LASER SYSTEM
E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract
Femtosecond optical pulse interacts with the electron
beam in the two-period undulator and produces energy
modulation within a slice of the electron bunch. Then theelectron beam enters the first part of the X-ray undulator
and produces SASE radiation with 100 MW-level power.
Due to energy modulation the frequency is correlated to thelongitudinal position, and the largest frequency offset corresponds to a single-spike pulse in the time domain whichis confined to one half-oscillation period near the central
peak electron energy. After the first undulator the electron
beam is guided through a magnetic delay which we use toposition the X-ray spike with the largest frequency offset
at the ”fresh” part of the electron bunch. After the chicane
the electron beam and the radiation enter the second undulator which is resonant with the offset frequency where
only a single (300 as duration) spike grows rapidly. The
final part of the undulator is a tapered section allowing toachieve maximum output power 100-150 GW in 0.15 nm
wavelength range.

INTRODUCTION
With the realization of the fourth-generation lightsources operating in the X-ray regime [1, 2], new attoscience experiments will become possible. In its initialconfiguration the XFEL pulse duration is about 100 fs,
which is too long to be sufficient for this class of experiments. The generation of subfemtosecond X-ray pulses
is critical to exploring the ultrafast science at the XFELs.
The advent of attosecond X-ray pulses will open a new
field of time-resolved studies with unprecedented resolution. X-ray SASE FEL holds a great promise as a sourceof radiation for generating high power, single attosecond
pulses. Recently a scheme to achieve pulse duration down
to attosecond time scale at the wavelengths around 0.1 nm
has been proposed [3]. It has been shown that by using
X-ray SASE FEL combined with terawatt-level, sub-10fs Ti:sapphire laser system it will be possible to produce
GW-level X-ray pulses that are reaching 300 attoseconds
in duration. In this scheme an ultrashort laser pulse isused to modulate the energy of electrons within the femtosecond slice of the electron bunch at laser frequency.
Energy-position correlation in the electron pulse results inspectrum-position correlation in the SASE radiation pulse.
Selection of ultra-short X-ray pulses is achieved by us-

MOBOS02

ing the monochromator. Such a scheme for production of
single attosecond X-ray pulses would offer the possibility
for pump-probe experiments, since it provides a precise,
known and tunable interval between the laser and X-ray
sources.
In this paper we propose a new method allowing to increase output power of attosecond X-ray pulses by two orders of magnitude. It is based on application of sub-10fs laser for slice energy modulation of the electron beam,
and application ”fresh bunch” techniques for selection of
single attosecond pulses with 100 GW-level output power.
The combination of very high peak power (100 GW) andvery short pulse (300 as) will open a vast new range of applications. In particular, we propose visible pump/X-ray
probe technique that would allow time resolution down tosubfemtosecond capabilities. Proposed technique allows to
produce intense ultrashort X-ray pulses directly from the
XFEL, and with tight synchronization to the sample excitation laser. Another advantage of the proposed scheme isthe possibility to remove the monochromator (and other Xray optical elements) between the X-ray undulator and asample and thus to directly use the probe attosecond X-ray
pulse.
Operation of 100 GW attosecond SASE FEL is illustrated for the parameters close to those of the European
XFEL operating at the wavelength 0.15 nm [1]. Optimization of the attosecond SASE FEL has been performed withthe three-dimensional, time dependent code FAST [5] taking into account all physical effects influencing the SASE
FEL operation (diffraction effects, energy spread, emittance, slippage effect, etc.).

HIGH POWER ATTOSECOND FACILITY
A basic scheme of the high-power attosecond X-ray
source is shown in Fig. 1. An ultrashort laser pulse is used
to modulate the energy of electrons within the femtosecond slice of the electron bunch at laser frequency. The
seed laser pulse will be timed to overlap with the central
area of the electron bunch. It serves as a seed for modulator which consists of a short (a few periods) undulator.
Following the energy modulator the beam enters the baseline (gap-tunable) X-ray undulator. In its simplest configuration the X-ray undulator consists of an uniform input
undulator and nonuniform (tapered) output undulator separated by a magnetic chicane (delay) as it is shown in Fig. 2.

Available online at http://www.JACoW.org

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 96-99

97

Figure 1: Schematic diagram of high power attosecond X-ray source.

Figure 2: Design of undulator system for high power attosecond X-ray source.
The process of amplification of radiation in the input undulator develops in the same way as in conventional X-ray
SASE FEL: fluctuations of the electron beam current serveas the input signal. When an electron beam traverses anundulator, it emits radiation at the resonance wavelength
λ = λw (1 + K 2 /2)/(2γ 2 ). Here λw is the undulator period, mc2 γ is the electron beam energy, and K is the undulator parameter. In the proposed scheme the laser-driven
sinusoidal energy chirp produces a correlated frequency
chirp of the resonant radiation δω/ω  2δγ/γ.

few mJ can result in electron energy modulation amplitude
higher than 30-40 MeV. In few-cycle laser fields high intensities can be ”switched on” nonadiabatically within a few
optical periods. As a result, a central peak electron energy
modulation is larger than other peaks (see Fig. 3). This relative energy difference is used for selection of SASE radiation pulses with a single spike in time domain. Single-spike
selection can effectively be achieved when electron bunch
passes through a magnetic delay and output undulator operating at a shifted frequency.

Our concept of attosecond X-ray facility is based on theuse of a few cycle optical pulse from Ti:sapphire laser system. This optical pulse is used for modulation of the energy of the electrons within a slice of the electron bunchat a wavelength of 800 nm. Due to extreme temporal confinement, moderate optical pulse energies of the order of a

Operation of proposed attosecond facility is illustrated
with Figs. 4-6. The input undulator is a conventional 0.15
nm SASE FEL operating in the high-gain linear regime.
This undulator is long enough (60 m) to reach 100 MWlevel output power (see Fig. 2). After the input undulator
the electron beam is guided through a magnetic delay (chi-Single-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 96-99

Figure 3: Left plot: electric field strength within femtosecond laser pulse. Right plot: energy modulation of electron
bunch at the exit of the modulator.

Figure 4: Energy in the radiation pulse versus undulator
length. Marks 1, 2, and 3 show the end points of the 1st,
2nd, and 3rd undulator sections, respectively.

Figure 6: Shot-to-shot fluctuations of the radiation pulse
after monochromator with 0.5% linewidth tuned to the frequency of the main maximum. Undulator length is 100 m.

cane). The trajectory of the electron beam in the chicane
has the shape of an isosceles triangle with the base equal
to L. The angle adjacent to the base, θ, is considered tobe small. Parameters in our case are: L = 4 m, θ = 1.5
mrad, compaction factor Lθ2 = 8µm, extra path lengthLθ2 /2 = 4µm, horizontal offset Lθ/2 = 3 mm. In thepresent design we have only 4 µm extra path length for theelectron beam, while the FWHM length of electron bunch
is about 50 µm. Calculations of the coherent synchrotron
radiation effects show that this should not be a serious limitation in our case.
Passing the chicane the electron beam and seed SASE
radiation enter the output undulator operating at an offset
frequency. We use a magnetic delay to position the offset frequency radiation at the ”fresh” part of the electron
bunch. This seed single spike at an offset frequency starts
interacting with the new set of electrons, which have no energy modulation, since they did not participate in the previous interaction with optical laser pulse. This is the essenceof the ”fresh bunch” techniques which was introduced in[4].
In the output undulator seed radiation at reference frequency plays no role. However, single spike at an offset

frequency is exponentially amplified upon passing throughthe first (uniform) part of the output undulator. This part islong enough (30 m) to reach saturation. The power level atsaturation is about 20 GW. The most promising way to extend output power is the method of tapering the magnetic
field of the undulator. Tapering consists in slowly reducing the field strength of the undulator field to preserve theresonance wavelength as the kinetic energy of the electronschanges. The strong radiation field produces a ponderomotive well which is deep enough to trap the particles. The
radiation produced by these captured particles increases
the depth of the ponderomotive well, and they are effectively decelerated. As a result, much higher power can beachieved than for the case of a uniform undulator. At the total tapered undulator length of 20 m, the single-spike poweris enhanced by a factor of five, from 20 GW-level to 100
GW-level. Figure 6 shows temporal characteristics of theradiation pulse at the exit of the undulator after monochromator with 0.5% linewidth. It is seen that the method proposed in this paper allows direct production from XFEL of
single 100 GW-level X-ray pulses with FWHM duration of
300 as.

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99

Figure 5: Temporal (left column) and spectral (right column) evolution of the radiation pulse along the undulator. Upper,
middle, and lower plots correspond to the undulator lengths of 57, 85, and 100 m. Dashed line shows energy modulationof the electron bunch.

CONCLUSION
Today there are at least two possible attosecond X-ray
sources for light-triggered, time-resolved experiments associated with the X-ray SASE FEL: the ”attosecond X-ray
parasitic” [3] and the ”attosecond X-ray dedicated” source
mode proposed in this paper. The simplest way to obtainattosecond X-ray pulses from XFEL is to use ”parasitic”
technique which is proposed in [3]. It also would offer
the possibility of providing a beam to a pump-probe experiments with the XFEL that has a precise, known andtunable time interval between the laser and X-ray sources.
More power of attosecond pulse could be obtained using
the XFEL for dedicated attosecond X-ray pulse production
as described in this paper.

REFERENCES[1] P. Audebert et al., “TESLA XFEL: First stage of the X-ray
laser laboratory – Technical design report (R. Brinkmann etal., Eds.)”, Preprint DESY 2002-167.
[2] The LCLS Design Study Group, LCLS Design Study Report, SLAC reports SLAC- R521, Stanford, 1998.
[3] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Optics
Communications 237(2004)153.
[4] L. H. Yu and I. Ben-Zvi, Nucl. Instrum. and Methods
A393(1997)96.
[5] E. L. Saldin, E. A. Schneidmiller and M. V. Yurkov, Nucl.
Instrum. and Methods A 429(1999)233.

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Y.-C. Chae et al. / Proceedings of the 2004 FEL Conference, 100-103

AN EXPERIMENTAL STUDY OF THE BEAM-STEERING EFFECT ON
THE FEL GAIN AT LEUTL’S SEGMENTED UNDULATORS*
Y.-C. Chae#, A.H. Lumpkin, M. Erdmann, J.W. Lewellen, and S.V. Milton
Advanced Photon Source Argonne National Laboratory Argonne, Illinois 60439 USA
Abstract
The electron trajectories at the low-energy undulator
test line (LEUTL), a self-amplified spontaneousemission (SASE) free-electron laser (FEL) facility at
Argonne, were routinely corrected during the user run
in order to deliver maximum radiation power to theuser. Even though we knew from experience that SASE
gain at the segmented undulators was dependent on the
trajectory, the quantitative understanding of steering
effects associated with the specific trajectory waslacking. Recently Tanaka et al. [1] proposed ananalytical model for the single-kick error (SKE) effect.
Since the LEUTL has eight segmented undulators, we
performed the first measurement of SKE on the FEL
gain. In the experiments we varied the corrector
strength up to the critical angle, and the gain over theundulator was measured for each corrector setting. The
results were compared with the analytical model and
GENESIS simulations. We also measured the e-beam
positions and SASE intensities over the undulators. The
experimental data were analyzed and their results werereproduced by GENESIS simulation. The simulation
condition, including the measured not-so-ideal
trajectory, was used to predict performanceenhancements that could be achieved by upgrading ebeam current, e-beam emittance, or trajectory control.

EXPERIMENTAL SETUP
The low-energy undulator test line (LEUTL) is theAdvanced Photon Source’s self-amplified spontaneousemission (SASE) free-electron laser (FEL) facility,
which has shown high gain and saturation near 530 nm
and 385 nm, as reported elsewhere [2]. The schematicof the facility is shown in Fig. 1, which includes a
photocathode rf-gun, a 650-MeV linac, 3-screen
emittance measurement area, and undulators withdiagnostic stations between them.

Figure 1: Schematic of APS SASE FEL experiment.
___________________________________________*Work supported by the U.S. Department of Energy, Office of Basic
Energy Sciences, under Contract No.W-31-1090-ENG-38.
#
chae@aps.anl.gov

MOBOS03

The experiments were performed around the fifth
undulator ID-5, which also includes a horizontally
focusing quadrupole, a steering coil, and a reflecting
mirror that transports the radiation to VUV cameras, as
shown in Fig. 2.
VUV-5

VUV-4

Q4, H4

ID-5

Q5, H5Figure 2: Schematic of a segmented undulator used forsingle-kick-error (SKE) measurement; shown are
quadrupoles Q4 and Q5 with steering coils H4 and H5,
mirror and cameras VUV-4 and VUV-5, and the fifth
undulator ID-5 over which we measure the gain of
SASE radiation.
During experiment we steered the orbit by using theH4 corrector. For a given H4 strength we record theradiation images by using cameras VUV-4 and VUV-5
before and after undulator ID-5. The undulator
radiation by SASE was used to measure the gain overthe undulator. The coherent transition radiation (CTR)
was used not only to measure the electron beam’s
microbunching but also to measure the beam’s positionin order to estimate the steering angle. The CTR isgenerated by interaction of a 6-µm-thick Al foil and thebeam, as describe in Ref. [3]. The angle estimate isbased on the fact that in the horizontal plane theundulator is a drift space where the e-beam’s trajectoryis straight. For each radiation type, SASE or CTR, wetook near-field and far-field imaging. Because of thestatistical nature of the SASE process, we took 100
images of each type of radiation for a given steering
angle.
At the beginning of the experiment we established areference orbit that should provide exponential gain
over ID-5 but should not be saturated there. The
experimental conditions were radiation wavelength
λ=130 nm, beam energy E=439 MeV, charge Q=250
pC, FWHM pulse length σt=250 fs, energy spread
σE=0.15%, and normalized emittance εx/εy=4.5/3.5 π
mm-mrad, respectively. The measured SASE intensity
along the undulators is shown in Fig. 3, where two
results from processing near-field and far-field images
are presented. The horizontal axis refers to the location
after the nth-undulator.
Radiation power or intensity shown in Fig. 3 wasestimated by integrating the intensities of image asfollows: 1) project 100 images into the horizontal orvertical axis in order to obtain the profile in either

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plane, 2) take the average of 100 profiles to make asingle profile representing the average state of themeasurement condition, 3) set the baseline of the
profile to zero as a background removal, and 4)
integrate the profile in order to obtain the total intensity.
Thus this total intensity represents the averaged powerof 100 radiation pulses resulting from a given
experimental condition. Since the background of the
profile is different in the horizontal and vertical planes,
the resultant intensities Ix and Iy are not necessarily thesame. In order to have a unique quantity, we take theaverage of the two quantities I=(Ix+Iy)/2. The unit ofintensity obtained this way is arbitrary, but the realradiation power is proportional to this quantity so that
we can estimate the gain.

determined. We observed that the far-field images ingeneral provide better-defined profiles with higher
intensities. Thus we decided to use far-field images inmeasuring the intensity of the SASE pulse in the SKE
experiment where we vary the steering angle.

SINGLE-KICK ERROR (SKE)
EXPERIMENT
According to Tanaka’s model [1] the gain will bedegraded by the SKE due to two effects: 1) themismatch between incoherent radiation with angle ofincidence and coherent radiation with its wave-front
normal in the z-direction and 2) the smearing of microbunching. Since the analysis of microbunching is
incomplete when providing the results in bounded form,
we only refer to the first case where we compare theexperiment and the theory. The model predicts that thegain will be degraded according to
Lg ' =

where x = θ / θ c . The

Lg
1 − x2

critical

(1)

,

angle

is

definedas θ c = λ / Lg , where λ is the radiation wavelength
Figure 3: The z-dependent SASE power measurements
at ID-2,4,5,6,7; both far-field and near-field results areincluded for comparison.

Figure 4: Horizontal profiles of undulator radiation
images at two different locations at ID-2 and ID-4. The
images from ID-2 in small-gain are displayed on theleft and the ones from ID-4 in exponential gain arecompared on the right. The far-field images in red
provide better-defined profiles than the near-field
images in black which have broader shoulders.
Far-field and near-field images were examined inorder to explain the discrepancies shown in Fig. 3. We
found that radiation profiles from near-field images
have a broader shoulder than the far-field images
shown in Fig. 4, which were taken at VUV-2 andVUV-4. Whether this shoulder resulted from thevariation in trajectory or from the reflection in the lighttube due to the limited acceptance is yet to be

and Lg is the gain length of ideal trajectory, and θ is thesteering angle.
After we established the reference trajectory
described in the previous section we adjusted the angleof trajectory by varying the corrector H4. A calibration
was performed on H4 and found that it can steer 0.34
mrad/A. Since the critical angle of this experiment wasestimated to be 0.4 mrad we decided to vary H4 by ±1
A with the respect to the currently set -0.7 A. For each
H4 setting we measured the intensities at VUV-4 andVUV-5. Even though VUV-4 measurements shouldn’t
depend on the H4s, the repeated measurements werenecessary in order to make sure that we could detect
drift of beam condition while we were taking data forfive hours.
The intensities as a function of H4 are shown at the
top of Fig. 5. The black curve represents the intensity at
VUV-4 showing we maintained steady beam operation,and the red curve gives the results at VUV-5 showing
the significant variation on average power over the H4s.
We also note large fluctuations at VUV-5, acharacteristic of exponential gain regime. The ratio of
average power between VUV-4 and VUV-5 is the gain
to be compared with the SKE model of Eq. (1). At thesame time we also acquired CTR images. The centroidsof images representing the e-beam positions are also
shown in Fig. 5 as a function of H4.
Data shown in Fig. 5 were processed in terms of gain
and steering angle. The result is fitted by Eq. (1) withtwo parameters, the offset angle θ0 in slightly
generalized x=(θ0-θ)/θc and the gain length Lg. We
found θ0 close to zero and Lg equal to 1.6 m. The
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shown in Fig. 6. Since the critical angle with λ=130 nm
and Lg=1.6 m is 0.28 mrad, two data points whose
steering angles are greater than 0.3 mrad are out ofrange but still had small gain. One data point near 0.1
mrad, whose gain is far smaller than theory predicts,
corresponds to the corrector setting H4=-0.2 A where
the beam position didn’t respond to the setting, as was
revealed in Fig. 5. Thus we are suspicious about thisdata point, and we may disregard its validity in its gain.
Other than that we have good agreement between themeasurement and the model prediction.

Figure 5: SASE radiation intensities measured bycameras VUV-4 and VUV-5 as a function of H4 (top)and electron beam position estimated by CTR images
as a function of H4 (bottom)

simulation we found the solution at 380 A, and in the
SASE simulation the solution was 550 A for a given
250-fs pulse length.
Once we settled on the beam parameters, we varied
the corrector in the GENESIS simulations in asegmented undulator configuration; both steady-stateand SASE simulations were performed. All results,
including experiment, theory, and simulations, areincluded in Fig. 7 and show good agreement with eachother. We note that the theory and steady-state
simulations have better agreement because theanalytical model assumed DC beam. The results bypulsed beam, which represents a more realistic
situation, indicates that the ideal gain length should beslightly shorter than 1.6 m in order to have a better fit.

Figure 7: Gain vs. steering angle: experiment (diamondsymbol), theory (black line), steady-state (SS)simulation (green line with symbol), time-dependent(SASE) simulation (blue line with symbol).

TRAJECTORY ANALYSIS
Eq. (1)
Lg=1.6 m

Figure 6: Measured gains as a function of steering
angle compared with theory (Eq. (1)).

COMPARISON WITH SIMULATION
We used the GENESIS program [4] in order tocompare the experimental results with simulation. The
simulation conditions were the same as theexperimental condition specified in the previous
section. In the simulation we needed to vary the beam
current in order to find the condition resulting in thegain length equal to 1.6 m. In the steady-state

MOBOS03

As we verified the steering effect quantitatively, we
gained a better understanding of the importance oftrajectory control in the segmented undulators.
However, we questioned how much we could improve
the FEL performance by correcting the trajectory. With
this as motivation, we tried to reproduce by simulations
the measured trajectory and z-dependent gains. Then,the simulation conditions found this way could be used
to benchmark the effectiveness of trajectory control vs.
upgrading other beam parameters such as beam current
and beam emittances.
The first requirement for trajectory analysis is todetermine the trajectory. Instead of relying on beam
position monitors (BPMs) installed in the LEUTL
tunnel, we used CTR images for determining e-beam
positions. As usual, 100 shots of images were taken at
the camera stationed between the undulators.
The trajectory responsible for the gain shown in Fig.
3 has been determined experimentally, and its results
are depicted in Fig. 8, which includes the centroid
coordinates of the e-beam and the alignment laser on
the viewing screen. The difference between the two
will be the beam position with respect to the alignment

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laser; this trajectory is shown at the bottom of Fig. 8.
Since not all stations have VUV or diagnostic cameras,
we could only measure positions at VUV-2,4,5,6,7.
Even though we measured both horizontal and vertical
positions, we only took the horizontal trajectory into
account in our simulation.

Figure 8: Trajectory measurement along the undulators
by using CTR images: (top) electron beam centroid,(middle) alignment laser beam, (bottom) electron beam
positions with respect to the alignment laser at VUV2,4,5,6,7.
Since our measured trajectories were limited, we
tried several simulated trajectories with right betatronoscillations. The most successful “guesstimate” isdepicted in Fig. 9 together with measured beam
positions. With these simulated trajectories we could
reproduce the z-dependent gain quite accurately, as
shown in Fig. 10. Because of this good agreement ingain measurement, we use this simulated trajectory
testing in several performance upgrading scenarios.

arbitrary but within an achievable envelope in the near
future as gun technology develops. Trajectory control
requires improving BPM electronics in terms ofsensitivity and gain bandwidth. The combination of
improvements in both beam and trajectory is the ideal
upgrade path, but we emphasize controlling trajectory
could be easy and its effect would be immediate as
evidenced by the simulation study shown in Fig. 11.

Figure 10: Measured gain at ID-2,4,5,6,7 and thecorresponding simulation results. Power is normalized
by the power at ID-2 or VUV-2.

Figure 11: Comparison of performance upgrade
options: 1) trajectory correction, 2) current increase, 3)
emittance reduction.

SUMMARY
We measured the SKE effect for the first time, andwe obtained good agreement between theory,
experiment, and simulation. We also analyzed ameasured trajectory to show that improving trajectory
could be as important as improving the beam qualities.

REFERENCES
Figure 9: Measured beam positions and their simulated
trajectories used in the GENESIS simulation.
For definite comparison we put three upgrade
scenarios into one picture: 1) increase the beam current
from 950 A to 1250 A, 2) reduce the beam emittancefrom 4.5/3.5 π mm-mrad to 3/3 π mm-mrad, and 3)
correct trajectory to an ideal trajectory. The assumed
amount of current and emittance improvement are[1] T. Tanaka et al., “Consideration on an Alignment
Tolerance of BPMs for SCSS Undulator Line,”
Proc. 25th International FEL Conference,
September 9-12, 2003, Japan[2] S. V. Milton et al., Science 292, 2037 (2001).
[3] A. H. Lumpkin et al., Phys. Rev. Lett. 86, 79(2001).
[4] S. Reiche, Nucl. Instrum. Methods Phys. Res. A
429, 243 (1999).

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START-TO-END INJECTOR AND LINAC TOLERANCE STUDIES FOR
THE BESSY FEL∗
M. Abo-Bakr† , M.v. Hartrott, J. Knobloch, B. Kuske, A. Meseck, BESSY, Berlin, Germany
Abstract
BESSY is proposing a soft X-ray FEL user facility in
Berlin, delivering short and stable photon pulses in the
wavelength range of 62 nm ≤ λ ≤ 1.2 nm by utilizing up
to four cascaded High Gain Harmonic Generation (HGHG)
stages [1]. To optimize the FEL performance of the cascaded HGHG stages extensive Start-to-End (S2E) simulations have been carried out. To test the quality of the chosenconfiguration with respect to the sensitivity towards various
error sources tolerance studies from the injector to the linac
end have been performed. Procedures and results of thesestudies are presented.

INTRODUCTION
Based on it’s experiences in operating high brilliant synchrotron light sources the Berliner ElektronenspeicherringGesellschaft für Synchrotronstrahlung (BESSY) is proposing a 2.3 GeV linac-based single-pass Free-Electron Laser(FEL) user-facility for the wavelength range from 62 nm≤ λ ≤ 1.2 nm. To generate very short photon pulses of≤ 20 fs duration and to ensure stable radiation output a cascaded High Gain Harmonic Generation (HGHG) scheme
has been designed. A detailed description of the BESSY
FEL can be found in the recently completed Technical Design Report [1].
Due to the FEL process the quality of the seeded partof the electron bunch, mainly the energy spread, after one
HGHG stage is significantly reduced and no longer suitable for further stages. For that reason the “fresh bunchtechnique” [2] is applied, providing a fresh part of the electron bunch to to all HGHG stages and the final amplifier.
Taking timing jitter sources and synchronization limits into
account, a flat top pulse of about 700 fs duration is required.
In combination with the requested 1.8 kA peak current a total bunch charge of 2.5 nC will be needed.
To deliver such an electron beam to the FEL lines, a very
long bunch of 40 ps FWHM duration is generated in thephoto-injector. By means of two magnetic bunch compression stages at energies of 220 MeV and 750 MeV in combination with an energy-position correlation in the longitudinal phase space (chirp) the longitudinal bunch density andthus the peak current is increased to the requested values.
Aim of this studies was to verify that compression, timing and energy variations at the linac end due to the expected “shot-to-shot” errors stay within tolerable limits.
∗ Funded by Bundesministerium fr̈ Bildung und Forschung, the state ofBerlin and the Zukunftsfonds Berlin† Michael.Abo-Bakr@bessy.de, Albert-Einstein-Strasse 15, 12489
Berlin, Germany

MOPOS03

For that purpose, start-to-end simulations have been performed, beginning at the injector cathode and ending at thefirst HGHG undulator entrance.

ERROR SOURCES AND THEIR EFFECTS
In the simulations, errors in the injector and linac part areinvestigated, that influence mainly the dynamics of the longitudinal phase space. Nevertheless, the horizontal emittance can also be affected due to the peak current dependency of wake field and CSR effects.
Injector: for the injector (rf gun and first, eight-cavity“booster” module), timing errors and intensity variationsof the photo cathode laser are considered as well as phaseand amplitude errors of the rf fields in the injector gun andthe booster cavities.
For the main linac tolerance studies, phase and amplitude rf field errors are considered. No error correlation between neighbouring linac cavities is assumed. Vibrations
and field strength variations of the magnets on a “shot-toshot” time level haven’t been considered as well as vibrations of the rf modules, which would cause the electron
bunches to scan “off axis” transverse electric field components in the cavities. Mechanical vibrations of the cavities
are considered within the microphonics simulations, incorporated into our assumptions on cavity phase and amplitude errors.

Figure 1: Single error simulations for the BESSY FEL injector: longitudinal phase space at the booster module end
for ±2.5 ps timing jitter (blue), ±1 MV/m gun amplitude(red) and ±5◦ gun phase errors (green). The reference
curve is also plotted (black).

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At the end of the booster module, all injector errors resultin a time and energy jitter of the bunch center with respect
to the undisturbed bunch. In addition, the momentum position correlation (chirp) is changed, when the bunch passes
the booster module with a time or, equivalently, a phasejitter. All injector error sources couple by “time of flight”
effects in the non-relativistic part of the injector. Thus theresulting time, energy or chirp jitter at the injector end can
not be easily associated to a single error source.
In Figure 1 longitudinal phase space distortions at theend of the booster module due to injector errors are shown.
For demonstration exemplary single error types such as±2.5 ps timing jitter, ±1 MV/m gun amplitude and ±5◦
gun phase have been applied. In all cases the mean energy
and z-position (for a fixed time of flight) changes as wellas the momentum chirp. The effects of gun amplitude andphase errors dominate at the chosen error weighting, while
the changes due to the timing jitter are small.
Main linac: the effect of injector errors on the final longitudinal phase space at the linac end are illustrated in Figure 2. Both a mean energy jitter and a time jitter of thebunch are investigated.
The main effect of an energy jitter from the injector is
the transformation into a time jitter in the bunch compressors and thus at the linac end (upper graph of Figure 2).
For an HGHG FEL with several “fresh bunch” stages thiscauses two problems: to ensure, that the seeding laser hits
the electron bunch always in its flat top, high current part,the flat top length has to be increased at both ends by the
expected time jitter. If the jitter exceeds the expectations,either the initial seed for the first HGHG stage or the lastseed for the final amplifier interacts with a lower current
region on the bunch edges. In both cases the final radiation
output might be significantly reduced.
A second problem is a variation of energy looking to a
fixed longitudinal bunch position, just like the HGHG seeds
do. It is caused by the the time jitter at the linac end inconnection with the momentum chirp, which was required
for the bunch compression. As every HGHG stage is optimized for a special energy this leads to a mismatch of theseeding and the insertion device resonant wavelength. Theenergy modulation and, later on, the bunching and the radiator output is reduced.
A time jitter from the injector not only leads to a time jitter at the linac end, with all the drawbacks just mentioned.
It also strongly influences the bunch compression, by modifying the momentum chirp (lower graph in Figure 2), which
can cause a significant output power degradation of a cascaded HGHG FEL.
To little compression results in a lower peak current witha longer flat top. The smaller peak current reduces the radiator output of the first HGHG stage, which acts as seed forthe second one. Clearly the reduced seed power produces
less momentum modulation in the second modulator. Thus
the output power of the second radiator is not only reducedby the lower peak current but also by the smaller bunching.
Too much compression leads to a higher peak current
with a shorter flat top. If the flat top becomes too short,again either the first or the last seed hits the edges of the flat
top with less peak current. Even if this is not the case, toohigh peak currents can be disadvantageous: the increased
output of the first radiator produces a stronger momentum
modulation in the second modulator. Of course the strengthof the dispersive section, converting the momentum into acurrent density modulation, is fixed, and one will end up
with an over-compressed bunch. This reduces the output of
the second radiator, but is counteracted to a certain degreeby the higher peak current.
Finally, also in the case of an injector time jitter thesliced energy varies, leading again to a mismatch of seeding and resonant wavelength, as already described above.

TOLERANCE BUDGET

Figure 2: BESSY HGHG FEL: variations of the final longitudinal phase space (high energy beamline) due to energy(top) and timing (bottom) jitter from the injector.

Assumptions on the error sizes arise from experiences,made with PITZ at DESY/Zeuthen, the FZ Rossendorf andthe Max Born Institute (MBI) and result from RF control
simulations.
Two cases have been investigated: “case 1” with errors
as they are presently already reached in the mentioned laboratories and “case 2” with decreased errors, as they are
assumed to be in reach within the next few years. Listed inTable 1 are the considered (rms) errors of the longitudinal“shot-to-shot” tolerance budget.
The limited synchronization between the photo-cathodelaser and the rf system determines the timing jitter. A 500 fs
rms-jitter can be assumed today, with future state-of-theart systems this value could be further reduced by 50% orSingle-Pass FELs

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M. Abo-Bakr et al. / Proceedings of the 2004 FEL Conference, 104-107

case 1
cath. laser
injector gun
linac cav.

jitter / psbunch charge (rel.)phase / ◦amplitude (rel.)phase / ◦amplitude (rel.)case 20.5
0.25
1×10−2
1.0
0.2
−3
5×10
2×10−30.1
3×10−4

Table 1: BESSY FEL: longitudinal tolerance budget.
more. For the integrated laser intensity stability, defining
bunch charge fluctuations, an rms error of 1% was recently
measured at PITZ [3].
Phase and amplitude errors have also been adopted frommeasurements at PITZ. A 1◦ phase error and a 3 × 10−3
relative amplitude error has been deduced [4], limited by
the thermal stability of the normal conducting cavity. Withan extended cooling scheme and a direct measurement of
the rf amplitude and phase in the gun, allowing for fast rf
feedback, a further reduction to the values used for “case2” seems to be feasible.
Values of 1 × 10−4 and 0.1◦ for the relative stabilityof the rf amplitude and for the phase errors of the superconducting linac cavities are based on measurements at
Rossendorf [5] and on rf feedback simulations [6].

SIMULATION TECHNIQUES
Two codes have been used for the tolerance studies:
ASTRA [7] for the injector and ELEGANT [8] for the linac
part. To get a sufficient statistics, 100 runs were performed for each of the two cases. With ASTRA 25000
macro-particles were tracked, taking space charge forces
into account. The output particle distribution in the 6D
phase space is converted to the ELEGANT input format. WithELEGANT the particle distributions were tracked under the
influence of wake and CSR fields. To reduce noise in thelongitudinal density distribution, the number of particles
was raised to 100 000, keeping the characteristic bunch parameters unchanged.

bunch parameters.
There is one effect, that will reduce the arrival time variations at the linac end: in contrast to the simple examples in
Figure 2, the real time and energy variations from the injector are correlated. This correlation is produced by the off
crest passage trough the booster module, adjusted to produce the bunch compression chirp. For that reason the time
jitter is compressed just like the bunches them self. In theframe of the simple examples, shown in Figure 2, the final
arrival time variations caused by injector time and energy
jitter have opposite signs and will cancel partially.
For “case 2” arrival time and energy variations reducesignificantly to about 0.4 ps and 30 keV, respectively (rms).
In this case much smaller disturbances of bunch timing andshape are expected.
Main linac: the results of the ELEGANT linac simulations
are shown in Figure 4. Histograms of the central bunch arrival time and energy are plotted in Figure 4a and 4b. Compared to the injector values, the time variations are strongly
reduced due to the correlation of the injector jitter. No significant difference between the two error cases occurs forthe arrival time variation, which indicates a nearly full compression of the correlated injector time jitter. In contrast therms value of the energy variation is strongly reduced for the“case 2” scenario, compared to the “case 1” value.
In Figure 4c and 4d histograms of the distribution of thehorizontal emittance and energy spread are shown. Bothvalues are averaged over all slices, weighted by the slice
current. The variation of the horizontal emittance is lessthan 20% and 10% for “case 1” and “case 2”, respectively.
For the energy spread, there is no big difference between
the two error scenarios, most of the bunches have values
around 1×10−4 .

SIMULATION RESULTS
Injector: in Figure 3 histograms of the ASTRA injector
simulation results at the injector end (E = 130 MeV) are
shown.
For “case 1” the arrival time jitter is about 1.2 ps while
the energy variation is 85 keV (rms). Comparing the rms
time jitter with the “single error case”, even stronger modifications of the bunch compression have to be expected aspresented in Figure 2. Also for the energy variation, therms value is close to the assumptions for the “single errorcase” example. Thus disturbances of the longitudinal phasespace have to be expected in an order as shown in Figure 2,
which would represent a severe distortion of the electron

MOPOS03

Figure 3: Injector simulation results: histograms of thecentral bunch arrival time (top) and energy (bottom) variation at the injector end (case 1: red, case 2: blue).

M. Abo-Bakr et al. / Proceedings of the 2004 FEL Conference, 104-107

107

Figure 4: Linac simulation results: histograms of the variations of the central bunch arrival time (a), energy (b), the sliced
horizontal emittance (c) and the sliced energy spread (d) at the linac end. The relative rms values of the momentum (e)and peak current (f) variations as function of the longitudinal position are drawn. (case 1: red, case 2: blue)
In Figure 4e and 4f the rms values for the sliced meanenergy and peak current variations of all runs of each caseare plotted versus the longitudinal position. This is of major importance for the HGHG process, as it describes thebunch parameter changes for every HGHG stage. The maximum energy variations occur in the head of the bunch andreach 6×10−4 for “case 1” and 3×10−4 for the second scenario. The momentum acceptance of the final amplifier ofthe most critical four stage HGHG is about 1×10−3 , which
is about 2σ even with “case 1”. The maximum peak current
variations do not strongly differ for “case 1” and “case 2”
and amount 11% and 8% respectively.
Simulations on the FEL radiation performance under the
influence of single error sources (energy, current, emittance, energy spread) show relative output variations on theorder of the assumed relative errors compared to the ideal
case, but no drastic decrease [9].

CONCLUSION
S2E simulations for the BESSY FEL injector and linac
have been performed. Final distortions of the longitudinal
phase space are dominated by error sources in the injector.
Time and energy jitters at the injector end are transformedby the bunch compressors and yield tolerable values forboth investigated error cases, where “case 2” with smaller
error assumptions clearly delivers smaller final distortions.
A reliable proof of FEL power losses due to the estimated bunch distortions can only be done, using the sim-

ulated realistic bunches to perform S2E FEL simulations,where all variations of the sliced bunch parameters aretaken into account.

REFERENCES[1] “The BESSY Soft X-ray Free Electron Laser, Technical Design Report”, March 2004, eds.: D. Krämer, E. Jaeschke, W.
Eberhardt, ISBN 3-9809534-0-8, BESSY, BERLIN (2004).
[2] L. H. Yu, I. Ben-Zvi, “High-Gain Harmonic Generation ofSoft X-Rays with the Fresh Bunch Technique”, NIM-A 393,
96 (1997).
[3] J. H. Han, et al., “Conditioning and High Power Test of the
RF Guns at PITZ”, Proc. of the 8th EPAC, Swiss (2004).
[4] D. Lipka, PhD thesis, Berlin (2004).
[5] A. Büchner, et al., “Noise Measurements at the RF Systemof the ELBE Superconducting Accelerator”, FZR, Dresden,
Germany, Proc. the 7th EPAC, France (2002).
[6] A. Neumann, J. Knobloch, “RF Control of the Superconducting Linac for the BESSY FEL”, Proc. of the 8th EPAC, Swiss(2004).
[7] K. Floettmann, “ASTRA user’s manual”,
http://www.desy.de/ mpyflo[8] M. Borland, “elegant: A Flexible SDDS-Compliant Code forAccelerator Simulation”, Advanced Photon Source LS-287(2000).
[9] B. Kuske, et al., “Impact Studies of Bunch Parameter Variations on the Performance of the BESSY HGHG FEL”, thisproceedings.

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D. Krämer / Proceedings of the 2004 FEL Conference, 108-111

A MULTISTAGE HGHG-SCHEME FOR THE BESSY SOFT X-RAY FELMULTIUSER FACILITY*
D. Krämer# on behalf of the BESSY Soft X-ray FEL Design Team,BESSY, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
Abstract
2nd generation FEL facilities in the VUV to soft X-ray
range delivering reproducible ultra short photon pulses at
an energy level of mJ/pulse will open up new physicalfrontiers. Tuneability of photon-wavelength and variablebeam polarization as well as synchronization to externallasers will be essential for the future ultra-fast timeresolved pump-probe experiments utilizing these novel
FEL base synchrotron light sources. Furthermore, using a
RF photoinjector in combination with a CW
superconducting (s.c.) linac, free selectable pulse
repetition rates and pulse pattern can be realized.
Distributing the electron bunches to different FEL-lines
allows effective multi-user operation.
Following this approach BESSY proposes a soft X-ray
HGHG-FEL multi-user facility for the VUV to soft X-ray
range.

INTRODUCTION
Ultra-short pulses from free electron lasers will be thetool in future time-resolved fs-physics experiments.
However there is an on-going debate on the best FEL
scheme how to derive intrinsic stable photon beam as ismandatory for any future multi-user FEL facility. The
cascaded High-Gain-Harmonic-Generation (HGHG)-FEL
scheme as pioneered by BNL [1], is the most promising
scheme in achieving high performance reproducible andstable fs-photon pulses in the soft X-ray wavelength range
λ QPi.e. photon energies up to 1 keV.
In the HGHG approach a seed from an external highpower fs-laser co-propagates with the electron bunch
through an undulator (modulator), modulating theelectron energy if the resonance condition

λL =

λU
(1 + K 2 )2γ 2is met, where λL denotes the laser wavelength, λU is theundulators period, γ is the electron Lorentz factor and K
the undulator field parameter. The imprinted energy
modulation has a period length equal to the laser
wavelength λL and an envelope corresponding to the seedpulse, increased by the slippage of electrons relative tothe laser field over the NU undulator periods.
In a following dispersive section the energy modulationis transferred into a spatial density modulation. The
bunching structure reflects the laser fundamental
wavelength and its harmonics h⋅λL. In a second undulator(radiator), tuned to be in resonance to a specific harmonicn⋅λL, the micro-bunches will emit coherently when themodulation depth ∆γ fulfills the condition ∆γ ≥ nσγ ,where σγ is the electron beam energy spread. The
resulting photon output is used as the seed field of a next
HGHG stage.
Thus the stages consist of a sequence of modulator dispersive section - radiator, the last stage followed by afinal amplifier. In this long undulator, the FEL
amplification process is brought to saturation at thedesired wavelength.
Generation of stable ultra-short photon pulses thus is
the result of the high-quality characteristics of theexternal optical fs-seed pulse in the first HGHG-stage
dominating the statistical noise features from self
amplified spontaneous emission.
Two to four HGHG stages are needed to down-convert
the seed laser wavelength from the tunable frequency
multiplied high power fs-Ti:Sa laser (λ ≈ 230 - 460 nm) to
the desired range in the FEL-lines.
To avoid degradation of the FEL process in the various
HGHG stages of the cascade, the “fresh bunchtechnique” [2] is applied, i.e. the photon field and theinteracting electrons are delayed with respect to eachother. Thus there is always a new, “unused” part of theFig. 1: Foot print of the BESSY soft X-ray user facility with three independent FEL-lines serving three beam lines
each. The total length of the facility is approximately 400 m.

_________________________________________*Funded by the Bundesministerium für Bildung und Forschung, the State of Berlin and the Zukunftsfonds des Landes Berlin#kraemer@bessy.de

MOPOS04

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109

D. Krämer / Proceedings of the 2004 FEL Conference, 108-111

electron bunch interacting with the electromagnetic fieldfrom the preceding HGHG-stage.

THE BESSY SOFT X-RAY USER
FACILITYThe Technical Design Report for the BESSY Soft X-ray
FEL based on the multi-staged HGHG scheme waspublished recently [3]. This FEL-user facility will operate
three FEL-lines in parallel, spanning the photon energies
24 eV – 120 eV, 100 eV – 600 eV and 500 eV– 1000 eV,
delivering pulses of   IV IZhm) duration at variablebeam polarization. Fig. 1 gives a foot print of the machinelayout.
A superconducting 2.3 GeV CW-linac is used as driverin the FEL process. In combination with an injector (1kHz repetition rate, to be replaced by a superconducting
photoinjector at a later stage of the project) highflexibility is achieved with respect to pulse repetition rate
and pulse pattern, providing the opportunity to adjust to
the experimenters specific needs.

FEL Output Simulations
To derive detailed information on the photon beam
properties, time-dependent simulations have been
performed in a start-to-end approach [4,5], using amodified version of GENESIS 1.3 [6]. Typical results oftime resolved power distribution and spectral power
distribution as calculated for the low-energy and mediumenergy FEL-lines are depicted in figure 2.

effect, the energy modulation imprinted in the modulators
differs along the interacting part of the electron beam.
Optimizing for maximum photon beam brilliance, thoseelectrons corresponding to the seed pulse center typicallywill be overbunched when having passed the dispersive
section and thus perform synchrotron oscillations in the
ponderomotive bucket. As a result sidebands are
generated in the spectral distribution. These sidebands
which are pronounced only at the low energy part of thespectrum due to the slippage effect. This effect repeats inthe following HGHG-stages. Thus the higher the numberof stages the sideband structure becomes more and more
complex and pronounced. Means to suppress the effectare described elesewhere [7].
Based on the simulation results the main performanceparameters of the BESSY-FEL are listed in table 1.
Comparing the FEL parameters to a 3rd generation lightsource as BESSY II, the gain in peak brilliance is morethan 10 orders in magnitude.

Table 1: Main performance parameters of the BESSY
X-FEL. Values in brackets refer to an s.c. injector asplanned at a later phase of the project.
Parameter

Value

Unit

No. of FEL lines

3

No of beamlines

9 (15)

Electron energy

2.3

GeV

Emittance

1.5

π mm mrad

Bunch length

290

µm

Peak current

1.75

kA

Beam power

18 (150)

kW

Wavelength range

51 – 1.24

nm

Photon peak power

1.5 – 14GW

Ave. Power

0.26 – 0.02

W

Beam size

14 – 160µm

Divergence

27 – 140µrad

Pulse duration

< 20

fs

Figure 2: Time-resolved power distribution (top) andspectral power distribution (bottom) calculated for the
low-energy and medium energy FEL at wavelength of 10
and 2 nm .

No. of pulses in train

3 (1)No of photons/pulse

2⋅10 – 7 ⋅10

The calculations correspond to the high energy end of
the two and three fold staged FEL-lines, corresponding toa wavelength of 10.3, and 2.0 nm. In all cases a 17 fs(rms) Gaussian seed pulse of 500 MW peak power was
assumed.
The simulation results show a constant power level anda reasonable clean spectrum for the FEL photon beam.
However, as the interacting electrons experience a nonconstant seed due to the seed pulse shape and the slippage

Peak brilliance

6⋅1029 – 1.3 ⋅1031

Repetition rate

1 (25)
11kHz13(s mrad2 mm2
0.1% bw)-1

The RF-Photoinjector
Operation of the BESSY-FEL is planned at a 1 kHz
repetition frequency at the three FEL-lines. Thus theinjector has to deliver bunch trains containing three single
bunches. The spacing of bunches will be 3 µs, acompromise between an acceptable duty cycle of theSingle-Pass FELs

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D. Krämer / Proceedings of the 2004 FEL Conference, 108-111

room-temperature gun cavity and the demands on the
linac RF-system with respect to beam loading.
To generate the electron bunches at a charge of 2.5 nC a
RF photoinjector based on the PITZ design [8] is intended
to be used. Calculations show that with a short rise anddecay time of about 3 ps and a 40 ps “flat-top” intensity
profile photocathode laser-pulse a normalized slice
emittance of less than 1.5 π mm mrad can be achieved[9]. Thus the PITZ-type photogun modified to higher
repetition rates will be the technical starting point for the
BESSY-FEL.
However, a superconducting RF-gun, as is presently
under construction by a FZR-BESSY-MBI-DESY
consortium, will replace the injector later on.

5⋅10-5 of the system over a time scale of hours[12]. Figure
3 depicts a single kicker pulse as generated by the newpulser. The pulser repetition rate is 1 kHz, the pulse width
less than 3 µs, compatible with the bunch spacing.

The CW-Linac
The superconducting acceleration structures are basedon the TESLA linear collider modules that havedemonstrated reliable operation at TTF [10]. The TESLA
modules consist of eight niobium 9-cell cavities, each
module being 12 m long. 18 modules are needed for the
220 m long 2.3 GeV linac. The operation field of ~16
MV/m CW is the economical optimum with respect toinvestments and long-term operation costs. Minor
modifications are required to adapt the (pulsed) TESLA
technology for CW. The changes are due to the increased
He-flux from the cavities (20.5 W/cavity) requiring amodest enlargement of the two-phase He supply line.
To confirm the basis for a reliable CW operation an
detailed qualification program started at BESSY. Test of
couplers and tuners, optimization of cryogenic parameterssuch as bath temperature are performed. For this purposea Horizontal Bi-Cavity Test facility (HoBiCaT) has been
set up [11].
Tests of new concepts for damping microphonics - mostimportant in our CW operation - are under preparation.
The test bench also will allow optimization at realistic
conditions during RF source development, allowing for a
cost-optimized specification for the 144 units of 1.3 GHzpower sources. Commissioning of the bench is inprogress. 1.8 K LHe is provided from an existing Linde
TCF50 cryogenic plant connected to a pumping station.
Two 9-cell cavities completely manufactured andprocessed by industry have been delivered and areavailable now for testing.

The Beam Delivery System
A kicker system will be used to extract single bunchesfrom the main linac into the low and medium energy
FEL-lines at beam energies of 1.0 and 2.3 GeV
respectively. Extreme tight tolerances in the order of ∆θ/θ≈ 5⋅10-5 are required on the relative stability andreproducibility of the extraction angle θ.
As the kicker stability is determined primarily by thepower converter, a pulser design was developed based on
IGBT power semiconductors.
After careful design of the pulser geometry to minimize
intrinsic inductivities and optimization of grounding, themeasurements revealed a peak to peak stability of ∆θ/θ 

MOPOS04

Figure 3: Single pulse as achieved with the new highstability pulser.

The Beam Collimation
Beam collimation to protect the undulators modules
from electron losses and dark-current will be achieved by
a compact 43 m long dedicated beamline between linac
and undulators sections. The collimator acts as transverseand longitudinal phase space filter avoiding degradationof the radiation sensitive NdFeB undulator structures. For
transverse collimation round apertures in absorber blocks
are used. Particles outside the tolerable transverse
acceptance intercept the absorbers.
Energy collimation is achieved with apertures locatedin a closed dispersion bump in a dogleg structure. The
present system[13] is optimized for an acceptancebandwidth of 5% in energy spread.

The Undulator Sections
For the three FEL-lines in total 120 m of undulators ofdifferent period lengths is needed to ensure a proper
matching between modulator and radiator of the various
stages, ranging from λu = 122 mm to 28.5 mm. A
minimum gap of 10 mm is sufficient to cover the fullwavelength range. In each case the undulators are variable
gap devices, the radiators of the last HGHG-stage and thefinal amplifier undulators will follow the ellipticalpermanent magnet design now known as APPLE III
design.
The modulators are very short undulators (< 3 m each).
The radiators and final amplifiers however will be built
up from segments of typically 3.5 m in length. Thesesegments are spaced by 0.95 m long intersections
equipped with phase shifters, focusing quadrupole
magnets, steering elements, vacuum pumps and a variety
of diagnostic elements as OTR, wire scanner and beam
position monitors for beam characterization andmanipulation, see figure 4.

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D. Krämer / Proceedings of the 2004 FEL Conference, 108-111

technology making use of hardware developments forhigh energy physics colliders and/or hard X-ray FELs.
Future options such as seeding with future intense
short-wavelength High Harmonic Generation (HHG)
lasers (λ ∼ 30 nm) as well as options to expand thenumber of FEL-lines from three to five have been
incorporated into the design of the soft X-ray FEL.
The flexibility of the CW-accelerator together withfeatures as continuous wavelength tuning, variable beampolarization, will efficiently open-up the field of ultra-fasttime resolved spectroscopy allowing to take advantage ofthe specific characteristic of seeded FELs, i.e. transverseand longitudinal coherence of ultra-short pulses at highest
peak brilliance.

ACKNOWLEDGEMENTS
Figure 4: 3-D model of the compact intersection region
with components for beam focusing, steering, diagnostics
and vacuum pumps.
Special attention has been paid to the undulator
vacuum chamber to avoid beam degradation arising fromwakefields. An all Cu-vacuum chamber with a beam ductof surface roughness < 100 nm (rms) is favored for thedesign.

Beamlines
The three FELs will be equipped with three beamlines
each: optimized for high resolution experiments, a “whitelight” beamline without any monochromatization and ahigh intensity station conserving the short pulse structureof the FEL beam. Table 1 gives the main parameters forthe high-energy (HE) FEL beamlines as an example. Data
were calculated from detailed ray-tracing.
Dedicated undulators using the spent beam from the
FEL are planned at a later phase of the project.
Table 1: Main parameters for the HE-FEL beamlines.
Beamline

Bandwidth
(meV)

Pulse
length(fs)

Pulse
energy(nJ)

Energydensity(mJ/cm2)High
resolution

20 - 33

650 – 120

2.4 – 100.23 – 1.4

White
light

2000

10

11000

120000

Short
pulse

800

11

600

250

FEL
output

2000

10

15000

1000

CONCLUSIONS AND OUTLOOKThe proposed seeded soft X-ray FEL facility ideallywill complement the 3rd generation synchrotron lightsource BESSY II. The machine is based on existing

The author acknowledges the contributions from the
BESSY staff as well as the help from many colleagues at
BNL, Cornell, DESY, MBI-Berlin, TU Dresden andForschungszentrum Rossendorf in preparing the BESSY
Soft X-ray FEL TDR.

REFERENCES[1] I. Ben-Zvi, F. Di Mauro, S. Krinsky, L.H. YU, Nucl.
Instrum. and Meth., A304 (1991)181.
[2] L.H. Yu, I. Ben-Zvi, Nucl. Instrum. and Meth. A393
(1997)96.
[3] The BESSY Soft X-ray Free Electron Laser, TDR
BESSY March 2004, eds.: D. Krämer, E. Jaeschke,
W. Eberhardt, ISBN 3-9809534-0-8, BESSY, Berlin(2004).
[4] M. Abo-Bakr, M.v. Hartrott, J. Knobloch, B. Kuske,
A. Meseck, Start-to-End Tolerance Studies for the
BESSY FEL, this proceedings.
[5] B. Kuske, M. Abo-Bakr, A. Meseck, Impact Strudies
of Bunch Parameter Variation on the Performance of
the BESSY HGHG FEL, this proceedings.
[6] S. Reiche, Nucl. Instrum. and Meth. A429(1999)243.
[7] A. Meseck, M. Abo-Bakr, B. Kuske, The Influenceof the Seed Pulse Shape on the Output Performanceof the BESSY Multi-stage HGHG-FEL, theseproceedings.
[8] F. Stephan et al., Recent Results and Perspectives of
the Low Emittance Photo Injector at PITZ, theseproceedings.
[9] F. Marhauser, Photoinjector Studies for the BESSY
Soft X-ray FEL, EPAC 2004.
[10] R. Brinkmann, K. Flöttmann, J. Rossbach, P.
Schmüser, N. Walker, H. Weise (editors), TESLATechnical Design Report, Part II – The Accelerator,
DESY-2001-011 (2001).
11] J. Knobloch, W. Anders, A. Neumann, D.
Pflückhahn, M. Schuster, Status of the HoBiCaT Test
Facility at BESSY, EPAC 2004.
[12] O. Dressler, J. Feikes, J. Kuszynski, Kicker Pulser
with High Stability for the BESSY FEL, EPAC 2004.
[13] T. Kamps, Collimation System for the BESSY FEL,
this proceedings.

Single-Pass FELs

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B. Kuske et al. / Proceedings of the 2004 FEL Conference, 112-115

IMPACT STUDIES OF BUNCH PARAMETER VARIATIONS ON THE
PERFORMANCE OF THE BESSY HGHG FEL∗
B. Kuske † , M. Abo-Bakr, A. Meseck, BESSY, Berlin, Germany
DEVIATION FROM CONSTANT BUNCH
Abstract
PARAMETERS
In the recent past interest has grown in FEL designs
offering alternatives to the SASE principle. BESSY proposed a High Gain Harmonic Generation (HGHG) soft Xray FEL, composed of three independent FEL-lines utilising 2 to 4 HGHG stages. Modulators and radiators in sucha scheme are kept short, to stay away from the exponential
regime of the FEL process and only the final amplifier (FA)reaches saturation. Therefore, the mechanisms of how theelectron beam properties generated by the gun and the linac
influence the radiation output differ from what is known in
SASE devices. Shot to shot variations and the influence ofrealistic bunch profiles are considered, as well as requirements arising from the use of the fresh bunch technique.

In the design of the BESSY FEL it was assumed, that thebunch parameters do not vary along the bunch. The design
values of the bunch parameters are listed in Table 1.

INTRODUCTION

When the energy spread, the emittance or the currentof the bunch differ from their design values at the end of
the linac, it is not possible to retune the FEL in order toimprove its performance. These cases will be discussed
first. In case of an offset in the central electron energy, it
is possible to change the gap of the undulators and restore
the design output. Deviations in the central energy will betreated in the next paragraph. Beam sizes and trajectory
offsets can be corrected using the optics in front of the FEL
and between the HGHG stages, and will not be considered.
After a short reminder of how these parameters determine
the HGHG process, the effect of their deviations from thedesign values will be discussed.
Energy spread: The energy spread of the bunch at theend of the linac, σγ , is modified during the passage throughthe undulators due to spontaneous emission of synchrotron
radiation. Furthermore, an additional energy modulation is
introduced to the bunch by the interaction with the seeding field. For harmonic generation, the imprinted modulation depth ∆γ, has to fulfill ∆γ ≥ nσγ , with n theharmonic number sought in the modulator. Therefore, thelarger the energy spread the weaker the bunching on theseeding frequency after the dispersive section. In the radiators, a smaller energy spread supports the amplification
process as more particles fulfill the resonance condition.
Emittance: When the transverse emittances, εx,y , arereduced, the radiation power is concentrated on axis, andthe amplification process in the radiators is enhanced. Additionally, the energy spread induced to the bunch during
the passage through the undulator is linked to the transverse
emittances, as longitudinal energy is tranfered to the transverse velocities. This effect depends on εn /λs , where εnis the normalised emittance and λs is the resonant wavelength, i.e. its importance grows with every stage, resp.
wavelength reduction.

BESSY recently presented the technical design reportfor a linac-based soft X-ray FEL, designed as a multi-user
facility [1]. Three independent beamlines are planed andwill supply photons in the spectral range from 0.02 keV ≤h̄ω ≤ 1 keV . The FEL is designed as a High Gain Harmonic Generation (HGHG) structure, to avoid the known
restrictions of a SASE device and in lack of high-power
short-wavelength seeding lasers that could be used forseeding at the desired wavelength. As in every beam based
radiation source, the achieved bunch parameters, such asenergy, energy spread, emittances, current, and the like, determine the radiation quality. Different to storage rings, notonly deviations from design parameters have to be investigated. Due to jitter, mainly in the gun, but also in the linac,bunch properties will vary shot to shot. In addition, as the
fresh bunch technique is applied, the longitudinal profile ofthe bunch is of major importance. In an HGHG cascade,only the final amplifier takes the FEL process to saturation,
whereas all other undulators stay in the linear regime. Consequently, the mechanisms of how varying bunch parameters influence the final performance differ strongly fromthose in the SASE case. Performance improvements in
one stage might be lost in the following stage, while minor bunching or less seed power might still lead to adequat
output one stage later. The paper will cover different aspects of bunch parameter deviations. All calculations are
performed for the two stage low energy FEL line, using thetime-dependent computer code GENESIS [2]. Even in thiscomparatively short set up (the other lines cover three andfour stages) the computational efforts are considerable.
∗ Funded by the Bundesministerium für Bildung und Forschung(BMBF), the State of Berlin and the Zukunftsfond Berlin† Bettina.Kuske@bessy.de

MOPOS05

Table 1: Nominal bunch parameters.
bunch parameter
design valueenergy spread
2.0 × 10−4
emittancex,y
1.5 × 10−6
m radpeak current
2.1
kA
gamma (low energy)
1996.09
beam sizex,y< 1.0 × 10−4m

Available online at http://www.JACoW.org

113

spectrum [a.u.]

0

0

1
0.8
0.6
0.4
0.2

0
51 51.5 52 52.5 53
λ [nm]

FA

1e+07

0.2

1e+06

0.1
0

0.05 0.1
t [ps]
radiator 1

0.3

power on axis [W]

0.1

modulator 2

0

1e+05
10000

0.05 0.1
t [ps]

1
0.8

radiator 2

spectrum [a.u.]

0.2

1e+08

bunch. 5th harm.

0.3

modulator 1

spectrum [a.u.]bunch. 5th harm.

B. Kuske et al. / Proceedings of the 2004 FEL Conference, 112-115

0.6
0.4
0.2

0

1
0.8

0.05 0.1
t [ps]
FA

0.6
0.4
0.2

0
0
10.3 10.35 10.4 10.45 10.3 10.35 10.4 10.45
λ [nm]
λ [nm]

Figure 1: Development of the bunching in the modulators and the spectral power of the radiators and the FA, when the
average bunch current is altered by ±10%.

Fig. 1 shows the development of the bunching in themodulators, and the spectral power of the radiators and thefinal amplifier for the 2 stage low energy FEL line. The
three curves depict the reference case with the design current (black) and two cases with a reduced (green) and a enhanced bunch current (red). A 10% deviation in the bunch
current hardly influences the bunching rate created in thefirst modulator (upper left), but leads to a 30% increasein spectral power emitted by radiator 1 (lower left). The
bunching rate produced in the second modulator (center
top) reflects the different seed powers of radiator 1. In thecase of the higher seeding power, though, the particles are
already overbunched, as can be detected from the reduced
flat top of the green curve. This overbunching leads to therise of side maxima and a reduction of the peak power inthe spectrum of radiator 2 (center bottom). The peak powerin the case of the reduced bunching is similiar, and both lie
20% below the design current. In the final amplifier (rightbottom), the reduced current case still reaches the reference
spectral power by saturating at a later point in the undulator. The higher current case shows an increase of the spectral peak power by 20% due to the extra current.

1.4
maximum spectral power [a.u.]

Current: The higher the bunch current, the higher isthe radiation power emitted by the bunch even far awayfrom exponential gain. The bunching in the modulators
is slightly enhanced by the additional radiation. The dominant effect of current changes shows in the radiators, wherea higher bunch current directly leads to an increased spectral power.

1.2
energy spread

1emittances x,y

0.8
current

0.6
-60

-40

-20
0
20
deviation from reference in %40

60

Figure 2: Peak spectral power as a function of bunch parameter offsets in percent.

Fig. 2 shows relatice changes in the peak spectral powerat the end of the final amplifier as a function of offsets in thebunch parameters in percent. Clearly, the output power depends strongest on the bunch current. This differs from the
SASE experience, where f.e. the emittance has a stronger
influence on the power. When the bunch current increases,
overbunching limits the performance.
Changes in the energy spread can be large according tostart-to-end simulations. The energy spread plays a mayor
role in the modulators, in the interaction between the seedradiation and the bunch. The output of the radiators corresponds to the bunching rates created in the previous modu-

Single-Pass FELs

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B. Kuske et al. / Proceedings of the 2004 FEL Conference, 112-115

about 1/4 of the expected value. The reason is, that, aslong as the seed laser wavelength stays within the bandwidth of the modulator, the energy modulation on the seeding frequency will be enhanced and the following radiator is seeded with the respective harmonics. During thepassage through the radiator the central frequency of thespectrum slowly drifts from the harmonics of the seeding
frequency towards the resonant wavelength of the radiator.
The shorter the radiator, the smaller the wavelength shift.
Also in this respect, the HGHG setup is more relaxed thana SASE device. The effects of jitters in the seeding wavelength, though, yet have to be investigated, as well as theinfluence of shot to shot variations in the beam sizes andtrajectories.
nominal γ∆γ = −10e-3∆γ = 10e-3∆γ = −2∗10e-3∆γ = 2∗10e-31spectral power [a.u.]

lators. While the spectra of radiator 2 still reflect the changing energy spread, the output of the FA increases slightly
for deviating σγ . The overall change in spectral power issmall.
It should be pointed out, that for the design values thesaturation point of the final amplifier was chosen well inside the device, leaving space for fluctuations of whateverkind. As a result, a slower amplification process, due to minor parameters might still saturate at a later point, and evenat higher power than the reference. An excess of power, due
to advantageous bunch parameters might get lost, when theamplification process saturates too early, and overbunchingsets in. As the final amplifier consists of 3 undulators only,
opening gaps will be too crude to compensate this effect.
In a sense this is a stabilising mechanism that reduces theoutput fluctuations.
In the case of small emittance changes, the results are
dominated by the point of saturation in the FA rather thenby the emittance value. For growing emittances the expected power reduction sets in. For smaller emittances,
overbunching dominates the positive effects, the reductionin spectral peak power is below 20% for ±40% emittancechanges.

0.8
0.6
0.4
0.2

SHOT TO SHOT VARIATIONS
0

Jitter in the gun and linac parameters will lead to unavoidable shot to shot variations in the parameters of thebunches reaching the FEL. Start-to-end tolerance simulations [3] predict typical shot to shot rms deviations forthe emittance of 0.14mm mrad, for the energy spread of
0.8 × 10−4 for the low energy FEL line and for the current of ≤ 200 A. The studies presented in the previous
paragraph cover ≥ 2σ of the expected variations, so the expected fluctuations in the FA output seem to be tolerable,
as long as single error sources are concidered.
Effects leading to shot to shot variations in the transverse
size and position of the bunches have not yet been studied.
Whereas constant offsets in the central bunch energy, γ
can be counteracted by adjusting the undulator gaps, shot
to shot variations of γ could well be problematic, as the resonant wavelength will be shifted, or worse, particles might
run out of the resonance condition, and the FEL process
might not get started. Start-to-end simulation show, thatthe expected gamma variations depend on the position inside the bunch and are largest at the head and the tail ofthe bunch, where rms values of up to 6 × 10−4 can bereached. The resonance condition predicts shifts of the resonant wavelength of
∆γ
∆λ
= −2
λ
γ

(1)

Fig. 3 shows spectra of the final amplifier of the low energy FEL line, for bunches with the design γ (black) andwith central energies shifted by ±1 × 10−3 and ±2 × 10−3(solid and dashed lines). As expected, the central wavelength is clearly shifted, but it is shifted by only 6 × 10−4 ,MOPOS05

10.34

10.36
10.38
λ [nm]

10.4

Figure 3: Spectra of the final amplifier for bunches withoffsets in the central energy of ±1 × 10−3 (solid line) and±2 × 10−3 (dashed line).

REALISTIC BUNCH PROFILE
In order to study the effects of a realistic bunch profile, abunch with 1.4 ps total length, extracted from start-to-end
simulations [3] has been tracked through the low energy
FEL line. In such a bunch, all parameters vary slice to slice,
f.e. there is an energy chirp needed for the bunch compression and the current distribution approaches a flat top
profile. As only small parts of the bunch are used in each
HGHG stage, the bunch has been cut into twelve 120 f s
long pieces for the simulations. This corresponds roughly
to the spacing sought for the fresh bunch technique. As
the properties of the seeded part of the bunch spoil during the passage through a HGHG stage, the seeding radiation for the next stage has to be shifted to a fresh, unperturbed part of the bunch. In the two stage HGHG-FEL,
f.e., three consecutive parts of the bunch are used. The
averaged properties of each of the twelve bunch parts are
depicted in Fig. 4. While the central energies (top) varyaround the design value (line), the design current of 2100A
is only approached by the central four bunch parts (center).
The emittances and the energy spread stay well below thedesign values (bottom). The beam size is twice the design
value horizontally, and the first three parts have a consider-B. Kuske et al. / Proceedings of the 2004 FEL Conference, 112-115

able horizontal offset (not shown).

current [A]

gamma

2050
nominal gamma

2000
1950

2500
2000

nominal current
4

1500
1000

6

5
7
bunch parts

σ(γ), ε *10e5 [m rad]500
nominal abs. energy spread

0.3
nominal emittance

0.2
0.1
0

-0.2

-0.1

0
z [mm]

0.1

CONCLUSION

In an first attempt, these bunch parts have been tracked
through the first HGHG stage, without any readjustment.
Fig. 5 shows the resulting spectra of the first radiator.
Clearly, the frequency shift due to the energy slope in thebunch is detectable. As above, Eq. 1 is not fulfilled. The
achieved peak power basically reflects the current distribution. Part 5 radiates best, but still the peak power is only
60% of the design value, since the resonance condition is
not met anymore.
1

spectrum [a.u.]part 5the bunch part that is actually used. Although the averaged
bunch parameters of part 5 are close to, and better than thedesign values, it reaches only 80% of the required power inradiator 1. For part 4, the nominal values are reached. Bothparts have a 50µm horizontal offset that has not been compensated. The even smaller emittance of part 4 apparently
over compensates the lack of current and the trajectory mismatch.
Although the radiation generated by part 4 is comparable
to the reference case, only 80% of the bunching is achieved,
when it is used to seed part 5 in the second modulator. In
radiator 2, the power rises only slowly for part 5, and finallyreaches 1/3 of the expected value. In addition, the central
wavelength of the spectrum is shifted by 1 × 10−3 to lower
frequencies. This shift is caused by the energy ramp of thebunch, despite the adjustment of the undulators. Due tothe ramp, the dispersion sections following the modulators
not only transform the energy modulation into bunching,but, in addition compress the bunch, and thus shift the impressed wavelength to lower values. The optimisation of
the second stage under these circumstances requires further
investigations.

0.2

Figure 4: Bunch properties deduced from start-to-end simulations. Above: gamma, center: current, below: absolutenergy spread (black) and emittance (red).

0.8

115

part 6The effects of deviant bunch parameters have been studied for the BESSY low energy FEL line. Due to certain’self stabilizing’ effects of HGHG structures, offsets in the
averaged bunch parameters are tolerable in the order ofmagnitude, that is expected from start-to-end simulations.
Reductions in the bunching factor or spectral power that
occure in the early HGHG stages are at least partly compensated in the final amplifier, by a shifted saturation point.
When the early stages function too well, overbunching will
limit the final output. First studies using bunches extracted
from start-to-end simulations were presented. Unexpected
effects like a shift in the resonant wavelength caused by thedispersive sections in combination with the energy chirp ofthe bunch have to be included in further optimization procedures. Due to the fresh bunch technique, the bunch parameters vary for every HGHG stage, making the analysis
of performance limitations and the definition of acceptableparameter tolerances extremely difficult. In further studies
the three and four stage FEL lines will be investigated.

0.6
part 7

REFERENCES

0.4
part 40.2
0[1] The BESSY Soft X-ray Free Electron Laser, Technical Design Report, March 2004, eds.: D. Krämer, E. Jaeschke, W.
Eberhardt, ISBN 3-9809534-0-8, BESSY, BERLIN (2004)

part 8

51.4

51.6

51.8
52
λ [nm]

52.2

52.4

Figure 5: The power spectra of different bunch parts are
dominated by the respective current and gamma.

[2] GENESIS 1.3: A Full 3D Time Dependent FEL Simulation
Code, S. Reiche, Nuclear Instruments and Methods A429
(1999) p. 243[3] Start-to-End Injector and Linac Tolerance Studies for the
BESSY FEL, M. Abo-Bakr, M. v. Hartrott, J. Knobloch, B.
Kuske, A. Meseck, BESSY, Berlin, Germany, this proc.

In a second step, the K parameters of the modulators andradiators have been adjusted, each stage to the gamma ofSingle-Pass FELs

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A.M. Meseck et al. / Proceedings of the 2004 FEL Conference, 116-119

THE INFLUENCE OF THE SEED PULSE SHAPE ON THE OUTPUTPERFORMANCE OF THE BESSY ∗ MULTI-STAGE HGHG-FEL
A. Meseck, M. Abo-Bakr, B. Kuske, BESSY, Berlin, Germany
Abstract
The BESSY soft X-ray FEL is planned as a High Gain
Harmonic Generation (HGHG) FEL multi-user facility.
Three independent FEL-lines, fed by a superconducting
CW linac, will be provided to cover the VUV to soft Xray spectral range. In the HGHG scheme, the properties of
the radiation output are dominated by the characteristics ofthe laser seed. In this connection, the influence of the laser
pulse shape on the output characteristics, in particular on
the output spectrum is of high interest. We present simulation studies for the BESSY-HGHG-FELs and discuss theoutput performance for different shapes of the laser pulse.

INTRODUCTION
Based on the experience with its third generation lightsource, BESSY proposes a linac-based cascaded HGHGFEL multi-user facility. The target photon energy ranges
from 24 eV to 1 keV with a peak-brilliance of about1031 photons/sec/mm2 /mrad2 /0.1% BW, i.e. a peak powerof up to a few GW for pulse lengths less than 20 fs (rms).
The polarization of the output radiation will be variable.
The technical design report for the BESSY soft X-ray FEL
was published recently [1].
The BESSY HGHG multi-user FEL facility will consist of three undulator lines to cover the target photon energy range. Each line is seeded by a tunable laser covering the spectral range of 230 nm to 460 nm. The pulses
are assumed to have a Gaussian profile, a peak power of
500 MW, and a pulse duration of about 15 fs (rms).
Two to four HGHG stages are necessary to reduce existing laser wavelengths to the desired range of the BESSY
FEL. Each stage consists of a modulator - dispersive section - radiator structure, for more details on the HGHGstages see [1, 2]. The last radiator is followed by the socalled final amplifier. It is seeded at the desired wavelengthand the amplification process is brought to saturation.
For a Gaussian-shaped seed, only a part of the interacting
electrons experience the full power due to the seed shapeand the slippage effect. The impressed energy modulation mirrors the Gaussian profile of the seed. The strengthof the dispersion section can be adjusted for the peak energy modulation at the center of the seeded part or for asomewhat lower energy modulation including the flanks.
The second case provides the maximum output power ofthe following radiator, since more electrons are optimallybunched. In this case the electrons at the center, which
experience the full power of the seed are somewhat overbunched. The overbunched electrons perform synchrotron∗ Funded by the Bundesministerium für Bildung, und Forschung, thestate of Berlin and the Zukunftsfonds Berlin.

MOPOS06

oscillations in the ponderomotive bucket. The resulting
modulation of the emitted radiation frequency causes theside spikes (sidebands) [3]. The more electrons are overbunched the stronger is the growth of the sidebands. Thiseffect is repeated in the following stages. In this way the
number of sidebands in the spectrum adds up from stage tostage. Due to the slippage in the radiators and final amplifier, the sidebands are shifted to one side.
The sidebands can be avoided by optimizing the dispersion sections for the peak energy modulation, as described in [4]. In this case the bunching is of more Gaussian shape. The resulting radiation power and pulse length
are reduced compared to the overbunched case, since lessflank-electrons are optimally bunched. The losses in the integrated power are due to the reduction of the pulse length,
i.e. the peak power suffers only slightly. Neverthelessthe loss of integrated power and the reduction of the pulse
length which inhere in this approach might be undesirable.
Therefore other possibilities to avoid the sidebands are ofinterest.
The sidebands are due to the overbunched electrons inthe seeded part of the bunch. The shape of the impressedenergy modulation in connection with the strength of thedispersion section determines whether the electrons are
overbunched or not. Therefore the sidebands can also be
avoided by adjusting the shape of the energy modulation
instead of reducing the dispersion strength. In this case one
would expect that the integrated power and pulse length do
not suffer in spite of more spectral purity. As the shape of
the impressed energy modulation is mainly determined by
the profile of the laser seed, the shape of the seed pulse canbe adjusted to optimize the shape of the energy modulation. Note that, due to the slippage, the impressed energy
modulation is not an one-to-one copy of the seed shape.
In this paper, we present simulation studies for different
laser-pulse shapes for the BESSY-HGHG-FELs and discuss the output performance in terms of power and spectrum purity. The calculations have been performed with thetime-dependent 3-D-simulation code GENESIS [5]. The
different laser seed profiles in the time domain are generated with a modified version of the GENESIS output
routine. Note, that the chosen seed-pulse shapes should
demonstrate the influence of the seed shape in a HGHGFEL rather than represent realistic laser radiation profiles.

SIMULATION STUDIES
Seed Pulse Shapes
In order to avoid the overbunching and ensure the maximum output power of the radiator a constant energy modulation in the interacting part of the bunch seems to be ben-Available online at http://www.JACoW.org

A.M. Meseck et al. / Proceedings of the 2004 FEL Conference, 116-119

117

Figure 1: The different shapes of the seed pulses used in
the simulation studies.
eficial. Using a box-shaped seed a nearly constant energy
modulation of the interacting electrons can be achieved. As
the slippage of the seed in the modulator as well as the slippage of the emitted photons in the radiator have to be taken
into account, the expected output of the radiator is not boxshaped.
Figure 1 shows the different shapes of the seeds used
for the present simulation studies. In addition to the simulations with the Gaussian and the box-shaped seeds, also
simulations with increasing and decreasing seed power are
performed to investigate the slippage effects.

First Stage

Figure 2: The resulting bunching factors on the fifth harmonic after the first dispersion section of the two-stage
HGHG-FEL for different seed cases.
The resulting bunching factors of the fifth harmonic after
the first dispersive section for the two-stage HGHG-FEL[1] are shown in figure 2. The dispersion strength is adjusted to maximum radiator power and for retaining pulse

Figure 3: The power distribution (top) and the spectrum(bottom) of the first radiator of the two-stage HGHG-FEL
for different seed-pulse shapes.
lengths if procurable. As expected, the bunching caused by
the box-shaped seed is not fully box-shaped. Due to theslippage, there exist electrons in the interacting part, which
do not experience the peak power during the whole passage
through the modulator. For the maximum power of the following radiator, the strength of the dispersion section has
to be adjusted such that these edge electrons are bunched
optimally. In this case the central electrons experience a tohigh dispersion strength, which leads to an over bunchingof them. The flanks of the bunching caused by the boxshaped seed are steeper than those of the Gaussian shaped
seed, while the flanks of the increasing-power and decreasing power seeds are roughly as steep as those of the Gaussian seed in spite of the upright edges of the corresponding
seed shapes.
The bunching maxima of the increasing- and decreasing
power cases are shifted relative to each other but this shift
is much smaller than the shift by the seed shapes itselfs.
The slippage effect seems to mitigate these seed characteristics. Due to the fact that the integrated seed powers forthese both shapes are lower than for the Gaussian and boxshaped cases, the resulting maximum bunching factors are

Single-Pass FELs

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A.M. Meseck et al. / Proceedings of the 2004 FEL Conference, 116-119

also lower.
The power distributions and the spectra of the first radiator for different seeds, shown in figure 3, point at theeffects of the slippage and overbunching. The higher peaks
at the right side of the power distributions for the Gaussian and box-shaped cases are caused by the slippage. The
dips in the power profiles originate from the overbunching, which increases during the passage through the radiator. The maxima for the other two seed cases are shifted
according to the bunching factors. For these cases, the electrons are not yet overbunched but the radiator outputs arefar from the maximum results.

Second Stage

Figure 4: The Bunching on the fifth harmonics after thesecond dispersion section of the two-stage HGHG-FEL for
different seed cases.
The output of the first radiator is used as a seed for thesecond stage. Figure 4 shows the bunching factors on thefifth harmonics after the second dispersive section for thetwo-stage HGHG-FEL. The dip in the bunching for thebox-shape case is not an overbunching effect but rather it
mirrors the shape of the seed radiation, i.e. the output of
the first radiator. This can be concluded from the spectrumof the second radiator, figure 5b, where the sidebands arevery small. The flanks of the bunching profile for the boxshaped case are no more steeper than the Gaussian case.
Although the peaks of the power distributions for the different seeds, figure 5a, have roughly the same values, thespectral distributions differ strongly. The high sideband in
the spectrum of the Gaussian case points to a strong overbunching which is also indicated by the deep dip in the corresponding power distribution. The spectrum of the boxshaped case is pure and its maximum is roughly as high as
the Gaussian case. The spectrum of the increasing- and decreasing power cases are also pure but the maximum spectral powers suffer from the reduced pulse length similar
to the purity-optimized case described in [4]. The relative
shift between the spectral maxima is not only reduced but

MOPOS06

Figure 5: a)The power (top) and b) spectrum (bottom) of
the second radiator for different seed-pulse shapes.

also the order of the maxima is changed compared to thespectra of the first radiator.

Final Amplifier
Using the output radiation of the second radiator as seed
for the final amplifier, one would expect, that the properties of the radiator outputs dominate the output characteristics of the amplifier. Figures 6a and 6b show that this istrue only for the Gaussian and box shaped case. For theincreasing- and decreasing power cases, the properties of
the radiator outputs are not fully retained during the amplification process. The spectral purity is reduced comparedto the radiator output and the shift between the maxima of
the spectrum seems to increase.
A comparison of the results of the final amplifier for theGaussian, box-shaped, and purity-optimized case [4], figure 7, shows that a box-shaped seed leads to a spectral purity as high as a purity-optimized case, i.e. reduced dispersion strengths, while the output power is roughly as highas for a Gaussian seed. Although the pulse duration of
the box-shaped case is longer than of the purity-optimized
case, it is not as long as the Gaussian case. This might be119

A.M. Meseck et al. / Proceedings of the 2004 FEL Conference, 116-119

Figure 6: The power and spectrum of the final amplifier fordifferent seed-pulse shapes.

Figure 7: A comparison of the temporal and spectral powerof the final amplifier for the Gaussian, box-shaped, andpurity-optimized case [4] is shown.

originate from the flanks of the Gaussian distributed seedpulse.

REFERENCES

CONCLUSION[1] The BESSY Soft X-ray Free Electron Laser, Techniacal Design Report March 2004, eds.: D.Krämer, E. Jaeschke, W.
Eberhardt, ISBN 3-9809534-08, BESSY, Berlin (2004)

The simulation studies show that the performance of a
HGHG-FEL can be further optimized by adjusting the seedpulse shape. For the BESSY two-stage HGHG-FEL a boxshaped seed pulse can be used to achieve notable more
spectral purity with only a minor loss of power comparedwith the FEL output for a Gaussian seed. Nevertheless thesimulations with the increasing and decreasing seed powershow also that due to the slippage, the shape of the radiation pulse changes during the passage through the FELline. Therefore the seed pulse shape should be adjusted foreach of the three BESSY FEL-lines separately, in order topreserve the benefits of a well adjusted seed.

[2] L.H. Yu, J. Wu, Nucl. Instrum. and Meth. A 483 (2002) 493[3] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, The physics offree electron lasers, Springer-Verlag Berlin Heidelberg, 2000
[4] A. Meseck, M. Abo-Bakr, B. Kuske, Output Variability of the
BESSY Soft X-Ray FEL, EPAC 2004
[5] S. Reiche, Nucl. Instrum. and Meth. A 429 (1999) 243

ACKNOWLEDGEMENT
The authors would like to thank A. Gaupp for very fruitfull discussions concerning the physics of the free electron
lasers and the HGHG scheme.

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J.-P. Carneiro et al. / Proceedings of the 2004 FEL Conference, 120-122

VELOCITY BUNCHING SIMULATIONS FOR THE DESY VUV-FEL
J.-P. Carneiro∗ , B. Faatz, K. Floettmann
DESY, Hamburg, Germany

INTRODUCTION
The injector of the VUV-FEL consists of a 1.5 cell
RF gun operating at 1.3 GHz surrounded by 2 solenoids(a bucking and a main) and followed by a cryomodule(ACC1) containing eight TESLA type superconducting
cavities. A high quantum efficiency Cs 2 Te photo-cathodeis inserted into the half-cell of the RF gun and allows the
production of high charge bunches when illuminated by theUV light of a laser pulse (20 ps FWHM) with a wavelengthof 262 nm. The optimal operation of the injector requires,for emittance compensation purposes, that the four firstcavities of the cryomodule operate with a lower accelerating field (∼12.5 MV/m) than the four others (∼20 MV/m).
The RF-induced curvature of the longitudinal phase spaceis corrected by the use of a third harmonic cavity installedat the exit of ACC1. Five cryomodules and two magnetic
compressors will then accelerate the beam to 1 GeV andcompress it down from σ z 2 mm to σz 62 µm. Under
optimal operation, the beam peak current at the entrance of
the undulator is expected to be ∼2.5 kA, for a slice emittance <1.5 mm-mrad (in the radiation part) and a total energy spread of σ E ≤1 MeV. The radiation pulse is then expected to be in the order of ∼200 fs FWHM for a peak
power in the GW level.
In the present status of the VUV-FEL, a shorter laser
pulse length (∼10 ps FWHM measured with a streak camera) is available and the last cryomodules have not yet been
installed. Furthermore, the third harmonic cavity is underdevelopment ([1]) and will not be available for use in the
VUV-FEL within 2 to 3 years. Without this element, only ashort part of the electron bunch can present at the undulator
entrance the required beam properties (peak current, emittance and energy spread) to induce SASE radiation. Reference [2] indicates that a possible way to operate the VUVFEL under these starting conditions is to use a low charge
beam (0.5 nC) together with both magnetic compressors.
At the entrance of the undulator, the bunch presents thena slice with a peak current of 1.3 kA, a normalized emit∗ Jean-Paul.Carneiro@desy.de

MOPOS07

VELOCITY BUNCHING PRINCIPLE
The velocity bunching is based on the phase slippage between the electrons and the RF wave for a non-relativistic
beam [3]. Reference [4] suggests, for the VUV-FEL, to use
the first cavity of the first cryomodule (located ∼2.5 metersfrom the photo-cathode) to compress the bunch by velocity
bunching.
This scenario, presented in Figure 1, shows ASTRA [5]simulations of the RMS bunch length as a function of thephase of the first cavity of ACC1 (relative to an acceleration on crest) keeping the phase of the other cavities to a
maximum energy gain.
7
6

6 nC
3 nC
1 nC
0.5 nC

5z

The TESLA Test Facility is currently being upgraded toreach in its final stage as a user facility SASE radiation at awavelength of 6 nm. After a brief description of the layout
and status of the VUV-FEL, this paper presents start-toend simulations studying velocity bunching as a scenario
for the first operation of the accelerator.

tance <1.5 mm-mrad and a local energy spread of about
300 keV inducing a SASE radiation pulse of 15 to 50 fs
at a wavelength of 30 nm. In this paper, we study an alternative option for the start-up of the VUV-FEL based on
velocity bunching and on which no magnetic compression
is used.

σ [mm]

Abstract

4
3
2
1

0
−100

−50
0
50
Phase First Cavity ACC1 [Deg]100

Figure 1: ASTRA [5] simulation of the RMS bunch length
versus the phase of the first cavity of ACC1 (relative toacceleration on crest) for different charges. Outputs at theexit of ACC1 (z=13.6 m).
Four different bunch charges Q are studied and the outputs are taken at the exit of ACC1, at z=13.6 m. The
main parameters of the injector used for these simulations
were determined from measurements during the conditioning: field on the gun of 40 MV/m and accelerating fieldon the cavities of ACC1 of ∼12 MV/m. The beam enters

Available online at http://www.JACoW.org

121

J.-P. Carneiro et al. / Proceedings of the 2004 FEL Conference, 120-122(a)Table 1: Main beam characteristics for nominal and velocity bunching operations and for different charges. FromASTRA [5]. Outputs at z=13.6 m.

SASE FEL OUTPUTSThe ELEGANT outputs were tracked in the undulator
using the FEL code GENESIS [8]. The transverse distribution of the beam has been taken as gaussian with the appropriate emittance and the longitudinal one as given by
ELEGANT. The peak of the current distribution has beenmatched into the undulator focusing structure.
The undulator of the VUV-FEL is made of six segments(of 4492 mm each) separated with doublet focusing and diagnostics blocks between. The undulator period is set at

0.8

4

0.6

3

0.4

2

0.2

1

−2

−1.5

−1

−0.5
s [mm]

0

0.5

0
1

(b)

DISTRIBUTION AT Z=203 METERS

1.4

7

1.2

6

1

5

0.8

4

0.6

3

0.4

2

0.2

1

0
−2.5

−2

−1.5

−1

−0.5
s [mm]

0

0.5

0
1

(c)

Current [kA]

ELEGANT [7] has been used to track the compressedbunch obtained by velocity bunching from the exit of
ACC1 to the entrance of the undulator (z=203 m). The
four charges studied in the previous paragraph were transported along the VUV-FEL linac, taking both bunch compressors as drifts. The field on the cryomodules ACC2,
ACC3 and ACC4 was ∼14 MV/m in order to get a totalenergy of ∼440 MeV. Figure 2 shows the beam current andslice emittance distributions at the entrance of the undulator for Q=0.5 nC, 1 nC and 3 nC. It is clear from these figures that first, the velocity bunching induces a sharp peak(∼100 µm) at the head of the bunch and second, that theslice emittance in the peak keeps reasonable values (∼5mm-mrad for ∼1 kA). The slice energy spread in the peak(which has not been plotted) stays below 200 keV.

5

0
−2.5

Current [kA]

the first cavity with a total energy of ∼4.7 MeV and exits the cryomodule with an energy of ∼107 MeV. Figure
1 indicates that a minimum bunch length is obtained for aphase of -86 ◦ . Table 1 presents the beam characteristics
from ASTRA simulations at z=13.6 m for an optimized(laser diameter on the photo-cathode and solenoid field) operation of the injector under nominal (all cavities on crest)and velocity bunching (-86 ◦ ) cases. The table shows thatthe use of velocity bunching enables a significant increaseof the peak current (from 50 A to 1.2 kA for Q=1 nC)
but it also degrades the projected emittance and the energy
spread. The charge Q=6 nC corresponds to the maximum
charge extractable from the RF gun using a laser diameterof 5 mm at 40 MV/m (maximum available, from [6]).

1Transverse Emittance [mm−mrad]

Velocity Bunching
In
n
∆En
[kA] [µrad] [MeV]
0.65
3.2
0.58
1.2
5.1
0.72
1.8
8.6
0.91
2.1
15.6
1.35

Transverse Emittance [mm−mrad]

Nominaln∆En[µrad] [MeV]
1.3
0.13
2.0
0.15
5.3
0.33
9.9
0.57

2

10

1.6

8

1.2

6

0.8

4

0.4

2

0
−2.4

−1.4

−0.6
s [mm]

0.2

Transverse Emittance [mm−mrad]

In
[kA]
0.03
0.05
0.10
0.16

Current [kA]

Q
[nC]
0.5
1.0
3.0
6.0

0
1

Figure 2: Current and slice emittance distributions at theentrance of the undulator (z=203 m) for bunch charges of(a) 0.5 nC, (b) 1.0 nC and (c) 3 nC. Bunch head for s>0.
From ELEGANT [7].

Single-Pass FELs

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J.-P. Carneiro et al. / Proceedings of the 2004 FEL Conference, 120-122

(a)

Q
[nC]
0.5
1.0
3.0
6.0

0.8
0.7

Power [GW]

0.6

Pulse duration
FWHM [fs]
80
65
100
500

Mean power
[GW]
0.2
0.5
1.0
1.0

0.5

Table 2: Main radiation power characteristics.
0.4
0.3
0.2
0.1
0
0

50

s [µm]

100

150

(b)

Power [GW]

1

0.5

0
0

50

s [µm]

100

150

(c)

The simulations presented in this paper show that the velocity bunching applied to the VUV-FEL produces bunches
whose characteristics enable the SASE process in the undulator. However, it is important to notice that the spacecharge effects along the linac (mainly the longitudinalones) have not been taken into consideration and can have asignificant impact on the beam dynamics, especially for thehigh charge cases (3 nC and 6 nC). These effects should bestudied in the future. First experimental studies of velocity
bunching at the VUV-FEL began in June 2004 where thecompression of the bunch has been observed with a pyrodetector located downstream of ACC1 for a phase of thefirst cavity of about -90 ◦ . More experiments on this subjects are foreseen in the VUV-FEL in the next months.

REFERENCES

4[1] T. Kabibouline et al., TESLA-FEL-2003-01, May 2003.

3.5[2] E. Saldin, E. Schneidmiller and M. Yurkov, TESLA-FEL-0406, to be published.

3[3] L. Serafini and M. Ferrario, “Velocity Bunching in PhotoInjectors”, AIP conference proceeding 581, p. 87-106, 2001.

2.5
2[4] Ph. Piot and K. Floettmann, “ An upgraded injector for the
TTF FEL user facility”, EPAC2002, Paris, France.

1.5[5] K.
Floettmann,
ASTRA
User
Manual,http://www.desy.de/∼mpyflo/Astra− dokumentation/.

1
0.5
0
0

27.3 mm with an undulator parameter of K=1.23. GENESIS outputs of the radiating part of the distributions, corresponding to the peak in the current distribution shown in
Figure 2, are shown in Figure 3 for the cases 0.5 nC, 1 nC
and 3 nC. They show the power distributions at a position
where the first peak reaches saturation, corresponding approximately to minimal spectral bandwidth. Table 2 shows
the main characteristics of the radiation at the same positions, together with the 6 nC case.

CONCLUSION

1.5

Power [GW]

Saturation length[m]
15.23313.26815.23319.165[6] S. Schreiber, private communication.
50s [µm]

100

150[7] M. Borland, Advanced Photon Source LS-287, Sept. 2000.
[8] S. Reiche and B. Faatz, TESLA-FEL-2001-09.

Figure 3: Radiation power at position of minimum spectral
bandwidth for bunch charges of (a) 0.5 nC, (b) 1.0 nC and(c) 3 nC. From GENESIS [8].

MOPOS07see123

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 123-126

THE POTENTIAL FOR THE DEVELOPMENT OF THE X-RAY FREE
ELECTRON LASER: GENERATION OF SASE RADIATION
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

LAYOUT OF XFEL

Abstract
We present a concept of a universal FEL beamline covering continuously wavelength range from 0.1 to 1.6 nm
at a fixed energy of the electron beam. FEL beamline accommodates three undulators (SASE1-3) installed one after another. The first undulator, SASE1, is optimized for
operation at the wavelength range 0.1-0.15 nm. Our study
shows that such tunability range almost does not affect operation at the shortest wavelength of 0.1 nm. Operationof two other FELs (SASE2 and SASE3) is not so critical,
and nominal tunability range is chosen to be by a factor oftwo (2-4 nm, and 8-16 nm, respectively). The length of theundulators is chosen such that continuous wavelength tunability can be provided by means of extra opening the undulator gaps, or by tuning to the frequency doubler modeof operation. Changing of undulator gaps in different partsof SASE2 and SASE3 undulators allows one to tune themodes with high output power (sub-TW level), or for effective generation of the second harmonic. The latter featuremight be important for future pump-probe experiments.
Also, recently proposed attosecond SASE FEL scheme isforeseen for implementation.

INTRODUCTION
For the design of the XFEL laboratory and the undulators the requirements with respect to photon energy range
and tunability are important. The FEL laboratory will provide intense photon beams in the X-ray regime. Within
the upper limit for generation of XFEL radiation at about
15 keV (0.08 nm) a wide range of photon energies has tobe provided [1, 2, 3]. The lower energy cutoff is practically determined by the availability of the other sources, inparticular the DESY TTF soft X-ray FEL facility which isforeseen to deliver FEL radiation with wavelength down to
2 nm in its third harmonic [4].
The superconducting linac is capable of supplying thepulse rate needed to support a farm of X-ray undulators.
The proposed XFEL source will consist of three FEL beamlines. All together we expect that up to a hundred experimental stations can be distributed among the three undulator beam lines according to the needs of the user community.

Available online at http://www.JACoW.org

The accelerator will be operated at 10 Hz repetition rate
providing bunch trains of up to 4000 electron bunches
within one bunch train. All electron bunch trains will be
guided into one electron beamline and dump. The electron
beam transport line takes every bunch train and delivers it
to the 1st SASE undulator (see Fig. 1). The performance of
the FEL depends critically on the parameters of the electron
beam. The optics between the undulators is especially designed to ensure the desired beam quality. The two bending
magnets with a 10 mrad bending angle provide the parallel
shift of the beam axis by a distance of 0.5 m, then the electron beam reaches the entrance of the 2nd SASE undulator.
To bend the beam into the undulator, magnets operate in a
DC mode with improved field stability. The photon beamsof the 1st and 2nd SASE undulators have to be separated bya distance of 2 m in the experimental hall, which is realized
by a deflection angle of about a one mrad. After passing
all three undulators, the electrons are stopped in the beam
dump. All three photon beamlines can be operated in parallel.
At a fixed electron energy the magnet gap of the FEL
undulator can be varied mechanically for wavelength tuning. The wavelength range 0.1-1.6 nm at a fixed electronenergy of 17.5 GeV can be covered by operating the XFEL
with three undulators which have different periods. These
SASE undulators can be placed behind each other assuming that the subsequent undulator radiates at longer wavelength. It is a great advantage that accelerator and electron beam transport line in new scheme of multi-user facility operate at fixed parameters and that a fast ”electron
switchyard” is not required. In order to avoid the need fora costly additional tunnels and shafts, the XFEL source isdesigned such that accelerator, all three SASE undulators,
electron beamline, and three photon transport beamlines
are installed inside the same (5 m diameter) tunnel.

Table 1: Specification of undulators

SASE1
SASE2
SASE3

λr
nm
0.1-0.15
0.1-0.4
0.4-1.6

λu
mm
39
47.9
64.8

gap
mm
10-12
10-19
10-20

Bw
T
0.8-1
0.6-1.3
0.8-1.7

Lw
m
150
150
110

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 123-126

Figure 1: Sketch of a X-ray SASE FEL source.
Table 2: Specification of photon beam properties∗
Units
SASE1
SASE2
SASE3
Wavelength range
nm0.1-0.15
0.1-0.4
0.4-1.6
Photon energy range
keV
12.4-8.3
12.4-3.1
3.1-0.8
Peak power
GW
10
20
20
Average power
W
40
80
80
Photon beam size (FWHM)
µm
90
60
60
Photon beam divergence (FWHM) µrad
1.1
2.2
6.6
Coherence time
fs
0.22
0.25
0.5
Spectrum bandwidth (FWHM)
%
0.08
0.14
0.3
Pulse duration (FWHM)
fs
100
100
100
2 × 1012
4 × 1012
Number of photons per pulse#
5 × 1011
16
16
Average flux of photons#/sec
2 × 10
8 × 102 × 1017
Peak brillianceB
2.5 × 1033 1.4 × 1033 8 × 1031
Average brillianceB
1 × 1025
6 × 1024
3 × 1023∗
Parameters are calculated for nominal electron energy of 17.5 GeV and middle of tunability range (see section 4 formore details). Average characteristics are calculated for 10 Hz repetition rate, and 4000 pulses per one train. Brilliance iscalculated in units of photons/sec/mrad2 /mm2 /(0.1% bandwidth).

CONTROL OF THE AMPLIFICATIONPROCESS WITH SASE SWITCHERS
Although the electron beam leaving the 1st SASE undulator has acquired some additional energy spread, it is stilla good ”active medium” for the 3rd SASE undulator at theend. In this scheme it will be possible to provide in parallel hard (around 0.1 nm) and soft (around 1 nm) X-rays
for two photon beamlines (after-burner mode of operation).
Normally if a SASE FEL operates in saturation, the qualityof the electron beam is too bad for the generation of SASE
radiation in a subsequent undulator which is resonant at a
few times longer wavelength. On the other hand, to operate
XFEL at the requested radiation wavelengths, three undulators are needed. The new method of SASE undulatorswitching based on a rapid switching of the SASE process
proposed in this paper is an attempt to get around this ob-

MOPOS10

stacle. This approach could be a very interesting alternative
to the SASE undulator-switching based on ”electron beamswitchyard”. The same goal, rapid switching between different SASE undulators, can be achieved in a more technically reliable way at less expenses.
There are two approaches to solving the problem of
rapidly switched FEL. The first one focuses on the development of electromagnetic phase shifter embedded in theother components needed inside the undulator insertion.
Second, electron energy shifter, can also be used. The technique of using a phase shifter as a switch relies on the factthat dependence of the FEL gain on the phase between theelectron beam modulation and the radiation field, acting on
the electrons is very strong. It is apparent that the electron’s
relative position within a radiation wavelength will determine whether it consistently gains or loses energy as it trav-

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 123-126

Figure 2: Electromagnetic phase shifter for a rapid switching of the SASE process in the 0.1 nm undulator.

Figure 3: The second way to a rapid switching of the SASE
process in the 0.1 nm undulator. Conceptual layout of theelectron (photon) energy shifter.
els through the undulator. Optimal suppression is obtained
when phase shift is such that most of electrons fall into accelerating phase and after passing through the phase shifter
the electrons start to absorb power from electromagnetic
wave. For the purpose of phase switching, electron beam
has to be slightly delayed (about of Angstrom) as comparedto the radiation beam. This is done by a suitably designed
magnetic chicane called a phase shifter [5] (see Fig. 2).
It consists of three horizontal magnets. The length of thecenter one is doubled because it needs twice the strength.
The total length of phase shifter is about 20 cm. It uses
electromagnets at an excitation level which is low enough,so that water cooling is not needed. For trapezoidal mode afrequency of 1 Hz is specified with a switching time of lessthan 10 ms. This kind of insertion device can be embedded
between two neighboring undulator segments.
Another interesting approach is that of photon (electron)
energy shifter. This method of beamline switching is based

Figure 4: Installation of an energy shifter for a rapid
switching of the SASE process. The quadrupole separationof a FODO lattice is large enough so that an accelerator
structure of length 2 m can be installed.

125

on the accelerator technique. In this case the SASE undulator beamline consists of an input undulator, and an
output undulator separated by an accelerator module (seeFig. 3). The typical FEL amplification bandwidth in the
X-ray wavelength range is of the order of 0.1%. The offset
photon energy 0.2% corresponds to electron energy shift of
15 MeV. By shifting the energy of the electron beam, one
can effectively switch output undulator off. So the effective length of the undulator system can be rapidly varied.
The RF switch consists of RF accelerator module with total
voltage V0  15 MeV. We select 1.3 GHz structure basedon standing-wave room temperature cavities with gradientof 8 MV/m. The quadrupole separation of an undulator
FODO lattice is large enough so that relatively short (2 m)accelerator structure can be installed (see Fig. 4). Each RF
switch would require one klystron TH 2104. This klystronis used for the TTF RF gun. The RF switch is operated
with full beam loading and with design beam parameters.
The average heat load of the accelerator cavity amounts
to 20 kW which has to be removed by the cooling water.
DESY is now developing similar room temperature accelerator structure for research unit PITZ at DESY Zeuthen[6].

EXTENDED POSSIBILITIES BEYOND
STANDARD (SASE) MODE OF
OPERATION
The developments discussed in this paper concern also
the increased FEL output radiation power. The mostpromising way to achieve the goal is the method of tapering the magnetic field of the undulator. Tapering consists in
slowly reducing the field strength of the undulator field topreserve the resonance wavelength as the kinetic energy ofthe electrons changes. Figure 5 shows the design principleof a high-power undulator. The first stage is a conventional
X-ray SASE FEL. The gain of the first stage is controlledin such a way that the maximum energy modulation of theelectron beam at the FEL exit is about equal to the local
energy spread, but still far away from saturation. Whenthe electron bunch passes through the dispersion section
this energy modulation leads to effective compression of
the particles. Then the bunched electron beam enters thetapered undulator, and from the very beginning produces
strong radiation because of the large spatial bunching. Radiation field produces a ponderomotive well which is deep
enough to trap the particles, since the original beam is relatively cold. The radiation produced by these captured particles increases the depth of the ponderomotive well, andthey are effectively decelerated. As a result, much higher
power can be achieved than for the case of a uniform undulator. At the total undulator length of 150 m, the FEL output at 0.2 nm is enhanced by a factor of 8, from 20 GW to
150 GW. With the proposed variable gap undulator design
this option would require only installation of a dispersion
section. Our study has shown that the required net compaction factor of the dispersion section is about a fraction

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 123-126

Figure 5: Three schemes for 2nd SASE undulator. Only one type of undulator magnet structure is needed. The radiation
wavelength will be tuned by changing the gap. The total magnetic length is 150 m
of µm. The quadrupole separation of an undulator FODO
lattice is large enough so that relatively short (4 m) dispersion section can be installed. An undulator taper could
be simply implemented as a step taper from one undulator
segment to the next.
The specification of the 2nd SASE undulator in uniform
mode of operation gives a range of wavelengths between
0.2 and 0.4 nm. It was concluded that most experiments
which are not interested in particular resonance effects will
benefit from using photon energies close to 0.1 nm. A design was conceived that enables to obtain XFEL radiation
at a close to 0.1 nm wavelength at two of the three SASE
undulators simultaneously. The problem to be solved is
how to extend the higher photon energy cutoff of the 2nd
SASE undulator up to 12 keV. In this paper we propose
to use an efficient frequency doubler for the 2nd and 3rd
SASE FELs [7]. In its simplest configuration the frequency
doubler consists of an input undulator, and an output undulator separated by a dispersion section. After passing
through the dispersion section the bunched beam has not
only a fundamental radiation frequency component, butalso has considerable intensity in its harmonics. It is possible to have an input undulator operating at one frequency,
and an output undulator operating at double of this frequency (see Fig. 5). The radiation in the output undulator will then be excited by the harmonic component in theelectron beam, and the FEL will operate as a combinationof frequency multiplier and amplifier.
Another perspective development is an attosecond modeof operation. A technique for the production of attosecond X-ray pulses is based on the use of X-ray SASE FEL
combined with a femtosecond laser system [8]. It is important that this attosecond scheme is based on the nominal XFEL parameters, and operates in a ”parasitic” mode
not interfering with the main mode of the XFEL operation.
It can be realized with minimum additional efforts. The

MOPOS10machine design should foresee the space for installation ofmodulator undulator and a viewport for input optical system. Many of the components of the required laser system
can be achieved with technology which is currently being
developed for applications other than the attosecond X-ray
source.

REFERENCES[1] ”Conceptual Design of 500 GeV e+ e− Linear Collider with
Integrated X-ray Facility” (Edited by R. Brinkmann et al.),DESY 1997-048, ECFA 1997-182, Hamburg, May 1987.
[2] TESLA Technical Design Report, DESY 2001-011, edited
by F. Richard et al., and http://tesla.desy.de/.
[3] P. Audebert et al., “TESLA XFEL: First stage of the X-ray
laser laboratory – Technical design report (R. Brinkmann etal., Eds.)”, Preprint DESY 2002-167.
[4] “A VUV Free Electron Laser at the TESLA Test Facility
at DESY. Conceptual Design Report”, DESY, TESLA-FEL
95-03, Hamburg, June, 1995.
[5] J. Pflueger and M. Tischer DESY Print TESLA FEL 200008, DESY, Hamburg, 2000.
[6] V. Paramonov, private communication.
[7] J. Feldhaus et al., Preprint DESY 03-092, 2003. Nucl. Instrum. and Methods A, in press.
[8] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Preprint
DESY 04-013, 2004. Opt. Commun., in press.

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 127-130

127

ATTOSECOND X-RAY SOURCE FOR LIGHT-TRIGGERED
TIME-RESOLVED EXPERIMENTS ASSOCIATED WITH THE X-RAY
SASE FEL
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract
We describe a technique for the production of attosecond X-ray pulses which is based on the use of X-ray SASE
FEL combined with a femtosecond laser system. A fewcycle optical pulse from a Ti:sapphire laser interacts withthe electron beam in a two-period undulator resonant to 800
nm wavelength and produces energy modulation within aslice of the electron bunch. Following the energy modulator the electron beam enters the X-ray undulator andproduces SASE radiation. Due to energy modulation thefrequency is correlated to the longitudinal position within
the few-cycle-driven slice of SASE radiation pulse. The
largest frequency offset corresponds to a single-spike pulsein the time domain which is confined to one half-oscillation
period near the central peak electron energy. The selection of single-spike pulses is achieved by using a crystal monochromator after the X-ray undulator. Our studies show that the proposed technique is capable to produce
300-attoseconds long single pulses with GW-level output
power in the 0.1 m wavelength range, and is applicable to
the European X-Ray Laser Project XFEL and the Linac Coherent Light Source at SLAC.

INTRODUCTION
Brilliance, coherence, and timing down to the femtosecond regime are the three properties which have the highest
potential for new science to be explored with an XFEL. In
its initial configuration the XFEL pulse duration is about
100 femtoseconds [1, 2]. Even though this is a few hundreds times shorter than in third generation light sources, it
can probably be further reduced to about 10 femtoseconds[3, 4, 5]. A novel way to generate sub-10-fs x-ray pulses –the slotted spoiler method has been proposed recently [6].
This method is based on spoiling the beam phase density ina part of the electron bunch so that this part will not lase,while preserving lasing in a short length of the bunch. The
FEL performance of the spoiled beam approach was computed using the time-dependent GENESIS simulation. It
has been shown that it is possible to produce X-ray pulses
with duration of 3-4 fs FWHM for nominal LCLS bunch
compression parameters [6, 7].
Recently an approach for the generation of attosecond
pulses combining fs quantum laser and harmonic cascade(HC) FEL scheme was proposed in [8]. The HC FEL
scheme has the potential to produce coherent light down

Available online at http://www.JACoW.org

to wavelengths of a few nm in an undulator sequence [9].
The analysis presented in [8] shows that this technique has
potential to produce 100 as long radiation pulses with MWlevel of output power down to 1 nm wavelength.
The shortest possible X-ray pulse duration generated by
XFEL is limited by the intrinsic bandwidth of the SASE
process. In the case of the European XFEL and the LCLS,
the FWHM bandwidth near saturation (at 0.1 nm) is about
0.1%, indicating a 300-as coherence time determined by
the bandwidth product. Recently a scheme to achieve pulse
durations down to 400-600 attoseconds at a wavelength of
0.1 nm has been proposed [10]. It uses a statistical propertyof SASE FEL high harmonic radiation. The selection of asingle 10-GW level attosecond pulses is achieved by using a special trigger in data acquisition system. A promising scheme for attophysics experiments using this approachhas been studied and could be implemented in the XFEL
design [1].
In this paper we describe a new method to allow reducing
the pulse length of the X-ray SASE FEL to the shortest conceptual limit of about 300 as [11]. It is based on the application of a sub-10-fs laser for slice energy modulation of theelectron beam, and application of a crystal monochromator for the selection of single attosecond pulses with GWlevel output power. Optimization of the attosecond SASE
FEL has been performed with the three-dimensional, timedependent code FAST [12] taking into account all physicaleffects influencing the SASE FEL operation (diffraction effects, energy spread, emittance, slippage effect, etc.).

GENERATION OF ATTOSECOND PULSESFROM XFEL
A basic scheme of the attosecond X-ray source is shownin Fig. 1. An ultra short laser pulse is used to modulate
the energy of electrons within the femtosecond slice of theelectron bunch at the seed laser frequency. The seed laser
pulse will be timed to overlap with the central area of theelectron bunch. It serves as a seed for a modulator which
consists of a short (a few periods) undulator. Following
the energy modulator the beam enters the X-ray undulator.
The process of amplification of radiation in this undulator develops in the same way as in a conventional X-ray
SASE FEL: fluctuations of the electron beam current serveas the input signal. The proposed scheme for the generation of attosecond pulses is based on frequency-chirping

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 127-130

40

80

20

60

P [GW]

E-E0 [MeV]

Figure 1: Schematic diagram of attosecond X-ray source.

0

-20

-40

20

5

10

15

20

t [fs]

Figure 2: Energy modulation of electron bunch at the exitof the modulator.

the SASE radiation pulse. When an electron beam traverses
an undulator, it emits radiation at the resonance wavelength
λ = λw (1 + K 2 /2)/(2γ 2 ). Here λw is the undulator period, mc2 γ is the electron beam energy, and K is the undulator parameter. The laser-driven sinusoidal energy chirp
produces a correlated frequency chirp of the resonant radiation δω/ω  2δγ/γ. After the undulator, the radiation is passed through a crystal monochromator which reflects a narrow bandwidth. Since the radiation frequency
is correlated to the longitudinal position within the beam,a short temporal radiation pulse is transmitted through themonochromator.
In the following we illustrate the operation of an attosecond SASE FEL for the parameters close to those of theEuropean XFEL operating at the wavelength 0.1 nm [1].
The parameters of the electron beam are: energy 15 GeV,
charge 1 nC, rms pulse length 25 µm, rms normalized emittance 1.4 mm-mrad, rms energy spread 1 MeV. Undulator
period is 3.4 cm.
In the present scheme an electron beam with slice modulation of the energy passes through the undulator and produces SASE radiation. Since only a small fraction of thebunch is modulated (10 fs versus 200 fs of FWHM electron
pulse duration, see Fig.2), the total energy in the radiation

MOPOS11

40

0

5

10

15

20

t [fs]

Figure 3: Temporal structure of the central part of the radiation pulse (single shot). Undulator length is 120 m. Dottedline shows energy modulation of the electron bunch (seeFig. 2).

pulse remains approximately the same as in the case of nonmodulated electron beam, and saturation is achieved at an
undulator length of about 120 m. Figure 3 shows a view of
the central part of the radiation pulse. The dotted lines inthis figure show the initial energy modulation of the electron beam. The temporal structure of the radiation pulse
has a clear signature of the slice energy modulation. The
FEL process is strongly suppressed in the regions of theelectron bunch with large energy chirp, and only regions of
the electron bunch with nearly zero energy chirp produce
radiation.
The plots in Fig. 4 show the spectrum of the radiation
pulse. A signature of the slice energy modulation is reflected by the tails of the spectrum. Each of three clearlyvisible bumps in the averaged spectrum corresponds to a
local extremum of the energy offset shown in Fig. 2. The
bump marked as M1 corresponds to the central peak energy
offset. The bump M2 corresponds to the neighboring two
positive energy offsets. The bump M3 comes from the areas of the electron bunch with negative energy offset. The
single-shot spectrum (shown as grey line) exhibits an oscillatory behavior near bumps M2 and M3 . That is due to an

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 127-130

30

M3

0.2

0.1

0.0

-0.8

-0.6

20

10

0

-0.4

0.3

-0.8

-0.4

0.0

M1

M2

Normalized spectrum

Normalized spectrum

Normalized spectrum

0.3

0.2

0.1

0.0
0.0

0.4

0.2

∆ω/ω [%]∆ω/ω [%]

0.4

0.6∆ω/ω [%]

Figure 4: Spectrum of the radiation pulse produced by modulated electron bunch. Undulator length is 120 m. Middle:
complete spectrum. Left and right plots show enlarged tails of complete spectrum. Solid line is averaged spectrum.
Dashed line is averaged spectrum of non-modulated electron beam. Mark M1 shows tuning of monochromator for single
pulse selection. Marks M2 and M3 show tuning of the monochromator for selection of two pulse sequence (see Fig. 5).
3

P [GW]P [GW]

1.0

0.5

P [GW]

3

2

1

1

0.0

5

10

15

20

0

2

5

t [fs]

10

15

20

0

5

10

t [fs]

15

20

t [fs]

Figure 5: Averaged temporal structure of the radiation pulse behind monochromator tuned to single spike (left plot) andtwo pulse sequence selection (middle and right plots).

2.0

P [GW]

interference of two radiation wave packets with close frequencies coming from different parts of the electron bunch.
Other maxima can be hardly distinguished, since they arelocated within the bandwidth of the main spectrum.
Figure 4 gives a clear idea about separation of the attosecond radiation pulses. Positioning of the monochromator to different maxima of the spectrum allows us to selectsingle pulse, or a two pulse sequence of attosecond duration. The calculation involves the following steps. The
FEL simulation code produces 3-D arrays for the radiation
field in the near zone. This field is recalculated into thefar field zone, and is subjected to the Fourier transform.
The latter result is convoluted with the reflectivity function of Ge(111) monochromator, and is subjected to inverse
Fourier transform giving temporal structure of the radiation
pulse behind the monochromator.
By selecting the frequency offset of the monochromatorto the position marked as M1 in Fig. 4, we select single
pulses. Their properties are illustrated with Figs. 5 and 6.
An analysis of single pulses shows that their pulse duration
is about 300 as, the average power has GW-level, and theradiation pulse energy is about a µJ. The larger width of
the averaged curve is partially due to shot-to-shot fluctuations of the position of the radiation pulse (a fraction ofcoherence time). Note that shot-to-shot fluctuations of theradiation energy after monochromator are suppressed significantly due to ultra short duration of the lasing fraction

1.5
1.0
0.5
0.0
10.0

10.5

11.0

11.5

t [fs]

Figure 6: Temporal structure of the radiation pulse behindmonochromator tuned to single spike selection (mark M1
in Fig. 4). Thin curves are single shots, and bold curve isaverage over many pulses.
of the electron bunch [13]. An advantage of single-pulse
selection is the small background from the main radiation
pulse due to a large offset from the resonant frequency.
By positioning of the monochromator central frequency
to the spectrum bumps M2 or M3 one can select a two pulse
sequence as illustrated in Fig. 5. Two pulses are separated
by two or one oscillation period of optical laser depending on the choice of the monochromator tuning. Note that
due to the statistical nature of the SASE process the timeSingle-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 127-130

Figure 7: Scheme for femtosecond resolution pump-probe experiments based on the generation of the 100 GW-levelattosecond X-ray pulses directly from X-ray SASE FEL.
jitter between two pulses is about 200 as, a fraction of thecoherence time. One should not wonder that pulse amplitudes differ visibly for the case of pulse separation by one
laser oscillation period. This is a typical nonlinear effectrelated to the sensitivity of the FEL process to the sign andthe value of the energy chirp. Although the energy modulation amplitude is the same in both maxima, the shape ofthe energy chirp is asymmetric.

schedule.

REFERENCES[1] TESLA Technical Design Report, Supplement, DESY2002167, edited by R. Brinkmann et al., and http://tesla.desy.de.
[2] The LCLS Design Study Group, LCLS Design Study Report, SLAC reports SLAC-R-593 (2002), and http://wwwssrl.slac.stanford.edu/lcls/CDR.

CONCLUSION[3] C.B. Schroeder et al., Nucl. Instrum. and Methods
A483(2002)89.

Attosecond X-ray FEL described here is an ideal tool
for organization of pump-probe experiments (see Fig. 7)[11, 14]. Indeed, attosecond X-ray pulse is naturally synchronized with its fs optical pulse, and time jitter is cancelled. Usual optical elements are used for seed laser beam
splitting and tunable delay. It should be possible to achievea timing accuracy close to duration of the half period of
the seed laser pulse (1 fs), allowing an unprecedented insight into the dynamics of electronic excitations, chemical reactions, and phase transitions of matter, from atoms,
through organic and inorganic molecules, to surface, solids
and plasma.
It is important that proposed attosecond scheme is basedon the nominal XFEL parameters, and operates in a ”parasitic” mode not interfering with the main mode of the
XFEL operation. It can be realized with minimum additional efforts. The machine design should foresee the spacefor installation of modulator undulator and a viewport for
input optical system. Many of the components of the required laser system can be achieved with technology which
is currently being developed for applications other than theattosecond X-ray source. As a result, a laser system could
be developed over the next few years and can meet the
XFEL requirements well in advance of XFEL construction[4] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt.
Commun. 205(2002)385.

MOPOS11[5] S. Reiche, P. Emma, and C. Pellegrini, Nucl. Instrum. andMethods A507(2003)426.
[6] P. Emma et al., Phys. Rev. Lett. 92(2004)074801.
[7] M. Cornacchia, et al., SLAC-PUB-10133, December 2003.
[8] A. Zholents and W.M. Fawley, Preprint LBNL-54084,
LBNL, Berkeley, 2003.
[9] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt.
Commun. 202(2002)169.
[10] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt.
Commun. 212(2002)377.
[11] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt.
Commun. 237(2004)153.
[12] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A429(1999)233.
[13] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A507(2003)101.
[14] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt.
Commun. 239(2004)161.

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 131-134

131

THE POTENTIAL FOR THE DEVELOPMENT OF THE X-RAY FREE
ELECTRON LASER: MULTI-USER PHOTON DISTRIBUTION SYSTEMFOR XFEL LABORATORY
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract

facilities [1, 2, 3].

X-ray photon beam from a SASE FEL undulator is inprinciple a single user tool, just like an optical laser. Therefore, the operation and amortization cost cannot be easily
spread over many simultaneous experiments. To avoid prohibitive cost for each experiment, a new XFEL laboratory
scheme is proposed. A photon beam distribution system
based on movable multilayer X-ray mirrors can provide an
efficient way to generate a multi-user facility. Distributionof photons is achieved on the basis of pulse trains and it ispossible to partition the photon beam among a few tens independent beamlines thereby obtaining many users working in parallel. The second way to increase the numberof simultaneous experiments is based on the working witha series of perfect crystals in transmission (Laue) geometry. The later concept is the basic idea of the Troika beamline at ESRF. In principle, a hundred of photon beamlines
with different experiments can be served by a single XFEL
source.

INTRODUCTION
The preferred layout of a SASE FEL is a linear arrangement in which the injector, accelerator, bunch compressors
and undulators are nearly collinear, and in which the electron beam does not change the direction between accelerator and undulators. On the other hand, a X-ray FEL laboratory should serve several tens, may be up to a hundred
experimental stations which should operate independently
according to the needs of the user community. The present
paper describes a beam distribution system which allows to
switch the FEL beam quickly between many experiments
in order to make efficient use of the source. Many applications require only very high peak brilliance. Such experiments for which average brilliance and wavelength are notcritical, could operate simultaneously at the same radiation
wavelength.
Each FEL source emits only one photon beam. Therefore, the operation and amortization costs cannot be easily
spread over many simultaneous experiments. To avoid prohibitive cost for each experiment, new photon beam distribution scheme is proposed. It would specifically partition the photon beam among a few tens independent beamlines thereby obtaining many users working in parallel. Our
analysis shows that proposed mult-user photon distribution
schemes may be implemented at future upgrades of XFEL

Available online at http://www.JACoW.org

MULTI-USER DISTRIBUTION SYSTEMBASED ON MULTILAYERS
The technical approach adopted in this variant of XFEL
laboratory design makes use of movable multilayer X-ray
mirrors. Layered synthetic materials – multilayers – arelayered structures with usually two alternating materials: a
low and high density materials. They play an important rolein synchrotron X-ray optics [4, 5, 6, 7]. They provide lessenergy resolution but correspondingly more flux and keep
the angular beam divergence constant (in the ideal case).
Typical multilayers used as optical elements at third generation synchrotrons provide a spectral bandwidth of 1 to
5%. Typical glancing angles are of the order of a degree
and thus lie between the mrad wide angles of X-ray mirrors and the much bigger 10 degree wide Bragg angles ofsingle crystals. The angular acceptance of X-ray multilayer
mirror is of the order of one mrad (for a bandwidth 1%). Asa rule, from 100 to 400 periods participate in effective reflection in such mirrors. About 90% peak reflectivity wasachieved for wavelengths around 0.1 nm. Computer simulations are in very good agreement with experimental results in all cases so that efficiencies can be safely predicted.
The concept of photon beam distribution system is very
simple. Figure 1 shows relevant photon beamline configuration. The distribution of pulse trains among the different user stations can be done by movable deflectors. A
schematic diagram of a movable deflector is shown in Fig.
2. Its key components include rotating multilayers andmultifacet reflector. The advantages of multilayer as movable photon beam deflector are based on two factors: thelarger deflection angle compared to X-ray mirrors; and thelarger angular acceptance compared to crystals. The multilayer mirror angular acceptance is of the order of one mrad,and is well matched to the natural opening angle, (from one
to a few µrad), of an XFEL source. In order to achieve
stable photon beam deflection the alignment accuracy ofmultilayer deflectors must be less than 0.1 mrad. It is believed that technology, presently in advanced development
for applications other than XFEL, will enable rotating multilayers to satisfy these requirements. The initial photon
beam is transformed into 5 beams. The switching mirrors
need to rotate at a frequency of 1 Hz such that each user
actually receives one train of pulses with a full duration ofSingle-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 131-134

Figure 1: Proposed SASE undulator beamline for studies with maximum X-ray flux. The distribution of photons isachieved on the basis of pulse trains and it is possible to serve 5 user stations with repetition rate 1 Hz.

Figure 2: Concept of the photon beam deflector based on
multilayer X-ray mirror. Using rotating multilayer mirrors as switching elements between the multifacet reflectors makes it possible to provide X-ray radiation for many
user stations.
1 ms per second. Note that even if the photon beam is distributed among many users, the peak flux per user remains
untouched (apart from the losses in the deflector system).
Such a scheme, which adopts multilayer deflector concept,
allows one to increase the total number of user stations byusing standardized X-ray optical components.
An attractive feature of the distribution system based on
movable multilayers is the absence of no apparent limitations which would prevent operation at even hundred user
stations (per SASE undulator) simultaneously. All users
will receive the photon beam of identical (and high) quality. Every time deflection process happens only once during one pass of the photon beam through the deflector unit
with only three multilayers, and the problem of the absorption of the radiation in the distribution system does not exist
at all. Another advantage comes from small (one to a fewµrad) angular divergence of the FEL radiation. As a result, in an extended sequence of deflectors (say, a few tensof meters), photon beam properties (spot size) remain unchanged. The larger number of beamlines, the smaller isthe macropulse repetition rate per user station. Note also

MOPOS12that even if the beam is distributed among 50 users, themacropulse repetition rate per user will still be 0.1 Hz. It
is important to note that for many experiments this may
not be a difficulty and the macropulse (4000 pulses) per 10
seconds is more than sufficient. Photon intensity integrated
over macropulse is equivalent to an intensity integrated per
an hour at synchrotron radiation sources today. Anotherattractive feature of the proposed photon system is a highdegree of flexibility: if some user will request a full photon flux for a while, this can be done simply by means of”freezing” motion of the multilayers for a while such thatfull photon flux is directed to dedicated user station.

MULTI-USER DISTRIBUTION SYSTEMBASED ON CRYSTAL DEFLECTORS
Photon beam distribution system based on movable multilayers is one of the alternatives under consideration toextend the XFEL capability to a few tens users working
in parallel. The second potential candidate for the XFEL
laboratory to progress into multi-user facility class is that
distribution system based on (fixed) crystal deflectors. Figure 3 shows a schematic layout of the photon distribution

Figure 3: Photon beam distribution system setup based on
crystal deflectors for simultaneous multi-user mode of operation at 0.1 nm

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 131-134

Figure 4: Basic principle of the XFEL multi-user distribution system. Using Laue diffraction in Si crystals as amethod of photon beam deflection it is possible to provide
X-ray radiation for many user-station simultaneously.
system. This is a farm of multi-station SASE undulator
beamlines, working with a series of transmission crystal
deflectors. Advantage of this scheme is the possibility ofusing not only the diffracted photon beam, but also thetransmitted ”broadband” SASE beam for downstream experimental stations operating at different photon energies(see Fig. 4). The latter concept is the basic idea of the
Troika beamline at ESRF [8, 9, 10]. Note that even if thephoton beam is distributed among a few tens of users, thepeak brilliance per user remains untouched (apart from thelosses in the deflector system). In the case of end stations
the direct photon beam is used.
The relative spectral bandwidth for Laue reflection is
independent of the wavelength or glancing angle of Xrays and is given merely by properties of the crystal andthe reflecting atomic planes. In particular, it implies thatthe choice of a crystal and reflecting atomic planes determines the spectral resolution. For example, one canconsider Si(111) crystals, which have FWHM bandwidthof ∆λ/λ  1.2 × 10−4 in Laue transmission geometry.
Deflectors at photon beam lines are fabricated from silicon. The main advantage of the silicon is the availabilityof almost perfect synthetic monocrystals, with high transparency. The reason is that semiconductor industry has created a huge demand for defect-free, perfect single crystal.
In order to maintain a high transmission through the deflectors for the downstream stations, it is necessary to limit
the absorption in the 10 deflectors to about 50% at 0.1 nm.
The thickness of the one crystal must therefore not exceed
15 µm. The angular acceptance of silicon deflector is of
the order of 20 µrad for a wavelength of 0.1 nm, and iswell matched to the natural opening angle, (one µrad), ofan XFEL source.
The use of a Laue deflector can be extremely advantageous in the case of high thermal loads, because the beamis almost entirely transmitted, and only a small part is absorbed. At 0.1 nm an average power of 40 W (2 mJ×
5 trains/s × 4000 pulse/train) at the 1st SASE undulator
exit corresponds to a normal incidence power density of 50
W/mm2 at the distance of 1000 m from the undulator for abeamsize (FWHM) of 1 mm. The absorbed power per one
deflector is about 2 W.
Silicon has the advantage of a high heat conductivity and133

Figure 5: Electron (photon) energy shifter as a switchingelement between 3 beamline clusters. Conceptual layout.
high damage threshold, thus achieving good performanceat high power load. It is well known that when crystal plateis cooled, the thermal deformation results in a slope error
composed of a bending and bump component. Briefly, thethermal deformation of the crystal induced by heat load
depends on the ratio α/k, where α and k are the thermal
expansion coefficient and the thermal conductivity of thecrystal, respectively. This ratio is strongly temperature dependent for silicon. The ratio α/k is zero at 125 K, andabout 50 times smaller at liquid-nitrogen temperature (77K) than at room temperature.
The time-averaged power and power density at large distance from the SASE undulator are comparable to thoseof the third generation synchrotron radiation sources. For
example, the brightest X-ray beams at ESRF facility are
produced by in-vacuum undulators. These undulators emit
about 0.5 kW of X-ray power in the central cone and thepower density, at the position of the silicon monochromator 30 m from the source, is about 200 W/mm2 . Coolingtechniques such as cryogenic cooling of Si have become
standard at the third generation sources. The thermal deformation of the silicon crystal, which is indirectly cooled byliquid nitrogen, was studied experimentally and by finiteelement analysis. Excellent agreement between the experimental measurements and theoretical results was observed.
There is the best high-power working point for the crystal,
when the power is raised to the point where the maximum
temperature reaches 125 K. At this temperature the ratio
between the thermal expansion and the thermal conductivity is zero [11].
The advantage of operating single-crystal-silicon deflector at cryogenic temperatures is obvious. Lowering thetemperature of silicon from room temperature to liquidnitrogen temperatures improves the so-called figure of
merit, k/α, by 50-fold. A thin crystal is desired so thata large fraction of the incident beam would be transmitted,
hence reducing the absorbed power in the deflector that has
to be removed by the liquid nitrogen.
Although XFEL sources are designed primarily to generate brilliant X-rays with moderate energy 5-15 keV, highenergy X-rays are of great usefulness. In particular, highenergy focused beam is quite attractive for structural studies of amorphous solids and liquids and for diffraction studies of crystalline materials because of its extinction-free nature. The analysis shows that strong harmonic growth canSingle-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 131-134

Figure 6: 1st SASE undulator beamline. A photon beam distribution system based on combination movable multilayers
and crystals in transmission (Laue) geometry can provide efficient way to generate a multi-user facility.
be expected in SASE XFELs. When a beam is strongly
bunched in the sinusoidal ponderomotive potential formedby the undulator field and the radiation field of fundamental frequency, the electron beam density spectrum develops
rich harmonic contents. Coherent radiation at the odd harmonics can be generated in a planar undulator and significant power levels for the third harmonic can be reached
before the FEL is saturated. Explicit calculations show thatthe power of the transversely coherent third-harmonic radiation can approach a fraction of a per cent of the fundamental power level.

energy peak-width of 10−3 and thus, using the whole SASE
radiation peak, the flux is more than 10 times higher thanthat obtained with crystal deflector.
Both types of deflectors are important, their roles arecomplementary, and one type cannot replace the other. Figure 6 shows the optimal beamline configuration. The first
20 beamlines are planned to be multi-purpose beamlines
for experiments with maximum X-ray flux. In this case21st ... end-stations use the photon beam distribution system working with transmission crystal deflectors.

In this paper we propose to utilize the third harmonic
radiation from the XFEL. Four upstream transparent deflectors, which adopt so-called ”Laue transmission geometry” concept, enable us to perform five different experiments simultaneously. High-energy X-rays are associatedwith a large penetration power, which makes it possible touse relatively ”thick” silicon deflectors. The thickness of
one crystal is 0.1 mm. The other main difference between
diffraction at high energies and at conventional energies is
the smaller Bragg angles. In particular for the 1st orderSi(111) reflection at 0.03 nm the deflection angle is about
0.1 rad.

REFERENCES

The distribution of pulse trains among the different
beamline clusters can be done by a photon (electron) energy shifter pulsed at 5 Hz. It directs every other photon
pulse train into a second cluster of photon beamlines. Thismethod of pulse train distribution is based on the accelerator technique. In this case the SASE undulator beamline
consists of an input energy shifter, SASE undulator, andoutput energy equalizer (see Fig. 5). Using photon energy
shifter as switching element between 3 clusters of photon
beamlines makes it possible to provide simultaneously Xray radiation for 5 × 3 = 15 user station. Distribution ofphotons is achieved on the basis of pulse trains. Each user
station actually receives one, two, or three pulse trains offull length at 1 Hz repetition rate.
It should be noted that crystal deflector performances
are complementary to those of multilayer deflectors, whose
bandwidth is much wider but whose photon flux is muchhigher. Crystal deflectors have a band-pass of the order of
10−4 , which is unnecessary narrow in many experiments.
On the other hand, the fundamental SASE radiation has an

MOPOS12[1] TESLA Technical Design Report, DESY 2001-011, edited
by F. Richard et al., and http://tesla.desy.de/.
[2] P. Audebert et al., “TESLA XFEL: First stage of the X-ray
laser laboratory – Technical design report (R. Brinkmann etal., Eds.)”, Preprint DESY 2002-167.
[3] The LCLS Design Study Group, LCLS Design Study Report, SLAC reports SLAC- R521, Stanford (1998) andhttp://www-ssrl.slacstanford.edu/lcls/CDR.
[4] D. Windt, Appl. Phys. Lett. 74(1999)2890.
[5] E. Majkova et al., ”Nanometer-scale period multilayers:
thermal stability study”, report at the 7th International Conference on the Physics of X-ray Multilayer Structures, Sapporo, Japan, 2004.
[6] P. Deschamps et al., J. Synchrotron Rad. 2(1995)124.
[7] Ch. Morawe et al., SPIE Proc. 4145(2000)61.
[8] G. Grübel et al., J. Phys. IV C9(1994)27.
[9] G. Grübel et al., Rev. Sci. Instrum. 67(1996)1.
[10] M. Mattenet, T. Schneider, and G. Grübel, J. SynchrotronRad. 5(1998)651.
[11] Lin Zhang et al., J. Synchrotron Rad. 10(2003)313.

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 135-138

SUB-TERAWATT MODE OF OPERATION OF X-RAY SASE FEL
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract
Application of dispersion section in combination with
undulator tapering is an effective tool for achieving extremely high output power of XFEL. In the first part of theundulator the gap is fixed, and amplification process is developed as in usual SASE FEL. When energy modulationof the electron beam becomes to be comparable with local energy spread, the electron bunch passes via dispersion
section resulting in an effective compression of the electron
bunch. Then bunched electron beam enters the second halfof the undulator where the gap is tapered for effective extraction of the energy from the electron bunch. Our studies
show that output radiation power can reach a sub-TW level
in Angstrom wavelength range.

INTRODUCTION
Baseline design of present XFEL projects [1, 2, 3, 4] assumes only standard (SASE FEL) mode for production ofradiation. Recent developments in the field of FEL physics
and technology form a reliable basis for perspective extensions of the XFEL facilities. Relevant study for possible
perspective developments of LCLS within next ten years
since its commissioning has been presented in [5].
The first stage of the European XFEL facility assumes
installation of five radiators, and three of them are SASE
undulators. Present concept of an XFEL facility assumes
to cover continuously wavelength range from 0.1 to 1.6 nm
at a fixed energy of the electron beam. This is achieved
with three undulators (SASE1-SASE3) [6]. A VUV option (SASE4) is under consideration, too [7]. Optimizationof undulator parameters (see Table 1) has been performed
for the electron beam parameters presented in the Supplement to TESLA XFEL Technical Design Report: peak current 5 kA, rms normalized emittance 1.4 mm-mrad, andinitial energy spread of 1 MeV. All undulators are planar,
variable-gap devices with an identical mechanical design.
The first undulator, SASE1, is optimized for operation at

Table 1: Specification of undulators

SASE1
SASE2
SASE3
VUV

λr
nm
0.1-0.15
0.1-0.4
0.4-1.6
1.6-6.4

λu
mm
39
47.9
64.8
110

gap
mm
10-12
10-19
10-20
19-37

Available online at http://www.JACoW.org

Bw
T
0.8-1
0.6-1.3
0.8-1.7
0.7-1.6

Lw
m
150
150
110
80

the wavelength range 1-1.5 nm. Our study shows thatsuch tunability range almost does not affect operation at
the shortest wavelength of 0.1 nm. Operation of two other
FELs (SASE2 and SASE3) is not so critical, and nominal tunability range is chosen to be by a factor of two (24 nm, and 8-16 nm, respectively). The length of the undulators is chosen such that continuous wavelength tunability
can be provided by means of extra opening the undulator
gaps, or by tuning to the frequency doubler mode of operation. It should be noted that wide wavelength tunability
range of the proposed XFEL concept is not the only important feature. Changing of undulator gaps in different partsof SASE2 and SASE3 undulators allows one to tune themodes with high output power (sub-TW level), or for effective generation of the second harmonic (see Fig. 1). The
latter feature might be important for future pump-probe experiments. Also, recently proposed attosecond SASE FEL
scheme is foreseen for implementation [8, 9].
The developments discussed in this paper concern theincreased FEL output radiation power.

STANDARD SASE MODE OF OPERATIONIn this section we present main characteristics of XFEL
source operating in a standard mode, i.e. conventional
SASE mode. Figure 2 shows evolution of the averaged radiation power along undulator length. Saturation occurs at
the undulator length of about 100 m. Figures 3 shows temporal and spectral structure of the radiation pulse at saturation. Increase of the undulator length results in moderate
growth of the radiation power, but this happens mainly due
to the growth of the sidebands. As a result, radiation spectrum spreads, and brilliance drops down.

HIGH-POWER MODE OF OPERATION
Application of dispersion section in combination with
undulator tapering is an effective tool for achieving extremely high output power of XFEL and avoiding problemsof sideband growth in the nonlinear regime. Tapering consists in slowly reducing the field strength of the undulator
field to preserve the resonance wavelength as the kinetic
energy of the electrons changes. Figure 1 shows a concept of a universal undulator allowing implementing different modes of XFEL operation: standard SASE, frequency
doubler, and high power. The first stage is a conventional
X-ray SASE FEL. The gain of the first stage is controlledin such a way that the maximum energy modulation of theelectron beam at the FEL exit is about equal to the local

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 135-138

Figure 1: Three schemes for 2nd SASE undulator. Only one type of undulator magnet structure is needed. The radiation
wavelength will be tuned by changing the gap. The total magnetic length is 150 m.

At the total undulator length of 150 m, the FEL output

100

P [GW]

80
60
40
20
0
-100

-50

0

50

100

t [fs]

30
Normalized spectrum

energy spread, but still far away from saturation. The left
plot in Fig. 4 shows the phase space distribution of particles
in a slice of the bunch. Such a picture is typical for every
spike. The modulation amplitude is small, but there isvisible energy modulation with an amplitude of about thevalue of the local energy spread. When the electron bunch
passes through the dispersion section this energy modulation leads to effective compression of the particles as it isillustrated the right plot in Fig. 4. Then the bunched electron beam enters the tapered undulator, and from the very
beginning produces strong radiation because of the large
spatial bunching. Radiation field produces a ponderomotive well which is deep enough to trap the particles, since
the original beam is relatively cold. The radiation producedby these captured particles increases the depth of the ponderomotive well, and they are effectively decelerated. As
a result, much higher power can be achieved than for thecase of a uniform undulator.

20

10

0

-0.4

-0.2

0.0

0.2

∆ω/ω [%]<P> [GW]

150

Figure 3: Temporal and spectral structure of the radiation
pulse at saturation. Undulator length is 100 m. SASE FEL
operates in a standard SASE mode.

100

50

0

0

50

100

150

z [m]

Figure 2: Average radiation power versus undulator length.
Solid line: high power mode of operation. Dashed line:
standard SASE mode. Radiation wavelength is 0.2 nm.

MOPOS14

at 0.2 nm is enhanced by a factor of 8, from 20 GW to
150 GW (see Fig. 2). Figure 5 shows time structure of theradiation pulse at the undulator exit. It is seen that tapering procedure provides extremely high power of individual
spikes, up to sub-TW level. Such features of the radiation may be useful for applications studying nonlinear processes. Figure 6 shows spectral structure of the radiation
pulse. One can see that it does not contain a signature of

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 135-138

Figure 4: Phase space distribution of the particles in a slice before (left plot) and after (right plot) the dispersion section.

0.8

Normalized spectrum

15

P [TW]

0.6

0.4

0.2

0.0

10

20

30

10

5

0

40

t [fs]

-0.2

0.0

0.2

∆ω/ω [%]

0.8

Figure 6: Spectral structure of the radiation pulse for
SASE2 tuned for high power mode of operation. Radiation wavelength is 0.2 nm, undulator length is 150 m.

0.6
P [TW]

-0.4

0.4

50

0.2

6

8

10

12

14

t [fs]

Figure 5: Temporal structure of the radiation pulse for
SASE2 tuned for high power mode of operation. Lower
plot shows enlarged view of the upper plot. Radiation
wavelength is 0.2 nm, undulator length is 150 m. Dashedline shows power level of standard SASE FEL at saturation.

P [GW]

40
0.0

30
20
10
0

10

20

30

40

t [fs]

Figure 7: Temporal structure of the radiation pulse (seeFig. 5) reflected by thin Si (111) crystal. Central frequency
corresponds to ∆ω/ω = −0.1% (see Fig. 6). SASE2 tuned
for high power mode of operation. Radiation wavelength is
0.2 nm, undulator length is 150 m.
sidebands, and the spectrum width does not differ from thatof conventional SASE, while peak radiation power is muchhigher. The radiation filtered through a crystal (Si (111))
monochromator (see Fig: 7) has high peak power comparable with standard SASE level, but with much less spectrum
width.

REFERENCES[1] “Conceptual Design of 500 GeV e+ e− Linear Collider with
Integrated X-ray Facility” (Edited by R. Brinkmann et al.),DESY 1997-048, ECFA 1997-182, Hamburg, May 1987.

Single-Pass FELs

138

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 135-138[2] TESLA Technical Design Report, DESY 2001-011, edited
by F. Richard et al., and http://tesla.desy.de/.
[3] P. Audebert et al., “TESLA XFEL: First stage of the X-ray
laser laboratory – Technical design report (R. Brinkmann etal., Eds.)”, Preprint DESY 2002-167.
[4] The LCLS Design Study Group, LCLS Design Study Report, SLAC reports SLAC- R521, Stanford (1998) andhttp://www-ssrl.slacstanford.edu/lcls/CDR.
[5] M. Cornacchia et al., SLAC-PUB-10133, December, 2003.
[6] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, DESY
Print TESLA FEL 2004-02.
[7] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, DESY
Print TESLA FEL 2004-04.
[8] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt.
Commun. 237(2004)153.
[9] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt.
Commun. 239(2004)161.
[10] J. Feldhaus et al., Preprint DESY 03-092, 2003. Nucl. Instrum. and Methods A, in press.

MOPOS14

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 139-142

DESIGN FORMULAS FOR VUV AND X-RAY FELS
E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
Simple formulas for optimization of VUV and X-ray
SASE FELs are presented. The FEL gain length and the
optimal beta-function are explicitly expressed in terms of
the electron beam and undulator parameters. The FEL saturation length is estimated taking into account energy diffusion due to quantum fluctuations of the undulator radiation. Examples of the FEL optimization are given. Parameters of a SASE FEL, operating at the Compton wavelength,
are suggested.

INTRODUCTION
At the first stage of a SASE FEL (self-amplified spontaneous emission) [1] design one looks for the dependenceof the FEL saturation length on the wavelength, electron
beam parameters, undulator parameters, and beta-function.
Usually the parameters are optimized for the shortest design wavelength since the saturation length is the largest
in this case. The saturation length is proportional to thegain length (e-folding length) of the fundamental transverse
mode (see [2] for more details). The gain length can befound by the solution of the FEL eigenvalue equation.
The eigenvalue equation for a high-gain FEL, including
diffraction of radiation, emittance, and energy spread, wasderived in [3, 4]. There exist approximate solutions [5, 6]of this equation. The exact solution was presented in [7]as well as an approximate solution (with a limited validity
range). The latter solution was fitted [7] using 3 dimensionless groups of parameters, and 19 fitting coefficients.
An approximate solution, that fits the exact solution in theentire parameter space with high accuracy (better that 1 %),was presented in [8]. A numerical algorithm for finding thisapproximate solution is very fast and robust. It was used toobtain the main results of this paper.
In this paper we present the fitting formula for the FEL
gain length written down explicitly in terms of the beamand undulator parameters. This formula is not universal,
but it provides a good accuracy (better than 5 %) in a typical parameter range of VUV and X-ray FELs. We present
the formula without derivation since it was not derived analytically. In some sense the parametric dependencies were
guessed, and then the fitting coefficients were found fromthe solution of the eigenvalue equation. For instance, weused only 2 fitting coefficients for the gain length with the
optimized beta-function. The formulas of this paper allow
one to quickly estimate FEL saturation length, including
the effect of energy diffusion in the undulator due to quantum fluctuations of the undulator radiation. In addition,

Available online at http://www.JACoW.org

we present two practical examples of using our design formulas: optimization of SASE FEL with negligible energy
spread, and the limitation on SASE FEL wavelength taking
into account quantum diffusion. In particular, we suggest
for the first time the set of parameters for a SASE FEL operating at the Compton wavelength.

GAIN LENGTH FOR THE OPTIMIZEDBETA-FUNCTION
Let us consider an axisymmetric electron beam with acurrent I, and a Gaussian distribution in transverse phasespace and in energy [7, 8]. The focusing structure in the undulator is a superposition of the natural undulator focusing
and an external alternating-gradient focusing. The eigenvalue equation [7, 8] is valid under the condition [8]:


λr
Lf
 min 1,2πβ2πwhere Lf is the period of the external focusing structure,β is an average beta-function,  is the rms emittance of theelectron beam, and λr is the FEL resonant wavelength. The
resonance condition is written as:λr =λw (1 + K 2 )
.
2γ 2

(1)

Here λw is the undulator period, γ is relativistic factor, andK is the rms undulator parameter:
K = 0.934 λw [cm] Brms [T] ,(2)Brms being the rms undulator field.
In what follows we assume that the beta-function is optimized so that the FEL gain length takes the minimal value
for given wavelength, beam and undulator parameters. Under this condition the solution of the eigenvalue equation
for the field gain length can be approximated as follows:
Lg  Lg0 (1 + δ) ,

(3)

where


1/2

(n λw )5/6 (1 + K 2 )1/3
,
2/3
KAJJ
λr

(4)

5/4
σγ2
n
IA
.
9/8 (KA2
2 1/8
I λ1/8JJ ) (1 + K )
r λw

(5)

Lg0 = 1.67

IA
I

and
δ = 131

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 139-142

Figure 1: Gain length versus resonant wavelength for thefollowing set of parameters: λw = 3 cm, K = 1, I = 2.5
kA, n = 2 µm, σE = 1 MeV. Undulator is planar, resonance is maintained by tuning electron beam energy, betafunction is optimized for each case. Line is the solution of
the eigenvalue equation [8], and the circles are calculatedusing formula (3).
The following notations are introduced here: IA = 17 kA
is the Alfven current, n = γ is the rms normalized emittance, σγ = σE /mc2 is the rms energy spread (in unitsof the rest energy), AJJ = 1 for a helical undulator and
AJJ = J0 (K 2 /2(1 + K 2 )) − J1 (K 2 /2(1 + K 2 )) for aplanar undulator, J0 and J1 are the Bessel functions of thefirst kind.
The formula (3) provides an accuracy better than 5 % in
the domain of parameters defined as follows
2π
<5
λr


2 

1 2π
δ < 2.5 1 − exp −
2
λr
1<


βopt  11.2

IA
I

1/2

3/2 1/2

n λw(1 + 8δ)−1/3
λr KAJJ(8)

Note that dependence of the gain length on beta-function israther weak when β > βopt .
Finally, let us note that the saturation length cannot be directly found from the eigenvalue equation. However, withan accuracy 10-20 % one can accept the following estimate:(6)

Lsat  10 Lg(7)

EFFECT OF QUANTUM DIFFUSION IN
AN UNDULATOR

Note that the condition (6) is usually satisfied in realistic
designs of VUV and X-ray FELs when one does optimization for the shortest wavelength (defining the total undulator length). The condition (7) is practically not a limitation.
To illustrate the accuracy of the formula (3) we present a
numerical example. The following nominal operating point
is chosen: λr = 1 nm, λw = 3 cm, K = 1, I = 2.5 kA,
n = 2 µm, σE = 1 MeV, energy is 2.8 GeV, undulator isplanar. We scan over different parameters and compare thegain length calculated with formula (3) and by solving the
eigenvalue equation [8]. The results are presented in Figs.
1-6. We have carefully checked the accuracy of formula(3) for different combinations of dimensional parameters
entering (4) and (5). The deviation of the approximate formula (3) from the solution of the eigenvalue equation [8] isindeed defined only by the parameters 2π/λr and δ, andis within 5 % in the above specified domain.
We also present here an approximate expression for the
optimal beta-function (an accuracy is about 10 % in theabove mentioned parameter range):

MOPOS15

Figure 2: Gain length versus undulator period for the following set of parameters: λr = 1 nm, K = 1, I = 2.5
kA, n = 2 µm, σE = 1 MeV. Undulator is planar, resonance is maintained by tuning electron beam energy, betafunction is optimized for each case. Line is the solution of
the eigenvalue equation [8], and the circles are calculatedusing formula (3).

(9)

Energy spread growth due to the quantum fluctuationsof the spontaneous undulator radiation can be an important
effect [1, 10] in future SASE FELs. The rate of the energy
diffusion is given by [11]:
dσγ2
14
=
λc re γ 4 κ3w K 2 F (K) ,
(10)
dz
15
where λc = 3.86 × 10−11 cm, re = 2.82 × 10−13 cm,
κw = 2π/λw , andF (K) = 1.42K + (1 + 1.50K + 0.95K 2 )−1for helical undulator
F (K) = 1.70K + (1 + 1.88K + 0.80K 2 )−1
for planar undulator(11)

To estimate the FEL saturation length, we accept the following scheme. First, we neglect energy diffusion and finda zeroth order approximation to the saturation length from

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 139-142

Note that in the latter formula the powers are somewhat
simplified. Comparing Eqs. (9) and (12), we can introduce
an effective parameter
δeﬀ =Figure 3: Gain length versus undulator parameter K for thefollowing set of parameters: λr = 1 nm, λw = 3 cm,
I = 2.5 kA, n = 2 µm, σE = 1 MeV. Undulator is planar,resonance is maintained by tuning electron beam energy,
beta-function is optimized for each case. Line is the solution of the eigenvalue equation [8], and the circles arecalculated using formula (3).

δ + δq,1 − δq(14)

which should be used instead of δ in (7) to check the applicability range and in (8) to estimate the optimal betafunction.
Although formula (12) is rather crude estimate, it can beused for quick orientation in the parameter space with aposteriori check using a numerical simulation code.

OPTIMIZED FEL WITH A NEGLIGIBLE
ENERGY SPREAD
Formulas, presented in the previous Sections, can beused for the optimization of undulator parameters as soon
as a specific type of the undulator is chosen. We demonstrate such a possibility with the planar NdFeB undulatorof which magnetic field can be described by the following
formula [9]:g
+ 1.52
Bmax [T] = 3.694 exp −5.068
λw



g
λw

2 

for 0.1 < g/λw < 1 (15)Figure 4: Gain length versus normalized emittance for thefollowing set of parameters: λr = 1 nm, λw = 3 cm, K =1, I = 2.5 kA, σE = 1 MeV. Undulator is planar, betafunction is optimized for each case. Line is the solution of
the eigenvalue equation [8], and the circles are calculatedusing formula (3).

where g is the undulator gap. The rms value of√the parameter K is given by Eq. (2) with Brms = Bmax / 2.
We assume that the energy spread effect on the FEL operation can be neglected (δ , δq → 0). Then, using (3), (2)and (15), we minimize the gain length for a given undulator
gap. The optimal undulator period is independent of λr , I
and n and is found to be(λw )opt [cm]  1 + 2 g [cm](9), (3)-(5). Then we calculate an induced energy spread in
the middle of the undulator from (10), add it quadraticallyto the initial energy spread, and find a new expression forδ. Then, using (9), (3)-(5), we find the first approximation
to the saturation length. Then we do the next iteration, etc.
∞δqn
The saturation length is then proportional to a series
n=0

and is given by
Lsat  10 Lg01+δ
,
1 − δq

(12)

where

δq = 5.5 × 104



IA
I

3/2

λc re 2n
11/4 5/4
λr λw(1 + K 2 )9/4 F (K)
KA3JJ
(13)

for g > 0.5 cm (16)The optimal value of K is then defined from (15) and (2),the electron beam energy - from (1), and the optimal betafunction - from (8). The minimal gain length can be expressed (in practical units) as follows:
5/6(Lg )min [m]  20

n [µm] g 1/2 [cm]2/3

I 1/2 [kA] λr [Å]

(17)

Using estimate of the saturation length (9), we findthe minimal wavelength at which SASE FEL can saturate
within the given undulator length Lw :(λr )min [Å]  3 × 103

5/4

n [µm] g 3/4 [cm]3/2

I 3/4 [kA] Lw [m](18)Single-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 139-142

Figure 5: Gain length versus current for the following set ofparameters: λr = 1 nm, λw = 3 cm, K = 1, n = 2 µm,
σE = 1 MeV. Undulator is planar, beta-function is optimized for each case. Line is the solution of the eigenvalue
equation [8], and the circles are calculated using formula(3).

Figure 6: Gain length versus energy spread for the following set of parameters: λr = 1 nm, λw = 3 cm, K = 1,
I = 2.5 kA, n = 2 µm. Undulator is planar, beta-function
is optimized for each case. Line is the solution of the eigenvalue equation [8], and the circles are calculated using formula (3).

SASE FEL AT THE COMPTONWAVELENGTH

I = 5 kA and n = 0.1 µm, the energy is 40 GeV. We
choose a helical undulator with λw = 2 cm and K = 0.7.
The optimal beta-function is about 35 m, and the saturationis reached within 200 m. Our estimates show that quantum
effects, other than energy diffusion, give small corrections
to the classical description and can be neglected.

Another example is the optimization of sub-Angstrom
FELs for which the effect of quantum diffusion in the undulator can play an important role. We consider the casewhen the energy spread is dominated by the quantum diffusion, and neglect initial energy spread (δ → 0). Optimizing undulator period and parameter K in (12), we get thefollowing estimate for the minimal wavelength1 :(λr )qmin [Å] 

4 n [µm]2/53/5I [kA] Lw [m](19)Note that in some cases the optimal undulator parameters can be impractical. In any case, the estimate (19) givesa lower limit. The following numerical examples show that
one can be close to this limit with technically feasible undulator parameters.
Let us consider the electron beam parameters (peak current and emittance) assumed in [12]. One of the examples, considered in [12], is a SASE FEL operating at λr =0.28 Å with I = 5 kA and n = 0.3 µm. Another example
is even more ambitious: λr = 0.12 Å with I = 5 kA andn = 0.1 µm.
We try to push the wavelength closer to the extreme
given by Eq. (19). In our first example we assume I = 5 kAand n = 0.3 µm. With these parameters the wavelength
λr = 0.1 Å can be reached at the electron beam energy 23
GeV in a planar undulator with λw = 2 cm and K = 1(with the gap g = 0.7 cm according to (15) and (2)). The
optimal beta-function is about 40 m, and the saturation
length is estimated at 160 m.
The second example is a SASE FEL operating at theCompton wavelength, λr = λc = 0.0234 Å (photon energy is 0.5 MeV). We assume the electron beam with
1 One can notice the difference with more crude estimate presented in[10]

MOPOS15

REFERENCES[1] Ya.S. Derbenev, A.M. Kondratenko and E.L. Saldin, Nucl.
Instrum. and Methods 193(1982)415[2] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, “ThePhysics of Free Electron Lasers”, Springer, Berlin, 1999
[3] K.J. Kim, Phys. Rev. Lett. 57(1986)1871[4] L.H. Yu and S. Krinsky, Physics Lett. A129(1988)463[5] L.H. Yu, S. Krinsky and R.L. Gluckstern, Phys. Rev. Lett.
64(1990)3011[6] Y.H. Chin, K.J. Kim and M. Xie, Nucl. Instrum. and Methods A318(1992)481[7] M. Xie, Nucl. Instrum. and Methods A 445(2000)59[8] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A 475(2001)86[9] TESLA Technical Design Report, DESY 2001-011 (2001);TESLA XFEL, Supplement, DESY 2002-167 (2002)[10] J. Rossbach et al., Nucl. Instrum. and Methods A
374(1996)401[11] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A 393(1997)152[12] M. Cornacchia et al., SLAC-PUB-10133 (2003)

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 143-146

THE FREE ELECTRON LASER KLYSTRON AMPLIFIER CONCEPT
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract
We consider optical klystron with a high gain per cascade pass. In order to achieve high gain at short wavelengths, conventional FEL amplifiers require electron beam
peak current of a few kA. This is achieved by applying
longitudinal compression using a magnetic chicane. In
the case of klystron things are quite different and gain of
klystron does not depend on the bunch compression in theinjector linac. A distinguishing feature of the klystron amplifier is that maximum of gain per cascade pass at highbeam peak current is the same as at low beam peak current without compression. Second important feature of the
klystron configuration is that there are no requirements on
the alignment of the cascade undulators and dispersion sections. This is related to the fact that the cascades, in our(high gain) case, do not need the radiation phase matching.
There are applications, like XFELs, where unique properties of high gain klystron FEL amplifier are very desirable.
Such a scheme allows one to decrease the total length ofmagnetic system. On the other hand, the saturation efficiency of the klystron is the same as that of conventional
XFEL.

INTRODUCTION
High gain FEL amplifiers are of interest for a variety ofpotential applications that range from X-ray lasers [1, 2] toultraviolet MW-scale industrial lasers [3]. There are various versions of the high gain FEL amplifier. A numberof high gain FEL amplifier concepts may prove useful for
XFEL applications. Two especially noteworthy ones are
the FEL amplifier with a single uniform undulator [1, 2]
and the distributed optical klystron [4, 5, 6, 7]. The highgain cascade klystron amplifier described in this paper is
an attractive alternative to other configurations for operation in the X-ray wavelength range (see Fig. 1).
Electron bunches with very small transverse emittanceand high peak current are needed for the operation of conventional XFELs. This is achieved using a two-step strategy: first generate beams with small transverse emittanceusing an RF photocathode and, second, apply longitudinal
compression at high energy using a magnetic chicane. Although simple in first-order theory, the physics of bunch
compression becomes very challenging if collective effects
like space charge forces and coherent synchrotron radiation
forces (CSR) are taken into account. Self-fields of bunches

Available online at http://www.JACoW.org

as short as 10-100 µm have never been measured and arechallenging to predict.
The situation is quite different for klystron amplifier
scheme described in our paper. A distinguishing feature of
the klystron amplifier is the absence of apparent limitations
which would prevent operation without bunch compression
in the injector linac. As we will see, the gain per cascade pass is proportional to the peak current and inversely
proportional to the energy spread of the beam. Since thebunch length and energy spread are related to each otherthrough Liouville’s theorem, the peak current and energy
spread cannot vary independently of each other in the injector linac. To extent that local energy spead is proportional
to the peak current, which is usually the case for bunch
compression, the gain will be independent of the actual
peak current. We see, therefore, that klystron gain in linear
regime depends only on the actual photoinjector parameters. This incipient proportionality between gain and I0 /σγ(I0 is a current and σγ is a local energy spread in units of
the rest electron energy) is a temptation, in designing an
XFEL, to go to very high values of I0 /σγ and very longvalues of bunch length. Starting with this safe scenario, one
may gradually increase compression factor getting shorter
FEL pulses with higher peak power (brilliance). Note thatthe average power (brilliance) is almost independent of thecompression factor. It is also worth mentioning that there
is a possibility [8] to get short (10 fs) radiation pulses forthe pump-probe experiments, having long (10 ps) electron
bunches. To illustrate further possible advantages of the
klystron amplifier, we describe a multi-user facility having
a ring geometry, and thus being similar to the 3rd generation synchrotron radiation facilities.

THE GAIN OF A KLYSTRON AMPLIFIER
A detailed theoretical analysis of a klystron amplifier
with a high gain per cascade can be found in [8]. Here
we present some results of that analysis.
The principle of klystron operation is simple and is very
similar to that of a multi-resonator microwave klystron. A
modulated electron beam radiates in a first undulator, andthe radiation modulates the beam in energy. Then the beam
passes a dispersion section where the energy modulationis converted into the density modulation which is muchhigher than the original one. In the second undulator the
beam with the enhanced density modulation radiates pro-Single-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 143-146

Figure 1: Schematic diagram of high gain cascade klystron amplifier
ducing much higher energy modulation etc. The process
can continue in several cascades up to saturation in the last(output) undulator. Since the gain per cascade is high, thephase matching (on the scale of the radiation wavelength)
between the beam and the radiation is obviously not required. An initial signal for such a device in VUV and
X-ray spectral range is the shot noise in electron beam.
We present here the expressions for a gain per cascade
for two different regimes of the klystron amplifier operation. In the first case the geometrical emittance of the electron beam  is small as compared to λ/(2π), where λ is
the resonant wavelength. In this case the beta-function in
the undulators can be chosen in such a way that the diffraction parameter, 2πσ 2 /(λLw ), is small (here σ is transverse
size of the beam and Lw is the length of an undulator segment). At the same time the effect of velocity spread due
to emittance on FEL operation can be neglected. After optimization of the strength of the dispersion section one getsthe amplitude gain per cascade [8]:A2JJ K 2 Nw I0,(1)(1 + K 2 ) σγ IA
where K is the rms undulator parameter, Nw is the numberof undulator periods per an undulator, IA = 17 kA is the
Alfven current, AJJ = 1 for a helical undulator andG0  4

AJJ = [J0 (Q) − J1 (Q)]for a planar undulator. Here Q = K 2 /(2 + 2K 2 ) andJn (Q) is a Bessel function of nth order.
In the opposite limit, 2π/λ  1, after optimizing betafunction and the strength of dispersion section one gets:
G0  2MOPOS16

A2JJ K 2 Nw I0(1 + K 2 ) σγ IA



λ
2π

2
.

(2)

In the latter case the diffraction parameter is big, andthe velocity spread due to emittance should be carefully
taken into account. Note that in contrast with a conventional SASE, the effects of emittance and energy spreadon longitudinal dynamics are separated in a klystron amplifier: emittance (energy spread) is important in undulators (dispersion sections). The noticeable feature of the results (1) and (2) is that the gain depends on the ratio I0 /σγ
and is, therefore, independent of compression factor in the
beam formation system. It is also interesting to note thatin the case of a small emittance the gain is defined by thelongitudinal brightness of the electron beam, while for alarge emittance - by total brightness (particles density in
6-D phase space).

Let us present an example for the case when the emittance is below diffraction limit and the undulator is planar.
With the numerical values λw = 3 cm, K = 1, γ = 103 ,the resonance value of wavelength is λ = 30 nm. If thenumber of the undulator period is Nw = 100, normalized
transverse emittance n = 2µm, and betatron function isequal to the undulator length, the diffraction parameter isabout 0.4. For a peak current of 100 A and a local energy
spread of 5 keV, appropriate substitution in (1) shows thatthe gain per cascade pass is about G0  102 (or, intensity
gain G20  104 ). In order to reach saturation in a klystron
amplifier, starting up from the shot noise, the total intensity gain should be of the order Nλ Nw [8], where Nλ is
the number of electrons per radiation wavelength. Thus,
for the considered set of parameters, one needs two cascades of amplification and the output undulator as shownin Fig. 1.

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 143-146

145

Figure 2: Diagram of a possible fourth-generation synchrotron facility using free-electron laser klystron amplifiers

Figure 3: Electron ring cell design. Using a klystron electromagnetic dispersion section as a switching element it ispossible to quickly switch off (on) the cell klystron amplifier thus providing multi-user capability. This design makes it
possible to make various wavelengths available in the XFEL laboratory quasi-simultaneously

Single-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 143-146

MULTI-USER DISTRIBUTION SYSTEMFOR XFEL LABORATORYAn X-ray laboratory should serve several, may be up toten experimental stations which can be operated independently according to the needs of the user community. On
the other hand, the multi-user distribution system has to satisfy an additional requirement. Passing the electron bunch
through the bending magnets must avoid emittance dilution
due to coherent synchrotron radiation (CSR) effects. Forvery short bunches and very high peak current, CSR cangenerate energy spread in the bending magnets and thus dilute the horizontal emittance. As a result, the preferred layout of a conventional SASE FEL is a linear arrangementin which the injector , accelerator, bunch compressors andundulators are nearly collinear, and in which the electron
beam does not change direction between accelerator andundulators.
The situation is quite different for the klystron amplifier scheme proposed in our paper. Since it operates without bunch compression in the injector linac, the problem
of emittance dilution in the bending magnets does not exist. An electron beam distribution system based on uncompressed electron beam can provide efficient ways to generate a multi-user facility - very similar to present day synchrotron radiation facilities. A possible layout of a soft
X-ray FEL laboratory based on an electron ring distribution system is shown in Fig. 2. The layout of the laboratory follows a similar approach as that used for synchrotron
light sources. The FEL user facility consists of an injector
linac and electron beam distribution system. The injector
is composed of a RF gun with photocathode and a main(superconducting) linac. In order to make efficient use of
the new source it is proposed to segment the full circumference of a distribution system into arcs which are repeateda number of times to form a complete ring. Each cell includes a two-cascade klystron and a bending magnet. A
specific realization of the electron ring cell is sketched inFig. 3. The electron beam transport line guiding electrons
from the injector linac to the experimental hall is connected
tangentially to one of the straight sections of the electron
ring. In order to obtain a useful separation between the experimental areas behind the photon beam lines, an angle of
36 degrees between two neighboring lines would be desirable. Thus, ten beam lines can be installed on a complete
electron ring. Using klystron (electromagnetic) dispersion
sections in each cell as switching elements it is possible toquickly switch the FEL photon beam from one experiment
to the other, thus providing multi-user capability. Users candefine the radiation wavelength for their experiment independently of each other to a very large extent, since theyuse different undulators. Injector linac and electron beamtransport lines operate at fixed parameters. At a fixed electron energy the magnet gap of the klystron undulators canbe varied mechanically for wavelength tuning. This design
makes it possible to make various wavelengths available in
the XFEL laboratory quasi-simultaneously. It is a great ad-

MOPOS16

vantage that injector and electron beam transport lines in
the new scheme of multi-user facility operate at fixed parameters and that an ”electron switchyard” is not required.
When a relativistic electron beam passes through the undulator, it emits incoherent radiation. This process leads
to an increase of the energy spread in the beam due toquantum fluctuations of the undulator radiation. This effect grows significantly with an increase in electron beamenergy, strength field and length of the undulator. This effect should be carefully taken into account when designing
multi-user distribution system. The expression for the rateof energy diffusion can be found in [9]. The next numericalexample illustrates the amplitude of the effect. If γ = 103 ,K = 1, λw = 3 cm, and the total length of the undulator
system is equal to 100 m, then the energy spread increase
due to quantum fluctuations is about 1 keV at the end of
the 10th klystron amplifier, and has a negligible effect on
the klystron performance.

CONCLUSION
The high-gain klystron amplifier described in this paper
is an attractive alternative to other FEL configurations for
operation in short wavelength range. A distinguishing feature of the klystron amplifier, operating in the VUV andsoft X-ray range, is the absence of apparent limitations
which would prevent operation without bunch compression in the injector linac. The scheme can also be adaptedfor generation of hard X-ray radiation. In this case one
should take into account quantum diffusion in the undulator. A consequence would be that some moderate compression would be needed (which could still be more safe than
the agressive compression required for conventional SASE
FELs [1, 2]).

REFERENCES[1] TESLA Technical Design Report, DESY 2001-011, editedby Richard et al., and http://tesla.desy.de[2] The LCLS Design Study Group, LCLS Design Study
Report, SLAC reports SLAC-R521, Stanford (1998) andhttp:www-ssrl.slacstanford.edu/lcls/CDR[3] C. Pagani et al., Nucl. Instrum. Methods A 455(2000)733[4] J.C. Gallardo, C. Pellegrini, Nucl. Instrum. Methods A
296(1990)448[5] V.N. Litvinenko, Nucl. Instrum. Methods A 304(1991)463[6] V.A. Bazylev, M.M. Pitatelev, Nucl. Instrum. Methods A
358(1995)64[7] G.R. Neil, H.P. Freund, Nucl. Instrum. Methods A
475(2001)381[8] E.L. Saldin, E.A. Scheidmiller, M.V. Yurkov, ”The Free
Electron Laser Klystron Amplifier Concept”, preprint
DESY 03-108, August 2003
[9] E.L. Saldin, E.A. Scheidmiller, M.V. Yurkov, Nucl. Instrum.
Methods A 381(1996)545

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 147-150

THE POTENTIAL FOR EXTENDING THE SPECTRAL RANGEACCESSIBLE TO THE EUROPEAN X-RAY FREE ELECTRON LASER IN
THE DIRECTION OF LONGER WAVELENGTHS
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract
The baseline specifications of European XFEL give a
range of wavelengths between 0.1 nm and 2 nm. This
wavelength range at fixed electron beam energy 17.5 GeV
can be covered by operating the SASE FEL with three undulators which have different period and tunable gap. A
study of the potential for the extending the spectral range
accessible to the XFEL in the direction of longer wavelengths is presented. The extension of the wavelength range
to 6 nm would be cover the water window in the VUV region, opening the facility to a new class of experiments.
There are at least two possible sources of VUV radiation
associated with the X-ray FEL; the ”low (2.5 GeV) energy
electron beam dedicated” and the ” 17.5 GeV spent beamparasitic” (or ”after-burner”) source modes. The second alternative, ”after-burner undulator” is the one we regard as
most favorable. It is possible to place an undulator as longas 80 meters after 2 nm undulator. Ultimately, VUV undulator would be able to deliver output power approaching
100 GW. A beam from this device could be run in pumpprobe mode with X-ray FEL.

INTRODUCTION
Baseline design of present European XFEL project [1]assumed only standard (SASE FEL) mode for productionof radiation. Recent developments in the field of FEL
physics and technology form a reliable basis for perspective extensions of the XFEL facility. In [2] we proposed
a concept of XFEL laboratory which will allow to implement perspective features from the very beginning of operation. These extra features include delivery of X-ray pulses
in the attosecond regime, increasing of the FEL power (upto sub-TW level), simultaneous multi-undulator capability.
The further development discussed in this paper concerns
the expanded photon energy range to VUV range. This
study will consider two possibilities: the first is based on”electron switchyard” technique (see Fig. 1). The electron
beam (at energy of 2.5 GeV) is . The electron beam (atenergy of 2.5 GeV) is extracted from the main linac andenters transport line, which guides it to the VUV undulator
located near the experimental hall. The beam distribution
system consists of two transport lines. The first beamline(2.5 GeV) directs one bunch train, coming to the ”water
window” undulator. The second beamline (17.5 GeV) takes
every other bunch train and delivers it to X-ray undulators.

Available online at http://www.JACoW.org

Figure 2 illustrates the second (baseline energy) option.
This alternative is the one we regard as most favorable. The
second option holds the energy at the baseline value (17.5
GeV) and chooses the undulator period length to match thewater window wavelengths. This alternative is the one we
regard as most favorable. Tables and present optimized
parameters of undulator and FEL performance applied to”water window” wavelength range with the electron energyof 2.5 GeV, and for the case of the maximum available energy (17.5 GeV). If the electron energy is that of the upper
limit of the range of the baseline design (17.5 GeV) the
undulator period length increases, for the resonant wavelength of 6 nm, from 4 to 11 cm. The FEL peak power isa factor of 10 higher for baseline energy (17.5 GeV). The
saturation length of ”water window” undulator at 17.5 GeV
is 80 m, against the 30 m of the low energy undulator.
The second option is the simplest way to obtain VUVradiation from the European XFEL. This is XFEL parasitic mode. All electron bunch trains will be guided into
one electron beamline and dump. The wavelength range
0.1-6 nm at fixed electron beam energy of 17.5 GeV canbe covered by operating the SASE FEL with four undulators which have different period and tunable gap. These
SASE undulators can be placed behind each other assuming that the subsequent undulator radiates at longer wavelength. It is a great advantage that accelerator and electron
beam transport line in this scheme operate at fixed parameters and that a fast ”electron switchyard” is not required.
In order to avoid the need for a costly additional tunnels
and shafts, the XFEL source is designed such that accelerator, all four SASE undulators, electron beam line, andphoton transport beamlines are installed inside the same (5m diameter) tunnel.

OPERATION OF FEL SOURCE AT
LONGER WAVELENGTH
Present concept of an XFEL facility assumes to covercontinuously wavelength range from 0.1 to 6 nm at a fixed(17.5 GeV) energy of the electron beam. This is achieved
with four undulators installed in a series in one electron
beamline. Optimization of undulator parameters has been
performed for the electron beam parameters presented in[1]: peak current 5 kA, rms normalized emittance 1.4 mmmrad, and initial energy spread of 1 MeV. All undulators
are planar, variable-gap devices with an identical mechani-Single-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 147-150

Figure 1: Schematic layout of the first possible strategy for VUV radiation. This scheme is based on the ”electron
switchyard” techniqueFigure 2: Schematic layout of the most favorable strategy for VUV radiation. In this scheme it will be possible to provide
simultaneously hard X-ray and VUV radiation beams (”after-burner” mode of operation)
Table 1: Specification of soft X-ray undulators for XFEL laboratory

Nominal option
Low energy option

Energy
GeV
17.5
2.5

λu
mm
110
38

gap
mm
19-37
10-20

Bu
T
0.7-1.6
0.4-1

Lu
m
80
35

Table 2: Specification of soft X-ray FELs for XFEL laboratory
Units Nominal∗ Low energy∗∗
EnergyGeV
17.5
2.5
Wavelength range
nm
1.6/6.4
1.6/6.4
Peak power
GW
100/100
10/20
Average powerW
400/400
40/80
Photon beam size (FWHM)
µm
60/90
90/90
Photon beam divergence (FWHM) µrad
11/27
11/30
Saturation length
m
70/80
18/32
∗
Operation in after-burner regime with rms energy spread of 8 MeV∗∗
Operation with nominal energy spread of 1 MeVMOPOS17

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 147-150

625

E = 2.5 GeV

E = 17.5 GeV

6.4 nm4

Erad [mJ]Erad [mJ]

20

2

10

5

10

15

20

1.6 nm5

1.6 nm0

6.4 nm

15

25

30

0
30

35

40

50

z [m]

60

70

80

90

z [m]

Figure 3: Energy in the radiation pulse versus undulator length. Left plot: low energy option (2.5 GeV). Right plot:
nominal energy option (17.5 GeV).
120

E = 17.5 GeV

λ = 6.4 nm

λ = 6.4 nm

300

80

P [GW]P [GW]

400

E = 2.5 GeV

100

60

200

40
100
20
0

50

100

150

200

250

300

0

350

50

100

t [fs]

150

200

8

350

E = 17.5 GeV

λ = 6.4 nm

6Normalized spectrum

Normalized spectrum

300

6
E = 2.5 GeV

4

2

0
-1.5

250

t [fs]

-1.0

-0.5

0.0

0.5

∆ω/ω [%]

λ = 6.4 nm
4

2

0
-1.5

-1.0

-0.5

0.0

0.5

∆ω/ω [%]

Figure 4: Temporal and spectral structure of the radiation pulse in saturation regime. Radiation wavelength is 6.4 nm.
Left column: low energy option (2.5 GeV). Right column: nominal energy option (17.5 GeV).
cal design. Optimized parameters of the undulator for bothcases are presented in Table . Calculations of the FEL characteristics are performed with time-dependent FEL simulation code FAST [3].
In this section, some examples will be given that shedlight on the differences between the undulator applied to
the VUV wavelengths with the electron energy of 2.5 GeV
and an undulator that is modeled for the baseline energy
17.5 GeV (after-burner undulator). The build-up of the radiation pulse energy along the undulator is shown in Fig. 3.
Requirements for FEL saturation at the shortest wavelength(1.6 nm) defines the undulator length: 35 m for dedicated
2.5 GeV option, and 80 m for 17.5 GeV after-burner option. Typical temporal and spectral structure of the radiation pulse from the VUV FEL operating at saturation arepresented in Figs. 4 and 5. For both options these structures are very similar, while peak power is much larger forthe after-burner option. At the wavelength around 1.6 nm
all key parameters of SASE FEL (peak power, photon flux,
brilliance) are by an order of magnitude higher for the afterburner option. This is an evident advantage for using highenergy electron beam to drive long-wavelength SASE FEL.

CONCLUSION
In this paper we performed direct comparison of two
possible options to extend wavelength range of European
XFEL towards 6 nm. The first option assumes to use electron beam extracted from the XFEL linac at the energy of
2.5 GeV. This beam is then transported via separate beamtransport line, passes through the undulator, and is dumped

Single-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 147-150

40

400

E = 2.5 GeV
30

20

10

0

λ = 1.6 nm

300
P [GW]P [GW]

E = 17.5 GeV

λ = 1.6 nm

200

100

50

100

150

200

250

300

0

350

50

100

150

t [fs]

200

250

10

λ = 1.6 nm

8E = 17.5 GeV

Normalized spectrum

Normalized spectrum

350

10
E = 2.5 GeV

6
4
2
0
-1.0

300

t [fs]

-0.5

0.0

0.5

∆ω/ω [%]

λ = 1.6 nm

8
6
4
2
0
-1.0

-0.5

0.0

0.5

∆ω/ω [%]

Figure 5: Temporal and spectral structure of the radiation pulse in saturation regime. Radiation wavelength is 1.6 nm.
Left column: low energy option (2.5 GeV). Right column: nominal energy option (17.5 GeV).
into the beam dump. Extra expenses for this option are as
follows. First, it requires to interfere XFEL linac in order to put extraction devices. Second, long beam transportline (of about two km long) is required. Third, it requires
separate beam dump. These evident disadvantages can not
be justified by relatively short undulator required (of about
35 meters). The second option, after-burner undulator isthe one we regard as the most favorable. It uses electron
beam with nominal energy of 17.5 GeV, and can be implemented in a parasitic mode of operation. It is possible toplace an undulator as long as 80 meters after 2 nm undulator. Ultimately, VUV undulator would be able to deliver
output power approaching 100 GW level (by an order ofmagnitude higher than for 2.5 GeV dedicated option). One
should also keep in mind the problem of the overall efficiency of the XFEL laboratory, i.e. increasing the number of simultaneously working user stations. It is evident
that 2.5 GeV option reduces the number of simultaneously
working user stations: when electron beam is directed into
the VUV branch, hard X-ray users need to wait. 17.5 GeV
VUV option works in a parasitic mode: VUV pulse is produced by the electron bunch which was used for productionof X-ray pulse in the previous undulator. Finally, in somemodes of operation, VUV FEL radiation could be used with
X-ray FEL radiation to do pump-probe experiments with
precise intervals between the sources.

MOPOS17

REFERENCES[1] P. Audebert et al., “TESLA XFEL: First stage of the X-ray
laser laboratory – Technical design report (R. Brinkmann etal., Eds.)”, Preprint DESY 2002-167.
[2] E. L. Saldin, E. A. Schneidmiller and M. V. Yurkov, DESY
Print TESLA FEL 2004-02, DESY, Hamburg, 2004.
[3] E. L. Saldin, E. A. Schneidmiller and M. V. Yurkov, Nucl.
Instrum. and Methods A429(1999)233.

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Y. Kim et al. / Proceedings of the 2004 FEL Conference, 151-154

START-TO-END SIMULATIONS FOR PAL XFEL PROJECT
Yujong Kim∗ , DESY, D-22603 Hamburg, Germany
J. S. Oh, M. H. Cho, I. S. Ko, and W. Namkung, PAL, POSTECH, Pohang 790-784, Korea
D. Son and Y. Kim, The Center for High Energy Physics, Daegu 702-701, Korea
Abstract

Table 1: Main parameters for PAL XFEL project.

At the Pohang Accelerator Laboratory (PAL), there is a
2.5 GeV S-band linac which is under operating as a fullenergy injector for the Pohang Light Source (PLS) storage ring. By installing a new S-band photoinjector, a new
0.7 GeV linac, and two new bunch compressors, the PLS
linac can be operated as an FEL driver for the PAL XFEL
project. To generate ultrashort, ultrabright, and coherent
X-ray FEL sources, we should supply high quality electron
beams to a long undulator. In this paper, we describe design concepts of the new injector, bunch compressors, linac
layout optimization, and various start-to-end (S2E) simulations on linac optimization and jitter.

INTRODUCTION
During the nominal operation of the PLS storage ring,
2.5 GeV PLS linac is operated as a full energy injector forthe ring, and its total injection time is within about 20 minutes a day. Since the PLS linac does not have any otherspecial dedicated service, the linac can be ideally converted
into the FEL driver for an X-ray FEL facility. To supply
femtosecond (fs) hard X-ray FEL sources, recently, Korean
government approved the PLS linac upgrade for the PAL
XFEL project. Under the fundamental mode operation of
the PAL XFEL facility, its tunable shortest wavelength is
3 Å, and FEL sources with more shorter wavelength can bealso available by various higher harmonic generation technologies [1]. Detail FEL related parameters for the PAL
XFEL project can be found in references [2] and [3], andits required electron beam parameters for 3 Å and 1 Å FEL
sources are summarized in Table 1. Generally, FEL source
properties strongly depend on the electron beam parameters such as slice and projected normalized rms emittances,slice rms relative energy spread, and peak current. And
these parameters are mainly determined by the injector system and bunch compressors (BCs) in the FEL driving linac.
Since the current 80 kV DC gun can not generate high quality electron beams, a new gun, two bunch compressors, anda new injector linac should be added to the existing PLS
linac to supply required electron beams for the PAL XFEL
project. However its overall modification must be minimized to reoperate the PLS storage ring within a limited
period. In this paper, we propose one possible linac layout
for the PAL XFEL project and describe various S2E simulation results with ASTRA and ELEGANT codes.
∗ E-Mail : Yujong.Kim@DESY.de, URL : http://www.desy.de/∼yjkim

Available online at http://www.JACoW.org

Parameter

Unit

3 Å / 1 Åbeam energy E
single bunch charge Q
slice normalized rms emittance ns

GeV
nC
µm

3.0 / 3.0
1.0 / 1.0
1.5 / 1.0

slice rms relative energy spread σδspeak current Ipk
undulator length for fundamental mode

10−4
kA
m

2.0 / 2.0
4.0 / 4.0
60 / 37

undulator length for the 3rd harmonicm· / 23INJECTOR FOR PAL XFEL PROJECT
Recently, by the help of a flat-top laser profile with about
9 ps (FWHM) length and about 1.5 ps rising and fallingtime, one BNL/SLAC/UCLA type S-band RF gun with a
14 MeV booster linac had generated high quality electron
beams with a projected normalized rms emittance of about
1.2 µm for 1 nC singe bunch charge [4]. After considering two facts that slice normalized rms emittance should besmaller than 1.0 µm to generate 1 Å FEL source, and projected and slice emittances can be diluted at bunch compressors due to the microbunching instability and CSR,
we determined that the PAL XFEL injector should supply much higher quality electron beams with a smaller projected normalized rms emittance [5]-[7].
This required higher quality electron beams can be generated by upgrading the BNL/SLAC/UCLA type S-band
RF gun with following steps [4]: First, transverse laser
profile will be improved to have a good homogeneous intensity, and longitudinal laser profile will be improved tohave a good uniform flat-top shape with a shorter risingand falling time. These improvements will help in reducing
emittance growth at head and tail regions due to the nonlinear space charge force [5]. Second, the maximum gradientat the cathode will be increased from current 100 MV/m to
120 MV/m which will also help in reducing space charge
force effects [8]. Third, we will align laser on the cathode and correct solenoid misalignments by the beam basedalignment. Fourth, several fine optimizations will be done
under 120 MV/m gradient: gun RF phase optimization to
get the maximum energy gain, laser pulse length optimization to control longitudinal space charge force, laser spotsize optimization at the cathode to control transverse spacecharge force and thermal emittance, solenoid current optimization to compensate emittance growth in gun region
due to space charge force and to reduce emittance growth
due to the none-zero magnetic field on the cathode [8], [9].

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Y. Kim et al. / Proceedings of the 2004 FEL Conference, 151-154

Figure 1: One possible linac layout (21JUL04 version) for PAL XFEL project.

Table 2: S2E simulation results for PAL XFEL project.

Figure 2: ASTRA simulation results on PAL XFEL injector: (left) projected normalized rms horizontal emittance
up to the end of X1B, and (right) slice normalized rms horizontal emittance at the end of X1B. Here the entrance of
X1A and X1B are located at 1.4 m and 5.4 m downstream
from the cathode, respectively.
Fifth, we will re-compensate the second emittance growth
due to space charge force in the drift space between gun
and the booster linac by installing the first S-band accelerating column (X1A) at the so-called Ferrario matching
point as shown in Figs. 1 and 2 [10]. Here, X1A has a lower
gradient to satisfy the Ferrario matching condition and thesecond accelerating column (X1B) has a higher gradient to
get a higher beam energy and to control Twiss parametersin X1B [10]. According to our ASTRA simulations for the
PAL XFEL injector, we may generate higher quality electron beams with a projected normalized rms emittance ofaround 0.94 µm by following above optimization steps. Its
simulation results are shown in Fig. 2, and its detail simulation conditions are summarized in Table 2.

BC FOR PAL XFEL PROJECT
Basic bunch compressor design concepts are well described in references [7] and [11]. The same concepts areused in designing bunch compressors for the PAL XFEL
project. Since dispersion is reversed inside of the S-typechicane, the chicane is generally useful in compensating
the projected emittance growth [12]. But its overall CSR
strength is much higher than that of the normal chicane
with four dipoles because S-type chicane has two additional dipoles [12]. Specially, if current density profile
and/or energy profile have a modulation before the S-typechicane, its CSR microbunching instability is stronger thanthat of the normal chicane [12].
To avoid slice parameter dilution due to the microbunching instability in BCs, we have adopted followings in our
linac layout as shown Fig. 1: First, to reduce overall CSR

MOPOS18

Parameter

Unit

Value

RF frequency of gun and linac
repetition rate
gun cell number

MHz
Hz
cell

2856
60
1.6

laser spotsize at cathode σx,ylaser pulse length (FWHM)

mm
ps

0.60
10

laser pulse rising and falling timenormalized thermal emittancemaximum longitudinal solenoid field

ps
µm
T

0.7
0.60
0.272

maximum gradient at the cathodegun phase from zero crossing
accelerating gradient in X1A

MV/m
deg
MV/m

120
32
18

accelerating gradient in X1B
X1A and X1B phase from on crest

MV/m
deg

30.5
0.0

projected emittance before BC1 / BC2
slice emittance before BC1 / BC2bunch length before BC1 / BC2

µm
µm
µm

0.94 / 0.99
0.81 / 0.81
894 / 110

beam energy before BC1 / BC2
projected energy spread before BC1 / BC2
slice energy spread before BC1 / BC2

MeV
%
10−5

442 / 700
1.90 / 1.31
0.92 / 4.30

projected emittance after BC2 / LINAC
slice emittance after BC2 / LINACµmµm

1.08/ 1.00
0.81 / 0.81

bunch length after BC2 / LINAC
beam energy after BC2 / LINAC
projected energy spread after BC2 / LINAC

µm
GeV
%

24.6 / 24.6
0.70 / 3.39
1.27/ 0.03

slice energy spread after BC2 / LINAC

10−4

2.44 / 0.29

strength, we choose only two bunch compressors with thenormal chicane instead of S-type chicane. Second, tokeep the slice rms relative energy spread at the entrance ofBC2 large, we put BC2 at a low beam energy of around
700 MeV. In this case, BC2 has still a large projected
rms relative energy spread of around 1.31%. Third, during compression in BCs, slice energy spread generally becomes larger to conserve the normalized longitudinal emittance. Therefore slice rms relative energy spread before
BC2 can be further increased up to 4.3×10−5 by compressing bunch length at BC1 strongly. Since the compression
factor at BC1 is high, we put BC1 at 442 MeV to avoid
any beam dilution due to space charge force. Note that
our linac layout can be also operated as the double chicane
mode only by turning off two S-band accelerating sections(X4 and X5) and by rematching optics [5], [7]. In this case,

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Y. Kim et al. / Proceedings of the 2004 FEL Conference, 151-154

LB = 0.3 m∆ L = 5.0 m

Tail

1.0 m

Head

0.33 mTail Electrons
QF QD

QD QD QF BM

Head Electrons

2.0 m

12.2 mQD QD QF

QD QF
2.8 m

17.0 mX−band Correction Cavity, −30.5 MeV
X3 S−band Linac, 473 MeV

Figure 3: BC1 layout for PAL XFEL project. BC2 chicane
has the same layout.

Figure 5: Slice parameters at the end of PAL XFEL linac.

Figure 4: Twiss parameters (left) and projected emittances(right) along PAL XFEL linac.

microbunching instability will be effectively damped [5].
To avoid projected emittance dilution due to CSR in
BCs, we have adopted followings in the PAL XFEL linac
layout as shown in Figs. 1 and 3: First, to reduce CSR,
we should choose a smaller momentum compaction factor
R56 of chicane. This is possible by choosing a somewhat
larger projected rms relative energy spread σδ [11]. After considering the emittance growth due to chromatic effect, we choose 1.90% at BC1. Second, we choose shortquadrupoles around BCs to reduce emittance growth due
to chromatic effect. Third, for a required R56 , we can reduce dipole bending angle (hence, CSR) further by using alonger drift space ∆L between the first dipole and the second one as shown in Fig. 3 [11]. Fourth, generally, CSR
is weaker at BC1, and CSR becomes stronger at BC2 asbunch length is compressed. Hence, we choose a higher
compression factor at BC1 and a lower compression factor at BC2 to reduce overall CSR effects in our two BCs.
Fifth, we reduce CSR further by installing a 4th harmonic
X-band accelerating column (X3X) before BC1 to compensate nonlinearities in the longitudinal phase space asshown in Fig. 3 [11]. Sixth, if we use a long linac between
BCs, the longitudinal short-range wakefield in the linac induces a small change in the longitudinal-phase-space chirping slope at head and tail regions, where charge is low.
In this case, projected emittance is increased due to overcompression at head and tail regions in BC2 [10]. Therefore we reduce the length of S-band linac between BCs to
reduce the projected emittance growth at BC2. Seventh, theprojected emittance dilution due to CSR can be reduced
further by forcing the beam waist close to the last dipole
where α-functions are zero, and β-functions are their minimum as shown in Fig. 4 [11]. Since chromatic effects be-comes smaller at BC2 due to smaller σδ , we choose muchhigher β-functions at the upstream of BC2 to give strong
focusing in BC2 as shown in Fig. 4(left) [11]. In this case,the projected emittance growth due to CSR can be effectively reduced at BC2.
To check performance of our linac layout, we have
performed S2E simulations with ASTRA and ELEGANT
codes as shown in Figs. 1 and 4(right), and as summarized in Table 2. Here emittance, energy spread, and bunch
length are estimated in normalized rms, rms relative, andrms, respectively, and slice parameters before BC2 (after BC2) are estimated at ±0.1 mm (±0.02 mm) core region. In these simulations, we have included all important
impedances such as space charge force in gun and X1 accelerating section, CSR and incoherent synchrotron radiation (ISR) in BCs, and short-range wakefields in all accelerating sections. According to our S2E simulations, allobtained slice parameters at the end of the linac are muchbetter than our requirements as summarized in Table 2 andshown in Fig. 5. Here small spikes in current are generated
by the weak over-compression at head and tail regions.

S2E SIMULATIONS ON JITTERTo relax jitter tolerance, we have adopted followings in
PAL XFEL linac layout as shown in Fig. 1, where each accelerating section from X2 to K12 has four S-band accelerating columns: First, tight jitter tolerance can be improvedby operating more klystrons in one accelerating section.
Therefore one klystron will be dedicated to two sequent Sband accelerating columns from X1 to X5 sections to relax
tight jitter tolerance there. Since X2AB (= X2A + X2B),
X2CD, X3AB, and X3CD will be operated by their own
klystrons under the same RF conditions, X2AB, X2CD,
X3AB, and X3CD have the same jitter sensitivity [5]. Since
jitter tolerance is loose at the downstream of BC2, one
klystron will be dedicated to four sequent S-band accelerating columns from K2 to K12 sections. Second, tightjitter tolerance can be looser by operating S-band accel-

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Y. Kim et al. / Proceedings of the 2004 FEL Conference, 151-154

the help of newly developing advanced RF low level control system, rms phase error and rms voltage error can becontrolled within 0.01 deg and 0.01%, respectively [13].
Therefore we expect that the PAL XFEL facility can supply stable FEL sources to users.
Table 3: Jitter sensitivity and tolerance at PAL XFEL.

Figure 6: The most sensitive jitter sources in PAL XFEL
linac: (top left) wavelength of FEL source versus gun timing jitter, (top right) saturation length versus gun timing
jitter, (bottom left) saturation power versus gun timing jitter, and (bottom right) photon beam arriving time versus
current error in BC1 magnet power supply.
erating columns around BCs with a low gradient of about
15 MV/m. To investigate the jitter sensitivity Js and jitter
tolerance Jt at the PAL XFEL linac, we have performed
S2E simulations with ASTRA and ELEGANT codes. By
applying an artificial jitter or error to each component, thenby monitoring its impact on FEL performances, we can determine the jitter sensitivity of the component. In this paper, we assume that jitter is uncorrelated, and all components do not have any misalignment.
After considering users’ requirements on photon beamstability, we have used following four constrains in determining the jitter sensitivity: First, peak-to-peak (p2p)change in wavelength of FEL source should be within±0.25%. Second, p2p change in saturation length should
be within ±5.0%. Third, p2p change in saturation powershould be within ±20.0%. Fourth, p2p change in bunch
arriving time should be within ±25 fs. The most sensitive
jitter source in wavelength, saturation length, and saturation power is the gun timing jitter, and the most sensitive
jitter source in bunch arriving time is the current error ofmagnet power supply for BC1 as shown in Fig. 6. Here theMing Xie model is used in estimating FEL performances,which are averaged in 80% core slices.
By repeating above processes, we have determined jitter sensitivities and jitter tolerances
all linac compoofn2nents, which satisfy a relation of
i=1 (Jt,i /Js,i ) < 1,
where n is the total number of all considered linac components. Investigated bunch-to-bunch jitter sensitivities andjitter tolerances are summarized in Table 3. Here Tol. (p2p)
and Tol. (rms) are jitter tolerances which are estimated in
p2p and rms respectively.
Recently, it was reported that gun timing jitter can becontrolled within several tens of fs by newly developing
laser-RF synchronizing and timing technologies, and by

MOPOS18

Jitter parameter

Unit

Sensitivity

Tol. (p2p)

Tol. (rms)

gun timing ∆Tcharge ∆Q/Q
X1AB ∆φ

ps
%
deg

-0.24
-3.00
-0.14

0.24
3.00
0.06

0.08
1.00
0.02

X1AB ∆V /V
X2AB ∆φ
X2AB ∆V /V

%
deg
%

-0.06
-0.10
-0.11

0.06
0.06
0.06

0.02
0.02
0.02

X3X ∆φX3X ∆V /V

deg
%

+0.17
+0.29

0.06
0.06

0.02
0.02

BC1 ∆I/I
X4AB ∆φ
X4AB ∆V /V

%
deg
%

+0.02
-0.64
-1.17

0.02
0.06
0.06

0.007
0.02
0.02

BC2 ∆I/I
K2 ∆φ
K2 ∆V /V

%
deg
%

+0.11
-83.3
+1.70

0.02
0.06
0.06

0.007
0.02
0.02

SUMMARY
By putting BC2 at a lower energy region, by using ashort linac between BCs, and by choosing high compression factor at BC1, slice energy spread before BC2 is about
4.3×10−5 , which is large enough to control microbunching
instability at BC2. In this case, optimized beam parametersat the end of PAL XFEL linac are also much better than ourrequirements, and growths of slice and projected normalized rms horizontal emittances in BCs are only 0.0 µm and0.14 µm, respectively, even though peak current is about
4.0 kA. We expect that the PAL XFEL facility can supply
stable FEL sources to users if jitter sources are controlled
by newly developing advanced technologies.

REFERENCES[1] L. H. Yu, Phys. Rev. A 44, 5178 (1991).
[2] J. S. Oh, et al., Nucl. Instr. and Meth. A 528, (2004) 582.
[3] J. S. Oh, et al., in these proceedings.
[4] J. Yang et al., J. Appl. Phys. 92, 1608 (2002).
[5] Yujong Kim et al., in Proc. EPAC2004, 2004.
[6] Yujong Kim et al., Nucl. Instr. and Meth. A 528, (2004) 427.
[7] Yujong Kim et al., in these proceedings.
[8] C. Travier, Nucl. Instr. and Meth. A 340, (1994) 26.
[9] B.E. Carlsten, Nucl. Instr. and Meth. A 285, (1989) 313.
[10] LCLS CDR, SLAC-R-593, 2002.
[11] Yujong Kim et al., Nucl. Instr. and Meth. A 528, (2004) 421.
[12] http://www.desy.de/∼yjkim/TESLA S2E 2003 10.pdf[13] S. Simrock, in Proc. LINAC2004, 2004.

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G. Lambert et al. / Proceedings of the 2004 FEL Conference, 155-158

SEEDING HIGH GAIN HARMONIC GENERATIONWITH LASER HARMONICS PRODUCED IN GASES
G. Lambert*, B. Carré, M. E. Couprie, D. Garzella, Y. Mairesse, P. Salières, CEA, DSM/SPAM, 91
191 Gif-sur-Yvette, France, A. Doria, L. Giannessi, ENEA C.R. Frascati, Italy,
T. Hara, H. Kitamura, T. Shintake, SPring-8/RIKEN Harima Institute, Hyogo 679-5148, JapanFree electron Lasers employing High Gain Harmonic
generation (HGHG) schemes are very promising coherent
light sources in the soft X-ray range. They offer bothtransverse and longitudinal coherence, while Self
Amplified Spontaneous Emission schemes have a limited
longitudinal coherence. We propose here to seed a HGHG
experimental setup with high harmonics produced by a
Ti:Sa femtosecond laser focused on a gas jet in the 10010 nm spectral region. The implementation of thisparticular laser harmonics source as a seed for HGHG isinvestigated.
Semi
analyticalandnumerical
1D calculations are given, for the cases of the SCSS,SPARC and ARC-EN-CIEL projects.

INTRODUCTION
In order to reach very short wavelengths in systems
based on Free Electrons Laser (FEL) [1,2], and to havemore compact and fully temporally coherent sources, aHigh Gain Harmonics Generation (HGHG) configuration[3] is studied here, in which an external laser source isseeded into a modulator, thus allowing a strong
prebunching of the e-beam. The use of a long radiator
section can lead to the consistent emission of radiation athigh order harmonics of the seeding source while
reproducing its longitudinal and transverse coherence. A
very promising scheme is the one where the seeding
source is already in the XUV range, provided by the
harmonics of the Ti:Sa laser generated in gas. Intense,
ultra-short laser harmonics can be now generated down to
10 nm [4]. We propose to use these laser High Harmonics(HH at λ wavelength) as the seed for a high gain FEL
amplifier radiating at λ or λ/3 and to extract its third andfifth non linear harmonics [2,5]. This scheme isconsidered for different installations: first on SCSS
(Spring-8 Compact Sase Source, Japan) [6] and SPARC(Sorgente Pulsata e Amplificata di Radiazione Coerente,
Italy) [7] for demonstration experiments, second on ARCEN-CIEL (Accelerator-Radiation Complex for ENhanced
Coherent Intense Extended Light, France) [8] and BATES(MIT, USA) [9] for efficient X-ray generation. SCSS andSPARC are projects of linac-based FEL, providing acompact SASE source with high brightness in the X-ray
range. ARC-EN-CIEL (AEC) is a proposal for an
innovative HGHG in the XUV range (Phase 1 is a firststep towards VUV). In this paper, we discuss the
prototype experiments on SCSS, AEC and SPARC,
including a brief description of the experimental setup
and theoretical estimate of the performances, the latter*guillaume.lambert@lure.u-psud.fr

Available online at http://www.JACoW.org

based on analytical formulae [1, 10] and 1D simulations
using PERSEO code [11].

THEORY OF HIGH ORDER HARMONICSPRODUCED IN GASESThe high harmonic generation in rare gas (Xe, Ar, Ne,
He) results from the strong non linear polarisationinduced by the strong laser field ELaser, at intensity 10141015 W/cm2. The process is qualitatively described in thesemi-classical “three-step” model [12, 13]. Close to laser
focus, for ELaser comparable to the intra-atomic field,
atoms ionize in the tunnelling regime [4] (step 1). The
ejected electrons are then accelerated by the laser fieldand gain a kinetic energy (step 2). Those which are driven
back close to the core may recombine to the ground state,emitting a burst of XUV photons (step 3). This three-stepprocess reproduces every half- optical cycle.

EXPERIMENTAL SET UP
Characteristics of High Harmonics in gases
A typical harmonic spectrum generated in Ne is displayedin fig. 1, illustrating the characteristic distribution of theodd harmonics into the "plateau" region, where theconversion efficiency is almost constant, and the "cut-off"region where the conversion efficiency rapidly drops
down. The conversion efficiency for high harmonic (HH)
generation remains relatively weak, typically varying
from 10-4 in the plateau to 10-7 in the cut-off.
Number of photons / pulses (approx.)

Abstract

Neon
plateau

CutoffthWavelength (nm)Fig. 1: High Harmonic spectrum in Ne.
The upper spectral limit is given by the “cut-off law”
[5, 14]. It states that the lighter the gas, i.e. the higher theionization potential and the laser intensity to which atom

Single-Pass FELs

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G. Lambert et al. / Proceedings of the 2004 FEL Conference, 155-158

can be submitted without ionizing, the higher the cut-offenergy. The HH therefore cover the 100-3 nm range (12400 eV). They have remarkable properties of ultra-shortduration (of a few 10 fs down to sub-fs), longitudinal [15]and transverse [16] coherence, good beam quality (small
divergence ~ 1mrad on laser axis), easily rotatable linear
polarization [17] and can be produced at relatively highrepetition rate (up to KHz). Finally it is possible tocontinuously tune the HH, e.g. by manipulating thespectral phase of the driving laser or by starting from two
driving frequencies [18].

magnetic chicane is inserted on the electron bunch path tosuperimpose the bunch and the XUV pulse at entrance ofthe modulator (Fig. 1).
ChicaneeModul.

Radiator

Linac

Telescope
Ti:Sa Laser

For the seed experiment, a HGHG configuration isforeseen with two undulators: the modulator (mod),which is chosen according to the wavelength of theseeded radiation, and the "radiator" (rad), providing ahigh gain. In SCSS and SPARC projects, the radiator
emitted wavelength is matched on the fundamental of themodulator (λrad=λseed). In AEC and AEC Phase 1 projects
it is matched on the third harmonic (λrad=λseed/3). The
table 1 shows the electron beam parameters, where IP is
the peak current, the undulators parameters, where NP is
the number of periods per section and NS the number ofsection, and the seeding parameters, where EH is the
harmonic energy per pulse, PH the harmonic power and D
the harmonic spot diameter.
Table 1: electron beam, undulator, and seeding
characteristics.

E (GeV)σγ
Q (nC)ε (π mmmrad)
IP (kA)AEC PhI
AEC
SCSSElectron Beam Characteristics
0.22
1
0.25
0.001
0.001
0.0002
1
1
1
1.7

1.5-2

1.5

IR filter

0.21
0.002
1

UV and IR
Light
Pump

A small size mirror serves to inject the XUV beam in
the FEL cavity and to adjust its position. The advantage inthis scheme is that all the XUV beam (~mm in diameter)
is injected; the constraint is that enough room should beavailable to accommodate the magnetic elements. So,
another arrangement, where the chicane is replaced by aholed mirror on the XUV beam, is envisaged in the
SPARC project (Fig. 2).
Holed mirror

A Ti:Sa laser system delivers pulses at 800 nm(Eph=1.55eV), which are converted into harmonics in thegas jet vessel. The harmonic pulses are then injected into
the modulator. In SCSS and ARC-EN-CIEL projects, a

e-

e-

e-

Radiator

Modul.

Linac

HGHG
Light

Gas JetTi:Sa Laser

1

Layout of the HGHG configuration seeded byharmonics produced in gases

Gas
BottleFig. 1: Layout of the seeding system with a chicane.

SPARC

0.8
0.6
0.2
0.15
Undulators Characteristics (Mod/Rad)
267/8914/4.64
60
160
λR (nm)38.9/2030/20
1528
λU (nm)K
1.76/1.14 2.27/1.26
1.39
1.36
NP
34/450160/1000
300
487
NS
1/1
1/1
2
6
Seeding Characteristics
H57=14 H13=60 H5=160
λseed (nm) H3=2675155EH (µJ)
PH (MW)
50
10
50
50
250
250
250
250
D (µm)MOPOS21

HGHG
Light

Gas JetBeams and undulators parameters

Projectse-e-

IR filter UV and IR
Light
Pump

Gas
BottleFig. 2 : Layout of the seeding system with a holed mirror.
The constraint is now that the hole should be
sufficiently small so that a high enough XUV energy isreflected.
In both schemes, the laser beam is eliminated using
various metallic filters which further select a finite
spectral range in the harmonic spectrum. Then the XUVbeam should be collimated to a small diameter (mm) bymeans of a telescope (spherical mirrors in afocal
geometry). The different mirrors should also improve, if
needed, the spectral selection of a particular harmoniccomponent, e.g. Mo/Si multilayer optics to select highorders in SCSS [19, 20]. The required multiple reflections
should not reduce the XUV energy by more than 50%.
Thus, if we consider a harmonics injection system basedon five optics the global reflectivity falls around 3%.

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G. Lambert et al. / Proceedings of the 2004 FEL Conference, 155-158

One dimensional code PERSEO

Output Peak Power (W)Perseo [11] is a library of functions reproducing themain properties of the desired FEL configuration in a 1D
simulation. The basic idea consists in the integration of
the pendulum equation coupled to the fields equations. A
typical simulation is shown in fig. 4.a,b where the growthof the output peak power on the fundamental and on thehigher order non-linear harmonics is represented asfunction of the longitudinal coordinate in the radiator. The
implementation of Perseo considered in this study allows
to inspect the energy modulation (fig. 5a) and theassociated bunching factor evolution (fig. 5b), during theparameters optimization. Finally in fig.6, the evolution of
the output peak power on the harmonics is shown as afunction of the seed power and the radiator length.

0.1
0.01
3
1 .10
4
.
21 10
5
b nh ) .
1 10
6
1 .10
7
1 .10
8
.
1 10

1 1

22

33

44
nh+ 1
nh

55

66

Fig. 5b: Evolution of the harmonics bunching factor (bnh)before the drift section for SPARC project versus theorder of harmonics (nh=1 is the fundamental).

Output Power (W)

CODES AND SIMULATIONS

4a

Input
P

ower

R

t
ia
ad

or

n
Le

gt

h

Fig. 6: Evolution of the SPARC Seeding HGHG output
peak power for the third non linear harmonics (53.3 nm)
versus input power and radiator length.

Analytical simulation

4b

Radiator Length (m)Fig. 4a, 4b: Evolution of the AEC SASE (a) and AEC
Seeding HGHG (b) output peak power at 6.5nm () andat their third (…) and fifth (---) non linear harmonics.

These simulations are based on an analytical 0D
approach in static mode, that is to say, with an average on
the transverse and longitudinal coordinates. The used FEL
formula come from G. Dattoli and P. L. Ottaviani [10].
The simulations allow to investigate the exponential
growth of the fundamental output peak power as afunction of the radiator length.
1000
Output Peak Power (MW)Energy (MeV)

20

10

0

10

100

10

1

0.1
20

0
0

1

2

3

4

5

6

5

25
20
15
10
Radiator Length (m)

30

35

Phase

Fig. 5a: Evolution of the energy modulation before thedrift section for SPARC project.

Fig. 7: Evolution of the AEC Seeding HGHG output peak
power at 6.5nm.

Single-Pass FELs

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G. Lambert et al. / Proceedings of the 2004 FEL Conference, 155-158

EXPECTED PERFORMANCES

Table 2: Saturation length (m) comparison with Perseo:
Seeding HGHG/SASE.
Fundamental
Output Radiation
(nm)
9.2
6.5
5.5
88.9
66.7
53
60
260
160

Projects
ARC-ENCIEL
ARC-ENCIEL
Phase 1SCSSSPARC

Saturation Length(Seeding/SASE)
(m)
2/7.5
3.5/7.5
7/12
3.5/5.5
4.5/7
6/12
4/7.5
4/6
6/8.5

400
300
200
100

0
1

10
WAVELENGTH (nm)100

Fig. 9: Output peak power of the λseed/3 harmonics
performances with a 1MW seed power and with beam
parameters coming from Table 1, for AEC (●), and AEC
phase 1 (■). <Pseed>≈0.1-0.5 W.

CONCLUSIONS

Figure 8 shows the expected results in terms of output
power made with Perseo.
1000
OUTPUT PEAK POWER (MW)OUTPUT PEAK POWER (MW)500

We can see in table 2 that seeding HGHG
configuration allows the saturations lengths to be reduced
from a factor of 1.5 to 2.

100

10

Using high laser harmonics generated in gas for seedingHigh Gain FEL amplifiers appears very interesting, since
the seed radiation is fully coherent, of ultra-short durationand tuneable in the XUV range. The seeding can reduce
the saturation length, leading to a more compact source.
The calculated performances roughly agree between 0 and
1D analysis. They show that high peak power (> MW)
could be obtained with this scheme.

REFERENCES
1

0.1
67

1

2

3

4 5 672

3

4 5 67

10
WAVELENGTH (nm)

100

2

3

Fig. 8: Output peak power of λrad, its third and fifth nonlinear harmonics for AEC (--▲--), AEC phase 1 (-*-),SCSS (-■-), SPARC (-♦-), and, for seed powers up to
1MW. <PRrad >≈0.1-0.5 W.
As we can see on the figure 4a and 4b, the output peak
power is lower by a factor of ~ 5 for a Seeding HGHG
configuration than for a SASE configuration. However, itremains high and now corresponds to fully coherent XUVpulses. For instance, if we seed the SPARC experiment at
260 nm, the fifth harmonic at 52 nm is generated at 0.25
MW output level, whereas seeding at 160 nm gives a fifth
harmonic at 32 nm of 0.15 MW peak power.
Figure 9 shows the expected results in terms of output
power obtained by the analytical simulations.

MOPOS21[1] F. Ciocci et al, IEEE Jour. Quant. Elec. 31 (1995)
1242.
[2] S. G. Biedron et al., Nucl. Inst. Meth. A 475 (2001)
401.
[3] L. H. Yu, I. Ben-Zvi, Nucl. Inst. Meth. A 393 (1997)
96.
[4] K. Midorikawa, Phys. Rev. Lett. 82 (1999) 1422.
[5] D. Garzella et al., Nucl. Inst. Meth. A 527 (2004).
[6] http://www-xfel.spring8.or.jp/scss/.
[7] Sparc Collaboration, Nucl. Inst. Meth. A 507 (2003)
345.
[8] ARC-EN-CIEL www.lure.u- psud.fr/congres/femto/.
[9] http://mitbates.mit.edu/xfel/.
[10] G. Dattoli, P. L. Ottaviani J. Appl. Phys., 95, (2004).
[11] www.perseo.enea.it.
[12] P. B. Corkum, Phys. Rev. Lett. 71 (1993) 1994.
[13] M. Lewenstein et al., Phys. Rev. A 49 (1994) 2117.
[14] G. Lambert et al., to be published in Jacow.
[15] P. Salières et al., Science 292 (2001) 902.
[16] L. Le Déroff et al., Phys. Rev. A 61 (2000) 043802.
[17] P. Salières et al., Adv. At., Mol., Opt. Phys. 41(1999) 83.
[18] H. Eichmann et al., Phys. Rev. A 51 (1995) R3414.
[19] Yu. A. Uspenskii, Nucl. Inst. Meth. A448 (2000)
147.
[20] T. Feigl et al., Nucl. Inst. Me

159

S.D.M. Di Mitri et al. / Proceedings of the 2004 FEL Conference, 159-162

ELECTRON BEAM SIMULATIONS FOR THE FERMI PROJECT AT
ELETTRAS. Di Mitri*, R.J. Bakker, C.J. Bocchetta, P. Craievich, G. D’Auria, G. De Ninno, B. Diviacco,
L. Tosi, V. Verzilov (Sincrotrone Trieste S.C.p.A., Area Science Park, 34012 Basovizza, Trieste,
ITALY)
Abstract
FERMI at ELETTRA is a project aiming at theconstruction of a single-pass user facility for the spectral
range from 100 nm to 10 nm. Starting point is the existing
1.2 GeV, 3 Ghz linac. Downstream of the linac two
undulator beamlines will serve the wavelength range from
100 nm to 40 nm and from 40 nm to 10 nm, respectively.
The former beamline will be based on a single-stage High
Gain Harmonics Generation (HGHG) scheme, while forthe latter a double stage HGHG scheme is foreseen.
In this paper we present the results of both numericaland analytical studies aimed to optimize the electron
beam characteristics for the 100-40 nm HGHG. In
particular, care has been taken to include realistic models
for the injector.

INTRODUCTION
The FEL-I phase of the Fermi at Elettra project
involves the construction of a single-pass FEL user
facility for the spectral range of 100 nm to 40 nm. The
laser will be driven by the existing normal conducting 1.2
GeV linac [1].
Studies on a reliable representation of the linac sections
and of their influence on the beam dynamics are here
presented; these topics are essential for realistic start-toend simulations, as well as to guarantee the final desired
beam quality (Table 1) [2].

LAYOUTFig.1 and Fig.2 show the scheme for the linac layout
and for the undulators line, respectively. As for the linac,
a new rf photo-cathode gun [3] provides a high quality
electron beam (see Table 2).

PRE-INJECTOR

1st BUNCHCOMPRESSORVERTICAL
RAMP

A 100 MeV pre-injector of two (2/3) π travelling wave
accelerating sections (TWs) gets the beam out of thespace-charge energy domain and creates an energyposition correlation suitable for the following bunch
compression.
An X-band harmonic cavity (HC) linearizes thecompression process in order to permit a uniform charge
density in the bunch and to remove excessive current
spikes which may drive the coherent synchrotron
radiation (CSR) instability.
After the chicane, five (3/4)π backward travelling wave
sections (BTWs) allow the beam to reach the fixed target
energy of 700 MeV. Quadrupole triplets between thesections provide the necessary transverse focusing.
Table 1. Electron beam target parameters at the end of thelinac for FEL-I stage.
FEL-I
Wavelength target
100 40nm
GeV
Beam energy
0.70
nCBunch charge
1.0
kA
Peak current
0.8
fs
500
Bunch duration (σt)
MeV
0.7
Energy spread (σδ)
1.5µm radEmittance
50
Hz
Repetition rate

The electron beam is taken to the surface undulator hallthrough a dogleg, which is achromatic and nearly
isochronous: its 5o bending angle avoid a further beam
quality degradation due to the CSR.
dispersive
regionmodulator

FEL-I

synchronizedseeding pulse
λo 250 nm

PHOTOINJECTOR

S1 – S5 LINACACCELERATINGSECTIONS

2nd BUNCHCOMPRESSOR

S6 — S7
for FEL-II

Fig.1 Schematic layout of the linac configuration for the
FEL-I and FEL-II stages.
simone.dimitri@elettra.trieste.it

Available online at http://www.JACoW.org

e- beam

HGHG λ/5

PLANARHIGH
HARMONICCAVITY

radiator

APPLE II

Fig.2 Set-up of the FEL-I undulators line based on asingle-stage HGHG mode of operation.

HGHG using an external laser as input seed isforeseen for FEL-I. Such a technique allows the
optimization of the stability and of the flexibility of thesystem, as well as the spectral properties of the output
signal. The undulators line consists of sections of about
2.5 m, separated by drift sections 0.75 m long dedicatedSingle-Pass FELs

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S.D.M. Di Mitri et al. / Proceedings of the 2004 FEL Conference, 159-162

to diagnostics and quadrupole focusing (FODO lattice).
Planar undulators will be used in the upstream areas,
where mainly the electron-bunching process is important.
APPLE-II type of undulators, allowing the control of thepolarization of the output signal, will be used to produce
the final radiation [1].

σδ ,i = 1.8 × 10-5 m. The emittance growth is limited to
10% in both planes by the optics arrangement.
Table 3. Electron beam parameters before and after thecompression.
Beam parameters
Electron energy (E)Bunch length (σz)
Energy spread (σδ)
Peak current (I)RF PHOTO-INJECTOR

Table 2. Electron beam parameters at the exit of the rf
photo-cathode gun. Simulations by ASTRA code.
Beam parameter
Gun field [MV/m]
Units
140
120
µm
330
340
Beam size rmsµm rad0.63
0.57
Normal. emittance rms
MeV
68Electron energy (E)
µm
930
900
Bunch length (σz)
%
0.27
0.21
Energy spread (σδ)
kA
0.102
0.104
Peak current (I)

BUNCH COMPRESSION
The beam distribution generated by ASTRA istransported by ELEGANT [7] to the magnetic chicane.
The appropriate energy-position correlation is created by
the “out of crest” acceleration in the second section of the
pre-injector.
The following HC is described by a π-mode standing
wave pill-box. It linearizes the longitudinal phase space inorder to increase the compression efficiency. Its
parameters are estimated by means of analytical formulas[8] and refined through an optimization in ELEGANT.
The bunch compressor is a symmetric structure of 4
rectangular bending magnets. The optics limits the effectsof CSR, mainly the transverse emittance growth and themicro-bunching in the energy distribution. CSR has beentaken into account also in the drifts following the dipoles.
A compression factor of 7 produces a peak current of 1
kA in a symmetric charge distribution, which may be
modified at occurrence by a proper setting of the HC andof the bunch compressor. The beam parameters before
and after the compression are listed in Table 3. The
present scheme provides R56 = - 1.1 × 10-2 m and T566 ×

MOPOS25

After
68.3
128
3.5
1.0

Units
MeV
µm
%
kA

LINAC
Wakefield in the BTW sections
The accomplishment of the FEL-I phase foresees thebeam acceleration in 5 linac sections, each giving amaximum energy gain of 150 MeV (conservative value).
The Green functions for the transverse and longitudinal
wakefield in the Elettra linac sections have been studied
and well defined through numerical calculations [9]. The
longitudinal wakefield interacts with the charged particles
changing their energy. Thus it perturbs the bunch energy
distribution inducing a correlated energy spread. The
FEL-I electron beam simulations presented here include
the longitudinal wakefield only, which is expected to bemuch stronger with respect to the SLAC-type [10] andTESLA [11] cases (Fig.3).
1400

1200

Longitudinal wake functions [V/pC/m]

Simulations have been performed with a maximum of
105 macro-particles for 1 nC of total charge.
The ASTRA tracking code [4] simulates the beam
generation in the rf photo-cathode gun and its transport tothe end of the first section of the pre-injector. It takes into
account 1D space-charge effects.
The new gun for the Fermi at Elettra project is a rescaled version of the LCLS gun model [3]; it comprises
an external solenoidal field of 0.3 T. Ferrario’s working
point [5] defines the distance from the cathode at which
the total emittance (geometric and thermal) reaches aminimum; here the emittance is freezed by the solenoid[6]. Table 2 lists the parameters of the electron beam at
the exit of the gun [3,6], in agreement with thespecifications for FEL-I (see Table 1).

Before
78.1
907
3.2
0.1

1000

800

600
BTW Elettra
400

200

SLAC−type

TESLA
0
0

0.2

0.4

0.6

0.8
s [mm]

1

1.2

1.4

1.6

Fig.3 Wake function (in V/pC/m unit) vs. longitudinalcoordinate behind the electron bunch in the ELETTRA,TESLA and SLAC-type accelerating sections. The origin
s=0 coincides with the unit charge position generating thewakefield.
Studies on the reliability of the ELEGANT tracking inpresence of wakefields have been carried out through a
comparison with results obtained from an analyticaltreatment of the wake potential [12,13]. The beamtransport has been investigated both for the case of asingle section (i) and for the whole linac (ii). A gaussian
distribution has been used as input, with initial central

S.D.M. Di Mitri et al. / Proceedings of the 2004 FEL Conference, 159-162

161

produce results differing to 30% as maximum, but thequalitative behaviour of the curves is still very similar.

energy and energy spread negligible with respect to thetotal energy gain.
In the analytical treatment the beam is propagatedthrough (3/4)π TW sections. The ELEGANT simulationis performed using analogous π-mode SW sections,instead [7]. Simulations show that the particle distribution
is practically unmodified by the propagation in one
accelerating section.
Fig.4 for case (i) and Table 4 for the case (ii) permit acomparison of the final correlated energy spread obtainedwith the two methods. In both cases the agreement isquite good; the discrepancies are in the tolerances of thedifferent wakefield implementations (few percent).
It is worth pointing out that there exists a minimum forthe correlated energy spread induced by the simultaneousinteraction of the accelerating field and of the wakefieldwith the electron beam. In particular, larger amplitudes of
the rf voltage (that is larger energy gains) counteract the
wakefield effect, thus reducing the growth of energy
spread.

Wakefield compensation
The evolution of phase space along the linac shows thatthe wakefields enhance a nonlinear region in the bunchenergy-position correlation, producing a minimum at δ ≈– 0.2% for the correlated energy spread (corresponding to
the highest peak in Fig.5); it is located in the bunch tail (t> 0 in Fig.6).

−3

Relative correlated energy spread

14

x 10

12
U0=90MeV10
U =120MeV

Fig.5 Frequency histogram of the relative correlated
energy spread in the elecron bunch at the exit of the FELI linac. A large amount of the particles assumes an energy
spread δ ≈ – 0.2%, as shown by the highest peak.

08

6
U =150MeV
04
U =180MeV
0

2
−50

−45

−40

−35

−30

−25

−20

−15

−10

−5

RF phase [degree]

Fig.4 Relative correlated energy spread as function of therf phase, at different energy gains in one accelerating
section of the Elettra linac. Comparison of results fromthe analytical treatment of the wake potential (solid lines)
and from ELEGANT tracking (dots).
Table 4. Results from the analytical method and
ELEGANT tracking along 5 linac sections.
Analytical
ELEGANT
MethodCentral Energy [MeV]
699.6
699.3
Relative Correlated
Energy Spread (rms)
0.44%
0.45%
Arbitrary initial conditions in the energy and charge
distributions cannot be described analytically in asatisfactory way. However, such distributions have been
approximated by means of known functions in theanalytical treatment. In these cases the two methods

0

The minimization of the correlated energy spread canbe performed in a similar way both by the analyticaltreatment and by ELEGANT: the rf phases are forced tothe minimum, accordingly with the constraint of a final
beam energy of 700 MeV. This condition requires thus
maximum peak voltages.
A very simple linac optimization foresees identicalparameters for the 5 sections, with maximum peakvoltage (150 MeV energy gain) and – 31o rf phase for an"out of crest" bunch acceleration. The optimization
provides σz = 128 µm and σδ = 0.2%, at a central energyof 699.5 MeV.
However, the FEL performance is determined by theuncorrelated slice-energy spread at the maximum current,i.e., the total energy spread over a cooperation length of
the FEL [14]. In our case the typical cooperation length(Lc) is less than 2 µm. From Fig.6 and Fig.7 it follows thatat the peak of the bunch-current the correlated energy
spread is linear. Hence, the total energy spread within acooperation length can thus easily be estimated byLc⋅σδ/2σz = 1.6⋅10-5, well below the limit stated in Tab.1.
We also note that the estimated peak current of ~ 1 kA for
FEL-1 fully satisfies the condition quoted in the table.

Single-Pass FELs

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S.D.M. Di Mitri et al. / Proceedings of the 2004 FEL Conference, 159-162

agreement with the specifications [1,2]. Moreover, a wide
fraction of the electron bunch is compatible with theseeded mode of operation; in this case, the central energy
deviation may be easily compensated by the tuning of the
wavelength through the gap variation of the undulator.

REFERENCES

Fig.6 Longitudinal phase space (relative correlated energy
spread vs. time) of the bunch at the exit of the FEL-I
linac. The rf phases of the accelerating sections have been
set for the wakefield compensation.

Fig.7 Current distribution along the bunch at the exit of
the FEL-I linac.

CONCLUSIONSElectron beam simulations for the FEL-I phase [1] of
the Fermi at Elettra project [2] have been performed.
Special care has been taken in the study of thelongitudinal dynamics in the Elettra linac sections.
A fast analytical algorithm has been developed [12,13]
to evaluate the evolution of the correlated energy spreadin presence of longitudinal wakefields [9], as well as tooptimize the rf phases for the wakefield compensation.
The algorithm provides the same results obtained by the
ELEGANT tracking on analytical beam distributions. It
allows qualitative estimations in more realistic cases.
The strong longitudinal wakefield in the Elettra linac
sections does not result to be critical for the FEL-I phase:the correlated energy spread has been minimized to the
0.2% rms value. It provides slice features in full

MOPOS25[1] R.J.Bakker et al., “Fermi at Elettra: 100 nm – 10 nm
single pass fel user-facility”, presented at EPAC04(July 2004, Lucerne, Switzerland).
[2] Fermi@Elettra Machine Project Update, Sincrotrone
Trieste (2003, Trieste, Italy).
[3] V.A.Verzilov et al., “Photo-injector study for the
ELETTRA linac FEL”, presented at FEL-2003(September 2003, Tsukuba, Japan).
[4] K.Flottman, “ASTRA, A Space Charge Tracking
Algorithm”, http://www.desy.de~/mpyflo/[5] M.Ferrario, SLAC-PUB 8400, 2000.
[6] P.Craievich, V.Verzilov, ST/M-03/02, Elettra (May
2003, Trieste, Italy).
[7] M.Borland, http://www.aps.anl.gov/asd/oag/[8] P.Emma, LCLS-TN-01-1 (November 2001, SLAC).
[9] P.Craievich, T.Weiland and I.Zagorodnov, “The shortrange wakefield in the BTW accelerating structure of
the Elettra linac”, presented at 8TH ICAP (June 2004,
St.Petersburg, Russia).
[10]T.Weiland, I.Zagorodnov, “The short range
transverse wake function for TESLA accelerating
structure”, TESLA Report 2003 – 11 (2003).
[11]C.J.Bocchettaetal.,“Overviewof
F E R M I @ E L E T T R A a Proposed Ultra BrightCoherent X-ray Source in Italy”, presented at
FEL2002 (9-13 September 2002, Argonne, Illinois,USA).
[12] A.Novokhatski, M.Timm and T.Weiland, “Single
Bunch Energy Spread in the TESLA Crymodule”(September 1999, TH Darmstadt, Germany).
[13] P.Craievich, G.D’Auria, S.Di Mitri, “Energy spreadin BTW accelerating structures at Elettra”, presented
at LINAC 2004 (August 2004, Lubeck, Germany).
[14] P.Emma, “Accellerator physics challenges of X-Ray
FEL SASE Sources”, Proc. of the EPAC2002, Paris,
France, p. 49 (2002).

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A. Renieri et al. / Proceedings of the 2004 FEL Conference, 163-166

STATUS REPORT ON SPARC PROJECT
A. Renieri*, M. Carpanese, F. Ciocci, G. Dattoli, A. Di Pace, A. Doria, F. Flora, G.P. Gallerano,
L. Giannessi, E. Giovenale, G. Messina, L. Mezi, P.L. Ottaviani, S. Pagnutti, G. Parisi, L. Picardi,
M. Quattromini, G. Ronci, C. Ronsivalle, E. Sabia, M. Sassi, A. Zucchini, ENEA, Centro Ricerche
Frascati, C.P. 65, 00044 Frascati, Italy
D. Alesini, M. Bellaveglia, S. Bertolucci, M.E. Biagini, C. Biscari, R. Boni, M. Boscolo,
M. Castellano, A. Clozza, G. Di Pirro, A. Drago, A. Esposito, M. Ferrario, D. Filippetto, V. Fusco,
A. Gallo, A. Ghigo, S. Guiducci, M. Incurvati, C. Ligi, F. Marcellini, M. Migliorati, C. Milardi,
L. Palumbo, L. Pellegrino, M. Preger, P. Raimondi, R. Ricci, C. Sanelli, M. Serio, F. Sgamma,
B. Spataro, A. Stecchi, A. Stella, F. Tazzioli, C. Vaccarezza, M. Vescovi, C. Vicario, M. Zobov,
INFN-Frascati, Italy
F. Alessandria, A. Bacci, I. Boscolo, F. Broggi, S. Cialdi, C. De Martinis, D. Giove, C. Maroli,
V. Petrillo, M. Romè, L. Serafini, INFN-Milano, Italy
D. Levi, M. Mattioli, G. Medici, P. Musumeci, INFN-Roma1, Roma, Italy
L. Catani, E. Chiadroni, S. Tazzari, INFN-Roma2, Roma, Italy
C.J. Bocchetta, M. Danailov, G. D'Auria, M. Ferianis, Elettra, Trieste, Italy
A. Cianchi, A. D'Angelo, R. Di Salvo, A. Fantini, D. Moricciani, C. Schaerf, Università di Roma
Tor Vergata, Roma, Italy
S. Reiche, J.B. Rosenzweig, G. Travish, UCLA, Los Angeles, CA, USA
D.H. Dowell, P. Emma, C. Limborg, D. Palmer, SLAC, Stanford, CA, USA
Abstract*
We review the status of FEL source activity of theongoing SPARC FEL experiment, developed within theframework of a collaboration among ENEA, CNR, INFN,
INFM, Sincrotrone Trieste and University of Rome Tor
Vergata. The project is aimed at realising a SASE-FEL
source, operating in the visible (around 500 nm), with anextended range of tunability down to the VUV (100 nm)
by the use of the mechanism of non-linear harmonic
generation. The development of the relevant activities
foresees the realisation of an advanced 150 MeV photoinjector source, aimed at producing a high brightness
electron beams, needed to drive a SASE-FEL experiment,
and a 14 m long undulator. We present the status of thedesign and construction of SPARC FEL device. In
particular we discuss the choice of the project parameters,
their optimisation and the sensitivity of the SPARC
performance to any parameter variation. We will show,
using start-to-end simulations, what is the impact of the ebeam and of the undulator parameters on thecharacteristics of the output laser field and in particular on
the amount of the non-linearly generated power at higher
harmonics.

*

Renieri@frascati.enea.it

Available online at http://www.JACoW.org

INTRODUCTION
The SPARC project, funded by the Italian Government
in 2003 with a 3 year time schedule, is an R&D activity
aimed to develop a high brightness photoinjector for selfamplified spontaneous emission free-electron laser(SASE-FEL) experiments. The installation of the machineat LNF will start on September 2004, and the first beam is
expected on June 2006. The SPARC [1] complex iscomposed of an RF gun driven by a Ti:Sa laser producing
10 ps flat top pulses that hit on a photocathode. The out
coming beam is injected into three SLAC accelerating
sections to feed a 14 m long undulator (Fig. 1).

Figure 1: SPARC project layout.

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The main goals of the project are:1. the generation of a high brightness electron beamable to drive a SASE-FEL experiment in the green
visible light and higher harmonics generation;
2. the development of an ultra-brilliant beam
photoinjector needed for the future SASE-FEL
based X-ray sources.

WORKING POINT OPTIMIZATIONThe beam current required by the FEL experimentpushes the injector design towards the limits of the stateof-the-art for what concerns pulse charge and pulse shape.
The design goal of the SPARC accelerator is to provide a
155 MeV bunch with projected emittance lower than 2µm and slice emittance lower than 1 µm. The SPARCFEL operates in the diffraction dominated range and peakcurrent is a key parameter for shortening the FEL gain
length. Once including possible errors in the undulator
system (see next section), the analysis of the SPARC FEL
operation shows that, in order to leave a significant
contingency margin to ensure full saturation and testingof harmonic generation, a safer parameter set requires abeam having 100 A in 50% of the slices with a slice
emittance ≤1 µm. For this purpose a new optimization
was performed, with start-to-end simulations andparametric sensitivity studies aiming to reduce the FEL
saturation length. The best result was obtained with ascaling approach [2] in which more charge is launchedfrom the cathode. The configuration that gives theminimum emittance corresponds to a working point with
1.1 nC and a pulse length of 10 ps. The overall result isthe reduction of the SASE-FEL saturation length from 12
to 9 m at 500 nm wavelength. The beam characterizationis shown in Fig. 2, while FEL power as a function of z as
obtained with the GENESIS code is reported in Fig. 3. In
Tab. 1 and 2 the final parameter sets are reported.

Figure 3: FEL power longitudinal evolution (λu = 2.8 cm,
K = 2.1413, I = 110 A).
Table 1: Injector parameters.
ELECTRON BEAM
Electron beam energy (MeV)
Bunch charge (nC)
Repetition rate (Hz)Cathode peak field (MV/m)
Peak solenoid field @ 0.19 m (T)Laser spot size, hard edge radius (mm)Central RF launch phase (deg)Laser pulse duration, flat top (ps)Laser pulse rise time 10%→90% (ps)Bunch energy @ gun exit (MeV)
Bunch peak current @ linac exit (A)RMS normalized transverse emittance @ linac
exit (mm-mrad); includes thermal comp. (0.3)
RMS slice norm. emittance (300 µm)
RMS longitudinal emittance (deg.keV)
RMS total correlated energy spread (%)
RMS uncorrelated energy spread (%)
RMS beam spot size @ linac exit (mm)RMS bunch length @ linac exit (mm)

155
1.1
1-10
120
0.273
1.13
33
10
1
5.6
100
<2
<1
1000
0.2
0.06
0.4
1

Table 2: FEL parameters.

Figure 2: “Slice” electron beam energy spread, peakcurrent, x and y emittances (PARMELA code).

MOPOS27

UNDULATOR & FEL
Undulator period (cm)
No. of undulator sections
Undulator parameter
Undulator field on axis (T)Undulator gap (mm)Undulator section length (m)Drifts between undulator sections (m)FEL wavelength (nm)Saturation length, geometrical (m)FEL pulse length (ps)
FEL power @ saturation (MW)No. of photons/pulse
FEL power @ saturation, 3rd harm. (MW)FEL power @ saturation, 5th harm. (MW)

2.8
6
2.16
0.83
9.25
2.13
0.36
500
< 14
8
> 80
1015
> 10
> 0.7

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A. Renieri et al. / Proceedings of the 2004 FEL Conference, 163-166

The SPARC project foresees the possibility ofextending the tunability range by exploiting the non-linear
generation of higher order harmonics. The understandingof the mechanism underlying such a process has requireda strong effort involving analytical and numerical means[3] and, as to the SPARC proposal, it has been shown that
it is possible to obtain a significant amount of coherent
power at higher order harmonics, which guarantees abrightness of third (170 nm) and fifth (100 nm) harmonic
two orders of magnitude only below the fundamental.

0.010

0.005
0.000
-0.005-0.010
0

109

8

10

12

14

λ=496.89 nm

108
107
106
105

3rd
5th

104
103
102
101
100

Fm
δ

Fp

6

Figure 5a: Longitudinal on axis field variation along thesix undulator sections due to the induced flexure.

power (W)UNDULATOR SYSTEM

δ'

4

Z

In this type of FEL one of the most significant
problems is that of reaching a good level of mechanicalprecision along the whole length of the undulator, which
is a flexible structure. It is therefore evident that one of
the first effects to be included in the optimization of thedevice is that of bending of the undulator section due tothe magnetic and gravitational forces (Fig. 4). The
variations of the longitudinal profile will be in turnresponsible of magnetic field variations, which will
provide a kind of inhomogeneous broadening and thus again reduction along with an increase of the saturation
length.
Fp

2

10−1
10−2
10−3

z

Fm

The problem of understanding the undulator bending
effects on the SASE-FEL dynamics has been consideredby merging two different points of view:a) a typical engineering approach [4], according towhich we have defined the maximum bending as afunction of the attractive forces and of the Youngmodules of the relevant materials;b) a method based on dynamical simulations [5][6],which have been able to evaluate the effects of agiven flexure on the laser performances.
An example of the effects due to the profile variations
on the final laser power and on the subharmonics is given
in Fig. 5, which shows how such an effect may become
significant for values of the maximum deflection above
10 µm. This example yields just an idea of the problems
arising within the study of the optimization of the device.
There are indeed other effects which cannot be consideredby their own and should be combined with the others, ase. g. those associated with the fact that the surface of theundulator poles assembly may not be perfectly parallel.
This fact may combine with possible misalignments
between undulator sections and it may induce a further
gain reduction (Fig. 6), which has been accurately
modelled [6].

0

1

2

3

4

5

6

7

8

9 10 11 12 13

Z (m)Figure 5b: Effect of the induced flexure on the power
evolution of the fundamental and higher order harmonics(solid: no flexure, dots: 10 µm maximum flexure in thecentre; Prometeo code).
109

λ=496.89 nm

108

power (W)

Figure 4: Flexure of the undulator upper and lower faces
induced by the attractive magnetic forces and the gravity.

107
106
105

rd

3

5th

104

3rd

103
102

th

5

101
100

10−1
10−2
10−3

0

1

2

3

4

5

6

7

8

9 10 11 12 13

Z (m)Figure 5c: As in Fig. 5b for 50 µm maximum flexure(Prometeo code).

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A. Renieri et al. / Proceedings of the 2004 FEL Conference, 163-166

109

power (W)108
107

Fluorescentscreen forElectrondetection

106
105
104
103
102
100
10−1

0

1

2

3

4

5

6

7

8

Chamberlength
L=20cmRadiation
deflecting
mirrorδ=0 µm,
δ=5 µm,
δ=25 µm,
δ=50 µm,
δ=100 µm,

101

10−2
10−3

CCD camera

Channel for
wake fields
suppression

λ=496.89 nm

To the vacuum

9 10 11 12 13

Z (m)Figure 6: Effect of undulator faces misalignment on thelaser power for different values of the maximum flexure δ(Prometeo code).

OPTICAL DIAGNOSTICS
The diagnostic layout is shown in Fig. 7; a diagnostic
chamber is positioned in correspondence of each
undulator section. Through these chambers the FEL
radiation is extracted and transported up to ameasurement station placed at the ending part of the FEL.

Strip-Line

Three
positionsmovement

Figure 8: Diagnostics chamber.
A non-interceptive diagnostics, which will be tested at
a later stage of the SPARC project, is based on theinteraction between the electron beam and a metal
grating. It has been shown that such a device is capable ofproviding quantitative information about the longitudinalbunch profile from the power spectrum of the emitted
coherent spontaneous radiation [7].

CONCLUSIONSThe SPARC project has been approved by the ItalianGovernment and funded in June 2003 with a schedule ofthree years. After the first year the project has been fully
defined and the major components have been ordered.

REFERENCES
C
U

C

C

C

C

U

U

U

U

U

W

W

W

W

W
OB

Figure 7: Diagnostic layout. U: undulator sections; C:diagnostic chambers; W: workstations for the analysis of
the radiation from each undulator; OB: optical bench.
The study and the design of the diagnostic chamber
foresee a series of conditions to be fulfilled. Among themthe most significant one is due to the reduced space
available for its installation. The distance between the
different undulator sections is about 36 cm and withinsuch a space it will be necessary to allocate, along withthe diagnostic chamber, the quadrupoles for the electron
focusing on the horizontal plane. The schematic layout ofthe diagnostic chamber is shown in Fig. 8. The diagnostic
chamber will host “pop-up” mirrors to extract the FEL
radiation as well as electron diagnostics, alignment
screens based on transition radiation and all necessary
ports to connect to the vacuum pumping system.

MOPOS27[1] SPARC Project Team, “SPARC Injector TDR”,(www.lnf.infn.it/acceleratori/sparc).
[2] J.B. Rosenzweig and E. Colby, “Advanced
Accelerator Concepts”, AIP Conf. Proc. 1995, Vol.
335, p. 724.
[3] G. Dattoli, L. Giannessi, P.L. Ottaviani and A. Torre,
J. Appl. Phys. (2004); G. Dattoli, these proceedings.
[4] A. Zucchini, “Considerazioni relative alla flessionedel supporto e dei magneti a causa del campo magnetico”, SPARC Tech. Note 03/007 (www.sparc.it).
[5] F. Ciocci, G. Dattoli, L. Mezi and P.L. Ottaviani,“The effect of the magnetic deflection on the FEL
evolution:a dynamical point of view”, SPARC Tech.
Note 03/005 (www.sparc.it).
[6] F. Ciocci, G. Dattoli, L. Mezi and P.L. Ottaviani,“Angular Tolerances in the SPARC undulator”,
SPARC Tech. Note 03/008 (www.sparc.it).
[7] G. Doucas, M.F. Kimmitt, A. Doria, G.P. Gallerano,
E. Giovenale, G. Messina, H.L. Andrews, J.H.
Brownell, “Determination of longitudinal bunchshape by means of coherent Smith-Purcell radiation”,
Phys. Rev. Special Topics – Accelerators and Beams
Vol. 5, 072802 (2002).

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R. Kato et al. / Proceedings of the 2004 FEL Conference, 167-170

ANALYSIS OF INTENSITY FLUCTUATIONS OF SASE
USING THE AR MODEL
R. Kato#, S. Kashiwagi, S. Isaka, C. Okamoto, T. Yamamoto, S. Suemine, G. Isoyama,
ISIR, Osaka University, Mihogaoka, Ibaraki, Osaka 567-0047, Japan
H. Sakaki,
J-PARC, Japan Atomic Energy Research Institute, Tokai, Naka, Ibaraki 319-1195, Japan
Abstract
Using the auto-regressive model analysis, we haveanalyzed the intensity fluctuation of the SASE producedwith the L-band linac and the FEL system at the Instituteof Scientific and Industrial Research, Osaka University. It
has been found that the fluctuation of the SASE intensity
is affected by the beam current in the frequency region
less than 0.1 Hz and that the contribution ratio of thebeam current to the intensity fluctuation of SASE isevaluated to be 18 % in the period longer than 100
seconds.

INTRODUCTION
We are conducting experimental studies on SelfAmplified Spontaneous Emission (SASE) in the infrared
region using the L-band linac at the Institute of Scientificand Industrial Research (ISIR), Osaka University [1-3].
The intensity of SASE fluctuates intrinsically because thenumber of coherent optical pulses generated in anelectron bunch changes statistically. In the actual system,
however, another factor producing intensity fluctuations
also shows up, namely instability of the linac. Generally
speaking, it is difficult to distinguish contributions ofthese two factors in measured intensity fluctuations. We
have applied the auto-regressive (AR) model, which isone of the techniques of statistical analysis and has beensuccessfully applied to analysis of instability of rf linacs[4,5], to evaluate the contribution of beam instability inthe measured data. In the AR model, the present data canbe expressed with a linear combination of the past dataplus white noise. By using the AR model analysis,contribution ratios of the beam fluctuations to the intrinsic
fluctuations of SASE in measured data can be evaluated.
In this paper, we will report results of the analysis ofintensity fluctuations of SASE measured at ISIR, Osaka
University, using the AR model.

LINAC AND MEASUREMENT SYSTEM
The L-band linac is equipped with a three-stage subharmonic buncher (SHB) system composed of two 1/12
and one 1/6 SHBs in order to produce an intense singlebunch beam with charge up to 91 nC/bunch. For the
single-bunch operation mode, the electron beam with apeak current up to 28 A (typically 18 A in our
experiments) and a duration of 5 ns is injected from athermionic gun (EIMAC, YU-156) into the SHB system.
___________________________________________#

After being compressed to a single-bunch, the electron
beam is accelerated to 11 - 32 MeV in the 1.3 GHz
accelerating tube. The electron beam is transported via anachromatic beam transport line to the wiggler for the FEL
system. It is the 32 period planar wiggler with the period
length of 60 mm. The K-value can be varied from 0.01 to
1.47. The main characteristics of the electron beam andthe wiggler are listed in Table 1. Light emitted by thesingle-bunch beam passing through the wiggler wasreflected with a downstream mirror, and led to themeasurement room via a 10 m long optical transport line,
which was evacuated with a rotary pump. The highvacuum in the beam transport line and the low vacuum inthe optical transport line were separated by a 0.2 mm
thick, 20 mm in diameter synthetic diamond window. The
optical light was detected with a Ge:Ga photoconductive
detector cooled with liquid-helium.
We measured the SASE intensity over a period of
approximately 12 minutes with an interval of 0.73 s,
together with the beam current measured at the entranceof the wiggler. The measured data are shown in Figure 1.
The SASE intensity shown by the red lines in the lower
part of the figure contains higher frequency components
due to the intrinsic fluctuations of SASE, as well as thelong-period variations, which are similar to those of thebeam current shown by the blue lines in the upper part of
the figure.

Table 1: Main parameters of the electron beam and thewiggler
Electron beam
Accelerating frequency
EnergyEnergy spread (FWHM)
Charge/bunch
Bunch length
Peak current
Normalized emittance
Repetition
Mode

1.3 GHz12.8 MeV
1.97 %
10-20 nC
20-30 ps
0.5 – 1.0 kA
150-200 π mm mrad
60 Hz
Single-bunch

Wiggler
Total length
Magnetic period
No. of periods
Magnet gap
Peak field
K-value

1.92 m60 mm
32120-30 mm
0.37 T
0.013-1.472

kato@sanken.osaka-u.ac.jp

Available online at http://www.JACoW.org

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beam current

0.8

0.32

0.6

0.3

0.4

0.28

0.2

0.26

0

SASE intensity [arb.units]

beam current [arb.units]

0.34

factors of the influences due to the each intrinsic noise
power contributing to the power spectrum are called thenoise power contribution ratios. By analyzing the noise
power contribution ratios, we can know which is the mostinfluential component in the system.

ANALYSIS WITH THE AR MODEL
Impulse response
The SASE intensity and the beam current shown in
Figure 1 are analysed with the impulse response analysis

SASE intensity
0.24

0

100

200

300

400

500

600

700

-0.2

3

(a) impulse to beam current

time [sec]AR MODEL
The AR model is a method for time series analysis [6].
It may be applicable to analysis of the feedback structure
in a complicated system consisting of mutually interacting
elements. For the AR model analysis of the feedback
system with two parameters, the present data X(n) can be
expressed by the linear combination of the past data X(nm), Y(n-m) and the white noise ex(n):impulse response [arb.units]

Figure 1: Beam current measured at the entrance of
the wiggler (upper) and the SASE intensity (lower)
over a period of approximately 12 minutes with aninterval of 0.73 s.

2.5

MOPOS30

1.5
1
0.5
0
-0.5
-0.2

0

0.2

0.4

0.6

0.8

1

1.2

time [min] X (n ) M  a xx (m ) a xy (m )  X (n − m )  e x (n ) , (1) Y (n )  = ∑  a (m ) a (m ) ⋅  Y (n − m )  + e (n )
yy
 m =1  yx
  y  

1.2(b) impulse to SASE intensity
1

impulse response [arb.units]

where M is a regressive number. The optimum regressive
number M is derived with FPE (Final prediction error)[7]or AIC (Akaike information criterion) [8]. Fitting the eq.
(1) to a set of time series data, we obtain the factor aij andthe noise ei. These factors and noises show the feedback
system modelled on the computer.
Assuming that the noises ex(n) and ey(n) are equal tozero, the system will either converge or diverge. When an
impulse noise is applied to the feedback system in thestationary state without noise, it will attenuate soon forthe stable system. By analysing the impulse response of
the system, it is possible to know how the perturbation
propagates with time among the components, and whether
the system is stable or not. This method is called “impulse
response analysis” and gives a physical image of the
feedback structure in the time domain. Although a delta
function impulse is applied to a component, its response
is not like the delta function, but has a tail, since thecomponent is influenced by its own past values and theother components.
The power spectrum is defined as the Fourier transformof an auto-covariance of the fluctuation data. Fractional

beam current
SASE intensity

2

beam current
SASE intensity

0.8
0.6
0.4
0.2
0
-0.2
-0.2

0

0.2

0.4

0.6

0.8

1

1.2

time [min]Figure 2: Impulse responses of the system for (a)impulse given to the beam current and (b) to the SASE
intensity. The blue and the red lines indicate temporal
responces of the beam current and the SASE intensity,
respectively. The impulse given to the beam current
influences the SASE intensity, but that to the SASE
intensity does not affect the beam current.

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R. Kato et al. / Proceedings of the 2004 FEL Conference, 167-170

100

-4

4.0 10-4

noise power conrtibution ratio [%](a) beam current

power spectrum [arb.units]

3.5 10self (beam current)
total

-4

3.0 10-4

2.5 10-4

2.0 10-4

1.5 10-4

1.0 10-5

5.0 100.0 10(a) beam current
80

40

20

0

0

0

0.1

0.2

0.3

0.4

0.5

0.6

self (beam current)
contribution from SASE intensity

60

0.7

0

0.1

0.2

3.5 10-2

3.0 10-2

2.5 10-2

2.0 10-2

1.5 10-2

1.0 10-2

5.0 10-3

0.0 10

0.5

0.6

0.7

100

(b) SASE intensity

noise power conrtibution ratio [%]power spectrum [arb.units]

-2

0.4

frequency [Hz]frequency [Hz]4.0 100.3

self (SASE intensity)
total(b) SASE intensity
80

40

20

0

0

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

self (SASE intensity)
contribution from beam current

60

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

frequency [Hz]frequency [Hz]Figure 3: Power spectra (a) of the beam current and (b)of the SASE intensity. The red lines indicate the power
spectra. The blue ones show spectra due to the own
intrinsic noise power contributing to the power
spectrum.

Figure 4: Noise contribution ratios (a) of the beam
current and (b) of the SASE intensity. The blue and the
red lines indicate the ratio of the power contribution
due to the beam current to the power spectrum and thatof the SASE intensity to the power spectrum,
respectively.

method. Results of the analysis are shown in Figure 3, in
which the order of the regressive number M is chosen to
be 4 with the AIC for the measured data. The upper panel(a) shows the response of the system when the impulse isgiven to the beam current and the lower panel (b) to the
SASE intensity. The vertical units in the figure are voltsand the horizontal ones are minutes. When the beam
jumps up from zero, SASE is generated and the intensity
goes down gradually as the beam current decreases, butwith a delay as shown in the panel (a). The result of theanalysis is, (a): impulse to the beam current influences the
SASE intensity, (b): impulse to the SASE intensity does
not affect the beam current. The result is quite reasonable

and does not contradict physical understanding. It showsthat the AR model can be successfully applied to themeasured data.

Power spectrum
Figure 3 shows results of the power spectrum analysis.
The power spectrum of the beam current in the panel (a)shows that the frequency component less than 0.1 Hz is
dominant and that the total spectrum is filled up with thepower spectrum of the beam current, which indicates thatthe beam current is not influenced by the SASE intensity.
On the other hand, the power spectrum of the SASE
intensity in the panel (b) shows no significant peaks, andSingle-Pass FELs

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R. Kato et al. / Proceedings of the 2004 FEL Conference, 167-170

it is flat and constant over the frequency range shown in
Figure 3. The total power spectrum in the panel (b),however, shows a peak centred at zero frequency, whichindicates the contribution of the other component, or the
beam current. This means that fluctuations of themeasured SASE intensity is composed of the lower
frequency component due to the beam current and thewhite component due to the intrinsic fluctuation of SASE.

no frequency dependence, while the peak shows up due tofluctuation of the beam current in the frequency region
lower than 0.1 Hz, of the total power spectrum of themeasured SASE intensity. The noise power contribution
ratio of the beam current to the intensity fluctuation of
SASE was evaluated to be 18 % in the period longer than
100 seconds.

Noise power contribution ratio[1] R. Kato, et al., Nucl. Instr. and Meth. in Phys. Res. A
445 (2000) 164.
[2] R. Kato, et al., Nucl. Instr. and Meth. in Phys. Res. A
475 (2001) 334.
[3] R. Kato, et al., Nucl. Instr. and Meth. in Phys. Res. A
483 (2002) 46.
[4] H. Sakaki et al., T.SICE Vol.35, No.10 (1999) 12831291.
[5] R. Kato, et al., Nucl. Instr. and Meth. in Phys. Res. A
528 (2004) 244.
[6] H. Akaike, Ann. Inst. Statist. Math., Vol. 20 (1968)
425-439.
[7] H. Akaike, Ann. Inst. Statist. Math., Vol. 23 (1971)
163-180.
[8] H. Akaike, IEEE Trans. Vol. AC-19 (1974) 716-723.

Figure 4 shows noise power contribution ratios of thepower spectra shown in Figure 3. The beam current is notaffected by the SASE intensity, but the SASE intensity isaffected by the beam current in the frequency region
lower than 0.1 Hz. The contribution ratio is about 18 % at
the frequency of 0.01 Hz.

SUMMARY
In order to evaluate the contribution of the beam
current to the intensity fluctuation of the SASE
numerically, we measured the beam current and the SASE
intensity simultaneously and analysed the measured datawith the AR model. The results of the analysis show thatthe power spectrum due to the SASE intensity alone has

MOPOS30REFERENCES

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LINAC LATTICE AND BEAM DYNAMICS FOR X-RAY FEL AT PAL
E.-S. Kim∗ , M. Yoon, D.-E. Kim and S.-J. Park
Pohang Accelerator Lab., POSTECH, Pohang, KyungBuk, 790-784 KOREA
Abstract

1 GeV new linac

The PAL-XFEL is a fourth generation light source
project to produce soft and hard X-rays which is basedon the self-amplified spontaneous emission (SASE) freeelectron laser. The XFEL facility consists of a new photoinjector, a 1 GeV new linac, a 2.0 GeV existing linac,
with two bunch compressors and long undulators to generate intense radiation. In this paper, we present lattice design of the linacs, bunch compressors, beam transport line,
tuneable matching sections for the 3 GeV soft X-ray FEL
facility and show results of start-to-end beam simulations
that have performed to estimate FEL performance in thedesigned lattice.

Six quadrupole magnets just after the injector are used tomatch the beta functions into the new linac. The 0.6 m long
X-band rf section is inserted just prior to the first bunch
compressor to obtain the better linearity of the energy-timecorrelation along the bunch. The X-band section is set tothe off-crest phase of -175 degree and the beam energy is
reduced by 19 MeV from 370 MeV to 351 MeV in the section, which has the gradient of 31 MV/m. L1 linac in the
new linac accelerates the beam from 135 MeV to 350 MeV
with off-crest angle of -25 degree and provides the linear
energy-time correlation that is required in the first bunch
compressor. The L1 linac consists of 4 3-meter S-band rf
structures. Because of the large off-crest rf phase angle
and relatively long bunch length, the rms energy spread in
L1 linac increases from 0.19 % to 1.41 %. L2 linac in the
new linac accelerates the beam from 350 MeV to 1.05 GeVwith off-crest angle of -25 degree and provides the linear
energy-time correlation that is also required in the second
bunch compressor. The L2 linac consists of 16 3-meter Sband rf structures and the rms energy spread in L2 linac
decreases from 1.5 % to 0.74 %.

INTRODUCTION
A 2.0 GeV linac in PLS had been used as an injector for
2.5 GeV PLS storage ring which is a third generation lightsource since 1994. Furthermore from September 2002, thelinac has being used for full energy injection of the 2.5 GeV
storage ring[1]. For this purpose operating time of the linac
is less than 10 %. With the requirement for next generation
light sources, the linac is being intensively considered as a
facility for soft[3] and hard X-ray FEL, which will include
the extension of the linac to achieve the energy of 3.0 GeV.
In this paper, we present concept of designed lattice andshow the results on the first start-to-end simulations for an
option of the soft X-ray FEL. For this simulation, injection beam in LCLS with energy of 135 MeV, emittance of
0.97 µm rms and bunch length of 870 µm rms and bunchcharge of 1 nC was utilized for the particle tracking[2].
Code ELEGANT[4,5,6,7] was used up to 3.0 GeV at undulator entrance to estimate the FEL performance in thedesigned FEL lattice. Figure 1 shows a designed schematicfor 3 GeV soft X-ray FEL in PAL.

LATTICE DESIGN
The designed PAL-XFEL facilities are composed of a 1
GeV new linac that will be constructed, one X-band section, two bunch compressors, a 2GeV existing linac, abeam transport linac, four matching sections and undulator beam lines. The Figure 2 shows Twiss parameters for
the PAL-XFEL from end of the injector to undulator entrance. The gun and injector linac are excluded in Figure 2.
In the following subsections, we will give investigations on
design concept, and beam and machine parameters in thedesigned lattice.
∗ eskim1@postech.ac.kr

Available online at http://www.JACoW.org

Two bunch compressors
Figure 3 shows the bunch compressors which exist in the
1 GeV new linac. Dispersion and beta functions around thefirst bunch compressor with R56 =16.3 mm are shown in
Figure 4.
X-band rf structure is upstream of the first bunch compressor. The first bunch compressor is designed compress a
870µm rms bunch to 198 µm rms. Results of longitudinalbeam simulations were used to set the bunch length of 198µm rms in incoming second bunch compressor. Dispersion
and beta functions through second bunch compressor with
R56 =22.4 mm are shown in Figure 5.
The second bunch compressor is designed compress a
198 µm rms bunch to 35 µm rms. The parameters of thefirst and second bunch compressors are listed in Table 1.
The bunch length after second bunch compressor can bevaried by controlling parameters of R56 in second bunch
compressor. Accordingly, the R56 of the second bunch
compressor is adjustable to satisfy requirements of the different bunch lengths for the option of the soft and hard Xray. Beta functions are kept to low values at the exit of thebunch compressors to minimize degradation of emittancedue to coherent synchrotron radiation. Each bunch compressor has also a short length of about 6 m to reduce theeffects of coherent synchrotron radiation.

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q=1nC
RF
Gun

2 GeV existing linac

M : Matching section
X-Linac

M

S-Linac

M

S-Linac

M

Undulator
L1
S-Linac

BCBC-1σz = 870 µmσδ = 0.19 %135 MeVσz=35 µm σδ= 0.07%

L2σz = 198 µmσδ = 1.5 %350 MeV

BCBC-2σz = 35 µmσδ = 0.74% Beam transport lineM(bending angle :10 deg)

1.05 GeV

3 GeV

1 GeV new linac

Figure 1: Schematic for a 3.0 GeV soft X-ray FEL in PAL.

Figure 2: Twiss parameters for PAL soft X-ray FEL frominjector exit to undulator entrance.

Existing linac
The existing linac begins at 90 m and ends at 235 m. It
includes 42 3-meter rf structures and they will be used forthe energy acceleration of 2 GeV for FEL facility. Newly
designed lattice for the existing linac is shown in Figure
6. The short bunch of 35 µm rms in the linac effectively
eliminates transverse wakefields as a source of emittance
growth and the rms energy spread decreases from 0.74 %down to 0.07 % in the linac. The rf phase angle in the linac
is set to -10 degree to improve energy stability.

Matching sections
Four matching sections are inserted in order to provide
adjustable beta-matching in each system of the designed
lattice. First matching section is located at the position between injector exit and L1 linac. Second one is inserted tomatch optics between the 1 GeV new linac and the existing
linac. Third one is inserted to match optics between the existing linac and the beam transport line. The optics matching at the undulator entrance is performed by fourth one to

MOPOS34

Figure 3: Twiss parameters for the 1 GeV new linac. It
includes two bunch compressors, 16 accelerating structures
and two matching sections. Matching sections are inserted
for matching of optics between injector and L1 linac, andbetween second bunch compressor and the existing linac.
Injector is excluded in this figure.
obtain average beta funtions of ∼10-meter in the undulator.
All matching sections are composed of six quadrupoles.
Figure 7 shows the beta functions in the matching section
between the new linac and the existing linac.

Beam transport line
Figure 8 shows dispersion and beta functions along 3
GeV beam transport line. The system with four dipole
magnets is used for beam transport between the existing
linac and undulator beam line, and a quadrupole triplet exists between dipole magnets. The net R56 in the four dipole
system is designed to have almost zero by making the dispersion function to be reverse sign in the center of the four
bending magnets. Each bending angle in the bending magnets with 1 m long is given by +5, +5, -5, -5 degree, respectively.

E.-S.. Kim et al. / Proceedings of the 2004 FEL Conference, 171-174

Figure 4: Beta function and dispersion functions aroundfirst bunch compressor. A X-band rf is located at upstreamof first bunch compressor. 12 S-band rf structures with offcrest phase of -25 degree are located at upstream of the
X-band rf section.

Figure 5: Beta function and dispersion functions aroundsecond bunch compressor. 12 S-band rf structures with offcrest angle of -25 degree are located at upstream of the second bunch compressor.

173

Figure 7: Beta functions in the tuneable matching section
between second bunch compressor in the new linac and theexisting linac.

Figure 8: Beta and dispersion functions in the beam transport line with four bending magnets. Each bending angle inthe bending magnets is +5, +5, -5, -5 degree, respectively.
First bending magnet corresponds to BAS2.
FEL. Our full simulation uses the beam that comes from the
LCLS photoinjector which produces charge of 1 nC, bunch
length of 2.9 ps rms, relative energy spread of 0.19 % rms
and emittance of 0.97 µm rms. The L1 linac is used for energy chirp before the beam enters the X-band rf section. A
bunch compression factor of 23.7 and a peak current of 10
KA in the bunch length of 105 fs rms were obtained by thesimulation. The bunch compression occurs at beam energyof 350 MeV and 1.05 GeV. Voltage and phase downstream
the bunch compressor were also optimized to reduce theenergy spread. Table 2 shows the beam parameters at theundulator entrance in the beam energy of 3 GeV.

Figure 6: Newly designed beta functions along the existing
linac. RF phase angle and energy acceleration for the FEL
schematic are set to 10 degree and 2 GeV, respectively.

RESULTS ON START-TO-END BEAM
SIMULATION
A start-to-end simulation using the code ELEGANT has
been performed to optimize beam parameters for soft X-ray

CONCLUSIONS
We have performed lattice design for the 3 GeV PALXFEL project and optics was designed to minimize degradation of the emittance and energy spread due to the CSR
and wakefields. Start-to-end beam simulations based on
the parameters for soft X-ray FEL were also performed.
These designed works have demonstrated the beam param-

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Table 1: Parameters of first and second bunch compressors.
Parameter
Beam energy
Ini. rms bunch length
Final rms bunch length
Ini. rms relative energy spread
Final rms relative energy spread
Magnetic field
R56
T566
Bending angle
Maximum dispersion
Length of bending magnet

1st BC
350 MeV870 µm
198 mm1.41 %
1.5 %0.5 T
16.3 mm-9.4 mm
5.04o-250 mm
203 mm

2nd BC
1.05 GeV
198 µm35 µm0.74 %
0.74 %
0.36 T
22.4 mm-33.8 mm
3.66o
-180 mm
203 mmTable 2: Beam parameters in the entrance of the undulator.
Parameter
Units Values
Beam energy
GeV3
RMS bunch lengthµm
35
RMS relative energy spread%
0.07
Norm. trans. emittance(H/V)µm
1.2/1.3
Bunch chargenC
1eters and feasibility of soft X-ray FEL with wavelength ofaround 30 Angstron in PAL.

REFERENCES[1] E.-S. Kim et. al, Proc. Particle Accelerator Conf., Portland,
p.3114 (2003).
[2] LCLS Design Study Report, SLAC-R-521 (1998).
[3] M.
Borland,APS
LS-287,
Sept.
http://www.aps.anl.gov/techpub/IsnotesTOC.html.

2000.

[4] M. Borland, XX International Linac Conf., Minterey, p. 833(2000).
[5] S. Reiche, et. al., SLAC-PUB-9369 (2002).
[6] P. Emma, LCLC-TN-o1-1, Nov. (2001).
[7] M. Yoon, et. al., In these proceedings.

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DESIGN STUDY ON 0.3-NM PAL XFEL
J. S. Oh, I. S. Ko, and W. Namkung, PAL/POSTECH, Pohang 790-784, Korea
Y. Kim, DESY, D-22603 Hamburg, Germany
Abstract

INTRODUCTION
PAL operates a 2.5-GeV electron linac, the 3rd largest in
the world, as a full-energy injector to the PLS storage ring[1]. The PAL 2.5-GeV linac can be converted to an X-ray
free electron laser (XFEL) facility driven by a selfamplified spontaneous emission (SASE) mode, which
supplies coherent X-rays down to 0.3-nm wavelength.
The undulator length has to be less than 60 m considering
available site area and reasonable cost. Table 1 shows thecomparison of single bunch specifications between the
PLS linac and PAL XFEL. The linac should supply
highly bright 3-GeV beams of which emittance of 1.5
mm-mrad, a peak current of 4 kA, and a low energy
spread of 0.02% [2]. Normalized emittance should be
improved 100 times, which requires a low emittance gun
and high gradient acceleration at low energy region topreserve the emittance. A suitable bunch compression
technique is important to realize the high peak current.
The performance and stability of the 2.5-GeV linac is also
challenging to meet the strict SASE requirements.

0.3-NM PAL XFELThe fundamental radiation wavelength λx of an
undulator is given by

λx =

λu
(1 + K 2 / 2), γ = Eo / 0.511, K = 0.934 Bu λu ,2γ 2where Eo is the beam energy in MeV, Bu is the peakmagnetic field of the undulator in Tesla, and λu is theundulator period in cm. Either a short-period undulator ora high-energy beam can provide short-wave radiation. A
short-period undulator is preferred for a compact FEL
machine. It is important to keep a reasonably large
undulator parameter K to obtain a short saturation length.
An in-vacuum mini-gap undulator can meet thisrequirement. This idea was introduced by T. Shintake for
the SCSS project at SPring-8 [3].
Each curve in Fig. 1 shows the undulator parameters of
the 0.3-nm PAL XFEL for saturation lengths of 40, 50, 60
m and beam energy of 2.5, 3.0, 3.5 GeV, respectively.
The possible solution that is reasonably economic, tomeet the saturation length of 50 m, is to use an undulator
with a 3-mm gap, 12.5-mm period and a 3-GeV beam.
For the saturation length of 50 m, the largest gap is 3.4
mm with 16-mm period at the beam energy of 4 GeV.
1.0

2.5 GeV
3 GeV

0.8
Undulator Gap [cm]

PAL is operating a 2.5-GeV electron linac as a fullenergy injector to the PLS storage ring. The PAL linac canbe converted to a SASE-XFEL facility (PAL XFEL) that
supplies coherent X-rays down to 0.3-nm wavelength. It
requires a 3-GeV driver linac and a 60-m long in-vacuum
undulator with a 3-mm gap and a 12.5-mm period torealize a hard X-ray SASE-FEL. The linac should supply
highly bright beams with emittance of 1.5 mm-mrad, apeak current of 4 kA, and a low energy spread of 0.02%.
FEL performance is very sensitive to electron beam
parameters. The beam quality is degraded along theundulator trajectory due to the energy loss and the wakefield. Also the FEL gain is reduced by errors in theundulator fields and beam trajectories. The preliminary
design details for the 0.3-nm PAL-XFEL are presented
with parametric analysis.

4 GeV
0.6

60 m
0.4

50 m
0.2

40 m
0.0

Table 1: Bunch specifications of PLS linac and XFELParameter
PLS Linac
PAL XFEL
Beam energy
2.5 GeV
3.0 GeV
Normalized emittance
150 µm
1.5 µm
FWHM bunch length
13 ps
0.23 ps
RMS energy spread
0.26%
0.02%
Bunch charge
0.43 nC*
1.0 nC
Peak current
33 A*
4 kA
Repetition rate
10 Hz
60 Hz
* 2-A gun current and 62% transmission

Available online at http://www.JACoW.org

0

1

2

3

Undulator Period [cm]Figure 1: Undulator period and gap length for 0.3-nm
SASE for saturation lengths (40, 50, 60 m) and beamenergy (2.5, 3, 4 GeV).
Table 2 summarizes the FEL parameters for a 0.3-nm
PAL XFEL. The undulator beta value is adjusted toobtain as short a saturation length as possible. Undulator
saturation length is approximately 20 times the 3D gain
length Lg. The peak brilliance of the PAL XFEL is 1012
time higher than the U7 undulator radiation from the PLS
3rd generation storage ring. The hard X-ray spontaneous

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J. S. Oh et al. / Proceedings of the 2004 FEL Conference, 175-178

radiation from the undulator of the PAL XFEL is also
1010 times brighter than the synchrotron radiation fromthe PLS bending magnet.

500-µJ, and 260-nm UV laser. It is accelerated to 7 MeV
by a high gradient of 120 MV/m.
E-gun
Accelerating Column
Bending Magnet
Bunch Compressor
Undulator
Beam Dump

Table 2: FEL parameters for 0.3-nm PAL XFEL
Undulator period [mm]12.5
Undulator gap [mm]3.0Peak magnetic field [T]0.97
Undulator parameter, K
1.14
Beta [m]15
1D FEL parameter4.3e-4
1D gain length [m], L1d
1.35
0.97
3D gain length correction, η∗
3D Gain length [m], Lg
2.67
Effective FEL parameter2.2e-4
Cooperation length [nm]63
Saturation length [m]52Peak power [GW]
2.1
Peak brightness [x 1032]**
1.4* Lg = (1+η) L1d** photons/sec-mm2-mrad2-0.1%BW

10m

30m

50m

100m

Scale

To 2.5 GeV
Storage Ring

K1 K2 K3 K4 K5 K6 K7 K8 K9 K10 K11 K12

X1 X2 X2X X3

To X-rayBeam Line

BC2

BC1

Figure 3: 3-GeV Linac for PAL XFEL.

Figure 2 shows 3D gain length correction and 3D gain
length according to normalized emittance, which arecalculated according to M. Xie [4]. An electron beam has
to match the transverse phase space for a diffractionlimited photon beam to get the minimum 3D gain
correction. The gain correction factor of the PAL XFEL islarger than the LCLS and the TESLA XFEL due to arather large normalized emittance relative to the naturalradiation emittance. However, due to the small periodic
length of an undulator, the gain length is smaller thanothers. Therefore, it is possible to realize a compact X-ray
FEL by using an in-vacuum undulator with small period
and a low energy linear accelerator.

The injector layout presented in FEL2003 is improvedin this work [2]. Instead of the dog-leg layout, the new
injector is aligned to the center line of the existing linac tosuppress as far possible as emittance degradation due to
CSR. All bunch compressors are included in the new
injector area to preserve the existing layout of PLS 2.5GeV linac. Figure 4 shows the layout of the new FEL
injector linac and gives details of BC1 which is almost thesame as the BC2 design. A suitable energy spread forbunch compression is provided by the modulator unit X2.
The 4th harmonic cavity X2X linearizes the non-linear
energy spread due to the RF curvature caused by the Sband modulator. The net chicane length is 12.2 m. The
total chicane length becomes 17 m including focusing
quadrupoles. The maximum beam offset in the middle ofthe bunch compressor is 33 cm.
R F-G U N

X1

X2

BC1

X 2X

X3

BC2

(a)
LB = 0.3 m

2.0

10

1.5

8

1.0 m

6

Tail Electrons∆ L = 5.0 m

Gain length (m)Gain correction

TESLA XFELPALXFELTESLA XFEL
1.0

0.5

2

4

6

Emittance/(λ x/4π)

8

10

QF QD

2.0 m

Head

Head Electrons
12.2 m0.33 mQD QD QF

QD QF
2.8 m

17.0 m

0
0

2

4
6
8
Εmittance/(λ x/4π)

10Figure 2: 3D gain correction factor and 3D gain length.

XFEL LINAC DESIGN
The existing 2.5-GeV S-band PLS linac can beconverted to X-ray FEL driver by adding a new S-band
FEL injector linac. Figure 3 shows the layout of the PAL
linac including a new undulator system. The FEL injector
linac consists of a laser-driven photo-cathode gun, three
S-band accelerating modules (X1, X2, X3), and twobunch compressors (BC1, BC2). The S-band photoinjector consists of a copper cathode and a 1.6-cell S-band
RF cavity. The photoelectron beam is generated by 10-ps,

MOPOS36QD QD QF BM

LCLS

2

LCLS
0.0
0

PALXFEL4

Tail

X−band Correction Cavity, −33 MeV
X2 S−band Linac, 475 MeV(b)Figure 4: New injector layout (a) and details of BC1 (b).
The lattice design of two bunch compressors is shownin Fig. 5. The lattice is optimised by the following
equation for the relative emittance growth [5]. The
optimum condition is given at the alpha value of about 0
and beta function of about 3.
∆ε

ε

5

= 1+

2
(0.22) 2 γ e2 N 2 θ LB 3 2( 4 ) [ LB (1 + α 2 ) + 9 β 2 + 6αβLB ]36 γε N β σ z

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J. S. Oh et al. / Proceedings of the 2004 FEL Conference, 175-178

BC1. The uncorrelated energy deviation at BC2 is larger
than the 1x10-5 that is required to suppress the microbunching instability.
Table 4: Beam parameters of bunch compressors
Parameter
BC1
BC2
Beam energy
442 MeV
700 MeV
Relative energy spread
1.84%
1.31%
Uncorrelated energy spread
9.2x10-6
4.3x10-5
Initial rms bunch length
820 µm114 µmFinal rms bunch length
114 µm26 µm
Compression factor
7.2
4.38
Initial projected emittance
0.90 µm
1.01 µm
Final projected emittance1.01 µm
1.12 µm
Figure 5: Lattice profile of two bunch compressors.
Against projected parameter dilution due to CSR andchromatic effect, adopted lattice design concepts are as
follows: long drift space to reduce bending angle for arequired R56, small bending angle at a large energy
spread, large compression factor at BC1 and small
compression factor at BC2. Strong focusing lattice aroundBCs to reduce CSR induced emittance growth, small
quadrupole length around BCs to reduce the chromaticeffects, smaller maximum beta-function of ~ 60 m at theentrance of BC1, larger maximum beta-function at theentrance of BC2 after reducing energy spread are also
effective. Against slice parameter dilution due to themicro-bunching instability, the following design concepts
are adopted: normal 4-bend chicane instead of S-typechicane, large relative uncorrelated energy spread at BC2
by putting BC2 in the low energy region, no laser beamheater or superconducting wiggler. Table 3 shows thedesign parameters of the bunch compressor BC1 and BC2.
Table 3: Design parameters of bunch compressors
Parameter
BC1
BC2
BC typeTwo stage Two stage
Bending angle
3.50°
1.45°
Momentum compaction R56 38.9 mm
6.70 mm
Chicane length12.2 m12.2 m
Dipole length
0.3 m
0.3 m
5.0 m
5.0 m
Drift length ∆L

SIMULATION
We examined beam parameters using the ASTRA codefrom the photo-injector to the X1 booster unit consideringstrong space charge effects in this region. The code
ELEGANT is used to design the main linac lattice fromthe X2 unit to the end of the existing linac. This code
includes CSR effects in the bunch compressor andgeometric wake field effects in the accelerating section.
Table 4 summarizes the simulated beam parameters forBC1 and BC2. All uncorrelated energy spread isestimated at ± 0.1 mm core region. Initial uncorrelated
energy spread at BC2 is increased after compression by

Figure 6 shows the energy spread and beam size before
BC1 and at the end of the linac, respectively. The energy
spread along the bunch length is well linearized by the Xband section (X2X) before BC1. At the entrance of BC1,energy spread is 1.835% and the beam size is 230 µm (σx).
At the end of the linac the energy spread is 0.033% andbeam size is 68.1 µm (σx). The longitudinal short-range
wake-field damps the energy spread so that the energy
spread becomes flatter and uniform.

(a)

(b)
Figure 6: Energy spread and beam size before BC1 (a)and at the end of linac (b).
Figure 7 shows the variation of the projected energy
spread and the bunch length along the linac. The relative
energy spread is continuously increased to 1.84% until theentrance of BC1 by the modulator unit to fit the necessary
compression factor at the BC1. The variation of energy
spread in BC2 is mainly caused by CSR effects and kept
reasonably low, which means the CSR is not so high in
BC2. Increasing the beam energy, the energy spread iscontinuously decreased to 0.033% at the end of the linac.
The large compression at BC1 and small compression at
BC2 are clearly shown in the figure. The bunch length iscompressed down to 26 µm after BC2.

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J. S. Oh et al. / Proceedings of the 2004 FEL Conference, 175-178

E = 3.389 GeVσδ = 0.033%

σz = 26 µm

Figure 7: Energy spread and bunch length along linac.
Figure 8 shows the beam quality at the end of linac.
The required beam parameters for FEL lasing at theundulator entrance correspond to dotted lines for the peakcurrent of 4 kA, normalized emittance of 1.5 µm, andenergy spread of 0.02%. The normalized emittance, that is
the most sensitive FEL parameter, is well below therequirement along the bunch, which gives reasonablemargin for saturation within a 60-m long undulator. The
lowest peak current along the bunch is about 20% lessthan 4 kA. The slice emittance is also 20% lower than thenominal value of 1.5 µm. Because the saturation length ismore sensitive to the emittance, it is possible to havesaturation along the whole bunch.

4.0 kA

1.5 µm

0.02%

Figure 8: Beam quality at the end of linac.

DISCUSSION
The bunch compressor design can be tuned to provide asuitable beam heating effect. Figure 9 shows the
distribution of uncorrelated energy spread along thebunch length before BC1 and after BC1, respectively. The
uncorrelated energy deviation within ± 1.0 mm bunchcore is 4 keV at the entrance of BC1. It is increased to 30
keV at the entrance of BC2 due to the high compression
factor at the BC1. Considering space charge forces, it will
be increased further, which helps to suppress microbunching instabilities.

Figure 9: Uncorrelated energy spread at the entrance of
BC1 and BC2.
In order to smoothly transfer the beam induced wall
current, nickel foil, plated with copper, is attached on thepole surface using the magnetic attractive force. The
practical smooth surface on commercially available metal
plate has a high aspect-ratio of surface roughness, which

MOPOS36

makes the energy spread due to the surface roughness
negligibly small enough. The energy spread due to theresistive wake field on the electron beams in the undulator
can be estimated by assuming the radius being equal tohalf of the gap and energy spread being half of the pipe
radius [3]. With the bunch charge of 1-nC, and the gap
size of 3 mm, undulator length of 60 m, the projectedenergy spread due to the resistive wall wake is 0.07% for
the bunch length of 26 µm. As the slippage length is 1.26
µm, the contribution to the slice energy spread is
negligible. The emittance growth due to transverse
resistive wall wake is less than 1% if the random
oscillation is kept less than 20 µm with a Gaussian beamaccording to reference [6]. The gap size of each undulator
can be tapered to adjust the resonant condition for the
reduced average beam energy due to the incoherent
synchrotron radiation loss.
The length of each undulator has to be at least 2xLg inorder to release the tight tolerance of longitudinal andtransverse misalignment [7]. The achievable radiation
power is reduced to 50% if the phase slip is π over thedrift section between the adjacent segments or theradiation is cut off at the drift section. As the saturation
length is 20xLg, the maximum number of segments is 10
and the minimum length of an undulator is 6 m for the
PAL XFEL.
The jitter and sensitivity analysis on the combined
parameter space is extensively studied in reference [8]. It
is still necessary to analyse the hardware upgrade schemeand the stability requirements with related technicalparameters.

ACKNOWLEDGMENTS
This work is supported by POSCO and the Ministry of
Science and Technology (MOST) of Korea.

REFERENCES[1] http://pal.postech.ac.kr/[2] J. S. Oh, et al., “0.3-nm SASE FEL at PAL,” Nuclear
Instruments and Methods in Physics Research A528,
582 (2004)[3] T. Shintake, et al., “SPring-8 Compact SASE Source(SCSS),” in Proc. the SPIE2001, San Diego, USA,
2001; http://www-xfel.spring8.or.jp[4] M. Xie, “Design Optimization for an X-ray Free
Electron Laser Driven by SLAC Linac,” LBL Preprint
No-36038, 1995
[5] T. Limberg, “Emittance Growth in the LCLS due toCoherent Synchrotron Radiation,” SLAC internal note,
Oct. 1997[6] LCLS CDR, SLAC-R-593 (2002)[7] T. Tanaka, et al., “Misalignment effects of segmented
undulator in self-amplified spontaneous emission,”
PRST-AB, 5(2002)040701[8] Y. Kim, et al., “Start-To-End Simulation of the PAL
XFEL Project,” 26th International FEL Conference and11th FEL Users Workshop, Trieste, Italy, 2004

179

S.J. Park et al. / Proceedings of the 2004 FEL Conference, 179-182

DESIGN STUDY OF LOW-EMITTANCE INJECTOR FOR SASE XFEL AT
POHANG ACCELERATOR LABORATORY*
S. J. Park#, J. S. Oh, E. S. Kim, J. Y. Huang, D. E. Kim, J. H. Park, S. H. Nam, M. H. Yoon, I. S. Ko,
S. G. Baik, and W. Namkung
Pohang Accelerator Laboratory, POSTECH, Pohang 790-784, Korea
Abstract
We report on the design study of the low-emittanceinjector for the SASE-XFEL that is being considered as
the possible choice for the next-generation light sources at
the Pohang Accelerator Laboratory (PAL), POSTECH.
The PAL XFEL will utilize existing 2.5-GeV linac
combined with a new 700-MeV linac, and aims to achieve
the SASE saturation at 3 Å with 3-GeV beam energy andmini-gap in-vacuum undulators. Requirements imposedon the beam quality are tight, e.g., the normalized rms
emittance at the entrance of the undulator should be lessthan 1.5 µm rad. Since the basic beam quality of the linac
is determined by its injector system, the injector systemshould be developed as soon as possible, well before thestart of the machine construction, which would greatly
help to find and solve potential obstacles in achieving therequired beam qualities. In this article, we report on our
preliminary design work on the injector system andscheme for the development of the system.

INTRODUCTION
The PLS (Pohang Light Source) in the PAL/POSTECH
is the 2.5-GeV light source with the full-energy injection
linac. The PLS linac uses 44 SLAC-style accelerating
structures powered by 80-MW klystrons and 200-MW
modulators. While it is the world 3rd in its beam energy, it
has been under-utilized with beam injections into thestorage ring only two times a day. Utilization of the PLS
linac as the 4th generation light source (PAL XFEL) has
been one of the hot issues in the PAL since last year, andrelevant design work has been performed. [1] As shown
in Ref. 1, the PAL XFEL aims to achieve 3-Å lasing with
3-GeV beam energy. This implies it requires very highquality beams at the entrance of the undulator. For the 4th
generation light source, we are going to add a new 700MeV linac, with a low-emittance electron gun and twobunch compressors, to the head of the main linac. In thisway, we could lessen the modification and shutdown
period for the main linac. The successful construction of
the new linac and the conversion of the main linac into
the 4th generation light source would require its electron
source be prepared as soon as possible with required
beam qualities. Due to these reasons, we have alreadystarted to construct the RF photo-injector system and will
test its performance in a dedicated test-stand.

DESIGN CONSIDERATION____________________________________________*Work supported by the MOST and the POSCO, Korea#
smartguy@postech.ac.kr

Available online at http://www.JACoW.org

In Table 1, we summarize requirements imposed to theinjector for the PAL XFEL.
Table 1: Injector requirements for PAL XFEL
Charge1 nC

Beam Energy

150 MeV

Repetition Rate

30 Hz

Emittance (normalized, rms)

< 1.2 µm rad

Energy Spread (rms)< 0.1 %

There are two representative schemes for XFEL
injectors. One is the LCLS-style injector based on the RF
photo-cathode gun and the emittance compensation by thegeneralized Brillouin flow (Invariant Envelope). Many
laboratories are demonstrating the practicability of thisscheme. [2][3][4] There is another unique approach at the
SCSS (SPring-8 Compact SASE Source) in the SPring-8.
The SCSS adopts thermionic DC gun with a single-crystal
cathode. The DC Gun is followed by a fast chopper and astanding-wave-type pre-buncher. The DC gun has alreadydemonstrated 1-µm emittance [5] at sufficiently highcharge. The success of this scheme seems largely dependon the transverse and longitudinal optics design in the
low-energy part from the gun exit to the beginning part of
the first accelerating structure.
As the injector for the PAL XFEL, we are going to
adopt the RF photo-cathode gun with the IE emittancecompensation scheme. The SCSS-style injector will bechosen as a backup option. This is because it does not relyon the laser for generating electrons, and this would makethe system inherently stable and reliable.
In order to deduce the basic requirements for therealization of the reliable RF photo-injector system, we
briefly mention on the IE emittance compensation.[6] The
transverse dynamics of charged-particle beams, with theperveance, κs, propagating through the linear focusing
channel, Kr, and accelerated at the rate of γ′ is describedby the following equation,

 γ′ 
κε2+ K rσ − 3s 3 − 3 n2 2 = 0
2 σβ γ σ β γ
β γ 

σ ′′ + σ ′ (1)

The rms beam size, σ and derived qualities (e.g.,
emittance) are damped as the beam is accelerated becauseof the non-vanishing σ′. This implies that the so-called
emittance oscillation is damped and the emittance can bemade frozen to a very low value under a certain condition.

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S.J. Park et al. / Proceedings of the 2004 FEL Conference, 179-182

This is achieved by providing proper matching conditions
at the accelerator entrance, in both the transverse and thelongitudinal planes, given by two equations below,

σ′=0
γ′=

2

σ

Iˆ
2 I 0γ(2)(3)(2) is to require the beam waist be formed at theaccelerator entrance, which is commonly done in linear
electron beam devices, e.g., klystrons. (3) is a newrequirement determining the accelerating gradient of thestructure with given beam size, σ and peak current, Iˆ .
The constant I0 in (3) is called the Alfvén current with thenumerical value of 17 kA.
Fig. 1 shows normalized emittance evolutions after the
RF gun and the emittance-compensating solenoid withand without the downstream acceleration. It is clearlyseen that the emittance and the beam size are frozen to acertain value with acceleration (thick lines), which
otherwise diverge (thin lines) due to the space-charge
repulsion force.

Figure 2: Variation of normalized emittance profiles(along z) with different rms bunch lengths. Bunch shape
is Gaussian with cut at +/- 5o. Shown are emittanceprofiles for different rms bunch lengths. Notice better
performance with larger rms length, i.e., more flat bunchshape.

Figure 3: Variation of normalized emittance profiles andbeam energies (along z) with different percent deviationsof gun solenoid current from the optimum value.
Figure 1: Comparison of beam rms sizes and normalized
emittance evolutions with (thick lines) and without (thinlines) acceleration. Accelerator entrance is located at z =1.5 m. Also shown are beam energy profiles (right scale).
Based on the principle of the IE emittancecompensation, we list up practical requirements for therealization of reliable XFEL injectors,!
!
!
!

Low-emittance electron gun (such as the RF gun +high-power laser with profile control capabilities)
High gradient booster accelerator with goodalignment
Solenoids with low field errors and good alignments
Low-jitter RF system

Without describing the above requirements in detail, theauthor presents in Fig. 2 - 5 some results from the
PARMELA simulations that have been done for
evaluating impacts of operation parameters on theperformance of the LCLS-type injector.

MOPOS37

Figure 4: Variation of normalized emittance profiles andbeam energies (along z) with different initial phases (w.r.t.
rf zero phase)

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S.J. Park et al. / Proceedings of the 2004 FEL Conference, 179-182

k r
),
2
k
f 2 = fπ (1 −)2 r

f1 = fπ (1 −Figure 5: Variation of normalized emittance profiles withdifferent alignment errors in the 1st accelerating column.
Errors are input in a cell-by-cell manner and are assumed
to be random with peak values as indicated.

FABRICATION OF RF GUN
We are fabricating the 1.6-cell RF photocathode gun(BNL Gun-IV type) for use in the injector test-stand thatwill be described in the next section. Another gun withsimilar design will be also fabricated for the femto-second
electron diffraction facility [7] that is being establishedwith the collaboration with the Chemistry department in
the KAIST (Korea Advanced Institute of Scientist andTechnology, Korea) and Dr. Xijie Wang at the BNL. At
the PAL, there has been active work on developing highpower klystrons for use in the PLS linac. Recently, we
have succeeded to fabricate an 80-MW pulsed klystronand all relevant facilities have been in-house established.
[8] This capability would play a vital role in developing
high-performance RF photo-injector at the PAL.
Before embarking in the fabrication of the RF gun, we
have prepared a cold model to check the tuning propertyof the gun cavities. See Fig. 6 for its appearance.

(2)where, f1 & f2 are resonant frequencies of half and fullcells,
fπ is the (required) π-mode frequency,
k is the coupling factor between the two cells =mode separation / fπ,
and r is the volume ratio between the two cells(= 1/0.6 = 1.67).
Using k = 1.16 x 10-3, r = 1.67, and fπ=2856 MHz, f1 =2853.861 MHz, f2 = 2854.717 MHz. Dimensions of eachcell can be determined from numerical calculation using
computer codes such as the SUPERFISH. Specificparameters of each cell are obtained by completely
detuning the other cells. Fig. 7 illustrates these procedures.
The upper two figures are SUPERFISH calculation forthe half (left) and the full (right) cells. After determining
independent cell dimensions, those two cells are
combined to yield the π-mode resonance at the required
frequency, fπ as shown in the lower figure in Fig. 7.

Figure 7: Scheme of determining cell dimensions.
Dimensions of each cell are determined by completely
detuning the other cells. (Upper figures) When both cells
are combined, π-mode resonance occurs at the required
frequency, fπ = 2856 MHz. (Lower figure)Network-analyzer measurement of the two resonantmodes in the gun cavity is shown in Fig. 8. With π-mode
resonance at the 2856 MHz, the mode separation between
the 0- and π-mode was 3.4 MHz. The suppression of the
0-mode is not done because the loop coupler used in thiscold model is wide-band.
Figure 6: Appearance of cold model of RF gun cavity.
It has two tuners and loop couplers installed at each cell,which allow easy checks of cavity tuning properties.
Tuning of each cell for resonating the gun cavity at the πmode with the required frequency (e.g., 2856 MHz) canbe done referring to the following equations [9],Single-Pass FELs

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S.J. Park et al. / Proceedings of the 2004 FEL Conference, 179-182

INJECTOR TEST-STAND
For the early development of the injector for the PAL
XFEL, we are going to setup a test-stand that is equippedwith a photo-cathode RF gun, an accelerating structure,
diagnostic devices, and a rf source system. See Fig. 10 for
the layout of the test-stand.
Klystron
Modulator

Figure 8: Network-analyzer measurement of the gun
cavity cold-model.
Transient response of the gun cavity to pulsed rf poweris important because of the mode beating phenomenon.
By applying pulsed rf to the full-cell coupler, timeevolution of cavity field was observed at the other couplerin the half cell. In Fig. 9 we show the time-profile of thecavity field together with the input rf waveform. The
rippling in the rising part of the cavity-field waveform isbelieved to be caused by the mode beating. Note theperiod of the rippling corresponds to the inverse of themode separation. Since the characteristic time of thestanding-wave cavity is proportional to the Q-factor of thecavity, measured transient period shown in Fig. 9 will bedifferent from the real gun that is made of brazed copper.
Also notice that the falling part of the cavity-field
waveform is a simple exponential decay, which would be
the indication of the enough decay of the 0-mode during
the rf pulse. The relevance of these observations to thepractical aspect of gun operation is that the pulse durationof the rf power input should be long enough to allow the
0-mode to decay sufficiently. Otherwise, the condition of
the cell balance will not be met and the beam quality isdeteriorated.

Figure 9: Transient response (upper trace) of gun cavity topulsed rf input (lower trace).
We will proceed to machine the gun cavity by the useof ultra-precision turning lathe. After brazing, theassembly will be baked with procedures similar to the
klystron fabrication. Whole fabrication will be controlled
by well-arranged quality-control procedures in order toachieve high performance and reliability.

MOPOS37

Quadrupole
Quadrupole
Magnets
Magnets

RF Gun& Solenoid

Accelerating Column& Solenoids

Wire Scanners

BAS

0
205

Laser

15000

Figure 10: Layout of planned injector test-stand for the
PAL XFEL.
We will employ standard diagnostics for measuring theemittance and the energy spread. Devices for measuringslice parameters will be also installed. Compact andmovable emittance analyzer would be very useful for
optimizing the delicate IE (Invariant-Envelope) emittancecompensation.

REFERENCES[1] J. S. Oh et al., NIM-A528, pp. 582-585.
[2] J. Yang et al., Proc. of the EPAC2002, pp. 1828-1830.
[3] V. Miltchev et al., these Proceeding.
[4] X.J. Wang et al., Proc. of the EPAC2002, pp. 18221824.
[5] K. Togawa et al., these Proceedings.
[6] R. Serafini et al., PRE-55, pp. 7565-7590.
[7] X.J. Wang et al., Proc. of the PAC03, pp. 420-422.
[8] S. J. Park et al., to be appear in Proc. of the APAC04.
[9] R. Bossart et al., Proc. of the EPAC92, pp. 10261028.

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M.H. Yoon et al. / Proceedings of the 2004 FEL Conference, 183-186

OPTIMIZATION OF A SOFT X-RAY SASE-FEL PARAMETERS AT
POHANG ACCELERATOR LABORATORY
M. Yoon∗ , J. E. Han, E.-S. Kim, PAL, POSTECH, Korea
Abstract
A free-electron laser (FEL) based on self-amplified
spontaneous emission has been designed. This FEL is utilizing the existing 2.5 GeV electron linear accelerator atPohang Accelerator Laboratory (PAL). The radiation wavelength was chosen to be in the water-window region 3-4 nm
which can be used for biological imaging. In this paper, it
is shown that the PAL is particularly suited for this wavelength if the existing linear accelerator is employed without
having major modification. For 4 nm wavelength, the saturated power is shown to be approximately 5 GW with asaturation length of about 30 m.

INTRODUCTION
Several free-electron lasers (FELs) based on selfamplified spontaneous emission (SASE) are under study,
construction or operation around the world including
LCLS, TTF, SCSS, LEUTL, VISA, etc. Among these, theLinac Coherent Light Source (LCLS) at Stanford Linear
Accelerator Center (SLAC) in USA and the TTF projectat DESY in Germany are under construction and aiming at
producing hard x-rays with 1.5 Å and 1.0 Å wavelength,
respectively. Recently, there is an increasing demand inthese facilities to have a capability of producing soft x-ray
radiation as well, 20-50 Å wavelength region. One of thepromising applications in this wavelength is x-ray microscopic imaging in the water-window region (23-44 Å), especially the imaging of biological specimens in their natural state. Due to large absorption differences between carbon and oxygen in the water-window region, the naturalcontrast between protein and water can be attained. In addition, due to short pulse nature of the radiation of the order of 100 femto second, a single-pulse exposure measurements can be carried out to obtain images of living cells
before the specimen changes in its structure caused by radiation damage.
The SASE principle is based on the FEL amplifier where
the initial spontaneous radiation near the undulator entrance is used as input electromagnetic (EM) wave. This
co-propagating EM wave combined with the undulator
field generates a beat (i.e. ponderomotive) wave whose
phase velocity is slower than the speed of light and canbe synchronized with electrons. Depending on the relative
phase with respect to the beat wave electrons can lose or
gain energy, causing micro-bunching of the electron beamof the order of the wavelength of the EM wave. The electrons in the micro-bunch then acts coherently to produce an
exponential growth of the radiation intensity which is pro∗ moohyun@postech.ac.kr

Available online at http://www.JACoW.org

portional to the square of the number of electrons at saturation. This SASE principle has been successfully demonstrated recently at UCSB, LEUTL at Argonne National
Laboratory (ANL) [1] and at DESY [2].
The wavelength of the output radiation through an undulator is given by
λ=


λU 
1 + a2U + γ 2 θ2 ,
2γ 2

(1)

where λU is the undulator period, γ is the ratio between theelectron energy and the electron rest energy 0.511 MeV,aU = K for helical and aU = √K2 for planar undulator.

U λU
Here, K is the undulator parameter given by K = eB
2πm0 cwith BU the peak magnetic field on the mid-plane of theundulator, m0 the electron rest mass, e and c the electron
charge and speed of light respectively. In Eq. (1), θ is theangle between the undulator mid-plane and the observation position. The equation shows that the radiation wavelength is inversely proportional to the beam energy squared.
Eq. (1) also shows that higher magnetic field (i.e., smaller
undulator gap) gives longer wavelength and this is due tothe fact that higher magnetic field reduces the magnitude ofthe longitudinal velocity of an electron beam.
Currently at the PAL, a 2.5 GeV electron linear accelerator (or linac) is used to inject electrons into the 2.5
GeV storage ring. The circulating electron beam in thestorage ring then emits synchrotron radiation during the
curved motion through bending magnets and insertion devices with a lifetime of 20 hours at maximum beam current
170 mA. Normally beam is injected two times per day andtime required for injection is less than 10 minutes. Thus
the linac is in stand-by mode for most of the time.
The electron energy of 2.5 GeV is particularly suited forsoft x-ray generation with a FEL. This paper concerns asoft x-ray FEL using the PAL injector linac. First, we introduce the parameter optimization of the soft x-ray. For
comparison purpose we consider two different energies ofan electron beam, 2.5 GeV and 3 GeV respectively. We
then show some characteristic feature of the FEL. Timeindependent and -dependent numerical simulation results
are depicted.

SOFT X-RAY FEL PARAMETERS
The amplification of the EM wave is due to the collective
instability of an electron beam. The instability produces
an exponential growth of the EM field intensity and of thebunching given by the bunching parameter:
N

B=

e
1 
exp
Ne

k=1



2πizk
λ


(2)

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M.H. Yoon et al. / Proceedings of the 2004 FEL Conference, 183-186

where zk is the longitudinal position of the kth electronwith respect to the bunch√ center, Ne is the total numberof electrons and i = −1. The growth saturates when
the bunching parameter is of the order of one. In onedimensional approximation the power growth before saturation is given byz1
P ≈ Pn exp(3)< Psat ,9Lg,1dU
is the one-dimensional gain length
where Lg,1d ≈ 4√λ3πρ
and Pn is the effective input-noise power proportional to
the square of the initial bunching parameter |B0 |2 and it is
the power for spontaneous coherent undulator radiation oflength Lg . Pn is proportional to the inverse of the num2eber of electrons in a coherence length (i.e. Pn ∼ ρ cEλ ). In
the case of SASE FEL, the saturation occurs approximately
after 20 gain lengths. The FEL performance is mainly described by the FEL parameter ρ which is given by

ρ=

1
γ


JJ(χ)

aU ωp
4 ωU

2/3
,

(4)

where ωU = 2πc
λU and ωp is the plasma frequency given2by n0eme 0 . Here ne is the electron density and 0 is thefree-space permeability. Note that the FEL parameter ρ is
1/3
proportional to ne . The function JJ(χ) is given by
1: helical undulator
JJ(χ) =J0 (χ) − J1 (χ) : planar undulator,
K2
th-order Bessel funcwhere χ = 4(1+K
2 /2) and Jn is the ntion. The radiated energy at saturation is roughly ρNe Ee ,where Ne is the total number of electrons. The number of
emitted photons per electron at saturation is then given byEe, where Eγ is the photon energy. The signifiNγ = ρ Eγcance of the FEL parameter ρ can be summarized as• Saturation length Lsat ∼ λρU• Radiation power at saturation Psat ∼ ρPbeam• Frequency bandwidth ∆ωω ∼ ρ,

where Pbeam is the peak power of the electron beam,
Pbeam = Ee Ip with Ip the peak current. Therefore highpeak current is desired to obtain high power at saturation.
In Figs. 2 and 3 we have not taken into account the undulator segments which will increase the saturation length as in
the case of Fig. 1.
In order for the collective instability to be developed thefollowing three conditions should be met:
• Electron beam emittance must match the diffractionλlimited emittance:  < 4π
• Beam energy spread must be smaller than the FEL paσrameter: γγ < ρ

MOPOS38• Gain length must be shorter than the Rayleigh length:
2πσ 2Lg < ZR = λ x , where σx is the rms size of theradiation.
When three-dimensional effect is considered, the FELgain length can be expressed by introducing a universal
scaling function [3]Lg = Lg,1d (1 + η(ηd , η , ηγ )) ,

(5)

where
ηd
η
ηγ

Lg,1d
Lg,1d
=
2kσx2
ZR



Lg,1d
4π
=
β
λ

 
Lg,1d
σγ
= 4π
.
λu
γ
=

(6)
In the above equations, ηd is the diffraction parameter, η isthe angular spread parameter, and ηγ is the energy spreadparameter. These scaling parameters measure the deviationof the beam from ideal case. M. Xie fitted η numericallywith 19 fitting parameters and listed the fitting coefficients
which will be omitted here [3]. The saturated power obtained empirically by fitting results is given by
Psat ≈ 1.6ρ

Lg,1d
Lg

2
Pbeam .

(7)

Table I shows the major beam and FEL parameters for 4
nm at PAL. It is seen that the undulator-gap height is 0.85
cm and the period is 3.3 cm. A moderate gap height waschosen to prevent possible deterioration of the beam quality from wake field and surface roughness. For planar undulator with Nd-Fe-B hybrid permanent magnet, the peakmagnetic field in the mid-plane is given by [4]

 2
g
g
+ 1.54
BU [T ] = 0.95 × 3.44 exp −5.08
λU
λU
g
0.1 <
< 1.0
λU
where g is the full gap of the undulator. This gives the peakmagnetic field on the mid-plane of 1.03 T and as a result
the undulator parameter K is 3.173 as Table I shows.

RESULTS
In order to obtain saturation power as a function of thelength, the GENESIS program was invoked, which is athree-dimensional simulation code for a SASE FEL. This
program has a capability of numerically integrating theequations of motion in time-independent or time-dependent
mode. Fig. 1 shows the power as a function of the undulator length. It is seen that the saturated power is approximately 5 GW and the saturation occurs at around 30

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M.H. Yoon et al. / Proceedings of the 2004 FEL Conference, 183-186

5εN (mm mrad)

4

10

10

9

10

8

10

3
Psat (GW)
4
6
8
10
12
14
16

2

1

0
1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Ip (kA)

Figure 2: Saturation power as functions of the normalized
emittance and peak beam current.

3.5

Lsat (m)
14
16
18
20
22
24
26

3.0

εN (mm mrad)

Table 1: Parameters of the 4 nm FEL.
Parameter
Radiation wavelength, λ (nm)42.5Electron beam energy, Ee (GeV)
3.3
Undulator period, λU (cm)Undulator full gap, g (mm)8.5
Undulator peak field
1.03
in the mid-plane, BU (T)Undulator parameter, K
3.173
Normalized rms beam emittance,
2.0n (µrad)3.0
Peak electron beam current, Ip (kA)
Rms energy spread, σγ /γ
6.01×10−4
Gain length (3-D), Lg (m)1.146
FEL parameter (3-D), ρ
1.32×10−3
FWHM bunch length, τB (fs)231
Gain correction factor, η
∼0.11
∼ 30
Saturation length, Lsat (m)∼5Saturation power, Psat (GW)

2.5
2.0
1.5
1.0

Power [W]

7

10

0.5

6

10

0.0

5

10

4

1

2

3

4

5

IP (kA)

10

3

10

2

10

0

10

20

30

40

Distance [m]Figure 1: Power as a function of the undulator length for 4
nm FEL. Undulators are assumed to be segmented.

m. Figs. 2 and 3 show the saturation power and the saturation length as functions of the normalized emittanceand the peak electron beam current. These figures wereobtained assuming undulators were not segmented so thatpower and saturation length were slightly different from thesegmented case. The saturation power increases as the normalized emittance decreases and the peak beam current increases. On the other hand the saturation length decreases
as the normalized emittance decreases and the peak beam
current increases. The natural emittance of 2 mm mrad andthe peak beam current of 3 kA have been chosen in view of
the reasonable performance of a rf photocathode electrongun.
To find the focusing requirement and therefore the optimal β functions, both the natural undulator focusing andquadrupole focusing by FODO structure were considered.
It is well know that the planar undulator gives a verticalFigure 3: Saturation length as functions of the normalized
emittance and peak beam current.
focusing due to edge effect of the magnet blocks and theequation of motion is given byd2 y
1+ 2 y = 0,dz 22ρwhere z runs along the longitudinal axis of the undulator.
The vertical transfer matrix due to a planar undulator istherefore√2ρ sin( √L2ρ )cos( √L2ρ )
,
(8)
My =
cos( √L2ρ )− √12ρ sin( √L2ρ )where L is the straight length of the undulator and ρ is theradius of curvature on the axis where the magnetic field is
peak.
To allow the space for quadrupole magnets and diagnostic instruments such as beam position monitors undulators
are split. The space requirement between undulator sections is such that the phase slip of the electron bunch behind the electromagnetic wave is integer multiple of the radiation wavelength: (c − v)t = nλ where v is the electron

Single-Pass FELs

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M.H. Yoon et al. / Proceedings of the 2004 FEL Conference, 183-186

speed n is an integer, and t is the gap-traversal time of theelectron. Therefore, for n = 1,K2
L ≈ λu 1 +.
(9)2This yields L = 19.916 cm.
Fig. 4 shows the horizontal and vertical β functions as
a function of the straight length. It is seen that average βfunction is about 4 m. Fig. 5 shows the saturation power

for s > 0 and Wz (s) = 0 for s < 0, where s isalong the longitudinal position of the test particle with respect to the particle generating field, Z0 = 120π Ω, s0 =(2a2 /Z0 σ)1/3 , σ is the conductivity of the chamber material, and a is the pipe radius. Table 1 shows that the full
gap height of the undulator was chosen to be 8.5 mm. Assuming 0.5 mm thickness of the vacuum chamber, Fig. 6
shows that the saturation power decreases about a factor of
2 when copper chamber was assumed.
10

10

9

With wakefield
Without wakefield

10

8.
βx
7.
6.
5.
4.
3.
2.
1.
0.0
0.0 1.

8

10

βy

7

Power [W]β (m)FEL FODO

4

10

2

10

0

10

20

30

40

Distance [m]

2.

3.

4.

5.

6.

7. 8. 9. 10.
Path length (m)

20
150
10
100
0

50

0

5

10

15

Saturation length [m]Power [GW]

5

10

3

and the saturation length as a function of the average βfunction. This figure indicates that the chosen 4 m average β value is reasonably optimized to yield high saturation
power and low saturation length.

020

β function [m]Figure 5: Saturation power and saturation length as a function of the average β function along the undulator.
Finally, effect of the wakefield due to the undulator vacuum chamber has been considered. In highly relativistic
approximation, the longitudinal wakefield due to a resistive
wall effect from a single electron is given by√
3s
4cZ0 1 −s/s0
e
cos
(10)
Wz (s) = − 2
πa
3
s0
√
2
2 ∞ x2 e−x s/s0
dx ,
−
π 0
x6 + 8MOPOS386

10

10

Figure 4: β function along the undulator and FODO focusing structure.

-10

10

Figure 6: Power as a function of the undulator length with(dashed) and without (solid) wakefield in the undulator.
Copper chamber with radius 3.75 mm was assumed.

CONCLUSION
In the paper we have described the SASE FEL to produce the soft x-ray. It is seen that with the present 2.5 GeV
rf linear accelerator at the Pohang Accelerator Laboratory,
the radiation of 4 nm wavelength can be produced with reasonable saturation power and the saturation length. The
wavelength are decreased to 3 nm if the electron energy isincreased to 3 GeV. Currently a design study is in progress
which includes the start to end simulation. More details of
this work is reported in these proceedings [5].

Acknowledgements
One of the authors (M. Yoon) would like to thank Dr.
Heinz-Dieter Nuhn at SLAC for his help and a numberof suggestions while carrying out this work. This work
was supported by Ministry of Science and Technology(MOST).

REFERENCES[1] S. Milton et. al. Science 292, 2037 (2001).
[2] R. Treusch and J. Feldhaus, Eur. Phys. J. D 26, 119 (2003).
[3] M. Xie, Proc. of the 1995 Particle Acc. Conf. (IEEE, Piscataway, NJ, 1995) p. 183.
[4] K. Halbach, J. Phys. (Paris) Collq, 44, C1-211 (1983).
[5] E.-S. Kim et. al., in these proceedigns.

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A.V. Elzhov et al. / Proceedings of the 2004 FEL Conference, 187-189

SIMULATING FEM AMPLIFIERS: FEATURES IN VARIOUS REGIMES*
A.V. Elzhov+, A.K. Kaminsky, E.A. Perelstein, S.N. Sedykh, A.P. Sergeev
Joint Institute of Nuclear Research, Dubna, Russia

Abstract
Results of previous experimental investigations ofCompton/Raman millimeter-wavelength FEL amplifiers
are analyzed in numerical simulations. Compact quasione-dimensional models under helical-trajectory approachare employed. A tare on the stationary trajectories due toradiation is inserted. Reasonable agreement between
simulation and experimental results is got in the regimes
with reversed guide magnetic field.

1 INTRODUCTION
A full-scale three-dimensional simulation of an FEL
amplifier allows one to get the best agreement between
the simulation and experimental data. However thecorresponding software possesses limited accessibility
and requires considerable computing resource. Moreover
not always one can distinguish principal physical factors
defining features of particular FEL amplification regime.
So use of compact approximate models seems to be
attractive if they take account of dominating physicalprocesses and allow one to determine parameters of
amplifier operating with an acceptable accuracy.
In this paper quasi-one-dimensional models underhelical-trajectory approach for various regimes of
millimeter FEL (FEM) amplifier are considered, theirapplicability taking into account the experimental data [1–4] and problems of numerical simulation [5] are analyzed.

2 FEL REGIMES AND MODELS
A Raman regime of an FEL amplifier in whichcollective effects dominate is valid under 3 conditions [6]:1°. The system is lengthy enough while the beam ishigh-dense so that several plasma oscillations get into the
λp/L ≤ 1.
(1)
system length:
Here λp = 2π/ωp, ωp is the relativistic plasma
frequency: ωp2 = 4πnee2/m0γz2γ0 where ne is the electron
beam density, m0 is the electron rest mass and γ0, γz are
the total and longitudinal relativistic factors.
2°. Transverse velocities are much less than criticalvalue [7]βw << βcrit ≡ F–1/2(2ωpc2 / vz03γz2kw)1/2.
(2)
Here kw = 2π/λw is the wiggler wavenumber (λw is the
wiggler period), vz0 is the initial longitudinal electron
velocity, F is the beam-waveguide fill factor.
This criterion is based on comparison of contributionof ponderomotive and Coulomb potentials and obtained inhelical-trajectory approach. Analyzing real experiments
one should use it with caution [6] for the complications___________________________________________* This work is supported by grant №03-02-16530 of RussianFoundation for Basic Research.
+ Corresponding author: A. Elzhov, E-mail: artel@sunse.jinr.ru

Available online at http://www.JACoW.org

such as reduction of the effective plasma frequency in a
waveguide, wiggler inhomogeneities, beam thermal
effects and guide magnetic field. So the model may beinsufficient for description of space-charge effects.
3°. Landau damping of the space-charge waves is not
significant (the space-charge wavelength is greater thanthe Debye length) [6]. This restriction is imposed by thebeam energy spread. For Gaussian distribution of electron
velocities this requirement [8] transforms to(δγ/γ)z < (L/2γ)(ωp/2c) ≡ πL/2γλp.
(3)Let us study a self-consistent spatial problem of
relativistic electron beam moving in the microwave fieldprovided the regime is stationary, the wave is a singlemode one and its amplitude is slowly varied with length.
Assuming the electrons obeying helical trajectories
with longitudinal velocity β⊥, we can write down a set of
equations for a Raman FEL accounting [9,10,11]:
dγ j
dZ

+

=

iβ ⊥ j2 2 β zj

ase

iψ j

+

2
2
c ω p 0γ z 0 Φ 0 β zj Fs . c . iψ j − iψ i
iee
+ c .c .
24ω 0c (k z + k w )

dθ j
dZ

=

1

β zj

−

1

β ph

(5),

− iθ

daˆ
e j
= η 0γ 0
dZ
γj

(4)
(6)

Here γj is the j-th electron’s relativistic factor;
Z = zω0/c is the dimensionless longitudinal coordinate, ω0is the amplifier operating frequency, kz is the longitudinalwavenumber. The phase variables are: θj is the electronto-wave one; ϕ is that of the complex RF amplitude ( â =aseiϕ), ψj = ϕ +θj is the total ponderomotive phase. The
variable as = eEs/m0ω0c is the dimensionless amplitude of
RF electric field. The gain factor is η0 = (Ib /IA ) (2κ0/N),
κ0 = aw/2γ0 [11], aw = eBw/(kwmc2) is the dimensionlessamplitude of the wiggler magnetic field, Alfven constantis IA = m0c3/e ≈ 17 kA; N is the wave norm; βzj and βph
are longitudinal electron velocity and phase velocity ofthe microwave respectively. Fs.c. is the attenuation factorof the space-charge wave, which is close to unity when
the requirement (3) is satisfied. The constant in Eq.(4) is~~β w2γ z2 Ω 0
β w2γ z2≡ 1−
Φ0 = 1−~2~2
1 + β w − γ 0 β z0 ag(1 + β w )Ω 0 − k w cβ z 0
where ag = eBg/m0c2kw = Ω0γ0/ckw is the dimensionlessamplitude of guide magnetic field with induction value of~
Bg, and β w = β⊥/βz0 is the extended wiggling parameter.
The same system is suitable for simulation of highgain Compton FEL if the Fs.c. term in (4) is removed.
A uniform longitudinal guide magnetic field allows
one to rise the electron beam stability relatively toSingle-Pass FELs

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A.V. Elzhov et al. / Proceedings of the 2004 FEL Conference, 187-189

transverse perturbations. But the trajectories became more
complicated. Particularly for the wiggler field of helicallysymmetric distribution generated by a sinusoidal surface
current in a bifilar helix [12], one can get a transcendental
equation for stationary trajectories for a narrow beam.
The electron trajectories are stable with respect to theexcitation of betatron oscillations, in two areas of beam
parameters and external fields. These areas are separated
by the vicinity of the cyclotron resonance where aperturbation of transversal oscillations results to their
exponential growth, so the helical trajectory approachassuming β⊥/βz << 1 becomes non-applicable.
The stationary trajectories were derived from external
magnetic fields (wiggler and guide ones) only. In a real
FEL an RF wave appears that the relations for the velocity
components should be derived more accurately.
Assuming as << aw, ag we consider the effect of the RF
wave as a tare for the motion over non-perturbed
stationary trajectories. The velocity vector of each particle

is resolved to "wiggler" and "radiation" parts: v = vw + vR.
The former is vw = (сβwcos kwz, сβwsin kwz, сβzw), thelatter is vR = (сβ⊥Rcos θ, сβ⊥Rsin θ, сβzR). The equation for
longitudinal momentum of the particle results in
γ

dβ zR
dϕ 
β  ckβ da s as sin ψ − w= w  s +cosψ +dZ
β z 0  ω 0 dZ β z 0 dZ+

1  dγ R dγ − βzdZ
β z 0  dZ  pwhere (dγ/dZ)p is the potential term of Eq.(4) (i.e. thesecond one on the right side).

3 FEL AMPLIFIER EXPERIMENTS ANDSIMULATION RESULTS
Basic parameters of FELs and electron beams inexperiments [1–4] are presented in Table 1.

Table 1. Parameters of millimeter-wave FEL amplifiers [1–4].
CESTA
JINR
I
Electron beam energy Eb, MeV
2.2
1.5
0.75
Electron current in wiggler Ib, A
500
50–70
90–119
Electron beam radius rb, cm
0.5
0.3–0.5
0.25
Initial energy spread of the electron beam, %
< 1.5
1–2
12
7.2
3.18
Wiggler period λw, cm
Wiggler magnetic field amplitude Bw, kGs
1.1
2.1
0.63
Guide magnetic field amplitude Bg, kGs
no
–1.4
4.06
35
35
33.9
RF wave frequency f0 = ω0/2π, GHz
Radiation spectral band (FWHM), GHz
0.16
0.2–0.3<0.16
Operating mode (cylindrical waveguide)
H11
H11
H11
RF power at the wiggler entrance, kW
8–10
6–20
8.5
RF power at the wiggler exit, MW
15
2–3
5.8
FEL amplifier efficiency, %
1.5
2–3
9
Spatial increment, dB/m
33
23
44
Saturation length, cm
~ 150
~ 120
~ 120

MOPOS47

MIT
II
0.75
300
0.25

III
0.75
300
0.25

3.18
1.47
10.92
33.9
<0.16
H11
8.5
4.2
2
38
~ 150

3.18
0.63
–10.92
33.9
<0.16
H11
8.5
61
27
41
~ 170

model with phase equation as (8). In this paper we allow
space charge using Eqs. (4), (8), (6) for the simulation.
3.0

lg (P/P0), P0 = 10 kW

Numerical simulation of microwave amplification andelectron beam bunching [9] for CESTA experiments [1,2]under Compton high-gain regime model agrees with theexperiment well. It is in conformity with the above
criteria for space-charge effects. The plasma wavelength~ 11 m much exceeds the interaction length. The relation(2) is not satisfied at least by an order of magnitude.
For the JINR FEL amplifier with reversed guidemagnetic field [3] the parameters are in the intermediate
range where no any interaction type dominates. (Parts of
the inequalities (1), (2) are comparable in pairs.) From(3), the Landau damping is negligible in this case.
The dispersion relation at non-zero guide magnetic
field stated in [7] at β⊥/βz << 1, as << aw, ag allows one totransform Eq. (5) todθ jc( k s + k w )1 ω p Φ0
(8)
=−
+
+
ω0
β zj
ω 0 β z0dZ
The previous simulation [13] for the parameters ofexperiment [3] had been performed under Compton

(7)

1
2
3

2.5
2.0
1.5

4

1.0
0.5
0.0

0

50

100

150

z, cm

200

250

300

Figure 1: RF power of FEL amplifier [3] versus length. The
experimental data are shown with dots. Curves 1,2,3 – Compton
model simulation [13] at the energy spread of: 1) 0; 2) 3%;
3) 5%; curve 4 – Raman model simulation for cold beam.

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A.V. Elzhov et al. / Proceedings of the 2004 FEL Conference, 187-189

Fig. 1 presents the results of RF power calculations[13] for different values of the initial energy spread of thebeam, and the spatial distribution of RF power obtained in
Raman model for cold beam (zero energy spread). The
experimental results [3] are depicted by dots. They took
an intermediate position between simulation results fromextreme models. This fact is in agreement with the idea ofcontinuity in the parameter space.
A detailed investigation of FEL amplifier with guidemagnetic field was carried out at MIT [4]. Three basic
regimes were studied: 1) positive (conventional-direction)
guide magnetic field with Larmor frequency less than thecyclotron resonance frequency; 2) positive guide field at
the other side from the cyclotron resonance; 3) negative(reversed) field (see Table 1). The experimental results
indicated that the reversed field regime turned out to be
most preferable by the beam current, spatial increment of
RF power, saturation level and energetic efficiency.
According to the estimation over all criteria (1), (2),(3), the space charge effect is sufficient for each regime.
The plasma wavelength (~ 20–30 cm) gets into theinteraction length several times. The inequality (2) issatisfied by over than one order of magnitude. The
limitation over thermal spread is practically absent: theright side of (3) amounts to several units.
So we have a definite Raman FEL amplifier. We
simulated it over Eqs. (4), (5), (6), (7).
At the small positive guide field (I) the operating pointis relatively near the cyclotron resonance. Transversal
oscillations of the particles grow much so that helicaltrajectory approach is not applicable, the solutions
become nonconvergent. In the regime of large guide field(II) the simulation yields an excessive level of the output
power. Though this discrepancy persists in the threedimensional simulation [5] also. According to the paper[14], an amplification depression in the regimes withpositive guide field may be caused by the competition
between the operating wave and high-frequency modes
excited from the noise level.
Bg = -10.92 kGs

lg (P/P0), P0 = 10 kW

4.0

1

3.5
3.0

2

2.5
2.0
1.5

3

1.0
0.5
0.0

0

20 40 60 80 100 120 140 160 180 200z, cm

Figure 2: RF power of FEL amplifier [4] versus length:experimental data (dots) and simulation results for different
values of the energy spread: 1) 2%; 2) 8%; 3) 10%.

For the reversed field case an acceptable agreementwith the experiment has been obtained in the distributionof the radiation power over the length (Fig. 2).
The difficulties in the simulation of the positive-fieldregimes, especially approaching the cyclotron resonance,
confirm the limited possibilities of quasi-one-dimensionalhelical-trajectory models for description of the particle
motion. For more adequate simulation of the FEL
amplification it is expedient to employ full-scale threedimensional models. One should foresee a possibility of
excitation of RF parasite modes, take into the account thefeatures of beam delivery to the interaction region andwiggler&solenoid inhomogeneties.

4 CONCLUSIONS
Series of numerical simulation of experiments [1–4] inhelical-trajectory approach in various FEL regimes havebeen carried out. The used models are compact and don’t
demand much computing resource. Simultaneously they
are suitable for simulation of regimes with reversed guidefield in order to define basic amplification parameters.
This may be employed during preparation of anexperiment for selection of amplifier operating
parameters.

5 REFERENCES[1] J. Gardelle, J. Labrouche, G. Marchese et al., Preprint
CESTA/5, 1996.
[2] J. Gardelle, J. Labrouche and J.L. Rullier, Proc. of
EPAC’1996, v. 1, p. 298.
[3] Yu.B. Viktorov, A.K. Kaminsky, S.B. Rubin at al.,Proc. of XI All-Union Seminar on Charged Particle
Accelerators, Dubna, 1989, v. II, p. 95 (in Russian).
[4] M.E. Conde and G. Bekefi, Nucl. Instrum. Meth.,
1992, v. A318, p. 109.
[5] A.K Ganguly and H.P. Freund, Nucl. Instr. and Meth.,
1993, v. A331, p. 501.
[6] H.P. Freund, Nucl. Instr. and Meth., 1993, v. A331,
p. 496.
[7] C.W. Roberson and P. Sprangle, Phys. Fluids B, 1989,
v. 1, N 1, p. 3.
[8] T.C. Marshall, “Free electron lasers”, New York –London, McMillan Publ. Co., 1985.
[9] E.A. Perelstein, L.V. Bobyleva, A.V. Elzhov,
V.I. Kazacha, Proc. of PAC’1997, p. 488.
[10] J.S. Wurtele, G. Bekefi, R. Chu and K. Xu, Phys.
Fluids B, 1990, v. 2, N 2, p. 401.
[11] N.S. Ginzburg and A.S. Sergeev, J. of Tech. Phys.,
1991, v. 61, p. 133 (in Russian).
[12] H.P. Freund and A.K. Ganguly, IEEE Trans. On
Plasma Sci., 1992, v. 20, N 3, p. 245.
[13] E.A. Perelstein, L.V. Bobyleva, A.V. Elzhov,
V.I. Kazacha, Problems of Atomic Science andTechnology, Series “Nuclear physics investigations”,
1997. N 2,3 (29,30), p. 78.
[14] A.T. Lin, C.C. Lin and K.R. Chu, Appl. Phys. Lett.,
1992, v. 60, N 3, p. 292.

Single-Pass FELs

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l. Werin et al. / Proceedings of the 2004 FEL Conference, 190-192

DESIGN CONSIDERATIONS FOR THE COHERENT RADIATOR,
FEL, IN THE MAX IV PROPOSAL
Åke Andersson, Mathias Brandin, Mikael Eriksson, Tue Hansen, Jörgen Larsson, Lars-Johan
Lindgren, Hamed Tarawneh, Sverker Werin, MAX-lab, Lund University, Box 118, S-221 00 Lund,
Swedenwith a wakefield and CSR analysis of the accelerator
system.

Abstract
The MAX IV proposal is a project for the next Swedish
synchrotron radiation source. Currently a design study is
produced with funding from the Swedish research council(VR). The first half of the project will be a double storage
ring (at 3 and 1.5 GeV respectively) but the second half
will be a coherent radiator, FEL, based on the 3 GeV linac
injector.

INTRODUCTION
After spending effort on a number of different solutions(such as [1]) a basic design is now being elaborated. Thisconsists of linac system providing a <1 nmRad sliced
emittance, <1e-4 sliced energy spread, 2 KA peak current
beam at 3 GeV which feeds three cascaded optical
klystrons and a radiator undulator to produce radiation
down to 1.5-3 nm at GW powers. The system will beseeded by a tunable laser system.
The linac system is foreseen to be normal conducting
operating up to 100 Hz.
To assure synchronisation the gun laser and the seed laser
share initial laser and amplifier.

BASIC LAYOUT INJECTOR AND LINACSYSTEM
The basic layout now being sketched consists of a coupleof building blocks which mainly show the ability of thesystem. This system will be adapted and optimised in thecurrent environment as part of the continuing design
work.
An injector system, which provides a suitable beam, hasalready been designed for the LCLS. As this is very muchin line with the needs of the MAX IV injector we initiallyassume a similar system. [2] (table 1)
The linacs will be based on the same linac technology as
already present in the new MAX-lab injector [3]. These
are 5.2 m long normal conducting 3 GHz structures fromACCEL equipped with SLED cavities. They will be
combined into 15 building blocks of one 35 MW klystron,
one SLED system and two linac sections, thus providing
100 MeV per linac (20 MV/m). An additional 2 blocks
will be used as back-up.
Two bunch compressors are foreseen to reach thenecessary peak current. These will be placed at 150 and
500 MeV or slightly higher energy. The compression
stages, strength and position, will be designed together

MOPOS51

NC v SC system
A normal conducting system is foreseen. A true CW
system (SC-system) will be limited by the drive lasers for
the PC-gun and the seeding to around 1 KHz. In thismode a linac such as the BESSY soft X-FEL will need awall power in the order of 5 MW (3 KW @ 2K [4]). By
going to semi CW operation the power will be reduced,
and so the repetition rate. A NC system as the MAX IV
system will be able to operate at 100 Hz needing a wall
power of 1.5 MW. The gain by a factor of 10 in repetition
rate is difficult to defend while regarding the increase inpower demand and the complexity of a SC-system.
An increase of the repetition rate can be achieved by
splitting the main laser pulse and generating several
synchronised gun (and seed) pulses with 30 ns separation.
These FEL pulses can also be chopped to different
experimental stations.
Table 1. The parameters of the LCLS injector
Charge1 nC
Bunch length
2.9 psEnergy150 MeV
Energy spread (integrated)
1*10-3 RMS
Energy spread (slice)
5*10-5 RMS
Emittance (slice)<= 0.8 umRad

COHERENT RADIATION AND OPTICALKLYSTRONS
The coherent radiation will be produced in a three stage
optical klystron (figure 1). In each step the fifth harmonic
will be extracted. The final stage will be an amplifier(“after burner”) to provide the necessary power.
By using an electron beam with a small sliced naturalenergy spread lower modulating electric fields are
required. Each stage will be supplied by electric fields
strengths in the GV/m range to achieve adequate
bunching.
It is important to match the electron beam optics to thedivergence of the radiation. A compact system is thus anecessity especially at the longer wavelengths (the 53 nmstage) as the divergence otherwise kills the field strengths
in the following modulator. Long undulators will of thesame reason not pay off.

Available online at http://www.JACoW.org

191

l. Werin et al. / Proceedings of the 2004 FEL Conference, 190-192

εx = 1*10-6 m Rad (rms)εx-slice = 0.5-1*10-6 m Rad (rms)σE/E-slice = 5*10-5 (rms)
σt = 2.9 ps (rms)Q = 1 nC
Î = 0.1 KA
Rep rate = 100 Hz

266

Ein = 5e8 V/mσex = σradσex = σrad /4-3
σrad = 0.3 10-3 m σrad = 0.3 10 m

Modulator 1

Buncher 1

λw = 0.12 m
K = 17.8
N = 17
L = 2.04 m

2.12

2 nm

εx-slice = ≤1*10-6 m Rad (rms)σE/E-slice = ≤1*10-4 (rms)
σt = 1 ps (rms)53.2

Delay 1

Ein = 1e9 V/mσex = σrad /4
σrad =0.4 10-3 m

Modulator 2

λw = 0.08 m
K = 9.7
N = 100
L = 8.0 m

λw = 0.08 m∆t= 50 fs K = 9.7
N = 25
L = 2.0 m

Ein = 5e8 V/mσex = σrad /3
σrad = 0.08 10-3 m

2.12 +
harm

3 GeV

εx-slice = ≤1*10-6 m Rad (rms)σE/E-slice = ≤1*10-4 (rms)
σt = ≥150 fs (rms)Î = 2 KAσex = σrad
σrad = 0.13 10-3 m

Buncher 2

Radiator 2
λw = 0.05 m
K = 4.8
N = 160
L = 8.0 m

10.6

Delay 2∆t= 20 fs

Ein = 3e9 V/mσex = σrad /4
σrad = 0.18 10-3 m
Modulator 3
λw = 0.05 m
K = 4.8
N = 40
L=2m

Buncher 3

σex = σrad
σrad = 0.06 10-3 m
Radiator 3

2.12

λw = 0.03 m
K = 2.87
N = 134
L = 4.02 m

P = 3 MWAmplifier 1

Delay 3
∆t= 10 fs

Radiator 1

53 nm

266 nmZrayl = 1 m
Lfoc = 1 m

Linac 2
BC2

2 nm

3 GHz
150 MeVNC

Linac 1
BC1

10 nm

LCLS

500 MeV

150 MeVMAX IV – Coherent radiator scheme

λw = 0.03m
K = 2.87

Figure 1. Schematics of the linacs and optical klystrons
The first HG stage can possibly use a bunch of lower
energy generated in a second electron gun to allow forless powerful seed lasers, but the basic design only uses
the fresh bunch technique.

GUN AND SEED LASER SYSTEM
A main Ti:Sa oscillator, synchronised to the RF-clock,
will provide the source both for the gun laser pulse andthe seed pulse. The gun pulse will be treated in a ps-laser(10ps), made top-hat and amplified thus controlling thecharge and spatial distribution of the electron pulse.
Another branch will be the FEL seed pulse which will bedirected to a Ti:Sa laser to provide the power for HHG ina gas cell where a harmonic of the around the 25th order
will be generated. The tunability in the Ti:Sa laser isenough to cover the distance between the harmonics inthe HHG process. Thus full tunability in the 30-50 nm
range can be achieved. It might turn out to beadvantageous to introduce an OPA before the HHG cell toprovide easier tuning over a larger range.

PERFORMANCE, CALCULATIONS AND
MODELS
The radiation propagation in the cascades has been
calculated by using an analytical approach focusing on
the retarded potentials of the fields. Thus the full
information on source point, divergence and relevant fieldstrengths is achieved. The preliminary results are shownin figure 1.
The amplifier in the system has been simulated in Genesis[5]. The necessary undulator length at 2 nm is around 13
m with powers around 3 GW. (figure 2.)

TEST FACILITY
A test facility is currently being planned at the MAXlaboratory together with BESSY to be utlised within the
EUROFEL co-operation (figure 3). It will make use of the
500 MeV linac injector recently put into operation. A firststage of a harmonic generation cascade will be installed
and the electron source will be upgraded to a photo
cathode RF-gun. Already available in the lab are a Ti:SA
laser, space for undulator installations and the electrontransport line. The same laser oscillator will feed both the
gun and be used as a seed pulse in a similar fashion as
depicted for the MAX IV. Initially seed pulses at 260 nm

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l. Werin et al. / Proceedings of the 2004 FEL Conference, 190-192

will be utilised and coherent radiation at the third (90 nm)
and fifth (53 nm) harmonic will be extracted.
In the test facility question like: benchmarking, electron
beam control and transport, laser synchronisation, laser
seeding, cascading etc. will be addressed.

Power at 2 nm
3,53,0Power (GW)

2,5
2,0

SUMMARY

1,5
1,0
0,5
0,0
0

5

10

15

20

Length (m)Electron beam optics (x and y resp.)

REFERENCES

35
30
Size (um) (RMS)

The design of the MAX IV coherent radiation source istaking form. The source will adopt the techniques of“second generation short wavelength FELs”: Seeding,cascading and harmonic generation. A 3 GeV NC electron
linac will provide a 100 Hz source which will generate
tunable GW power pulses in the range of 2 nm. Basic
simulations have been run using Parmela, Genesis andmodels using true field models.

25
20
15
10
5
0
0

5

10

15

20

Length (m)Figure 2. Amplification (top) and electron beam
optics (below) in the amplifier.

[1] M. Eriksson, L.-J. Lindgren, E. Wallen and S. Werin,
A cascaded optical klystron on an energy recovery
linac – race track microtron ,NIM A 507 (2003) 470[2] LCLS design report(http://www-ssrl.slac.stanford.edu/lcls/cdr/)[3] S. Werin et. al. Commissioning of the 500 MeV
Injector for MAX-lab, EPAC04, Lucerne 2004
[4] BESSY soft X-FEL design report(http://www.bessy.de/publicRelations/publications/files/TDR_WEB.pdf)[5] Genesis by Sven Reiche(http://corona.physics.ucla.edu/~reiche/)Figure 3. Placement of the test facility inside the MAX II storage ring.

MOPOS51

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S. Reiche et al. / Proceedings of the 2004 FEL Conference, 193-196

COHERENT RADIATION EFFECTS IN THE LCLS UNDULATOR∗
S. Reiche† , UCLA, Los Angeles, CA 90095, USA
Z. Huang, SLAC, Stanford, CA 94309, USA
For X-ray Free-Electron Lasers such as LCLS andTESLA FEL, a change in the electron energy while amplifying the FEL radiation can shift the resonance conditionout of the bandwidth of the FEL. The largest sources of energy loss is the emission of incoherent undulator radiation.
Because the loss per electron depends only on the undulator parameters and the beam energy, which are fixed
for a given resonant wavelength, the average energy loss
can be compensated for by a fixed taper of the undulator. Coherent radiation has a strong enhancement proportional to the number of electrons in the bunch for frequencies comparable to or longer than the bunch dimension. If
the emitted coherent energy becomes comparable to thatof the incoherent emission, it has to be included in the taper as well. However, the coherent loss depends on thebunch charge and the applied compression scheme and achange of these parameters would require a change of thetaper. This imposes a limitation on the practical operationof Free-Electron Lasers, where the taper can only be adjusted manually.
In this presentation we analyze the coherent emission ofundulator radiation and transition undulator radiation for
LCLS, and estimate whether the resulting energy losses are
significant for the operation of LCLS.

number of electron per bunch (≈ 5 · 109 ). In particular for
X-ray FELs the bandwidth of coherent emission is large
because the electron bunch is strongly compressed to reduce the FEL saturation length, and thus it excites higher
frequency components. In addition the particular compression scheme at LCLS [4] generates a current profile whichis rather flat with spikes at the edges than Gaussian (seeFig. 1). This increases the bandwidth of the excited frequencies. The two radiation processes, which can emit coherently in an undulator, are the undulator radiation and thetransition undulator radiation at the entrance and exit of theundulator.
14
12
10

I [kA]

Abstract

8
6
4
2
0
0.00

0.05

0.10
t [ps]

0.15

0.20

Figure 1: Current profile of the electron bunch in the LCLS
undulator, calculated by start-to-end simulations.

INTRODUCTION
Recent experiments [1, 2, 3] have shown successfully
the operation of free-electron lasers (FEL) in the modeof self-amplified spontaneous emission (SASE), startingfrom the spontaneous undulator radiation. This supports
the construction of SASE FELs in the X-ray regime [4, 5].
These 4th generation light sources allows for unprecedented brightness with Ångstrom spatial and femtosecond
time resolution for all branches of science [6].
For a successful operation of an X-ray FEL it is essential to keep the electron beam synchronize with the radiation field. Any externally induced loss in the electron energy will degrade the performance. However if the energychange is known it can be compensated by an adjustment in
the undulator field. The dominant contribution is the emission of incoherent undulator radiation [7], which is in thecase for X-ray lasers even larger than the maximum FEL
signal. Other sources are undulator wakefields, which havebeen already presented elsewhere (e.g. [8]).
In this presentation we calculate the contribution of coherent emission of radiation, which is enhanced by the∗ Work supported by the U.S. Department of Energy contract DEAC02-76F00515† reiche@physics.ucla.edu

Available online at http://www.JACoW.org

COHERENT UNDULATOR RADIATION
Undulator radiation is the dominant radiation source andis emitted mainly in the forward direction due to the strong
Doppler shift from the electron motion. The on-axis radiation can interact back on the electron beam, driving thefree-electron laser mechanism. For larger emission angle
with respect to the forward direction, the intensity drops
quickly and the emitted wavelength is red-shifted. However beyond a threshold angle the radiation wavelength iscomparable to the bunch length and the radiation adds up
coherently. In the following we estimate the emitted energy
due to the coherent enhancement by the particle distribution. Because we are integrating over a wide frequency
range and including all directions of observation, any approximation in our calculation is excluded.
The energy emitted per solid angle and frequency interval is given by

2


Q2 ω 2 ˜
d2 E2iω(t−
rn/c) 
=|I(ω)|  n × [n × β]e
dt ,
dωdΩ
16π 3 0 c
(1)
˜
with I(ω)
the Fourier-transformed current profile, n the
 the electron velocity in units ofvector of observation, βSingle-Pass FELs

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S. Reiche et al. / Proceedings of the 2004 FEL Conference, 193-196

the speed of light c, r the trajectory of the electron, andQ the bunch charge. For evaluation the transverse oscillation βx = K/γ sin(ωu t) is in the xz-plane, where γ isthe electron energy, K is the unitless undulator parameter,and ωu = cβ0 ku is the undulator wavenumber with ku =2π/λu and λu as the undulator period. Although the longitudinal velocity βz is modulated within a undulator period,
the average velocity is given by β0 = 1 − (1 + K 2 /2)/2γ 2 .
The dominant contributions in the integrations over t
arise from the transverse oscillation βx in the cross product and the transverse position rx in the argument of the
exponential function. The latter has the maximum amplitude (ωK/γωu ) sin(θ)  1 and can be expanded in Taylor
series. Both terms add up coherently as (K/γ) exp(iωu t)with the cross product n × [n × (ex + nx (ω/ωu )ez )].
The integral yield a sinc-function around the central frequency ω = ωu /(1−β0 cos θ), which is the resonant undulator wavelength, including the red shifting Doppler effect,when observed under an angle θ. Because the width of thesinc-function is the inverse of the number of undulator periods Nu , it selects only a narrow frequency window in theremaining integration over ω. We approximate the sincfunction by a Dirac-function δ(ωu − ω(1 − β0 cos θ)). The
integration over the frequency and the angle φ of the solid
angle dΩ = sin(θ)dθdφ yields

dE
dθ

2 

sin2 θ
1 + cos θ − 1−β0 cos θQ2 Lu K 2 ku2
32π0 γ 2
(1 − β0 cos θ)3
 
2


ωu

× sin θ I˜.
1 − β0 cos θ =(2)Under the condition ku σz  1 the total emitted power
is
=

ER

=

Q2 Lu K 2
and
32π0 σz2 γ 2
2γ 2
Q2 Lu K 2ln
96π0 σz2 γ 2
1 + K 2 /2

(3)

Figure 2: Suppression of the emitted energy due to thetransverse size σt of the electron bunch. The function S(x)depends on the ratio x = σt /σz .

Due to the transverse oscillation the average longitudinal velocity of the electron bunch is slower within the undulator than outside. The induced longitudinal accelerationof the short end pieces of the undulator, which match thestraight trajectory outside of the undulator with the sinusoidal trajectory within, causes the emission of transition
undulator radiation [9, 10]. The radiation footprint is similar to transition radiation [11], but there the emission is
produced by the boundary condition of the electric fieldat the surface. A similar radiation source is edge radiation [12, 13], when an electron enters or exits the field ofa bending magnet. However in transition and edge radiation the electron is modelled to come to a complete halt,
while for transition undulator radiation the electron is only
slowed down by ∆β = (K/2γ)2 .

(4)for a Gaussian and rectangular current profile, respectively.
For LCLS parameters (K = 3.63, γ = 27500 and σz = 20µm) the energy losses are EG = 6.4 µJ and ER = 40.5 µJ,
both three orders of magnitude smaller than the losses dueto the incoherent undulator radiation of 17 mJ [4].
The transverse extension of the electron bunch σt can
suppress the emission for very short bunches. Assuming a
Gaussian distribution in the transverse direction the form2˜
has then the additional
factor of the current profile |I(ω)|

MOPOS59

where Φ is the Error function. The function S(x) is shownin Fig. 2. For LCLS the ratio is about 1 and the reductionin the emitted energy is negligible.

COHERENT TRANSITION UNDULATOR
RADIATION

For our calculation we consider the cases of a Gaussian andrectangular profile with the rms bunch length σz and form
factors √ zsin2 ω 3σ
2 2c.
|I˜G (ω)|= e−ω σz and |I˜R (ω)| =3σ 2
ω 2 c2zEGfactor exp(−ω 2 σt2 sin2 θ/c2 ). The applied correction function S(σt /σz ) is then
√
2 2 2
2
S(x) = 1 − x2 πku σt ex ku σt (1+x )


ku σt
(1 + 2x2 ) ,
× 1−Φ
(5)
2

Low Frequency Approximation
In the low frequency model we assume that the change
in the velocity is instantaneously. The emission of a single
electron entering a undulator module is therefore

2
d2 E
Q2
βu sin θβd sin θ=−,dωdΩ
16π 3 0 c 1 − βu cos θ 1 − βd cos θ(6)where βu = 1 − (1 + K 2 /2)/2γ 2 is the velocity within theundulator and βd = 1−1/2γ 2 the velocity in the free space

S. Reiche et al. / Proceedings of the 2004 FEL Conference, 193-196

outside the undulator. If the electron would be stopped
completely (βu → 0) then the emission (Eq. 6) is identical with that of transition and edge radiation. Due to theinterference of the two terms in Eq. 6 the radiation is more
confined in the forward direction. Emission under large angles θ  1/γ is suppressed by a factor γ −2 in comparison
to transition and edge radiation.
The radiation patterns from the undulator entrance andexit interfere with each other with opposite signs andan additional phase factor exp(iω∆τ ), where ∆τ =(Lm /cβu )(1 − βu cos(θ)) is the retarded time-interval
when the electron enters and exits the undulator module,and Lm is the undulator module length. If the undulator
consists out of N modules additional terms arising with195

to sin2 (ωN τ )  1 for ω < 2πc/σz . We solve Eq. 7 numerically and express the suppression by the additional factor(9)
E = E0 · F (Ls /σz ) .
The function F is shown in Fig.3 and is quadratic/linear
for Gaussian/rectangular profile and small arguments. For
LCLS the suppression is 0.01, yielding a total emitted energy of 1.3 µJ, which is comparable in its magnitude to thecoherently emitted undulator radiation. It would require an
undulator of about 15 km for LCLS-like parameter in order to see no suppression by the destructive interference
between undulator entrance and exit.

N −1
2


sin2 (ω∆τ /2) sin2 (ωN τ /2)inωτ
iω∆τ 
e(1 − e) = 4,
sin2 (ωτ /2)n=0

τ = ∆τ +(Ld /cβd )(1−βd cos(θ)), and Ld the drift length,
separating two adjacent undulator modules. Including also
the excitation by the current profile, expressed by the form
˜
factor I(ω)
the angular distribution per frequency interval
becomes
d2 E
dωdΩ

=

Q2
16π 3 0 c× 4

βd sin θβu sin θ−
1 − βu cos θ 1 − βd cos θsin2 (ω∆τ /2) sin2 (ωN τ /2) ˜|I(ω)|2 .
sin2 (ωτ /2)

2

(7)

For a typical undulator the drift between two modules
corresponds to the slippage of a few resonant wavelength,
which is much shorter than the bunch length. As a result the phase difference ω(τ − ∆τ ) << 2π is negligible for frequencies excited by the bunch profile. Therefore
the two sine-functions sin(ω∆τ /2) and sin(ωτ /2) cancel
each other in good approximation in Eq. 7. Effectively the
undulator modules are joined together into one single longundulator module.
For very long undulator (N τ  σz /c) the sine-function
sin2 (ωN τ ) is fast oscillating and can be approximated by
its average value 1/2. In this case the integration over thefrequency is decoupled from the angle of observation θ,
yielding c π/4/σz and c π 2 /12/σz for Gaussian andrectangular profile, respectively. The resulting emitted energy is
Q2

E0 = √
2 π 3 0 σz
4 + K2K2
ln 1 +−1
2K 2
2

Figure 3: Function F for the suppression of the CTUR signal due to finite bunch length of a rectangular and Gaussian
profile (solid and dashed line, respectively).
It seems to be counter-intuitive that the energy loss occurs over the entire undulator length, while the emission
processes are spatially and temporarily localized at the entrance and exit of the undulator. But emission becomes
only distinguishable in the far field zone, which lies outside the undulator. At the location of the electron the velocity field is the dominant field. In this model of undulatortransition radiation the electrons are slower within the undulator and therefore the electrostatic field is less Lorentz
contracted. However it is not seen be all electrons instantaneously. The change in the field is seen immediately onlyby the trailing electrons, while it requires some distance tocatch-up with electrons ahead. This distance is the slippage
length. As seen in Fig.3 the electron bunch has reached almost electrostatic equilibrium after Ls > 3σz and only anegligible energy loss occurs further. At this point any retarded field information has propagated through the entire
bunch.

(8)

for the Gaussian profile and is higher by the factor π/3 ≈1.02 for the rectangular profile.
It is useful to point out that N τ is proportional to theslippage length of the radiation field within the undulator.
The limit, discussed above, is equivalent to the condition
that the bunch length is shorter than the slippage length
Ls = (λ/λu )z. Otherwise the radiation is suppressed dueHigh Frequency Limit
In the low frequency limit we assumed that the change
in the velocity is instantaneously, but in reality each undulator module has a short tapering section to match thestraight trajectory of the drift with the sinusoidal within.
Typically the tapering section is one or two undulator periods long. Note that the characteristic frequency, whichcan ‘probe’ the explicit tapering is of the order of the res-

Single-Pass FELs

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S. Reiche et al. / Proceedings of the 2004 FEL Conference, 193-196

onant wavelength of the FEL. Thus, the low frequency approximation is valid for all current profiles, except for the
micro-bunching, induced by the FEL process.
To estimate the high frequency dependence we refine ourmodel by assuming a linear change in the velocity over thetime interval δT . The acceleration is β̇ = (βu − βd )/δTfor entering the undulator module, yielding the profile ofthe electric field
E(τ ) =β̇e sin θ,4π0 cR [(1 − βd cos θ)2 − 2β̇τ cos θ] 32(10)where τ is the retarded time. The observed pulse length isδτ = (1 − cos θ(βd + βu )/2)δT . The spectrum for small
angle (θ  π/2) is

eiωδτ
1
e tan θ−Ẽ(ω =
4π0 cR 1 − βu cos θ 1 − βd cos θ√2 2
πϕe(1−βd cos θ) ϕ
(11)+× (Φ((1 − βu cos θ)ϕ) − Φ((1 − βd cos θ)ϕ)))
with
ϕ=

i

ωδT
2(βu − βd ) cos θ

.

(12)

1.0

| E(ω) / E(0) |2

0.8
γθ<<1

0.6

0.4

×

sin2 (ωr ∆τ /2) sin2 (ωr N τ /2).
sin2 (ωr τ /2)(13)

The radiation is strongly suppressed by two factors.
First, the decoherence effect due to the finite transverse
beam size confines the coherent radiation toward the forward direction θ  1/γ, where the sine-term in Ẽ suppresses the radiation. Second, the interference of undulator
entrance and exit is destructive because ωr ∆τ and ωr τ area integer number of π for any well tuned FEL, despite theenhancement N 2 from multiple undulator modules. However within a single undulator FEL, like the VISA FEL, thebunching occurs only within the undulator and there is nointerference with the undulator entrance.

CONCLUSIONFor X-ray Free-electron Laser the contributions of thecoherent undulator radiation and transition undulator radiation to the overall energy loss of the electron bunch is
negligible in comparison to the incoherent emission of undulator radiation. For CUR the emission is suppressed despite its enhancement by coherence because it requires theemission under an large angle so that the red shifted wavelength becomes comparable to the electron beam size. In
contrast the transition undulator radiation is broadband but
sees strong interference between the emission from the entrance and the exit of the undulator, which shifts the emission towards higher frequency and out of the bandwidth excited by the electron bunch. The possibility to measure thebunching factor in the FEL process is only given for longwavelength FELs, where other methods exist to accomplish
the measurement.

γθ=1
0.2

REFERENCES

γθ=4
0.0
0

5

10

15
ωδτ

20

25

30

Figure 4: Power spectrum of the radiation pulse from asingle electron at a single undulator entrance or exit.
Fig. 4 shows the spectra for different angle of observation. For larger value of θ > K/γ the pulse duration δτ
becomes larger, resulting in a stronger suppression of emission at a given frequency. As an example a LCLS like undulator is tapered over two undulator periods. The time ofobservation δτ is about 1.7 Å/c and even at the resonant
wavelength at 1.5 Å the spectral power is only dropped byabout 50% (ωδτ ≈ 7) for θ ≤ 1/γ.
Because the spectrum is not suppressed significantly at
the resonant wavelength, it might be considered to use
CTUR as a parasitic emission signal to measure the degreeof current modulation (micro bunching). With the assump2
˜= |b|2 δ(ω − ωr ) the resulting emitted energy
tion |I(ω)|
per solid angle becomesdEdΩ

MOPOS59

=

2 2
2
2
4|b|2
|Ẽ(ωr , θ)|2 e−ωr σt sin θ/cZ0[1] A. Tremaine et al., Phys. Rev. Lett. 88 (2002) 204801[2] S.V. Milton et al., Science 292 (2001) 2037
[3] V. Ayvazyan et al., Phys. Ref. Lett. 88 (2002) 104802[4] Linac Coherent Light Source (LCLS), SLAC-R-521, UC414 (1998)[5] TESLA-FEL 2001-05, Deutsches Elektronen Synchrotron,
Hamburg, Germany (2001)[6] C. Pellegrini and J. Stöhr, Nucl. Inst. & Meth. A500 (2003)
33[7] K.J. Kim, in AIP Conference Proceedings 184, M. Monthand M. Dienes, eds., (1989) 585[8] S. Reiche and H. Schlarb, Nucl. Inst. & Meth. A445 (2000)
155[9] K.-J. Kim, Phys. Rev. Lett. 76 (1996) 1244
[10] B.M. Kincaid, Il Nuovo Cimento 20 D (1998) 495[11] V.L. Ginzburg and I.M. Frank, Zh. Eksp. Teor. Fix. 16(1946) 15[12] O.V. Chubar and N.V. Smolyakov, J. Optics24 (1993) 117[13] R.A. Bosch, Proc. of the 1999 Particle Accelerator Conference, New York (1993) 2397

197

S. Reiche / Proceedings of the 2004 FEL Conference, 197-200

SPONTANEOUS RADIATION BACKGROUNDCALCULATION FOR LCLS∗
S. Reiche† , UCLA, Los Angeles, CA 90095-1547, USA
Abstract
The intensity of undulator radiation, not amplified by the
FEL interaction, can be larger than the maximum FEL signal in the case of an X-ray FEL. In the commissioning of a
SASE FEL it is essential to extract an amplified signal early
to diagnose eventual misalignment of undulator modules or
errors in the undulator field strength.
We developed a numerical code to calculate the radiation
pattern at any position behind a multi-segmented undulator
with arbitrary spacing and field profiles. The output canbe run through numerical spatial and frequency filters tomodel the radiation beam transport and diagnostic.
In this presentation we estimate the expected background signal for the FEL diagnostic and at what point
along the undulator the FEL signal can be separated fromthe background. We also discusses how much informationon the undulator field and alignment can be obtained fromthe incoherent radiation signal itself.

INTRODUCTION
Based on the successful demonstration of the SelfAmplified Spontaneous Radiation (SASE) Free-Electron
Lasers (FEL) principle at longer wavelength [1, 2, 3], several X-ray FELs have been proposed and are currently under construction [4, 5]. The unique properties of the highbrightness radiation source allows to study femto-second
processes with an Ångstrom spatial resolution, beneficial
for all branches of sciences [6].
For SASE FELs the seeding field is the spontaneous radiation, although only a small bandwidth is amplified by
the FEL process. The remaining part is emitted as a background signal, illuminating any detector to measure the
FEL radiation. Because the total emitted power scales withthe square of the energy of the driving electron beam [7],X-ray Free-electron lasers are more affected by the spontaneous radiation than FELs operating at longer wavelength.
It is essential to estimate the spontaneous radiation due tothree reason. First, the radiation power can be larger thanthe maximum FEL signal, yielding a large heat load on all
X-ray optics elements. Second, the energy loss is strong
enough to shift the electrons out of the FEL bandwidth,
unless it is compensated by a taper of the undulator field.
Third, spontaneous radiation overlaps with the FEL signal
and defines the background signal for the FEL measurements.
∗ Work supported by the U.S. Department of Energy contract DEAC02-76F00515† reiche@physics.ucla.edu

Available online at http://www.JACoW.org

From the FEL point of view it is essential to know the
spectral and angular distribution of the spontaneous distribution to optimize the experimental set-up for the highest
signal-noise ratio. Because the LCLS undulator lattice consists out of undulator modules and quadrupoles which arearrange with two short and one long drift sections between
modules and because the closest detector is not place inthe far field zone of the undulator, simple analytical calculations of the spontaneous radiation are not sufficient.
For that reason we developed a numerical code to calculate the explicit background signal at the detector location.
the algorithm is from first principle, based on the LienardWichert potential [8]. The initial results for the LCLS undulator are presented here.

ANALYTICAL MODEL
The total radiated power from the incoherent part of theundulator radiation is given by [7]Nu
Z0 Ieku γ 2 K 2 ,(1)
6
where Nu is the number of undulator periods, Z0 ≈ 377 Ω
is the vacuum impedance, I the beam current, e the electron charge, ku = 2π/λu the undulator wavenumber withλu as the undulator period, γ the electron energy in unitsof its rest mass energy, and K the undulator parameter. For
LCLS parameters the emitted power is 75 GW [5], about
10 times larger than the maximum FEL signal. Enhancement due to the coherent emission at longer wavelengths
are negligible.
Eq. 1 allows to calculate the total energy loss, which is
sufficient to derive the required taper of the undulator fieldin order to preserve the resonance condition. However itlacks any angular or spectral information. To calculate theradiation seen by a detector behind the undulator, the electric field is˙ = e n × [(n − β) × β] ,
E
(2)
 3R
4π0 c (1 − nβ)P =evaluated at the retarded time. Neither the direction of observation n nor the distance R between source and target
is constant for LCLS FEL , where the closest detector is
located 113 m behind the exit of the 130 m long, multisegment undulator.
The emission is the strongest due to the maximum
Doppler shift, where the electron moves parallel to the direction of observation, fulfilling the conditionnx
Ksin(ku z) =
γ
nz

.

(3)

Single-Pass FELs

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S. Reiche / Proceedings of the 2004 FEL Conference, 197-200

Eq. 3 is only valid for observation angles θ between 0
and K/γ in the xz-plane. Beyond that as well as in
the yz-plane the radiation intensity drops like the normal
synchrotron radiation with a characteristic fall-off of 1/γ.
Note that the signal from a single period is antisymmetric in the retarded time frame with respect to the emission time at z = λ/2. The forward direction shows alternating, equally spaced unipolar pulses. The pulses are
narrow due to the Doppler effect and excite a rich harmonic content of odd harmonics. To estimate the number of harmonics, we calculate the pulse length in the retarded time frame. The pulse shape is dominated by thedenominator in Eq. 2 and scales as E ∝ (1 − βz )−2 . Withβz = 1 − (1 + K 2 /2)/2γ 2 + (K 2 /4γ 2 ) cos(2cku t) the
full-width half maximum is given by√12) + K 2−1 2(1 −
∆T =
cos
.
cku
K2
In the retarded time frame it becomes∆τ =1 + K 2 /2
K2
∆T −sin(cku ∆T ) .
22γ
4cku γ 2

The ratio between resonant wavelength and FWHM of theobserved pulse length (c∆τ ) defines the harmonic content.
For LCLS parameters the value is 120.
For larger observation angles in the xz-plane pairs of adjacent unipolar pulses are shifted closer to each other tillthey merge to a single bipolar pulse at an angle of θ = K/γ
and beyond. The emission of each nth harmonic has n − 1knots in the xy-plane and is slightly more confined in theforward direction than the fundamental, because the observed pulses are wider due to the reduced curvature in theelectron trajectory, where Eq. 3 is fulfilled.

NUMERICAL MODEL
The program SPUR (SPontaneous Undulator Radiation)
has been written to calculated the radiation pattern from anarbitrary undulator lattice at any point behind the undulator.
It supports parallel architecture with a master-slave configuration using the Massage Passing Interface (MPI) method[9], where a master node assigns the work to slave nodes
and thus optimizes the CPU usage for asymmetric nodes or
unbalanced load upon a symmetric cluster.
Either the radiation pattern from a single electron onto
a two dimensional grid or from multiple electrons onto
a single point in space can be calculated, including single electron to single point configuration. The programis based on Eq. 2, calculating the time-domain signal in
the retarded time frame. Fourier transformation methodsof uneven sampled data [10] have shown an unacceptablelevel of noise, compared to standard Fast Fourier Transformation (FFT) of the signal, after it has been interpolated toan equidistant grid.
The undulator lattice can be defined down to each individual pole, including arbitrarily long drift sections be-

MOPOS60

tween undulator modules. The electron trajectory is analytical calculated for each undulator period with a step width,
sufficiently small enough to resolve all harmonics. In thecase for LCLS with more than 100 harmonics, at least 256
steps per period are required and then interpolated to a 4times finer grid in the retarded time frame to achieve convergence in the spectrum. For LCLS with a total of about
3700 periods it yields record sizes for the FFT of about 7
million sample points. Thus the memory demand is limited
to 100 MByte. To reduce the output for runs with a large
number of grid points, the spectrum can be downsampled
to a frequency resolution, lower than the maximum resolution ∆f /(λ/c) ≈ 1/Nu .

RADIATION PROPERTIESAt LCLS the first detector station is located 113 m behind the end of the undulator [4]. It is exposed to thehighest intensity of both FEL and spontaneous radiationcompared to the second diagnostic station, which is further downstream of the X-ray beam transport line. Due tothe close proximity of the first detector to the undulator, thecalculation of the radiation cannot be simplified by assuming the far field zone. First, the R−2 -dependence of theemission sources along the undulator with respect to the
fixed detector location is noticible. Second, the angle ofobservation is not constant for off-axis position, but shifts
towards larger values. As a consequence a systematic redshift dominates the width of the harmonics, which minimalvalue of 1/Nu can only be observed on-axis. While the intrinsic energy spread is smaller than 1/Nu , the finite beam
size and divergence has a non-negligible effect on the bandwidth as well.
At the detector location the peak intensity is 20 GW/cm2 ,illuminating an area of 6×2 cm2 (full width in the x- and ydirection). The observed total power is 75 GW, which has acontribution of 0.6 GW due to the coherent emission of thebunch profile [11]. Fig. 1 shows the intensity distribution
at the first detector location.

Figure 1: Intensity distribution of the spontaneous radiation
at the detector location, 113 m behind the LCLS undulator.
It is essential for the FEL amplification that all undulator modules are well tuned and aligned to the undulator

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S. Reiche / Proceedings of the 2004 FEL Conference, 197-200

BACKGROUND SIGNAL FOR THE FELRADIATION
The radiation power of the incoherent emission is about
75 GW and therefore 10 times larger than the expected saturation power level of the FEL at 1.5 Ångstroem. To improve the signal to noise ratio the incoherent backgroundsignal can be either cut by spatial aperture limitation or bybandpass filters. In this section we estimate the efficiency
of both methods. It excludes the frequency dependent sensitivity of the X-ray detector, which are typically less efficient at higher frequencies than at the FEL frequency [12].
The estimate, given below, is an upper limit for the detectedsignal.
Time-dependent FEL codes, such as Ginger or Genesis
1.3, cannot predict the total background signal, because
they model only a narrow bandwidth around the resonant
wavelength for an optimized calculation of the FEL process [13]. The typical full bandwidth in the FEL simulation of X-ray lasers such as LCLS and TESLA is between
5% and 10%. In addition the code discretize the radiation
field to a finite set of radiation modes, imposing a limit on
the maximum angle of emission. These cuts do not affectthe result of the FEL simulation because strongly diffracting modes as well frequency deviation larger than the FEL
bandwidth are amplified by the FEL process. To add thecorrect background signal, the spontaneous signal from the
FEL simulation is removed first by subtracting the linear
trend in the start-up process of the FEL signal. Then the
background signal, calculate by SPUR, is added.
The FEL signal is much more confined in the spatial direction than the spontaneous radiation. With an rms diffraction angle of about 1 µrad the FEL signal covers an area of
about 3 mm2 at the detector position 113 m behind the endof the LCLS undulator. A smaller aperture would cut the
FEL signal, which is not in the interest of the measurement. In the contrary the aperture has to be larger to allow
for jitter in the FEL beam centroid. The dependence of the

100.000

FEL Signal
10.000P [GW]

axis. The on-axis field requirement is ∆K/K ≈ 10−4 [5],which would be desirable to measure it for each undulator module individually. However this information cannot
be extracted from the radiation distribution and intensity,
which are insensitive to such small variation. The mostpromising measurement is the width of the harmonics ofthe on-axis radiation. While the fundamental harmonic has
an intrinsic width of about 1% – corresponding to 112 undulator periods per module – a change in the width on a percent level is difficult to measure, but the effect of a detuned
module becomes enhanced with higher harmonics. E.g. at
the 100th harmonics the shift in the wavelength due to a
detuning of ∆K/K ≈ 10−4 is 1% and thus comparable tothe intrinsic bandwidth. However the width can be broaden
by beam trajectory alignment and the beam emittance andthus obscure the measurement. It seems more beneficial
to derive the undulator field quality from the power versus
undulator position measurement of the FEL signal.

Spontaneous
Radiation

1.000
0.100
0.010
0.001
0.01

0.10

1.00

10.00

100.001000.00

A [mm2]

Figure 2: Detected power of the FEL signal and the spontaneous radiation for an aperture limit at the detector location, 113 m behind the undulator exit.
spontaneous radiation background signal and the FEL signal on the aperture is shown in Fig. 2. With an apertureof 1 mm2 0.9 GW of the spontaneous radiation is detected,
resulting in a signal-to-noise ratio of only 10:1. If the detector is array-based like a CCD camera, the measurement
is rather intensity than power based. In case for LCLS theratio between the intensities is 100 to 1, an improvement of
one order of magnitude compared to a collecting detector
with the aperture of 1 mm2 , mentioned above.
Spatial cuts are inferior to spectral cuts because even under the best circumstances a spatial aperture cannot filter
out higher harmonics. For high K undulator such as LCLS
a large number of odd harmonics are emitted on-axis, someof them with higher power than the fundamental. A significant reduction can be achieved when only the emission at
the resonant wavelength is collected. Although higher harmonics can contribute to the resonant wavelength due tothe red shift for larger emission angles θ, they can be filtered out by a loose spatial cut. For the second harmonic
the angle to shift the wavelength to the fundamental wavelength is 100 µrad and can be easily collimated by a 1 cm2aperture in front of the LCLS detector.
Due to the intrinsic width of δf /f0 = 1/Nu of the spontaneous signal the radiation at the resonant wavelength isconfined in the opening angle of

K
1
∆θ =
,
2γ Nu
with ∆θ = 1.5 µrad for LCLS parameters. This correspond to an emission of 1 MW per 0.1% bandwidth.
The full FEL signal falls within this bandwidth, yielding
a signal-to-noise ratio of about 104 :1. Even wider bandwidth cuts are still superior to the spatial collimation. The
detectable FEL signal for LCLS and various methods of
reducing the spontaneous background is shown in Fig. 3
From the point of view of detecting the FEL signal thesituation is improved when the FEL is operated at lower energy, because the saturation power has a weak dependence
on the energy while the incoherent radiation is 10 times
smaller for a FEL wavelength of 1.5 nm. In addition theSingle-Pass FELs

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S. Reiche / Proceedings of the 2004 FEL Conference, 197-200

1011

1010

exponential growth for optimum alignment and tuning.

solid - missteering of e-beamdashed - modules removed

REFERENCES

P [W]

109

[1] A. Tremaine et al., Phys. Rev. Lett. 88 (2002) 204801
108

FEL Signal
Spectral Cut: 0.1%
Spectral Cut: 1.0%
Spatial Cut: 1 mm2Spatial Cut: 4 mm2

107
6

10

105
0

20

40

60
z [m]

80

100

120

Figure 3: Detectable FEL signal for various method to reduce the background signal of the spontaneous radiation.

[2] S.V. Milton et al., Science 292 (2001) 2037
[3] V. Ayvazyan et al., Phys. Ref. Lett. 88 (2002) 104802[4] Linac Coherent Light Source (LCLS), SLAC-R-521, UC414 (1998)[5] TESLA-FEL 2001-05, Deutsches Elektronen Synchrotron,
Hamburg, Germany (2001)[6] C. Pellegrini and J. Stöhr, Nucl. Inst. & Meth. A500 (2003)
33[7] K.J. Kim, in AIP Conference Proceedings 184, M. Monthand M. Dienes, eds., (1989) 585

Table 1: Power level of the LCLS FEL and backgroundsignal for various spatial and spectral cuts at the near halldetector.
SignalFEL
Spontaneous Radiation
Spectral Cut: 0.1%
Spectral Cut: 1.0%
Spatial Cut: 1 mm2Spatial Cut: 4 mm2

1.5 Å
8 GW
75 GW
1 MW
10 MW
0.9 GW
3 GW

1.5 nm
4 GW
7.5 GW
100 kW
1 MW
9 MW
30 MW

[8] J.D. Jackson, Classical Electrodynamics, (John Wiley andSOns, New York, 1975)[9] Message Passing Interface Forum, Computer Science
Dept. Techincal Report CS-94-230, University of Tennessee, Knoxville (1994)[10] N.R. Lomb, Astrophysics and Space Science 39 (1976) 447[11] S. Reiche and Z. Huang,Coherent Radiation Effects in the
LCLS Undulator, presented at this conference.
[12] R. Bionta, private communication[13] Z. Huang and K.-J. Kim, Nucl. Inst. & Meth. A507 (2003)
65√
opening angle is increased by 10, so that the on-axis intensity drops by two orders of magnitude for spatial cuts.
Because the coherence angle is also increased the spectral
power in a narrow bandwidth is improved only by a factorof 10. Tab. 1 summarize the different power levels of the
FEL and background signal for the two limits in the FEL
wavelength of LCLS.

CONCLUSION
We have written a numerical code to calculated the background signal from the spontaneous radiation at a given location to detect the X-ray FEL signal. Due to the complex
lattice of the undulator and the close proximity of the detector the spontaneous radiation can be estimated analytically
only in crude approximation and detailed numerical calculations are required. With a given intensity distribution andthe associated spectrum of the background signal the X-ray
optics and detector can be optimized to maximize the signal
to noise ratio of the FEL signal.
Because the on-axis spectrum is rich in harmonics,
spatial collimation are less efficient than spectral filters(monochromators or dispersive optical elements). In theideal case, when only 0.1% of the spontaneous radiation
illuminates the detector the background signal is dropped
to 1 MW, while the FEL signal is not affected. Detectionof the FEL signal after 20 m of undulator becomes possible. All modules after that point can be examine by the

MOPOS60

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Z. Huang et al. / Proceedings of the 2004 FEL Conference, 201-204

Generation of GW-level, sub-Angstrom Radiation in the LCLS using a
Second-Harmonic Radiator ∗Z. Huang† , SLAC, Stanford, CA 94309, USA
S. Reiche, UCLA, Los Angeles, CA 90095, USA
Abstract
Electron beams are strongly microbunched near thehigh-gain free-electron laser (FEL) saturation with a richharmonic content in the beam current. While the coherent
harmonic emission is possible in a planar undulator, thethird-harmonic radiation typically dominates with about
1% of the fundamental power at saturation. In this paper,
we discuss the second-harmonic radiation in the Linac Coherent Light Source. We show that by a suitable design ofan second-stage undulator with its fundamental frequency
tuned to the second harmonic of the first undulator, coherent second-harmonic radiation much more intense than thethird-harmonic is emitted. Numerical simulations predictthat GW-level, sub-Angstrom x-ray pulses can be generated in a relatively short second-harmonic radiator.

INTRODUCTION
In a single-pass, high-gain free-electron laser (FEL)strong bunching at the fundamental wavelength can drive
substantial nonlinear harmonic bunching [1]. For a planar
undulator, third-harmonic radiation can typically reach 1%of the fundamental power level at saturation [2, 3]. While
comparable second-harmonic power has been observed at
the VISA [4] and the LEUTL [5] FELs and is in agreementwith the theoretical expectations [6], the second-harmonic
content is in general much smaller than 1% of the fundamental at very high-energy FELs such as the Linac Coherent Light Source (LCLS) [7]. To further increase the harmonic emission, a second undulator with its fundamental
frequency tuned to a harmonic number of the first undulator may be used [8, 9, 10]. A major concern of this method
is the effectiveness of the second undulator due to the increased beam energy spread induced by the nonlinear FEL
interaction in the first undulator. Another harmonic generation method for a self-amplified spontaneous emission(SASE) FEL [11], similar to the high-gain harmonic generation (HGHG) scheme for seeded FELs [12], proposes tooperate the first undulator in the linear regime for energy
modulation and to use a dispersion section for nonlinear
harmonic bunching. The relatively cold beam can then be
sent into a second undulator for effective harmonic generation.
The shortest-wavelength x-ray for the LCLS fundamental radiation is 1.5 Å. While there is a great interest inreaching shorter x-ray wavelengths such as the 0.86-Å 57 Fe∗ Work supported by the U.S. Department of Energy contract DEAC02-76SF00515.
† zrh@slac.stanford.edu

Available online at http://www.JACoW.org

Mössbauer spectroscopy, generation and saturation of the
FEL fundamental radiation at 1 Å or below is extremely
difficult with the present state of the art electron beams(see, e.g., Ref. [13]). In this paper, we show that thesecond-harmonic radiation in the main LCLS undulator isvery small and can be significantly enhanced by a secondharmonic radiator in order to expand the wavelength range
and scientific capabilities of the facility. Since the electron beam quality at x-ray wavelengths is usually limitedby the beam emittance rather than by the energy spread,
operating the first undulator at saturation does not severely
affect the performance of the second harmonic radiator. Instead, we find that by optimizing the focusing strength in
the second-harmonic radiator and by applying the appropriate undulator taper, we can effectively extract more than
10% of the fundamental power in a relatively short undulator, which can then operate parasitically to the first undulator. Fully three-dimensional, time-dependent FEL simulation code GENESIS [14] is used to predict the performanceof the second-harmonic radiator.

SECOND-HARMONIC CONTENT IN THE
MAIN LCLS UNDULATOR
The LCLS uses the last one-third of the SLAC linac(about γmc2 ≈ 14 GeV) to drive an x-ray SASE FEL at
the fundamental wavelength λ1 = 1.5 Å to reach a saturation power P1 ≈ 10 GW in a 100-m undulator. It is
expected that the third-harmonic power can reach 100 MW
near saturation. Although the second-harmonic bunching ishigher than the third-harmonic bunching due to the nonlinear harmonic interaction, only odd harmonics are emitted
in the forward direction. Even harmonics radiation can beemitted off-axis for a single electron and hence are present
for a beam with a finite transverse extension [15]. In addition, even-harmonic emissions may be enhanced for a misaligned beam trajectory [16]. Before investigating the performance of the second-harmonic radiator, we estimate inthis section the second-harmonic content in the main LCLS
undulator due to both of these two effects.
The electron motion in the undulator consists of a fast
wiggling oscillation and a slow betatron trajectory. Let us
write the transverse velocities as vx = c[K/γ cos(ku z) +x ] and vy = cy  , where K is the undulator parameter,λu = 2π/ku is the undulator period, x and y  are the transverse angles of the slow trajectory, and z is the undulator

Single-Pass FELs

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Z. Huang et al. / Proceedings of the 2004 FEL Conference, 201-204

distance. The longitudinal velocity is


dz
1
K2
2
2
2
= vz = v − v x − v y = c 1 − 2 − 2
dt
2γ
4γ

2

2
K
Kx
x + y 2cos(ku z) −− 2 cos(2ku z) −
. (1)
4γ
γ
2

P1

b1

b2

It is convenient to treat z as the independent variable,
and regard t as the electron arrival time at the undulator
distance z. Integrating Eq. (1) yields
K2
Kx
sin(ku z),sin(2ku z) +ct = ct∗ +
2
8ku γ
ku γ


1 + K 2 /2 x2 + y 2+ct∗ = 1 +
z,
2γ 2
2

(2)

where (x2 + y 2 ) is taken to be approximately constant after averaging over one FODO cell [17]. Thus, the average
longitudinal motion ct∗ is accompanied by a longitudinaloscillation at twice of the transverse wiggling frequency
cku , as well as another longitudinal oscillation at the wiggling frequency due to the coupling to the horizontal orbit.
We can change the time variable t to the ponderomotive
phase θ:θ(z) =(ku + k1 )z − ck1 t∗

(3)

8x ξ
sin(ku z),=(ku + k1 )z − ck1 t + ξ sin(2ku z) +K/γ
where k1 = 2π/λ1 = 2γ 2 ku /(1 + K 2 /2) is the fundamental wavenumber and ξ = K 2 /(4+2K 2 ). Inserting thisexpression into the paraxial wave equation (e.g., Eq. (2) ofRef. [6]) and expanding the exponent for 8γx ξ/K  1,
the nth harmonic field En (n = 1, 2, ...) is given by



∂
∇2⊥
ecKZ0 ∞+dθe−inθEn ≈ −
∂z
2ink1
γλ1
−∞
× einku z+inξ sin(2ku z) cos(ku z)Neδ (y − yj ) δ(θ − θj )

j=1


8xj
× δ (x − xj ) + inξ
sin(ku z)δ (x − xj )K/γKsin(ku z)δ  (x − xj ) ,
−
γku

(4)

where ∇2⊥ is the transverse Laplace, Z0 = 377 Ω is thevacuum impedance, δ  (x) = dδ(x)/dx, and the sum is overNe electrons.
Since both the FEL interaction and the betatron motion
occur on a length scale much longer than the fast wiggling
motion, we can average the current source (the right handside) of Eq. (4) over the wiggling motion. The first termin the square bracket contributes to odd-harmonic radiation in the forward direction. After summing over all electrons for the second term in the square bracket, we obtaineven-harmonic radiation due to trajectory errors with the

MOPOS63

Figure 1: Fundamental radiation power (black) and bunching (blue), second-harmonic bunching (red) along the main
LCLS undulator.
coupling strength 8nγxc ξ/K, where xc is the trajectory
angle of the beam centroid motion. Summing over all electrons for the last term of the square bracket yields evenharmonic emissions due to a finite beam size with the coupling strength K/(γku σx )) [6], where σx is the rms transverse size of the electron beam. Using a bunching paramNe
e−inθj |/Ne to characterize the current
eter bn = | j=1
thsource at the n harmonic, we can estimate the secondharmonic power P2 due to a finite beam size asP2 ≈ P1

K
γku σx

2 

[JJ]2
[JJ]

2

b22
,
b21

(5)

where the Bessel function factors are [JJ]= [J0 (ξ) − J1 (ξ)]
and [JJ]2 = [J0 (2ξ) − J2 (2ξ)]/2 = J1 (2ξ). Similarly, we
can estimate the second-harmonic emission due to trajectory errors asP2 ≈ P1

8γK(xc )2 1/2
2 + K2

2 

[JJ]2
[JJ]

2

b22
,
b21

(6)

where (xc )2 1/2 is the rms angle of the beam trajectory.
The evolution of the fundamental and the harmonicbunching is determined by the nonlinear interaction of thefundamental radiation field with the electron beam. Figure 1 shows GENESIS simulation of the fundamental andthe second-harmonic bunching for an average beta function β = 30 m in the LCLS undulator. The electron
beam is assumed to have a normalized transverse emittance γ = 1.2 µm, a peak current I0 = 3.4 kA, and an
initial rms relative energy spread σδ0 = 1 × 10−4 . For
simplicity, no drift spaces between undulator sections areincluded in our simulations. At the FEL saturation (aroundz = 86 m), we have |b1 | ≈ 0.30 and |b2 | ≈ 0.075. Taking K = 3.7 and λu = 3 cm, we obtain from Eq. (5)that P2 ≈ 50 kW for a perfect trajectory. For BPMs thathave a resolution of about 2-µm and are separated by about
4 m, the tolerable rms trajectory misalignment angle is(x0 )2 1/2 ≈ 2/4 = 0.5 µrad [18]. Assuming the FEL still203

Z. Huang et al. / Proceedings of the 2004 FEL Conference, 201-204

reaches saturation in the 100-m undulator, Eq. (6) yields
110 kW additional second-harmonic power due to the imperfect trajectory, still three orders of magnitude smaller
than the expected third-harmonic power.

COHERENT HARMONIC GENERATION
IN THE SECOND-HARMONIC RADIATOR
Since there is substantial second-harmonic bunching at
the FEL saturation, it should be possible to significantly
increase the second-harmonic radiation by using a secondstage undulator with its resonant wavelength tuned to thesecond-harmonic wavelength (i.e., λ2 = 0.75 Å) of the
LCLS. In this section, we study and optimize the performance of such a second-harmonic radiator. Table 1 lists
the parameters for a planar Nd-Fe-B undulator that is resonant at 0.75 Å. The undulator gap g = 5 mm and thepeak magnetic field B0 are determined by Halbach’s formula [19]. Since the field quality tolerance of the secondharmonic radiator is expected to be more relaxed than thefirst undulator, a helical undulator (with a wider gap) may
be used to generate circularly-polarized second-harmonic
radiation.
Table 1: Parameters for the LCLS second-harmonic radiator.
Parameter
symbolvalue
unit
undulator period
λu2
2.38
cm
undulator gap
g5
mm
peak magnetic field
B0
1.26
Tesla
undulator parameterK2
2.81
resonant wavelength
λ2
0.75
Å
undulator length
Lu243mtotal linear taper∆K2 /K2
0.25%
average beta function
β2 
15
m

For a pre-bunched beam entering the second-harmonic
radiator, the coherent radiation power is given by [20]I 2 Z0 K 2 [JJ]2
P2 = 0 2 2 2
8γ
4πσx

 Lu2
0

2

b2 (z)dz,(7)

where the Bessel function factor [JJ] is now evaluated forthe new undulator parameter K2 . We see that a smallertransverse beam size can generate more coherent radiation, but the increased angular spread also leads to a larger
spread in ponderomotive phase that degrades the bunching.
The phase spread due to the emittance can be estimatedfrom Eqs. (2) and (3) for the second-harmonic phase θ2 :

dθ2
2π
2π 2
.
(8)
σ =
=
dz
λ2 x
λ2 β2 
For the FEL that reaches saturation in the first undulator,
the micro-bunched beam has a rms relative energy spreadσδf ≈ ρ ≈ 4.5 × 10−4 , where ρ is the FEL parameter [21].

Figure 2: Radiation power in the second-harmonic radiatorfor (a) 15-m average beta, 0.25% linearly tapered undulator(red), (b) 15-m average beta, uniform undulator (blue) and(c) 30-m average beta, uniform undulator (black).
The resulting second-harmonic phase spread is

dθ2
4π
4π
σδf ≈
ρ.
=
dz
λu2
λu2

(9)

The optimal focusing strength is obtained when the righthand side of both Eqs. (8) and (9) are equal. Thus, an average beta function β2  ≈ λu2 /(2ρλ2 ) ≈ 15 m would generate the most coherent harmonic power without degrading
the bunching beyond the level caused by the energy spread.
Note that this value of the average beta function is abouta factor of 2 smaller than the average beta function in the
LCLS main undulator.
To simulate harmonic generation, GENESIS has been
upgraded to allow for up-conversion of its internal particle
distribution to higher harmonics. The particle phases areconverted by θn = nθ, filling n successive slices to keep
the spectral resolution of the simulation constant. It also
requires a change in the shot noise algorithm to provide thecorrect bunching statistics on all harmonics supported by
the simulation, and follows closely the method of harmonic
decomposition of the fluctuation in the particle phase [22].
For the second-harmonic generation, the electron distribution is extracted at a post-saturation distance z ≈ 90 m of
the first undulator (with b2 ≈ 0.06 instead of the maximum value 0.075). As seen in Fig. 1, the second-harmonicbunching is somewhat reduced from the maximum value
after saturation. If necessary, this reduction may be minimized by a slight increase of the initial energy spread witha designated energy-spread heater in the LCLS [23] to allow the FEL saturation at the end of the first undulator. The
electron transverse phase space is assumed to be properly
matched into the second undulator.
At this optimal focusing strength, the rapid build-up ofcoherent power in the second-harmonic radiator enables
tapering the undulator parameter K2 in order to trap sufficient electrons for effective harmonic generation. For
simplicity, we consider here only a linear taper that starts
at the beginning of the undulator. The taper strength isSingle-Pass FELs

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Z. Huang et al. / Proceedings of the 2004 FEL Conference, 201-204

Figure 3: Bunching parameter in the second-harmonic radiator for (a) 15-m average beta, 0.25% linearly tapered
undulator (red), (b) 15-m average beta, uniform undulator (blue) and (c) 30-m average beta, uniform undulator(black).

Figure 4: RMS beam size of the 0.75-Å radiation along thesecond-harmonic radiator.

REFERENCES[1] R. Bonifacio, L. De Salvo, and P. Pierini, Nucl. Instr. Meth.
A 293, 627 (1990).

then varied to maximize the output power. Figure 2 shows
SASE simulations of both tapered and uniform undulators
at β2  = 15 m. An 43-m tapered undulator with a taper
strength ∆K2 /K2 = 0.25 % generates more than 2 GW
output power at 0.75 Å, which is about one order of magnitude larger than that from the uniform undulator. Examination of Fig. 3 indicates the effectiveness of the undulator
taper in maintaining the second-harmonic bunching against
the phase spread from both the emittance and the energy
spread, while the bunching parameter drops almost independent of the focusing strength for a uniform undulator.
Figure 2 also shows that a larger beam size in the undulator (with β2  = 30 m) generates less coherent radiation
initially. Hence the undulator taper may not be as effective.
Finally, Fig. 4 shows that the radiation rms beam size
along the second-harmonic radiator follows closely to therms electron beam size (σx = 26 µm), indicating anearly diffraction-limited radiation at 0.75 Å. The relativerms spectrum bandwidth of the 0.75-Å radiation is about
0.05%, similar to the bandwidth of the saturated fundamental radiation at 1.5 Å in the first undulator. These x-ray
pulses from both undulators are naturally synchronized asthey are generated by the same electron beam.

CONCLUSIONS
Given that the LCLS reaches saturation in the planned
100-m undulator, the significant second-harmonic bunching can still be very useful in generating high-power,
shorter-wavelength coherent radiation which is otherwise
difficult to obtain with the current electron beam technology. The analysis and simulations presented in this paper
show that an second-harmonic radiator operating parasitically to the main LCLS undulator can effectively produce
GW-level, sub-Angstrom x-rays for scientific applications.
We thank P. Emma, J. Hastings, and K.-J. Kim for useful
discussions.

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Electron. QE-36, 275 (2000); Nucl. Instr. Meth. A 445, 53(2000).
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[5] S. Biedron et al., Nucl. Instr. Meth. A 483, 94 (2002).
[6] Z. Huang and K.-J. Kim, Nucl. Instr. Meth. A 475, 112(2001).
[7] Linac Coherent Light Source Conceptual Design Report,
SLAC-R-593, 2002.
[8] R. Bonifacio et al., Nucl. Instr. Meth. A 296, 787 (1990).
[9] W. Fawley et al., in Proceedings of the 1995 Particle Accelerator Conference, 219 (IEEE, Piscataway, NJ,1995).
[10] F. Ciocci et al., IEEE J. Quantum Electron. QE-31, 1242
(1995);.
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[13] M. Cornacchia, J. Synchrotron Rad. 11, 227 (2004).
[14] S. Reiche, Nucl. Instrum. Methods Phys. Res. A 429, 243(1999).
[15] M.J. Schmitt and C.J. Elliott, Phys. Rev. A 34, 4843 (1986).
[16] W.B. Colson, G. Dattoli, and F. Ciocci, Phys. Rev. A 31, 828(1985).
[17] S. Reiche, Nucl. Instrum. Methods Phys. Res. A 445, 90(2000).
[18] P. Emma, private communication.
[19] K. Halbach, J. Phys. (Paris) Colloq. 44, C1-211 (1983).
[20] L.H. Yu and J. Wu, Nucl. Instrum. Methods Phys. Res. A
483, 493 (2002).
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50, 373 (1984).
[22] W. Fawley, Phys. Rev. ST Accel. Beams 5, 070701 (2002).
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J.F. Schmerge et al. / Proceedings of the 2004 FEL Conference, 205-208

EMITTANCE AND QUANTUM EFFICIENCY MEASUREMENTS FROM A
1.6 CELL S-BAND PHOTOCATHODE RF GUN WITH MG CATHODE
J.F. Schmerge*, J.M. Castro, J.E. Clendenin, D.H. Dowell, S.M. Gierman, and R.O. Hettel, SLAC,
Menlo Park, CA 94025, USA
Abstract
A comparison of electron beam parameters from a 1.6
cell S-band rf gun with Cu and Mg cathode at the SLAC
Gun Test Facility are reported. The lower work functionof Mg compared to Cu theoretically increases thequantum efficiency for a fixed laser wavelength and also
increases the thermal emittance.
Slice emittancemeasurements at low charge (15 pC) set an upper limit on
the thermal emittance of 0.6 and 1.2 microns per mm
radius for the Cu and Mg cathodes respectively. The
longitudinal emittance measurements with both cathodes
exhibit large energy spreads emitted from the gun. The
measured quantum efficiency with no laser cleaning isapproximately 3 10-5 at 110 MV/m and 30° laser phase for
the Cu and 8 10-5 at 90 MV/m and 30° laser phase for theMg cathode.

INTRODUCTION
The cathode is one of the most important components ofa photocathode rf gun as it defines the quantum efficiency(QE) and the minimum achievable emittance or so called
thermal emittance. In addition the cathode also affects the
maximum attainable field in the gun due to rf breakdown
at the cathode to back plate joint. The ideal cathodewould exhibit high QE, low thermal emittance and would
not limit the maximum attainable field. A peak on axis
field of 120 MV/m is required in order to achieve anemittance of 1 µm with 1 nC of charge as desired for the
Linac Coherent Light Source (LCLS) [1]. The maximum
required field limits the choice of cathode materials tometals.
This paper reports the results of measurements made at
the SLAC Gun Test Facility with a Mg cathode. The
results are also compared with theoretical values andpreviously reported Cu cathode results [2]. The Cu
cathode used in the study is a 1 cm diameter, single
crystal (100 orientation) brazed into the polycrystalline
Cu back plate. After brazing, the cathode was polishedwith 0.25 µm diamond paste and installed on the gun in a
N2 environment. The 2 cm diameter Mg insert was
friction welded into the Cu back plate. After welding, theMg cathode and back plate surface were machined using
single point diamond tools. The cathode was offset fromthe lathe center to eliminate a machining defect at thecenter of the cathode. The Mg cathode was installed on
the gun in air so that the electric field on axis could bemeasured with a bead drop measurement.
The maximum field attained with the Cu cathode was
127 MV/m with reliable operation at 110 MV/m and____________________________________________*

schmerge@slac.stanford.edu

Available online at http://www.JACoW.org

typically 2 10-9 Torr vacuum pressure during electron
beam operation. The Mg cathode was limited to lower
fields due to rf breakdown. The maximum field achieved
was 107 MV/m with reliable operation at 95 MV/m and 5
10-10 Torr vacuum pressure with electron beam. For
comparison, a polycrystalline Cu cathode with no braze or
weld joint was operated up to 140 MV/m with reliable
operation at 125 MV/m.

THEORYThe definition of thermal emittance is shown inequation 1 where x is the beam position and px is thetransverse momentum [3]. Assuming a flat transverse
laser pulse shape and averaging over the electron energy
distribution leads to equation 2 where rcathode is the laser
beam radius, Ek is the electron kinetic energy in the metal
given by the sum of the Fermi energy and photon energy
and Eb is the metal barrier energy which is the sum of the
Fermi energy and work function less the Schottky barrier
reduction. Using the definition of QE as the number of
emitted electrons per incident photons, the QE can becomputed as shown in equation 3 where R is the opticalreflectivity. After integration the QE simplifies toequation 4 where EF is the Fermi energy.
ε n −thermal ≡

1
mc

x2

r

ε nthermal = cathode
2

Eb

∫

QE ≡ (1 − R ) min
E

1

px2

2 Ek
mc 2

cos −1

3/ 2
1/ 2
  Eb 2
E

E
 
1 −  E  + 2  b E  − 2  b E  
k 
k 
k 


 

1/ 2


E
E
6 1 +  b  − 2  b  
Ek   Ek 
 


Eb
E + E photon 2π

∫
0

∫N

electronsin Φdθ d ΦdE

30

Eb π 2π∫∫∫N

2electronsin Φdθ d ΦdE

0 0 0  Eb   Eb 1/ 2 1 +  E  − 2  E  
k 
k 



QE = (1 − R ) 
EF 

2

 Ek 

4

Thermal emittance is primarily a function of the Fermi
energy, work function and photon energy. The quantum
efficiency depends on the same parameters and is also
dependent on the optical reflectivity. The Cu and Mg
cathode parameters are listed in Table 1 along with thecalculated skin depth, QE and thermal emittance for 263
nm (4.71 eV) normal incidence photons. For the
calculation it is assumed the Cu cathode has a 110 MV/m

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J.F. Schmerge et al. / Proceedings of the 2004 FEL Conference, 205-208

Cu

Mg

Units

Work Function

4.59 [4]3.66 [4]eV

Fermi Energy

8.7 [5]

7.1 [5]eVPower Reflectivity

34 [6]

92 [7]%

Skin depth

25

19

nm

QE

11

21

10-5

εn-thermal

0.25

0.46

µm

The equations have been derived assuming a flat
cathode surface at absolute zero and electron-electron
scattering is ignored. Operation at room temperature
increases the reported thermal emittance and QE for the
Cu cathode by less than 2%. Temperature effects become
significant above about 300 C for Cu and approximately
2000 C for Mg. The inelastic mean free path (IMFP) for
electrons in Cu and Mg at 4.7 eV above the Fermi energy
is not well documented. From the literature the IMFP is
estimated to be on the order of 5 nm [5,8]. Since themean free path is less than the skin depth it must be
included for good agreement between theory andexperiment.
Including scattering will reduce thecalculated QE and thermal emittance as it will decrease
the average energy of photo-emitted electrons. Surface
roughness has two effects. First, sharp surface featurescause field enhancement that increase the Schottky effectand thus the QE and thermal emittance. Second, sinceelectrons are emitted from a narrow cone with respect tothe surface normal [3], roughness also affects the angular
distribution. This effect increases the thermal emittancebut has no effect on the QE. Both effects are localized
and must be averaged over the entire cathode.

MEASUREMENTS
The measurements reported here are performed with anearly Gaussian temporal pulse shape with approximately
2 ps FWHM duration. The transverse laser shape is flatand unless otherwise noted the radius is 1 mm. The laser
is incident on the cathode at near normal incidence. The
Cu cathode was operated at 110 MV/m and 30° laser
phase resulting in 5.7 MeV beam exiting the gun. The
Mg cathode was operated at 95 MV/m with 30° laser
phase resulting in 5.0 MeV beam unless otherwise noted.
All measurements are made with 15 pC of charge
corresponding to about 12 A of peak current unlessotherwise noted.

Quantum Efficiency
The QE is determined by measuring the laser energy
incident on the cathode with a Joule meter and the charge
exiting the gun on an insertable Faraday cup immediately
downstream of the gun. The measured QE versus the

MOPOS64108-5Parameterlaser phase for both cathodes is shown in figure 1. The
QE from the Mg cathode exhibits less phase dependence
than the Cu cathode because the Schottky effect is lesssignificant due to the lower work function.
In an attempt to increase the QE from the Mg cathode, ahigh intensity laser pulse was scanned across the cathodewith the rf off. A lens was inserted in the drive laser
beam path which reduced the 2 mm diameter beam to a 68
µm rms spot size. The maximum energy available at thecathode was 22 µJ resulting in a maximum fluence at thecathode of 800 µJ/mm2. With the maximum fluence
incident on the cathode there was no observable change inthe vacuum pressure. Likewise there was no measurable
increase in QE after the laser cleaning attempt. No
attempt was made to laser clean the Cu cathode.

QE (10 )rf field with 30° laser phase and 90 MV/m, 30° is
assumed for the Mg cathode.
Table 1: Cathode parameters assuming 4.71 eV photons at
normal incidence.

6
4
Cu

2

Mg

0
0

20

40

60

80

100

120

Laser Phase (°)

Figure 1: The QE versus laser phase. The peak field at thecathode is 110 MV/m for Cu and 90 MV/m for Mg.
The variation of QE across the cathode was alsomeasured by scanning a 130 µm rms laser beam over a
1.5 X 1.5 mm area on the Mg cathode. The rms QE
variation was 83% of the average and the minimum andmaximum QE were 44% and 660% of the average
respectively. The variation is probably due to localized
surface contaminants either lowering the work function oraltering the optical reflectivity. Since the Schottky effectis less significant for the Mg cathode it is unlikely thevariation is caused by rf field enhancement due tolocalized sharp features on the cathode. The QE
uniformity was significantly improved approximately 0.7
mm off center. Thus the laser was intentionally steered
off axis away from several hot spots to improve electron
beam uniformity for the emittance measurements reported
below.
Significantly less variation was observed on the Cu
cathode. The rms QE variation for the Cu cathode wasonly 11% of the average QE. The minimum andmaximum were 76% and 125% respectively of theaverage QE.

Longitudinal Emittance
Emittance measurements were made downstream of a 3
m SLAC linac structure located approximately 90 cm
downstream of the cathode. The longitudinal emittancewas determined by measuring the energy spread
downstream of a spectrometer magnet as a function of

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J.F. Schmerge et al. / Proceedings of the 2004 FEL Conference, 205-208

linac phase [2]. The technique is analogous to a quadscan for the transverse emittance measurements. A
relatively large energy spread exiting the gun wasobserved for both cathodes. As expected there is not asignificant difference in the longitudinal phase space with
the Cu and Mg cathodes.
Table 2 lists the electron beam longitudinal parameters.
All parameters were determined from a standard linear
least square error fitting routine. The emittance anduncorrelated energy spread listed in Table 2 areoverestimated due to non-linear energy-time correlation
terms. Better estimates of the uncorrelated energy spreadcan be determined using tomographic phase spacereconstruction [9]. With the actual beam phase space
distribution the true slice energy spread can be calculated
as opposed to the beam envelope which includes nonlinear correlated terms.

phase space for all ten slices and the total projected
emittance is shown in figure 2 for both cathodes.
The projected emittance is larger than the slice
emittance largely due to the phase space offsets in bothangle and position. The offsets are measured with respect
to the projected centroid and thus are not due to steering
errors but rather time dependent kicks. The kicks appear
independent of charge so they are not due to wakefields.
This suggests they originate at the gun or linac rf couplers[11]. The reversal of the head and tail with respect to thex axis between the two cathodes may be due to thedifferent gradients used on the cathode, the different linac
phase (Mg +19° and Cu +29°) or the fact that the beam
was steered slightly off center for the Mg case due to the
non-uniform electron emission. This will be investigatedin more detail in later experiments.

Parameter

Cu

Mg

Units

Emittance

2.5

2.8

keVps

Normalized Emittance

1.5

1.7

µm

Bunch Length

0.44

0.41

ps

Energy Spread

36

48

keV

Uncorrelated Energy Spread

5.7

6.9

keV

Linear Correlation

-81

-120

keV/ps∆ x' (µ rad)

Table 2: Longitudinal Beam Parameters at Linac
Entrance.

head

projected
-200

0

200

400

∆x (µm)∆ x' (µ rad)Slice Emittance
The transverse slice emittance is measured using aquadrupole scan technique on the identical screen used in
the longitudinal emittance measurements. Since thescreen is in a dispersive section, the linac phase can bevaried until the beam is sufficiently chirped at the screenthat the beam can be temporally sliced into 10 beamlets.
The energy-time calibration can be calculated since thelongitudinal beam parameters are known at the linac
entrance. The known beam matrix is propagated throughthe linac with the amplitude and phase settings used in thetransverse emittance measurement and the resulting linear
energy-time correlation is the calibration used todetermine the time axis for the slice emittancemeasurements shown later.
For the transverse measurements a total of five beam
parameters are fit in a least square fitting routine. In
addition to the three Twiss parameters, the phase space
offset with respect to the projection in both position andangle are also included. Thus a total of five parameters foreach slice are measured which determine both the positionand ellipse orientation in phase space. Previously wereported the slice emittance for the Cu cathode [10] and it
is repeated here after correcting the beam propagation
through the spectrometer. Also included are the slice
emittance results from a Mg cathode for comparison. The

1000
800
600
400
200
0 tail
-200
-400
-600
-800
-1000
-400

250
head
200
150
100
50
0
-50
-100
-150
-200
projected
-250
-500
-250

tail

0

250

500

∆x (µm)Figure 2: The upper plot shows the transverse phase space
for the Cu cathode and the lower plot for the Mg cathode.
The projected emittance is plotted as a red dashed line.
The minimum obtainable slice emittance is shown infigure 3 for both cathodes. The minimum emittance wasobtained by measuring the emittance as a function of theemittance compensating solenoid field. It was determined
empirically that the minimum emittance occurs when thesolenoid focal length is adjusted to produce a waist near
the linac exit.

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J.F. Schmerge et al. / Proceedings of the 2004 FEL Conference, 205-208

ε n (µ m)

The minimum slice emittance for the Cu cathode isapproximately 0.6 µm while the Mg cathode is higher
with 1.1 µm. The Cu results are in agreement with twoother Cu cathode measurements at different laboratories
using different techniques [12-13]. The measured values
represent an upper limit for the thermal emittance fromeach cathode. The Mg cathode produces a higher
emittance than the Cu cathode as expected although both
values are approximately a factor of 2.5 times higher than
the theoretical values listed in Table 1.
The emittance with the Mg cathode using a 0.5 mm
radius cathode was also measured with approximately 20
pC charge and 11 A of peak current. The minimum
emittance in this case was approximately 0.6 µm which isnearly half the value when the 1 mm radius laser wasused. While this is consistent with the expected behavior
due to thermal emittance (see equation 2) it is notconclusive that the measured emittance is equal to thethermal emittance. Experiments are underway to measure
the projected emittance directly exiting the gun to bettercharacterize the thermal emittance.
2.0
1.8
1.6
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0
-1.0

Cu
Mg

-0.5

0.0

0.5

1.0

Time (ps)Figure 3: Emittance versus time for both the Cu and Mg
cathodes. The projected emittance is plotted at t=0.

SUMMARY AND CONCLUSIONSThe transverse and longitudinal emittance in an S-band
photocathode gun with a Cu and Mg cathode have beenmeasured. No significant differences are observed in thelongitudinal phase space. The minimum transverse
emittance with a Cu cathode with 1 mm laser radius was
0.6 µm and 1.1 µm with the Mg cathode. The emittancefrom the Mg cathode decreased to 0.6 µm with a 0.5 mm
radius laser spot size. These measured values set upper
limits to the thermal emittance from Cu and Mg cathodes.
The measurements are a factor 2.5 times larger than
predicted by a theory that does not include temperatureeffects, surface roughness or electron-electron scattering.
Only surface roughness can increase the theoreticalemittance to the level of the measurements but it requires
significantly roughened surfaces. It is more likely that asource of emittance growth in the gun or linac iscontributing to the measured emittance. The time

MOPOS64dependent position and angle offsets observed in the beam
indicate the presence of a time dependent kick.
The QE was also measured from both cathodes. The
Schottky effect is less pronounced with the Mg cathodedue to the lower work function. The measured quantum
efficiency with no laser cleaning is approximately 3 10-5
at 110 MV/m and 30° laser phase for the Cu cathode and8 10-5 at 90 MV/m and 30° laser phase for the Mg
cathode. No increase in QE for the Mg cathode wasobserved after scanning the cathode with an 800 µJ/mm2
UV laser pulse.

ACKNOWLEDGEMENTS
The authors would like to acknowledge P. Pianetta for
helpful discussions and the entire SSRL staff for helping
to make this research possible. This work was supported
by Department of Energy contract DE-AC02-76SF00515.

REFERENCES[1] C. Limborg et al, NIM A528, (2004) 350-354.
[2] D. H. Dowell et al, NIM A507, (2003) 327-330.
[3] J.E. Clendenin et al, NIM A455, (2000) 198-201.
[4] R.C. Weast Editor, “CRC Handbook of Chemistry andPhysics 1st Student Edition”, (1988) E-78.
[5] S. Tanuma, C.J. Powell and D.R. Penn, Surface andInterface Analysis, Vol. 17, (1991) 911-926.
[6] M.J. Weber editor, “Handbook of Optical Materials”,(2002) 317.
[7] E.D Palik editor, “Handbook of Optical Constants ofSolids III”, (1998) 239.
[8] D.R. Penn, Physical Review B, Vol. 35, No. 2, (1987)
482-486.
[9] H. Loos et al, NIM A528, (2004) 189-193.
[10] D.H. Dowell et al, Proceedings of the 2003 Particle
Accelerator Conference, (2003) 2104-2106.
[11] D.H. Dowell et al, This conference, TUPOS56.
[12] W.S. Graves et al, Proceedings of the 2001 Particle
Accelerator Conference, (2001) 2227-2229.
[13] J. Yang et al, Proceedings of the 2002 European
Particle Accelerator Conference, (2002) 1828-1830.

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X.J. Wang et al. / Proceedings of the 2004 FEL Conference, 209-211

THE UPGRADE OF THE DUV-FEL FACILITY AT THE BNL
X.J. Wang*, H. Loos, J.B. Murphy, G. Rakowsky, J. Rose, B. Sheehy, Y. Shen, J. Skaritka, Z. Wu,
L.H. Yu, NSLS, BNL, Upton, NY 11973, USA
Abstract
The DUV-FEL linac is upgraded from 200 to 300 MeV
to enable the HGHG FEL to produce 100 µJ pulses of 100
nm light. This will establish the DUV FEL as a premieruser facility for ultraviolet radiation, and will enable stateof-the-art gas phase photochemistry research. Further
more, the upgraded facility will also enable several
critical R&Ds for future X-ray FELs, such as cascaded
and higher harmonic HGHG (n>5), and experimental
demonstration of the emittance spoiler for the LCLS .
The upgraded HGHG will operate at the 4th harmonicwith the seed laser at 400nm. The increase of the electron
beam energy will be accomplished by installing a 5th linac
cavity and two 45 MW klystrons. New HGHG modulator
and dispersion sections vacuum chambers will be
manufactured to accommodate new matching optics and8th harmonic HGHG. The status of the DUV-FEL
upgrade and other beam physics R&D opportunities arepresented..

INTRODUCTION
The Deep Ultra Violet Free Electron Laser (DUV-FEL),a laser linac facility at Brookhaven National Laboratory(BNL), is the world’s only facility dedicated to laserseeded FEL R&D and its applications. The high-gain
harmonic generation (HGHG) FEL at the DUV-FEL
reached saturation at 266 nm with 800 nm seeding [1] in
2002. Experiments were carried out at the DUV-FEL tofurther characterize the properties of the HGHG FEL andto demonstrate its fully coherence, stability andcontrollability. The narrower spectrum and better stabilityof the HGHG, compared to a self amplified spontaneousemission (SASE) FEL, were observed. Both the second
and third harmonic HGHG FEL outputs wereexperimentally
characterizedusingavacuummonochromator. The pulse energies for both harmonics(133 and 89 nm, respectively) were measured to be about
1 µJ, which is about one percent of the fundamental value
at 266 nm. A two-photon absorption auto-correlator with
100 fs resolution was developed to characterize the
HGHG output pulse length. It was experimentallydemonstrated that, the HGHG can produce output pulses
with lengths from 1 ps down to 250 fs by varying the seedlaser pulse length.
The first chemical science experiment – ion pairimaging, was successfully completed [2] at the DUVFEL. The ion pair imaging experiment used the HGHG’s
third harmonic output (89 nm) to study the super excitedstates of methyl fluoride, a highly flammable gas.
*_________________
Corresponding author: xwang@bnl.gov

Available online at http://www.JACoW.org

Velocity-mapped ion images of the fluoride ion, obtainedusing intense, coherent, sub-picosecond pulses of 86-89
nm light, revealed a low translational energy, implying avery high internal excitation in the molecule’s methyl
cation cofragment.
A series of workshops [3] was held at the NSLS tofurther explore the potential of the DUV-FEL facility, andto identify the future opportunities for chemical science,
beam physics and FEL. The participants of the July 2003
NSLS Chemical Dynamics Workshop identified that, a
VUV source with following properties will be a truly
unique source for chemical science and other applications:• Photon energy > 10 eV as a universal probe.
• Peak power > 1012 W/cm2 for nonlinear
process.
• 5x1013 ph/pulse for high sensitivity and single
molecule detection.
• Pulse duration ~100 fs for time-resolved
dynamics studies.
• Fully coherence for quantum physics andcoherent control.
The workshop participants enthusiastic recommended
that, the DUV-FEL facility be upgraded to make the FEL
fundamental ~100 nm with the properties listed above.
Further more, the upgraded DUV-FEL should be able toenable several critical R&Ds for future X-ray FELs, suchas cascaded and higher harmonic HGHG (n>5), andexperimental demonstration of the emittance spoiler for
LCLS [4].
In the rest of this report, the DUV-FEL upgrade options ,status, and beam physics R&D opportunities with theupgraded facility will be discussed.

THE DUV-FEL UPGRADEThe DUV-FEL accelerator system consists of a 1.6-cell
photo injector driven by a Ti:Sapphire laser system, and afour-section 2856 MHz SLAC-type traveling wave linac
that is capable of producing a 200 MeV electron beam.
The facility’s magnetic chicane bunch compressor
produces sub-picosecond-long electron bunches with apeak current of a few hundred amperes. The highbrightness electron beam travels down the 10 meter-longundulator to generate UV light with a fundamental
wavelength of 266 nm. There are two options for the
DUV-FEL to reach 100 nm fundamental. One is toreplace the NISUS undulator with a shorter period one,such as VISA undulator; the other is to increase theelectron beam energy (Fig.1).
After carefully considering cost, shutdown time andfuture experimental capabilities, the electron beam energy
upgrade to 300 MeV was chosen. The longer period

Single-Pass FELs

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X.J. Wang et al. / Proceedings of the 2004 FEL Conference, 209-211

NISUS undulator will make the cascaded HGHG easier torealize in the future.

FEL Scaling With NISUS & VISA
NISUS

λ [nm]

1000

100

λu = 3.89 cm
K=1
L = 10 m
Gap = 2.1 cm

λu = 1.8 cm
K = 1.2
L = 4+2 m
Gap = 0.6 cm

VISA

10

E [MeV]λ = λu (1+K2/2)/2γ2

Fig. 1: The DUV-FEL output wavelength vs. beam energy
for the two undulators.
Gun∆ = 5 MeV

∆ = 35 MeV∆ = 35 MeV Comp∆ = 65 MeV ∆ = 65 MeV 205 MeV

Gun∆ = 5 MeV

∆ = 55 MeV∆ = 65 MeV Comp∆ = 65 MeV ∆ = 65 MeV ∆ = 65 MeV

Various options for the HGHG seed laser injection werealso investigated. A four-steering-magnet chicane wasused for HGHG seed injection before the upgrade. The
electron beam was displaced about 8 mm at the HGHG
seeding station. The two steering magnets for the seedchicane before the seeding station were removed becauseof the space limitation. The on-line laser seed injection
using a mirror with a center hole was simulated. For thehole size of 3 mm diameter, about 80% of the seed laser
energy will be lost. A chicane is adopted for the upgradewith a new beam steering scheme. A special steering
magnet was designed so it can be install on top of the exit
cell of the newly installed linac. The diagnostic dipole
magnet will be used for the seed chicane with a opposite
polarity power supply.
For the upgraded DUV-FEL to be able to reach the 8th
harmonic, significant modifications of the HGHG
modulator were made. The minimum gap for themodulator before the upgrade is about 1.6 inch, and thegap for the 8th harmonic will be 0.93 inch. A new motor
drive mechanism was installed to achieve such small gap.
Fig.5 plots the pulse wire measurements for the electron
beam trajectories inside the modulator. The trim magnets
at both ends of the modulator will be adjusted to correct
the trajectory error for the higher harmonic operation.

Fig. 2: The old (top) and upgraded (bottom) DUV-FEL
linac configurations.
The old and upgraded DUV-FEL linac configurations areplotted in fig.2. The upgraded HGHG will operate at the
4th harmonic with the seed laser at 400nm. The increase of
the electron beam energy will be accomplished byinstalling a 5th linac cavity and two 45 MW klystrons.
New modulator and dispersion sections vacuum chambers
will be manufactured to accommodate new matching
optics and 8th harmonic HGHG. To make space for the
new linac, two quadrupole doublets were removed. A newquadrupole triplet was installed immediately after the
HGHG seeding station to achieve the beam matching for
the FEL (fig.3). Fig.4 plots the electron beam envelops
from the bunch compressor to the end of HGHG
amplifier.

Fig. 5: The pulse wire measurements for the electron
beam trajectories inside the HGHG modulator with trim
magnets. 1 – 8th harmonic, 2 – 7th, 3 – 6th, 4 – 5th.

Fig. 3: The DUV-FEL layout after the upgrade.

MOPOS67

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X.J. Wang et al. / Proceedings of the 2004 FEL Conference, 209-211

Fig. 4: The transverse electron beam envelops along the beam line, the HGHG amplifier (NISUS undulator) entrance isdownstream 21 m from the starting point.
In order to accommodate the tunable HGHG [5] andlaser heater [6] experiments, a much stronger HGHG
dispersion magnet is needed. The OK-4 dispersion
magnet on-loan from Duke was installed at the DUVFEL. The maximum R56 will increase from 0.35 mm to
4.2 mm after the upgrade.
The all hardware for the upgrade is installed; the initialenergy of the electron beam after the upgrade will belimited to about 250 MeV. The reason for that is, one of
the klystron tubes was damaged in May 2004. The RF
conditioning will start in early September of 2004.
Electron beam commissioning is expected shortly after.
The 4th harmonic HGHG with 800 nm seed laser will becommissioned in early December of 2004. 130 nm HGHG
will be commissioned in early 2005.

BEAM PHYSICS AND FEL R&D
The future R&D opportunities in FEL and beam physics
are discussed briefly in this section.
1. Seeded FEL R&D: though the basic properties andadvantages of the HGHG have been experimentallydemonstrated, there are still many significant challenges
to realize a X-ray FEL based on the HGHG. The large gapof the longer wavelength of the HGHG seed laser and the
X-ray users desired requires staging several HGHGs, i.e.,cascaded HGHG. We are exploring the possibility of
two-staged cascaded HGHG experiment in collaboration
with other groups. The proposed experiment will
demonstrate the staging and fresh bunch techniques.
To reduce the complexity of the cascaded HGHG, ahigher harmonic HGHG is desired. The higher electron
beam energy after the upgrade will make it possible tostudy the 8th harmonic. Higher harmonic HGHG will also
make it possible to investigate the degradation of HGHG
output, which scales as the square of the harmonic
number.
2. Other FEL R&D: The upgraded DUV-FEL offers
other unique opportunities for the FEL R&D. Twoexperiments now under consideration are emittancespoiler [4] and FEL gain enhancement by the inverse Free
Electron Laser (IFEL) micro-bunching [7]. Preliminary
estimation shows that, the FEL output pulse length will be
reduced from 1 ps to about 200 fs using emittance spoiler.

The HGHG modulator introduces electron beam energy
modulation via IFEL interaction. The large dispersion
magnet installed will allow us to optimize the electron
beam micro-bunching. A factor of 3 to 6 in peak current
enhancement is expected by the IFEL micr-bunching.
3. High-brightness electron beam R&D:
The
importance of electron beam quality becomes increasing
critical as the FEL going shorter wavelength. The gain
length measurement is one of the most powerful tools todetermine the 6-D quality of the electron beam. The
upgraded DUV-FEL facility will continue the BNL
tradition in high-brightness electron beam R&D. The
proposed experimental program will cover from electron
beam generation, compression to the preservation. An
BNL/LCLS/SPAC collaboration is established to study
the longitudinal laser pulse shaping on the transverse
emittance. The experiment will take advantage of thebroad bandwidth of the DUV-FEL laser system. We will
also to carry out the feasibility studies of generating the
femto-second kilo-Ampere electron beam using thelongitudinal emittance compensation technique[8].

ACKNOWLEDGEMENTS
The supports of BNL director office and NSLS aregratefully acknowledged. We appreciate the assistance ofProf. Y. Wu of Duke University for lending the OK-4
dispersion magnet. The work was performed under DOE
contract DE-AC02-98CH10886.

REFERENCES[1] L. H. Yu et al, Phy. Rev. Lett. 91, 074801-1 (2003).
[2] W. Li et al, Phy. Rev. Lett. 92, 083002-1(2004).
[3]http://www.nsls.bnl.gov/organization/Accelerator/highl
ights.htm.
[4]P. Emma et al, Phys. Rev. Lett. 92, 074801-1 (2004).
[5]. T. Shaftan et al, WEAISo1, this proceeding.
[6]Z. Huang et al, Phys. Rev. STAB. 7, 074401 (2004).
[7]Y. Liu, X.J. Wang et al, Phys. Rev. Lett. 80, 44184421(1997).
[8] X.J. Wang and X.Y. Chang, NIM A 507, 310–313(2003).

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EXPECTED PROPERTIES OF RADIATION FROM VUV-FEL AT DESY
(FEMTOSECOND MODE OF OPERATION)
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
For the next three years the nominal “long pulse” (200fs) mode of FEL operation at VUV-FEL, based on a linearized bunch compression, is not available due to the lackof a key element – a 3rd harmonic RF cavity. Essentiallynonlinear compression leads naturally to a formation of ashort high-current leading peak (spike) in the density distribution that produces FEL radiation. Such a mode of operation was successfully tested at VUV-FEL, Phase I. In thispaper we present optimized parameters of the beam formation system that allow us to get a current spike which isbright enough to get SASE saturation for the VUV-FEL,
Phase 2 at shortest design wavelength down to 6 nm. The
main feature of the considered mode of operation is the production of short (15-50 fs FWHM) radiation pulses with
GW-level peak power that are attractive for many users.
Main parameters of the SASE FEL radiation (temporal andspectral characteristics, intensity distributions, etc.) arepresented, too.

INTRODUCTION
The vacuum ultra-violet (VUV) free-electron laser(FEL) at the TESLA Test Facility (TTF), Phase I has
demonstrated saturation in the wavelength range 80-120
nm based on the self-amplified spontaneous emission(SASE) principle [1, 2, 3]. It was not simply a proof-ofprinciple experiment as it was planned at an early stage ofthe project. TTF FEL at DESY demonstrated an ultimate
performance for this class of coherent radiation sources inthe VUV wavelength range. It has been realized experimentally a unique mode of operation of SASE FEL producing radiation pulses of ultimately short duration, i.e. aboutcoherence time. Each radiation pulse of about 40 fs duration consisted of one-two wave packets. In other words,
TTF FEL produced radiation pulses close to Fourier limit.
The degree of transverse coherence was pretty high, too.
Peak power (averaged over ensemble) exceeded 1.5 GW.
Thus, TTF FEL produced nearly completely coherent (longitudinally and transversely) VUV radiation pulses with ultimate peak power. Number of photons in one mode exceeded the value of 1013 . Excellent properties of FEL radiation were used in the pioneering user experiments [4, 5].
The beam dynamics in TTF1 linac was nontrivial [3].
Due to nonlinear compression and small local energy
spread the short high-current (3 kA) leading peak (spike)in density distribution was obtained. Despite strong collective effects (of which the most critical was the longitudi-

THPOS66

nal space charge (LSC) after compression) this spike wasbright enough to drive FEL process up to the saturation for
the wavelengths around 100 nm.
For the next few years the nominal “long pulse” (200fs) mode of operation of the VUV-FEL at DESY (TTF2),
based on a linearized bunch compression, is not available
due to the lack of a key element – a 3rd harmonic RF cavity.
Essentially nonlinear compression leads naturally to a formation of a short high-current leading peak (spike) in thedensity distribution that produces FEL radiation. A shortcurrent spike regime is the natural solution for producing
short SASE pulses (that are requested by many users), provided that collective effects are tolerated.
In this paper we present the results of TTF2 linac optimization (with the codes Astra [7] and elegant [8]) for the
short spike regime. Choosing appropriate injector settings
and using two bunch compressors, one can tolerate collective effects on beam dynamics without 3rd harmonic cavity.
SASE FEL process is simulated with the code FAST [9]. It
is shown that the FEL can safely saturate even at the shortest design wavelength, 6 nm. SASE FEL output parameters(peak power, pulse duration, spectra, angular distributionsetc.) are calculated for 30 nm and 6 nm. With a GW level ofthe peak power one obtains short pulses in the range 15-50
fs FWHM.

OPTIMIZATION OF TTF2 LINAC
The nominal design of TTF2 [6] (see Fig. 1) assumes
the optimized injector and a linearized compression in two
bunch compressors, BC2 and BC3, with the help of the
3rd harmonic superconducting RF cavity being developed.
For the next few years this cavity will not be available, sothat this regime cannot be realized. The main potential advantages of such a regime (as compared to a short spike
regime) from the point of view of accelerator physicists

Figure 1: Schematic layout of the TESLA Test Facility,
Phase 2.

Available online at http://www.JACoW.org

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 212-215

3εx, εy [mm-mrad]

E [MeV]

453

452

451

2

1

450
0.0

0.2

0.4

0
0.0

0.6

0.2

0.4

0.6

t [ps]t [ps]

0.5

1500

0.4

I [A]

σE [MeV]

1000

500

0.3
0.2
0.1

0
0.0

0.2

0.4
t [ps]

0.6

0.0
0.0

0.2

0.4

0.6

t [ps]

Figure 2: Phase space distribution, current, slice emittanceand slice energy spread along the bunch at the undulator
entrance. Bunch charge is 0.5 nC. Bunch head is on theright. Only small part of the bunch is shown.
are: longer high-current (lasing) part of the bunch (withrms length σz ) is less sensitive to coherent synchrotron radiation (CSR) and LSC (for a given current these effects−1/3
and σz−1 , respectively); standard diagnostics
scale as σz(BPMs, screens) is better suited for such a regime since alarger fraction of total charge contributes to the lasing andone can hope that slice parameters do not differ strongly
from projected ones. On the other hand, the short spike
regime does not require very fine RF phase tuning andis, therefore, less sensitive to RF jitters (typical requirement for phase stability is δφ  2πσz0 /λRF , where σz0
is bunch length before compression and λRF is the wavelength of the accelerating RF field). From users’ point ofview, the short spike regime is advantageous for many experiments.
Two regimes of the spike formation were studied experimentally already at TTF1: the nominal one with only one
bunch compressor (BC2) [3] and the alternative one withtwo bunch compressors (BC1 and BC2). The latter regime
allowed one to get a longer spike after BC2 due to a mild
preliminary compression in BC1. The collective effects
could be efficiently tolerated this way. The question arises:
can the TTF1 experience be extrapolated to a different layout of TTF2 and much shorter wavelengths? In this paper
we give a positive answer: by using the optimized injector
and two bunch compressors (BC2 and BC3) one can obtaina short current spike and preserve its quality at the levelsufficient for lasing at short wavelengths (down to 6 nm,
the shortest design wavelength of TTF2).
The optimization of the beam dynamics in TTF2 linac
was done for the 30 nm case (beam energy 450 MeV). The
following simulation scheme was used in order to include
the most important effects. Simulation of the initial partof the machine (up to the first quadrupole) was performed
with Astra. The injector settings and beam parameters canbe found in [10]. Then the tracking was done with elegant

213

up to the end of the 4th accelerating module, including
CSR effects in both bunch compressors. The last part ofthe machine, up to the undulator entrance, was simulatedwith Astra using a simplified lattice (excluding dogleg) inorder to take into account space charge effects. The lowcurrent long tail of the bunch was cut out in this last part ofthe simulation.
For the nominal operation point the following main parameters were chosen. A Gaussian laser pulse with the 4 ps
rms duration was used to extract 0.5 nC from the gun (theother injector settings and beam parameters at the exit of
ACC1 can be found in [10]). Accelerating gradient is about
15 MV/m in the first three accelerating modules (ACC1-3)
and 8 MV/m in ACC4. The phase of ACC1 is 8 degrees
off-crest, in ACC2-4 beam is accelerated on-crest. The
beam energy is about 125 MeV, 380 MeV and 450 MeV
after ACC1, ACC3 and ACC4, respectively. The R56 areabout 18 cm and 10 cm for BC2 and BC3, respectively1 .
For these settings we have a mild compression in BC2, andthen a high-current spike (containing about 10 % of the total charge) in BC3. Combination of two phases, ACC1 andACC2-3, defines a slice (in the initial distribution) of which
the spike is made.
Slice parameters in the front part of the bunch at the undulator entrance are shown in Fig. 2. For the slice with amaximal current (1.3 kA) the mean geometric of x- and ynormalized emittances is about 1.5 mm-mrad, and the local
energy spread is about 300 keV. One may notice unusual
drop of slice emittances (well below the value of emittancein the best slice before compression) in the bunch head.
This behavior does not violate Liouville’s theorem (statingthat phase space density is conserved, not the slice parameters) and is explained by specific correlations between longitudinal and transverse phase spaces in the injector (see[3] for the detailed explanation). Longitudinal phase spacein Fig. 2 looks similar to that simulated in [3] for TTF1
case. However, the influence of energy chirp on the FEL
saturation length for 30 nm case is a small correction, i.e.
it is not that dramatic as it was in TTF1 case. It may become a dominating effect (for 30 nm case) if one does nottune the machine properly, i.e. if the spike becomes too
sharp.
Although we did the simulations for 30 nm case (450
MeV), we can do a simple generalization towards higher
energies. We assume that machine settings are the same
up to the end of BC3. Then we accelerate the beam up to
the required energy (say 1 GeV). Since space charge effectcannot be worse for higher energies, we can use the resultsof Fig. 2, and simply move the energy up. Although thisis a pessimistic estimate, in the following section we showthat even in this case one can safely reach saturation at 6nm.
To illustrate the sensitivity of the FEL operation to thenon-optimal settings of the accelerator, we simply changed
the charge extracted from the cathode, keeping other ma1 In [10] the R
56 of the BC3 is 4.9 cm. In order to get the same current
one should then accelerate beam off-crest in ACC2-3.

Single-Pass FELs

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 212-215

chine parameters untouched (see [11]) for more details).
One can see from the next section that the FEL saturation
at 30 nm should be relatively safely achieved, while a 6 nm
case must be carefully optimized.

RADIATION PROPERTIES
Simulations of the FEL have been performed with threedimensional, time-dependent simulation code FAST [9] using bunch parameters shown in Fig 2 for 0.5 nC case. In addition, a (non-optimized) 1 nC case was simulated in orderto show the total sensitivity of the machine to non-optimal
conditions [11]. Summary of the calculated FEL properties is shown in Table 1. More detailed information about
the radiation properties is presented in graphical form in
Figs. 3-5.
Figure 3 shows mean energy in the radiation pulse andrms fluctuations as functions of position along the undulator. One can see that for both charges saturation is reachedin the middle of the undulator for the wavelength of 30
nm. For the wavelength of 6 nm the (optimized) 0.5 nC
beam has a visible advantage, saturation is reached at theend of the 5th undulator module. The plots in Fig. 3
present numerical experiment of a specific measurement
being planned for TTF2 (similar procedure has been usedat TTF1). The interaction length is to be changed by meansof switching on electromagnetic correctors installed insidethe undulator. The value of the orbit kick provided by acorrector is sufficient to stop FEL amplification process
downstream the corrector. The radiation energy is measured by means of a radiation detector installed 18.5 m
downstream the undulator. When the FEL interaction issuppressed along the whole undulator length, the detector
shows the level of spontaneous emission collected from thefull undulator length into the detector aperture. Then FEL
interaction is to be switched on gradually along the undulator and the energy in the radiation pulse is recorded. Contribution of spontaneous emission depends on the angular
acceptance of the detector. In our simulations we used 10
and 5 mm diameter aperture for 30 and 6 nm wavelength,
respectively.
The energy in the radiation pulse fluctuates from shot toshot. The plots for standard deviation σ, are presented inFig. 3. At the initial stage fluctuations are defined mainlyby the fluctuations of the undulator radiation in the central cone. When the FEL amplification process takes place,fluctuations of the radiation energy are mainly given by thefundamental statistical fluctuations of the SASE FEL radiation [12]. A sharp drop of the fluctuations in the last partof the undulator is a clear physical confirmation of the saturation process. When the FEL amplifier operates in thehigh-gain linear regime, the value of parameter M = 1/σ 2
gives the number of spikes (wave packets) in the radiation pulse. This allows one to estimate the radiation pulse
length as τrad  M Lc /c. The cooperation length is about
Lc  2λLg /λu . The value of the power gain length Lg
can be measured experimentally from the gain curve (seeTHPOS66

Table 1: Expected parameters of the TTF FEL, Phase 2(femtosecond mode of operation)
Unitsbeam energy
bunch charge
peak current
normalized emittancebunch spacing# of bunches in a train
repetition rate
undulator period
undulator peak fieldaveraged beta-function
undulator length
radiation wavelength
power gain length
saturation length
radiation pulse energy
radiation pulse duration
radiation peak powerradiation average power
spectrum widthradiation spot size
angular divergence

MeV
nC
kA
µm
µs
#
#
cm
T
m
m
nm
m
m
µJ
fs
GW
W
%
µm
µrad

30 nm
option450

6 nm
option1000
0.5-1
1.3-2.2
1.5-3.5
1.6-3.5
up to 1800
up to 10 Hz
2.73
0.47 T
4.5
27
30
6
0.7-0.9
1.1-1.6
18-22
22-32
50-15015-50
2-4
up to 2 W
0.8
0.4-0.6
180-270 120-180
70-80
25-35

Fig. 3). Such an experimental technique has been provento be very useful during operation of TTF FEL, Phase I[1, 2, 3].
Properties of the radiation at 30 nm wavelength are expected to be similar to those obtained at TTF1 [1, 2, 3].
Number of modes in the radiation pulse is expected to be
M = 3 . . . 6 depending on the tuning of the driving beam.
As it was demonstrated at TTF FEL Phase I, we predict
some suppression (down to 40%) of the fluctuations of theradiation energy after a narrow band monochromator [13].
Radiation properties are expected to be distorted by the energy chirp along the lasing part of the electron bunch. First,
this is widening of the radiation spectrum. Second, spatial
distortion of the beam radiation mode takes place. This isreflected by the angular distribution of the radiation intensity in the far zone – appearance of the tails at large angles.

SUMMARY
Conclusion of our study is optimistic: femtosecond
mode of operation will allow overlapping complete operating wavelength range of the TTF FEL. Minimum wavelength will be mainly limited by the available energy of theelectron beam. Starting of operation at 30 nm wavelength
seems to be a reliable way to get success for the first lasing.
The next milestone for the TTF FEL would be the operation at the wavelength around 12 nm (linac energy about
700 MeV) that can be done without installation of additional hardware. With the third harmonic of the radiation

215

2

10

2

5

10

1

10

1

4

10

0

10

0

10

-2

10

-3

5

10

15

20

25

10

-1

10

-2

10

-3

10

30

20

10

10

20

0

25

5

10

z [m]

15

20

25

4

300

320

0.4

0.0

340

100

200

300

2x10

5

1x10

5

0

z = 18 m

z = 18 m

λ = 30 nm

0.8
I(θ)/I(0)Spectrum [a.u.]

3x10

5

400

r [µm]

λ = 30 nm-10∆ω / ω [%]

1

50

100

8x10

5

6x10

5

150

1.0

z = 22 mz = 22 m

4x10

5

2x10

5

0
-1.0

200

r [µm]

λ = 6 nm

λ = 6 nm

0.8
0.6
0.4
0.2

-0.5

0.0

0.0

0.5

0

10

20

30

40

50

θ [µrad]Figure 5: Summary of the radiation properties of TTF FEL
operating in the nonlinear regime at the undulator length of
22 m. Bunch charge is 0.5 nC (see Fig. 2). Radiation wavelength is 6 nm. Left column: temporal and spectral structure of the radiation pulse. Three single shots are shownwith different line shapes (solid, dashed, and dotted). Greyline shows profile of the bunch current. Right column: averaged distribution of the radiation intensity in the near andfar zone.

[3] M. Dohlus et
A530(2004)217.

al.,

Nucl.

Instrum.

andMethods[4] H. Wabnitz et al., Nature 420(2002)482.
[6] The TTF FEL team, “SASE FEL at the TESLA Test Facility,
Phase 2”, TESLA-FEL-2002-01, June 2002.

0.4

0.0

0

[5] L. Juha et al., Nucl. Instrum. and Methods A507(2003)577.

0.6

0.2

-2

0.0

320

[2] V. Ayvazyan et al., Eur. Phys. J. D20(2002)149.
0

1.0
5

310

[1] V. Ayvazyan et al., Phys. Rev. Lett. 88(2002)104802.

t [fs]

4x10

300

REFERENCES

0.6

0.2

280

290

z = 18 m

2

260

280

λ = 30 nm

0.8

I(r)/I(0)P [GW]

1.0

λ = 30 nm

0270∆ω / ω [%]Figure 3: Top: energy in the radiation pulse versus undulator length. Bottom: fluctuations of the energy in theradiation pulse versus undulator length. Left column corresponds to the case of bunch charge 0.5 nC (see Fig. 2).
Right column corresponds to the case of bunch charge
1 nC. Solid and dashed lines refer to the radiation wavelength 30 nm and 6 nm, respectively.

z = 18 m

0.4

t [fs]

z [m]

6

0.6

0.2

0

25

30

20

15

20

Spectrum [a.u.]

40

σ [%]

σ [%]

50

40

10

15
z [m]

50

5

3

1
5

z = 22 m

λ = 6 nm

0.8

2

z [m]

0

λ = 6 nmI(r)/I(0)-11.0z = 22 mI(θ)/I(0)10P [GW]

10

Erad [µJ]Erad [µJ]

E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 212-215

0

50

100

150

θ [µrad]Figure 4: Summary of the radiation properties of TTF FEL
operating in the nonlinear regime at the undulator lengthof 18 m. Bunch charge is 0.5 nC (see Fig. 2). Radiation
wavelength is 30 nm. Left column: temporal and spectral structure of the radiation pulse. Three single shots areshown with different line shapes (solid, dashed, and dotted). Grey line shows profile of the bunch current. Rightcolumn: averaged distribution of the radiation intensity inthe near and far zone.

it would be possible to reach the “water window” with thepulse duration on a 10 fs scale. This will greatly extend
possibilities for user experiments. In principle, saturation
at 6 nm can be achieved with five undulator segments. Replacement of the last segment with frequency doubler [14]will allow reaching 3 nm wavelength with GW level of output power.

[7] K. Flöttmann, Astra User Manual,
http://www.desy.de/~mpyflo/Astra dokumentation/.
[8] M. Borland, “elegant: A flexible SDDS-Compilant Codefor Accelerator Simulation”, APS LS-287, September 2000.
[9] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A429(1999)233.
[10] TTF2. Operation without 3.9 GHz cavity: Case 0.5 nC, 4 pssigma, magnetic compression,
http://www.desy.de/s2e-simu.
[11] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, “Expected properties of the radiation from VUV-FEL at DESY
(femtosecond mode of operation)”, DESY report TESLAFEL-2004-06, July 2004.
[12] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, The
Physics of Free Electron Lasers, Springer-Verlag, Berlin,
1999.
[13] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A507(2003)101.
[14] J. Feldhaus et al.,A528(2004)471.

Nucl. Instrum. and Methods

Single-Pass FELs

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G.P. Gallerano et al. / Proceedings of the 2004 FEL Conference, 216-221

OVERVIEW OF TERAHERTZ RADIATION SOURCES
G.P. Gallerano, ENEA, UTS Advanced Physics Technologies, P.O. Box 65, 00044 Frascati – Italy
S. Biedron, Argonne National Laboratory, Energy Systems Division, 9700 South Cass Avenue,
Argonne, Illinois 60439 USA
Abstract
Although terahertz (THz) radiation was first observed
about hundred years ago, the corresponding portion of theelectromagnetic spectrum has been for long time
considered a rather poorly explored region at theboundary between the microwaves and the infrared. Thissituation has changed during the past ten years with therapid development of coherent THz sources, such as solidstate oscillators, quantum cascade lasers, optically
pumped solid state devices and novel free electron
devices, which have in turn stimulated a wide variety of
applications from material science to telecommunications,from biology to biomedicine. For a comprehensive review
of THz technology the reader is addressed to a recent
paper by P. Siegel [1]. In this paper we focus on thedevelopment and perspectives of THz radiation sources.

average power level achievable in the region around 400
GHz is typically in the range 0.1 to 1 mW. Due to theircompactness, the range of application of these sources is
rapidly growing. A 200 GHz Gunn diode is being used asa source in a low cost imaging system under development
at RPI-Troy for security applications [3].

INTRODUCTION
Throughout this paper we will use a definition of theTHz region that extends over two decades in frequency,
covering the spectral range from 100 GHz to 10 THz.
This should allow a better understanding of the effort in
the extension of microwave electronics towards highfrequencies on one side and the development of photonic
devices from the optical region towards low frequencies.
According to this scheme, we will first cover the state of
the art of solid state oscillators and then move to gas andQuantum Cascade Lasers (QCL), which lie at the low andhigh frequency boundary of the THz region respectively.
A brief review of laser driven THz emitters will bepresented, which are the most widely used sources of THz
radiation. We will also briefly discuss the physicalprinciples of the generation of THz radiation from freeelectrons, describing the mechanism of Coherent
Spontaneous Emission and the development of table-top
Free Electron Laser (FEL) sources.

SOLID STATE OSCILLATORSElectronic solid state sources, like oscillators andamplifiers, are generally limited in frequency due to thetransit time of carriers through semiconductor junctions,which causes high frequency roll-off. High frequency
Gunn, IMPATT and TUNNET diodes are being developed
by several research groups [2]. They are rugged andcompact devices and can operate CW at room temperature
with a relatively narrow linewidth (10−6). A CW power ofabout 100 mW can be obtained around 100 GHz. The
output power falls off as 1/f2 and then as 1/f3 as thefrequency increases (see Fig. 1). Frequency multiplierswith two or more diodes are generally employed to reachfrequencies above 200 GHz, up to about 1 THz. The

FRBIS02

Fig. 1: State of the art results from GaAs and InP Gunn
devices. Numbers next to the symbols denote dc to RF
conversion efficiencies in percent (courtesy of H. Eisele,
University of Leeds, UK).

GAS AND QUANTUM CASCADE LASERS
The Far Infrared (FIR) gas laser and the quantum
cascade laser (QCL) are respectively the oldest and thenewest coherent source developed in the THz region. Gas
lasers date back to the sixties [4]. They are optically
pumped lasers, which use a CO2 laser to excite the rotovibrational levels of gas molecules at pressures in thembar range. The most widely used gas is methanol, which
provides a powerful (typically 100 mW) emission line at
118 µm. Gas lasers are line-tunable in the range 0.3 to 5
THz (1000 to 60 µm) although with limited power and arecommercially available by several companies, among
which Coherent Inc. and Edinburgh Inst. The technologyof FIR lasers has seen modest development in recent
years, as it has been the case of most gas lasers. However
they still are ideal sources for specific applications in

Available online at http://www.JACoW.org

G.P. Gallerano et al. / Proceedings of the 2004 FEL Conference, 216-221

which continuous tunability is not a must, like for
instance heterodyne spectroscopy and plasma diagnostics.
QCLs, the most recently invented optical lasers [5],have seen an impressive development in the THz region
during the past two years. In a Quantum Cascade Laser,
electrons are injected into the periodic structure of asuperlattice under electrical bias. They undergointersubband transitions with THz photon emission
excited by resonant tunneling through the multiple wells.
As a result a cascade process occurs, which gives name tothe source.
The first QCL to operate in the THz region wasdeveloped by a joint collaboration between NEST-Pisa
and the Cavendish Laboratory, Cambridge. It emitted at
4.4 THz providing about 2 mW of average power with
10% duty cycle at an operating temperature of 50 K [6].
Starting from this result, a great effort has been
undertaken by several research groups worldwide (NESTPisa, Cavendish-Cambridge, MIT, Sandia, Neuchatel
University), which has led to the record operating
temperature of 137 K pulsed and 93 K CW achieved at
MIT [7]. The group at MIT also holds the record of thelongest wavelength (~141 µm, 2.1 THz) QCL to date
without using magnetic fields [8], while the group at
Neuchatel has recently reported an average output power
approaching 50 mW [9]. 2.5 THz low threshold CW
operation has been obtained at NEST-Pisa [9]. Recent
progress in the QCL field also includes the developmentof THz QCLs using metal-semiconductor-metal
waveguides for mode confinement. This method will beadvantageous or even crucial as longer wavelengths areapproached.
Among the solid state lasers, we also recall the p-type
Ge laser [10], which can be tuned between 1 and 4 THz,but requires low temperature operation (20 K) and a large(1 T) applied magnetic field.

LASER DRIVEN THz EMITTERS
Today’s most widely used sources of pulsed THz
radiation are laser driven THz emitters based on
frequency down-conversion from the optical region. Twomain techniques have been developed to produce THz
radiation. The first one is based on a short pulse(femtosecond) Ti:Sapphire laser [11, 12], which
illuminates the gap between closely spaced electrodes ona photoconductor (e.g., silicon-on-sapphire or GaAs)
generating carriers, which are then accelerated by anapplied bias field (100 V). The resulting current transient,which is generally coupled to an RF antenna through astripline, radiates in a wide band at THz frequencies
corresponding to the Fourier transform of the laser pulse
time profile. The upper limit in frequency for thesedevices is given by the carrier recombination time in thesemiconductor and by the bandwidth of the stripline.
A similar terahertz spectrum can be obtained byapplying a sub-picosecond laser pulse to a crystal with alarge second-order susceptibility like ZnTe [13]. Due tothe nonlinear response of the crystal, photomixing occurs,
producing a time-varying polarization which in turn gives

217

rise to THz emission. In this case higher frequencies canbe reached due to the fast response of the crystal and to
the absence of any stripline or conductor. Both techniques
and the related electro-optical detection are at the basis of
most THz imaging systems [13, 14].
Laser driven solid state emitters also include CW
photomixers, in which offset-frequency locked CW lasers
are focused onto a photoconductor under bias. The laser
induced photocurrent is modulated at the laser difference
frequency and is coupled to an antenna, which emits THz
radiation [15]. In this case a narrow band continuous
wave emission is obtained, which can be tuned over afairly wide range by shifting the optical frequency of oneof the two drive lasers.
The typical frequency range covered by laser driven
solid state emitters is 0.2 to 2 THz or higher depending on
the laser pulse parameters. Average power levels range
from nanowatts to hundred microwatts and pulse energies
are typically in the femtojoule to nanojoule range.

FREE ELECTRON BASED SOURCES
Free electron based sources like Klystrons, Travelling
Wave Tubes (TWT), Backward Wave Oscillators (BWO)
and Gyrotrons have been extensively studied since themid of the past century to approach the high frequency
part of the microwave region. With the exception of
Gyrotrons, which are generally designed to reach highaverage power and deserve a review on their own [16],the above free electron sources suffer from simple
physical scaling problems, metallic wall losses and theneed for high magnetic and electric fields, as well as highelectron current densities as the frequency is increased.
For this reason, TWTs have received little attention as
candidate sources of radiation above 100 GHz.
The BWO [17] is a slow wave device where theelectrons spiralize through a corrugated structure in anaxial magnetic field interacting with the first spatial
harmonic of the backward wave. Indeed, in this region of
the dispersion relation, the phase velocity of the wave ispositive and the group velocity is negative. BWOs aretable top devices that can operate in the THz region atmoderate power levels (1 – 100 mW). The technology of
BWOs has been mostly developed in Russia and they are
now commercially available through companies in the US
and Europe. BWOs operate with an accelerating potential
in the range 1 to 10 kV and axial magnetic field of about
1 T. They can be tuned over tens of GHz by varying theaccelerating potential. A number of different BWOs canbe implemented in an integrated system to cover
altogether a wide frequency range extending from 30
GHz to 1.2 THz (see Fig. 2).
To overcome the necessity of reducing the physical sizeof the source components as the frequency is increased,different schemes have been developed to let the electrons
exchange momentum and allow photon emission. The
most frequently used one is the magnetic undulator
originally proposed by Motz [18], which was employedby Phillips in the Ubitron [19] back in 1960 to generate
mm-wave radiation and which led to the realization of the

FEL Oscillators

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G.P. Gallerano et al. / Proceedings of the 2004 FEL Conference, 216-221

5λ (mm)

20ν (GHz)

1
200

0.7

0.5

0.4

400

600

800

QS500

QS400

0.3

0.25

1000

1200

0.2
1400

Detected BWO output power (mW)QS6QS4 QS2
QS3100

QS1500
QS1000
QS700

10

QS350

QS260
QS300

QS200

1
0.1
0.01
Water vapor
absorption lines

0

10

20

30

40

50

-1

Frequency (cm )Fig. 2: Output power and spectral distribution of BWO devices employed in a CW spectroscopic system at the 1st
Physics Institute of the University of Stuttgart. (Courtesy of M. Dressel, University of Stuttgart)
first Free Electron Laser (FEL) in 1977 [20]. Other freeelectron devices are the Cerenkov FEL, based on theinteraction with a dielectric loaded waveguide [21], andthe Metal Grating FEL, based on the Smith-Purcell effect[22].

Coherent spontaneous emission
In his pioneering work on the undulator radiation [18],Motz pointed out that in a uniform electron beam thecontributions of individual electrons to the radiation field
are random in phase, and therefore the square of the total
field equals the sum of the squares of the individual
fields. If the electrons were bunched within a distancecomparable to the wavelength of the radiation, their fields
would add up in phase, resulting in the emission ofcoherent radiation with a power level several orders ofmagnitude higher than the non-coherent radiation
generated by a uniform beam. The idea of generating
coherent radiation in the THz region utilizing bunchedelectron beams, such as those produced by radiofrequency (RF) accelerators, was indicated in [18], anddifferent coupling structures, designed to extract energy ata harmonic of the bunch repetition rate, were investigated[23]. More recently the coherent spontaneous emission
from an RF-modulated electron beam at wavelengths
comparable to the electron bunch length has been theobject of renewed interest because of its relevance in thegeneration of short pulses of coherent THz radiation [24,FRBIS0225, 26]. Issues like the dependence of the emitted
radiation on the bunch shape [27] and the observation ofemission at discrete frequencies, which are harmonics ofthe fundamental RF [28], have also been addressed boththeoretically and experimentally and have led to therealization of compact FELs in the THz region [29, 30].

FEL Facilities and THz Synchrotron Sources
Historically, the first Free Electron Laser facility toprovide THz radiation to users has been the UCSB-FEL,
which is driven by an electrostatic accelerator andoperates in a quasi-CW mode. It provides tunableterahertz radiation in the region from 120 GHz to 4.8 THz(2.5 mm - 60 µm) with an output power in the range from
500 W to 5 kW and a pulse duration of 1 – 20 µs at 1 Hz
repetition rate [31]. Several facilities have been built to
operate in the infrared region and most of them can reachor plan to extend into the THz region. Besides the UCSBFEL, we recall here the Israeli EAFEL (100 GHz), basedon a 6MeV EN-Tandem Van der Graaff accelerator [32],the Stanford FEL (15 – 80 µm) [33], FELIX (3 – 250 µm)
with its planned FELICE extension for intracavity
experiments at FOM-Nieuwegein [34], CLIO at LUREOrsay, which has plans for a new hybrid resonator toreach wavelengths in the range 100 – 300µm [35], ELBE,
which has recently lased at 20 µm and has plans to extend
its operation to 150 µm [36], and the THz-FEL at
Novosibirsk, based on a CW energy recirculated linac

G.P. Gallerano et al. / Proceedings of the 2004 FEL Conference, 216-221(ERL) and providing about 100 W in the spectral range
120 – 180 µm [37].
The principle of coherent spontaneous emission is also
exploited to generate THz radiation from bending
magnets at FEL facilities and Synchrotron facilities.
About 100 W of CW radiation have been produced frombending magnets in the band from 0.1 to 3 THz at JLAB
[38]. The JLAB ERL accelerator overcomes some of thelimitations of conventional linacs and storage rings. It
produces 500 fs, 135 pC electron bunches at a very highrepetition rate (75 MHz) by using superconducting RF
cavities and recovering the energy of the spent electron
beam. Coherent THz emission from a linac driven beam
has been demonstrated at Brookhaven National Lab (seebelow). Coherent synchrotron radiation has also been
observed in storage rings [39, 40, 41, 42]. A coherent THz
beam line is operating at BESSY-Berlin and several
others are planned at Lawrence Berkeley National Lab(CIRCE), Cornell University, and Daresbury (4GLS).

Compact FELs and Table Top Free Electron
radiators
There also exist accelerator-based THz sources, which
can fit on or scale to the size of a table-top. They are
proof-of-principle experiments and should be looked
upon as ideas that can be specified and tailored forparticular types of experiments. Development work onelectron beam based sources is under way at several sites.
The RF-gun derived sources described below will benefit
from ongoing design work, especially if electron guns canbe made superconducting. Laser wake-field accelerators
are actively being researched as possible alternative
solutions for high energy systems and are still in the earlystages of development. Some of these sources could bedesigned to produce half-cycle pulses of THz radiation.
In a table-top free electron radiator based on an RF
modulated electron beam with short bunches, themodulator, klystron, waveguide, cooling, magnets,
electron gun, accelerating structure, and all otherperipheral accelerator components could easily be fitted
into the space of 3 cubic meters. The FEL-CATS source at
ENEA-Frascati [43] and the source under development at
ANL [44] are examples of this compactness. Further
engineering work and improved design in the X-ray
shielding of the accelerator will also increase thecompactness of these systems.
The coherent prototype radiator at Argonne National
Laboratory (ANL) employs three different cathode types– thermoionic, photo-gated thermoionic, or photocathode.
Even at a low RF repetition rate, as well as normal
conducting, relatively high average powers are achievable
if a laser gates the thermoionic cathode. The electron
beam pulse length changes depending upon the cathodemode of operation and the degree of compression.
Although this source is a prototype, it can be easily
adapted to a specific experiment and packaged into asmall space. The repetition rate, pulse width, average andpeak power can be improved significantly.

219

At ENEA-Frascati the recently built source FEL-CATS
utilizes a high-efficiency generation scheme based on themechanism of coherent spontaneous emission, whichallows operation in the frequency range between 70 GHz
and 0.7 THz. Tunable operation has been obtained in the
spectral region between 0.4 and 0.7 THz with a relative
linewidth of about 10% FWHM [45]. The radiation has apulsed structure composed of wave-packets in the 3 to 10
ps range, spaced at a repetition frequency of 3 GHz. A 5
microsecond long train of such pulses (macropulse) is
generated and repeated at a rate of few Hz. The measured
power in the macropulse is 1.5 kW at 0.4 THz.
The principle of operation of the source is based on thecoherent spontaneous emission from short bunches ofrelativistic electrons. The FEL source utilizes a 2.5 MeV
RF linac to generate the electron beam, which is injected
into a linearly polarized magnetic undulator composed of
16 periods, each 2.5 cm long with a peak magnetic fieldof 6000 Gauss. A second RF structure, called Phase
Matching Device (PMD), is inserted between the linac
and the undulator and is controlled in phase andamplitude to correlate the electron distribution in energy
as a function of time in the bunch [46]. In this way thecontributions to the total radiated field by individual
electrons in the bunch are added in phase, leading to amanifold enhancement of the coherent emission.
In the frame of a collaboration between University of
Maryland and the Brookhaven National Laboratory(Source Development Laboratory) a proof of principle
experiment based on the modulation induced on anelectron bunch has been recently carried out [47]. This
device uses a laser to generate a bunch train of electrons
through photoemission. Each bunch is about a picosecond
long, and they are separated by about a picosecond. Anelectron accelerator takes these short bunches andaccelerates them up to 70 – 72 MeV. At this point thebeam is intercepted by a mirror. When the environment
around the beam changes from vacuum to metal,transition radiation is emitted. Because of the way theelectrons are bunched, there is strong emission in theterahertz frequency range. The frequency spectrum can becontrolled by controlling the way the electrons are
initially bunched. The result is a tunable terahertz sourcethat could be used for a wide variety of additional
experiments.
At the Source Development Laboratory, Brookhaven
National Laboratory, a linac-based source of coherent
THz pulses has been developed. In this device electron
bunches are compressed to ~300 fs rms. The degree ofcompression can be varied with the perspective of
reaching 100 fs and possibly shorter pulse duration.
Electron bunches produce single-cycle coherent THz astransition radiation or dipole radiation. An energy perpulse of ~100 µJ and peak electric field up to > 1 MV/cm
has been demonstrated [48]. The method could be
improved to produce shorter electron bunches and abroader spectral range. A pulsed laser driving the linac
photocathode provides synchronized IR pulses forelectro-optic coherent detection of THz pulses.

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G.P. Gallerano et al. / Proceedings of the 2004 FEL Conference, 216-221

Advanced Energy Systems (AES) has plans to develop
a multi-watt (50 – 100 W eventual goal; 5 W in this initial
prototype), tunable, compact THz source.
Intense THz radiation from ultra-short electron bunches
has been generated by a laser wakefield-based linac at
Lawrence Berkeley Laboratory. This source is based on
the production of ultra-short (< 50 fs rms), high charge(0.3 – 5 nC) relativistic electron bunches by using a laser
excited plasma wave with large enough amplitude to trap
background electrons and accelerate them in mm distanceto 10’s of MeV. As the electrons exit the plasma, a burstof transition radiation is produced. The source
performance is controlled by the electron bunchproperties and the density and transverse size of theplasma at the exit boundary. The THz radiation is
intrinsically synchronized with an external laser andexperiments are underway to measure the THz pulse
structure with electro-optic sampling. Time averaged
spectra have been measured and show that the spectrumwith the present configuration is centered around 2 THz.
Whereas presently energy levels on the order of 0.1µJ/pulse have been collected, modeling indicates thatsignificantly higher power can be achieved by optimizing
the plasma properties (transverse size and longitudinal
profile) and could be as high as 100 µJ/pulse [49]. Further
progress on the laser driven accelerator performance isunderway, including the production of quasimonochromatic (few % energy spread) relativistic
electron bunches (100 MeV), which will lead to intenseradiation emission from conventional transition radiation
foils.

MICROFABRICATED SOURCES
A challenge for the future is the further reduction insize of compact FELs. A Smith-Purcell emitter using a
CW electron microscope gun as electron source has beendeveloped at Vermont Photonics [50], providing CW
power levels up to 10 microwatts at wavelengths in therange from 200 to 900 µm with an output bandwidth ofabout 1 to 2 cm−1. This source is devoted to research
applications like THz absorption spectroscopy, THz
pump/probe experiments in biology and nanotechnology,
test of bolometric arrays for THz astronomy, test of THz
imaging concepts. New developments are in progresswith corporate partners to provide output power in themW range and to extend the tuning range from 100 to1500 µm. Experiments and proposals are also in progress
at Chicago University [51] and Vanderbilt University,where a 45 – 65 kV gun equipped with a laser driven
needle cathode is being assembled to drive a miniaturized
Smith-Purcell emitter with a 200 µm period grating [52].
The device is designed to operate in the range 0.3 – 0.7
THz.
The possibility of using “Computer Controlled 3-D
Electron-beam Induced Deposition and Etching” torealize microfabricated Smith-Purcell emitters has been
investigated at NawoTech (Germany) [53].

FRBIS02

CalCreek Research (CCR) is developing miniaturized,
efficient traveling wave tube (TWT) amplifiers
incorporating micro-electro-mechanical systems (MEMS)
fabrication techniques [54]. The MEMS based TWT isdesigned to provide 10 W of RF power at 83.5 GHz with
5 GHz bandwidth for communication applications in
micro-satellites.

CONCLUSIONS
The development of a variety of THz sources has been
gradually filling the THz gap in recent years, providing
complementary characteristics in terms of frequency ofoperation, average and peak power.
Large scale FEL facilities are capable of providing highpower CW THz radiation while low-cost solid stateoscillators and QCLs are expected to drive the realizationof THz systems for a variety of applications in the near
future.
It has been shown that low-cost small size FELs canalso be built in the THz region. Their peculiar feature isthe capability of providing high peak power in the kW
range with peak electric field in the range 104 – 106 V/cm,
which is crucial for the investigation of non-linear
phenomena. The generation of ultra-short electron pulses(50 – 100 fs) will significantly increase the available
bandwidth of free electron THz radiators, andimprovements in RF-gun technology will make a tabletop high power CW source a possibility in the near future.

ACKNOWLEDGEMENTS
We gratefully acknowledge the contribution of allcolleagues at our home institutions and from various
laboratories worldwide, who have provided precious
information on the different THz sources.

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M.D. Shinn et al. / Proceedings of the 2004 FEL Conference, 222-225

HIGH AVERAGE POWER OPERATION OF A SCRAPER-OUTCOUPLED
FREE- ELECTRON LASER
M. Shinn*, C. Behre, S. Benson, M. Bevins, D. Bullard, J. Coleman, L. Dillon-Townes, T. Elliott,
J. Gubeli, D. Hardy, K. Jordan, R. Lassiter, G. Neil, S. Zhang
TJNAF, Newport News, VA 23606
Abstract
We describe the design, construction, and operation of ahigh average power free-electron laser using scraper
outcoupling. Using the FEL in this all-reflective
configuration, we achieved approximately 2 kW of stable
output at 10 um. Measurements of gain, loss, and output
mode will be compared with our models.

INTRODUCTION
Compared to other high average power laser systems,
an advantage of a free-electron laser (FEL) is there are noheat dissipation issues within the gain medium. However,when operated in an oscillator configuration, one must
mitigate and manage the effects of absorbed photons andthe resultant thermally induced distortion of the otherwise
spherical mirror surface. Previous analysis [1] andexperiment [2] have shown that this distortion, whensufficiently large, causes the output to saturate. The
obvious solution, to obtain low loss coatings andsubstrates, isn’t always possible at certain wavelength
ranges. For example, at 10.6 µm, the best outcoupler(OC) designs still have absorption levels in excess of
0.1% [3], which limits the extracted power to less than 10
kW [4]. In other wavelength regions such as the deep UV(< 150 nm) suitable substrates for outcoupling the output
don’t exist.
In these cases, some other scheme for outcoupling thelaser radiation from the resonator must be used. In FELs,
hole outcoupling is traditional [5], but is not particularly
efficient. For many high average power lasers it iscustomary to use a scraper mirror intracavity, i.e., anannular mirror were some fraction of the center of thelaser mode is transmitted, and the wings of the mode arereflected out of the cavity. [6] Usually scraper
outcoupling is used in positive branch unstable resonators,
where the gain is very high and the outcoupling fraction
may be large, e.g., > 30%. The gain in the majority of
FELs is not so high, and the wiggler in the FEL requires anegative branch unstable resonator, which adds its own
complications. We chose to use our existing nearconcentric resonator and place the scraper mirror close to
one of the end mirrors. Only one theoretical paper [7] hasbeen published on the use of an annular scraper, but to ourknowledge there are no experimental results. Therefore,
we analyzed this cavity configuration to confirm that wewould get efficient and stable output. Finding that it was
stable, we then proceeded to build and test it.

DESIGN AND IMPLEMENTATIONThe optical cavity configuration we modeled is shownin Fig, 1, and the resonator parameters are shown in Table
1. We chose to operate at ~ 10 µm, as we had beencommissioning the IR Upgrade FEL at this wavelength
using a conventional, transmissive outcoupling opticalcavity, and had mirrors readily available.
HR

HR
Wiggler

Scraper

Figure 1 Schematic layout of the FEL optical cavity withan annular scraper.
The solid arrows denote theoutcoupled beam, the dashed arrows denote the diffracted
beam that strikes the rear of the scraper.
Table 1 FEL resonator parameters
Parameter

Value

Cavity length

32.042 m

Rayleigh range

3m

Mirror radius of curvature

16.6 mScraper position

15.4 mScraper outcoupling

10%

Given the single pass gain of our optical klystron was ~30%, and the extraction efficiency is highest when theoutcoupling fraction is ~ 1/3 the gain [8], we designed thescraper to intercept 10% of the optical mode. This wasdone using the following analytical expressions [6]:The power transmitted for a gaussian beam of 1/e2
radius ω through a circular aperture of radius a is givenby: − 2a 2 (1)Ptrans = 1 − exp ω2 
In our case, we want Ptrans = 0.9, so a = 1.07ω.
At the position of the scraper (z=15.4m), the mode size isgiven by:*shinn@jlab.org

TUBOS03

Available online at http://www.JACoW.org

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M.D. Shinn et al. / Proceedings of the 2004 FEL Conference, 222-225

Item

Parameter

Material:

Cu

Diameter:

3.500 in (+ 0 in, - 0.005 in)Edge thickness:

0.500 in (+0 in, - 0.005 in)Mirror figure:10λ @ 632.8 nm

Surface roughness:≤ 1 µm rms

Actuation of the scraper was on a modified “ultraviewer”;
a linear insertion device that repeatedly maintainsalignment of the pitch and yaw axes to better than 50µrad. The outcoupled beam was in the horizontal plane,
and intercepted into a diagnostic beam dump (a power
meter with position sensing). Readout of the input andoutput temperatures is in our EPICS control system.
As mentioned earlier, as the mode traverses the scraper
there will be diffraction, which after reflection from theend mirror does not pass through the scraper aperture but
instead falls on the back of the scraper. Based on
simulations, this amounts to ~ 10% of the intracavity

power outcoupled by the scraper. This reflected laser lightpassed through an AR-coated viewport and was absorbed
by a Molectron PM5K power probe. This system had afaster response time than the diagnostic beam dump.

Figure 2 The scraper mirror. The mirror is moved in thevertical direction. At the bottom of the scraper is thecooling loop.
An IR camera imaged the surface. We could also use thisradiation to study the laser dynamics. When operating ina macropulsed mode we could insert a mirror before thepower probe and focus the light onto a Judson J15D12
cryogenically-cooled MCT detector.

RESULTS
Gain and loss measurements
Getting this system to lase was quite easy.
Inmacropulsed mode, the output from the MCT detector(Fig. 3) was used to optimize the system.
3

2.5

2

Intensity (au)

1

22
 
λz  
ω ( z) = ω 0 1 +(2)  πω 02    For our resonator configuration, ω0 = 0.003 m, and with λ= 10 µm, ω(z) = 1.66 cm. From the relationship between
a and ω, the radius of the hole in the scraper is. 1.78 cm.
This was the starting point for our simulations.
Simulations were carried out in both ZEMAX [9] andGLAD [10], with similar results. Given our interest in
determining the losses due to diffraction, we primarily
used GLAD.
Since we were most interested indetermining if the configuration was stable, we did thecalculations in a cold cavity, i.e., no gain. Rather than let
the power in the cavity decrease on each pass, we simply
reinitialized the power after each pass and let the modedevelop until the losses (and power) converged to a steadystate. These diffractive losses occur at two points, firstwhen the mode traverses the scraper, and then as it
approaches the wiggler vacuum chamber.
As the intracavity average power may be as high as
100 kW, the scraper should be thermally conductive andwater cooled. We chose copper for the substrate, with asimple loop of copper tube brazed to its periphery forcooling. (Fig. 2). To have high reflectivity, the scraper
was gold coated, using a RF magnetron deposition
process. As the wavelength is long, the surfaces did nothave to be polished to a high degree of flatness or
smoothness. Specifications are given in Table 2. The
polishing and coating were done in-house, and the opticalspecifications checked using a Wyko RTI4100 laserinterferometer and NT1100 noncontact profilometer. We
met or exceeded specifications; the mirror figure was 3
waves at 633 nm, and the roughness was 1 µm rms.
Table 2 Scraper specifications

1.5

1

0.5

0
-1.0E-04 -5.0E-05 0.0E+00 5.0E-05 1.0E-04 1.5E-04 2.0E-04 2.5E-04 3.0E-04 3.5E-04-0.5Time (sec)Figure 3 FEL output during a 250 µs macropulse.
We recorded the rise and decay of the macropulsed output
at higher resolution to determine the gain and loss. Thisis shown in Figs 4 and 5, respectively.
Analysis of the FEL output’s rise and fall allowed us todetermine the gain and loss/pass. These values are 16%
and 8%, respectively. The error bar on the measurements
is +/- 1%.
The lower than calculated gain was
unanticipated, since we had measured higher gain at thisFEL Oscillators

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M.D. Shinn et al. / Proceedings of the 2004 FEL Conference, 222-225

wavelength when operating the resonator with atransmissive outcoupler. We believe this was due to theaccelerator setup.

Intensity (au)10-1.50E-05-1.00E-05-5.00E-06

1
0.00E+00

5.00E-06

1.00E-05

0.1

Figure 6 IR image of light reflecting from the rear of thescraper onto a power probe.

0.01

Time (sec)Figure 4 FEL start up

High average power operation
When operating at high average power, we foundthe power probe and IR camera was beneficial in
optimizing the total output. Fig. 6 shows an image fromthe IR camera viewing the power probe.

pitch as the mirrors absorbed power, and the cavity length
would drift, first shorter, then longer. This madeoptimization problematic, and usually the cause of thelaser shutting off was the cavity length. Once thelaser was off, the mirrors would cool off and drift in the
opposite direction. Fortunately, we were able to track thisdrift and could get the cavity realigned quickly.

Intensity (a.u.)

10-1,00E-05

1
0,00E+00

1,00E-05

2,00E-05

3,00E-05

4,00E-05

0,1

Figure 5 FEL decay

Figure 7 Power trends. The purple trace is the outcoupledlight from the scraper. The yellow trace is the powerfrom the diffracted light off the rear of the scraper (0200W scale).

When operating at high average power, we found thepower probe and IR camera was beneficial in optimizing
the total output. Fig. 6 shows an image from the IR
camera viewing the power probe.
So long as the image remained circular, the mirrors were
well aligned and we had the highest output power - asmeasured on both the diagnostic dump and the diffracted
light power probe. The highest power measured was~1750 W, as inferred by measuring 139 W with the fast
power probe, and using an experimentally determinedratio between the diffracted to outcoupled light of 1:12.5.
A typical power trend is shown in Fig. 7. Once we wereabove 1 kW average power, note that each push up in
power was rather short, only a few minutes in length.
What was occurring was that both cavity mirrors would

Why was this occurring? Subsequent to testing the
scraper outcoupler, we added IR viewports and camerasthat enabled us to image the interior of the optical cavity
mirror vacuum vessels. What we found was that scattered
light was scattered into a wide enough cone that it fell on
the poorly cooled mirror fixturing hardware. These
components warmed up and as they expanded, theycaused the cavity length to grow longer. The more rapid
shortening of the cavity length was the result ofabsorption of laser light (and in the case of thedownstream mirror and its deforming assembly, THz andsecond harmonic light as well), that causes a thermalbump in the center of each mirror. The magnitude of thisbump (for each mirror) is of order 1 um, and develops in

0,01Time (sec)

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M.D. Shinn et al. / Proceedings of the 2004 FEL Conference, 222-225

the course of a few seconds, forcing us to initiallylengthen the cavity. There were other signs that the
scattered (and absorbed) light was excessive. We saw
pressure transients (as measured by the ion pumps) that
correlated with strong lasing. In addition, enoughscattered light was absorbed in a calcium fluoride vacuum
viewport situated just upstream of the wiggler (part of the
OCMMS hardware [11]) that it shattered. Clearly, better
control of scattered light needs to be in place. We aredesigning water-cooled absorbing shields that will beplaced before the mirror plane to minimize the heating
effects we saw. Treating the beam tube in the vicinity ofthe scraper, so it absorbs scattered light, is being
contemplated as well.
We can determine the amount of power absorbed bymeasuring the flow rate and temperature rise in the waterthat cools each cavity mirror. When lasing with a powerof 1500 W, the mirror upstream of the wiggler absorbed ~120 W, while the downstream mirror absorbed 310 W, thehighest value we have ever measured. We were able topartially compensate for the thermal bump by actively
deforming each mirror. Due to the high absorption (~1.7% of the intracavity power for the downstream mirror)
the uncompensated aberration lowered the lasing
efficiency to the point that we decided to pursue lasing ata shorter wavelength, where we had better mirrors. Muchlower loss 10 µm HR mirrors (absorption < 300 ppm) areavailable, and we are procuring them.
Table 3 Comparison between optical modeling andexperimental results
Model

Experiment

Loss/pass11%8%

Outcoupled/diffracted
power

10

12.5

CONCLUSIONS
We found that operation of a FEL in a scraperoutcoupled near-concentric cavity configuration lased
easily, and produced stable output. Experimentallyderived values for the loss and ratio of outcoupled todiffracted light were in good agreement (Table 3) with thevalues from our simulations. The outcoupling efficiencyof 92% is much higher than obtainable with a holeoutcoupler mirror.
We found that this cavity
configuration, using two high reflectors with backplane
cooling and active ROC control allowed us to outcouple ~1.75 kW. With a more conventional, edge-cooledtransmissive outcoupler with 0.4% loss, we could only
achieve 0.7 kW. If we had better mitigated the effects ofscattered light, and had lower loss coatings, we would
have easily achieved higher output powers. Clearly, thisdemonstration proves that the annular scraper outcoupler
can be used to produce high average power in wavelength
regions where substrate and/or coating absorption
precludes the use of a transmissive outcoupler.

ACKNOWLEDGEMENT
We thank the members of our review committee forsuggesting that we explore this cavity configuration
option. This work supported by the Office of Naval
Research, NAVSEA PMS-405, the Joint Technology
Office, the U.S. Night Vision Laboratory, theCommonwealth of Virginia, the Air Force ResearchLaboratory, and by DOE Contract DE-AC05-84ER40150.

REFERENCES[1] S.V. Benson et al. “Optical modeling of the Jefferson
Laboratory IR Demo FEL”, Nucl. Inst. and Meth.,
A407 401 (1998)[2] Stephen V. Benson, Joe Gubeli, and Michelle Shinn,“Mode Distortion Measurements on the Jefferson Lab
IR FEL” Nucl. Inst. and Meth. A483, 434 2002.
[3] D. Ristau et al, “Round-robin test on opticalabsorption at 10.6 µm” SPIE 2714 120 (1996).
[4] S.V. Benson, “What have we learned from thekilowatt IR-FEL at Jefferson Lab?“ Nucl. Inst. andMeth. A483 1 (2002).
[5] “Performance of Hole Coupling Resonator in the
Presence of Asymmetric Modes and FEL Gain”, M.
Xie and K.-J. Kim, Nucl. Inst. and Meth., A318
(1992) 877-884.
[6] A.E. Siegman, Lasers, University Science Books,
Mill Valley CA, 1986.
[7] R. Nagai, et al, “An optical resonator with insertablescraper output coupler for the JAERI far-infrared
free-electron laser”, Nucl. Inst. and Meth. A475 519(2001).
[8] G. Dattoli, L. Giannessi, and S. Cabrini, “Intensity
Saturation Mechanism in Free-Electron Lasers”,
IEEE J. Quantum Electron, 28(4) 770 (1992).
[9] Information on ZEMAX is available at
http://www.zemax.com/[10] In formation on GLAD is available at
http://www.aor.com/[11] M.D. Shinn, et al, “Design of the Jefferson Lab IR
Upgrade FEL optical cavity”, Nucl. Inst. And Meth.
A507 pp196-199 (2003).

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N.A. Vinokurov et al. / Proceedings of the 2004 FEL Conference, 226-228

STATUS OF THE NOVOSIBIRSK TERAHERTZ FEL*
V.P. Bolotin, N.A. Vinokurov#, D.A. Kayran, B.A. Knyazev, E.I. Kolobanov, V. V. Kotenkov,
V.V. Kubarev, G.N. Kulipanov, A.N. Matveenko, L.E. Medvedev, S.V. Miginsky, L.A. Mironenko,
A.D. Oreshkov, V.K. Ovchar, V.M. Popik, T.V. Salikova, S.S. Serednyakov, A.N. Skrinsky,
O.A. Shevchenko, M.A. Scheglov, Budker INP, Novosibirsk, Russia

Abstract
The first stage of Novosibirsk high power free electron
laser (FEL) was commissioned in 2003. It is based on thenormal conducting CW energy recovery linac. Now the
FEL provides electromagnetic radiation in the wavelength
range 120 - 180 micron. The average power is 200 W. The
minimum measured linewidth is 0.3%, which is close to
the Fourier-transform limit. The assembly of user
beamline is in progress. Plans of future developments are
discussed.

INTRODUCTION
A new source of terahertz radiation was commissioned
recently in Novosibirsk. [1]. It is CW FEL based on an
accelerator–recuperator, or an energy recovery linac(ERL). It differs from the earlier ERL-based FELs [2, 3]
in the low frequency non-superconducting RF cavities andlongerwavelength
operation
range.
Full-scale
Novosibirsk free electron laser is to be based on the fourorbit 50 MeV electron accelerator-recuperator (see Fig.
1). It is to generate radiation in the range from 3
micrometer to 0.2 mm [4, 5].
4
6

3

3

6

radiation in the FEL the beam passes once more throughthe accelerating structure, returning the power, and comesto the beam dump at the injection energy. Mainparameters of the accelerator are listed in Table 1.
Table 1: Accelerator parameters (first stage)
RF frequency, MHz
180
Number of RF cavities
16
Amplitude of accelerating voltage at one 0.7
cavity, MV
Injection energy, MeV
2Final electron energy, MeV
12
Maximum bunch repetition rate, MHz
22.5
Maximum average current, mA
20
Beam emitance, mm·mrad
2
Final electron energy spread, FWHM, % 0.2
Final electron bunch length, ns
0.1
Final peak electron current, A
10

The electron source is the 300 keV DC gun withgridded cathode. Recently we changed the cathode-grid
unit to the new one, and the charge per bunch increased to
1.5 nC.

FEL
2
1

5

Figure 1: Scheme of the accelerator-recuperator based
FEL. 1 - injector, 2 - accelerating RF structure, 3 - 180degree bends, 4 – undulator, 5 – beam dump, 6 – mirrorsof the optical resonator.

ACCELERATOR-RECUPERATOR
The first stage of the machine contains a full-scale RFsystem, but has only one orbit. Layout of the accelerator–
recuperator is shown in Fig. 2. The 2 MeV electron beamfrom an injector passes through the accelerating structure,acquiring the 12 MeV energy, and comes to the FEL,
installed in the straight section. After interaction withThe FEL is installed in a long straight section of asingle-orbit accelerator-recuperator. It consists of two
undulators, a magnetic buncher, two mirrors of the opticalresonator, and an outcoupling system. Bothelectromagnetic planar undulators are identical. The
length of an undulator is 4 m, period is 120 mm, the gap is
80 mm, and deflection parameter K is up to 1.2. One canuse one or both undulators with or without a magnetic
buncher. The buncher is simply a three-poleelectromagnetic wiggler. It is necessary to optimize therelative phasing of undulators and is used now at low
longitudinal dispersion Nd < 1.
Both laser resonator mirrors are identical, spherical, 15m curvature radius, made of the gold-plated copper, andwater-cooled. In the center of each mirror there is a hole.
It serves for mirror alignment (using the He-Ne laserbeam) and output of small amount of radiation. The
distance between mirrors is 26.6 m. The forward mirror______________________________________________*
Work supported by the Siberian Branch of Russian Academy of Science
under the integration grant #174.
*
vinokurov@inp.nsk.su

TUCOS01

Available online at http://www.JACoW.org

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N.A. Vinokurov et al. / Proceedings of the 2004 FEL Conference, 226-228

RF-Cavities

Bending Magnets
Undulators

Buncher

Quadrupoles

Mirrors

Solenoids

Outcoupler

Figure 2: Scheme of the first stage of the Novosibirsk high power FEL.

has the hole with the diameter 3.5 mm, and the rear one with the diameter 8 mm. The calculated transparency ofthe mirror with the 8-mm hole, at the wavelength 150
micron, is 1.5%. At this wavelength the measured roundtrip loss are near 7%. The output radiation pass throughtwo windows, which separated the FEL and accelerator
vacuum from the atmosphere. After the forward mirror
the additional iris and the normal-incidence quartz mirror
are installed. After the rear one there is a diamondwindow, tilted at the Brewster angle.
For FEL operation we used both undulators. Beamaverage current was typically 8 mA at the repetition rate
5.6 MHz, which is the round-trip frequency of the opticalresonator and 32-th subharmonics of the RF frequency
f0 ≈ 180 MHz.

RADIATION STUDY

100 kW. Therefore an electron efficiency is about 1%.
The typical radiation parameters are listed in Table 2.

Table 2: The radiation parameters
Wavelength, mm
0.12...0.18
Minimum relative linewidth, FWHM
0.003
Pulse length, FWHM, ns
0.05
Peak power, MW
0.6
Repetition rate, MHz
5.6
Average power, kW
0.2
To demonstrate the capabilities of our terahertz radiation
source we made a hole in a plexiglas (PMMA) cube (seeFig. 4). Using the short-focusing mirror the CW
breakdown in air was achieved (see Fig. 5).

The first measurements of radiation parameters werereported before [1].
Instead of the fine tuning of the optical resonator length
we tuned the RF frequency. The tuning curve is shown in
Fig. 3. The preliminary simulation results [6] demonstrate
a reasonable agreement with measured data.
1,0

Average power, a.u.

0,8Simulations
Experiment

0,6

0,4

Figure 4: The conic hole in the PMMA cube, done withthe terahertz radiation ablation. One division is 5 mm.

0,2

0,0
-5
-5
-5
-5
-6,0x10 -4,5x10 -3,0x10 -1,5x10

0,0

Detuning δf/f0
Figure 3: Dependence of the average power on the RF
frequency detuning.
The average radiation power, passed through the hole atthe rear mirror, was about 200 W. Taking into account the
7% loss, one get approximately 1 kW of power, extracted
from the electron beam. The electron beam power was

To transmit the radiation from the rear mirror hole touser stations, the beamline from the accelerator hall to theuser hall was built. It comprises of one spherical mirror
and 5 flat mirrors inside the stainless steel tubes. Now the
beamline is filled by nitrogen. It is separated from theaccelerator vacuum by the diamond window, and from theair by the polyethylene window. The beamline wascommissioned successfully, and some preliminary opticalmeasurements and experiments were done.

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N.A. Vinokurov et al. / Proceedings of the 2004 FEL Conference, 226-228

increase of the average current up to 0.1 A is underconsideration. As we have the two-section undulator,
further attempts to increase the FEL efficiency by theproper tapering looks promising.
The mechanical design of the second stage of the FEL
is in progress.

REFERENCES

Figure 5: The CW discharge in the focus of the parabolic
mirror.

FURTHER DEVELOPMENTS
We plan to increase further the output power. Factor two
may be obtained by the increase of the diameter of thehole in the rear mirror. The electron gun upgrade for the

TUCOS01[1] E. A. Antokhin et al. NIM A528 (2004) p.15-18.
[2] G.R. Neil et al. Phys. Rev. Lett. 84 (2000), p. 662.
[3] E.J. Minehara. Nucl. Instr. and Meth. A, V. 483, p. 8,
2002.
[4] N.G. Gavrilov et al. IEEE J. Quantum Electron., QE27, p. 2626, 1991.
[5] V.P.Bolotin et al. Proc. of FEL-2000, Durham, USA,
p. II-37 (2000).
[6] O.A. Shevchenko, A.V. Kuzmin, N.A. Vinokurov.
Numerical modeling of the Novosibirsk Terahertz FEL
and comparison with experimental results. These
proceedings.

S. V. Benson et al. / Proceedings of the 2004 FEL Conference, 229-232

229

HIGH POWER LASING IN THE IR UPGRADE FEL AT JEFFERSON LAB
S. Benson*, D. Douglas, M. Shinn, K. Beard, C. Behre, G. Biallas, J. Boyce, H. F. Dylla, R. Evans,
A. Grippo, J. Gubeli, D. Hardy, C. Hernandez-Garcia, K. Jordan, L. Merminga, G. R. Neil, J.
Preble, T. Siggins, R. Walker, G. P. Williams, B. Yunn, S. Zhang, H. Toyokawa†
TJNAF, Newport News, VA 23606, USA†
Photonics Research Institute AIST-Tsukuba Japan
Abstract
We report on progress in commissioning the IR
Upgrade facility at Jefferson Lab. Operation at highpower has been demonstrated at 5.7 microns with over 8.5
kW of continuous power output, 10 kW for 1 second longpulses, and CW recirculated electron beam power of over
1.1 MW. We report on the features and limitations of thepresent design and report on the path to getting evenhigher powers.

INTRODUCTION
At last years’ FEL conference we reported on firstlasing of the IR Upgrade FEL in the infrared region [1].
Turn-on and commissioning of that device went quitesmoothly and CW power of 300 W at 10 µm and 3 mA of
CW electron beam current at 80 MeV were demonstrated.
Two problems were noted—the FEL gain and power werelower than expected, and the mirror losses at 10 µm werehigher than expected. This paper will discuss how these
problems were overcome and how we intend to extend thepower even higher that we have to date. The paper will
describe the challenges we faced in the accelerator andour understanding of how to set it up to produce anelectron beam capable of high power. It will also describe
the challenge of running with over 100 kW of CW
circulating power in a free-electron laser.

ACCELERATOR CHALLENGES
The accelerator layout is shown in figure 1. By the
FEL 2003 conference almost the entire machine had been
installed and commissioned. The first arc still used a
dipole from the IR Demo machine [2], limiting the beamenergy to 80 MeV. We also used pairs of reworked IR
Demo sextupoles that limited operation to around 90 MeV
and were only in one of the two locations necessary fordispersion suppression. There were no octupoles installedin the second arc. Finally, only two of the three
cryomodules had been installed, limiting the energy toless than 90 MeV. In the fall of 2003 we took advantage
of a hurricane-induced downtime to install the final dipole
in the first arc. In early spring we upgraded the sextupoles
with bigger coils that allowed operation at up to 160 MeV
and installed the octupoles in the second arc. In May of2004 we installed the middle cryomodule, which has
operated with an accelerating voltage of over 80 MV withbeam, giving a total available accelerator energy of 170
MeV.
* email address felman@jlab.org

Available online at http://www.JACoW.org

Figure 1. Layout of the IR Upgrade FEL in its final
configuration. The beam starts at the injector at the upper
right, is merged with the full energy beam in an injection
chicane, accelerated up to as much as 160 MeV in three
cryomodules, transported to the optical klystron, and fromthere back to the linac. At the exit of the linac the energyrecovered beam is separated from the accelerated beam
and is dumped in a water-cooled copper dump.

The challenge of producing a high quality beam
The main reason for poor lasing performance last year
was a large growth in the longitudinal emittance between
the injector and the wiggler. To understand the tradeoffs
involved with reducing this growth it is useful to describe
the longitudinal matching around the accelerator.
The injector is designed to produce an uprightlongitudinal distribution at the entrance of the firstaccelerating module of the linac [3]. For our initial design
the injected bunch length was 1.5 psec rms and the energy
spread was 12 kV rms. The accelerator is designed totake that distribution and rotate it by 90 degrees in phasespace. The bunch length and relative energy spread at the
wiggler are then given by:
σ E,Iσω tan φσ t,W =and E,W =σ t,I(1)EL ω tan φ
EW
1+ EI / EL
where σE/t,W/I are the rms bunch lengths and energy
spreads at the injector and the wiggler, ω is the accelerator
frequency, φ is the off-crest phase, EL is the energy gain in
the linac, and EI and EW are the beam energies at the
injector exit and at the wiggler entrance. This equation
assumes that the quadrupoles and sextupoles in the firstarc are set to values that match the M56 and T566 of the arc
to the slope and curvature imposed on the beam by theaccelerator and thus perform a 90° rotation [4].

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The bunch length calculated using equation (1) for thedesign injector and the accelerator operated at 80 MeV, 15
degrees off-crest, should have had an rms bunch length at
the wiggler of 67 fsec and energy spread of 0.33%. In
fact the energy spread was close to 0.3%, but the bunch
length, measured using both a Martin-Puplett styleinterferometer looking at coherent OTR and a scanning
Michelson interferometer looking at the coherent
synchrotron radiation, was over 300 fsec rms and wassensitive to the transverse match in the machine. In
addition, the first arc magnet strengths that produced theshortest measured bunch were not those noted above thatrotated the phase space by 90 degrees. Finally, the rms
energy spread at the end of the wiggler should not dependon the sign of the phase with respect to the peak of thelinac’s accelerating phase (see equation (1)). In fact,
however, the energy spread was 50% larger on one side of
crest than on the other side. All these discrepancies
between the expected behavior and the accelerator
performance are due to longitudinal space charge (LSC)in the linac and transport [5]. The LSC leads tolongitudinal emittance growth and a tilt of the energy
distribution that alters the longitudinal match to thewiggler. We reduced the effects of LSC by modifying theinjector setup to increase the injected micropulse length to2.5–3.0 psec. This reduced the longitudinal emittance
growth, improved the FEL efficiency, and altered thelongitudinal match so that the design magnet strengths
were nearly optimal for the first arc. One cannot increase
the injected bunch length by an arbitrary amount. Due tothe energy acceptance of the FEL it is necessary to
decrease the off-crest phase angle to offset the increase inbunch length. This leads to problems with energy
recovery that will be discussed in the next section.
Using one family of sextupoles per arc it is possible toproperly set the T566 for the longitudinal match and tocancel the dispersion to first order. It is not possible tocorrect the second order dispersion, which leads to a
reduction in the efficiency of the FEL and to loss of haloat several points in the transport. This halo is produced in
the gun at different launch phases than that of theaccelerated bunches. The buncher cavity is set to bunchhigh charge bunches and strongly overbunches the halo.
The halo then has a large energy spread at the end of thelinac and, when the dispersion is corrected to only firstorder, grows dramatically in horizontal beam size at the
wiggler entrance. With two families of sextupoles wewere able to transport beam cleanly through the wiggler.
The efficiency also more closely matched predictions.
Once the third cryomodule was installed we had a newchallenge. The damping of the higher order modes(HOMs) in this cryomodule is not sufficient to raise thebeam breakup (BBU) threshold above 10 mA. In fact one
HOM was found to have a threshold of only 3 mA. We
found that, since there was only one mode with a low
threshold, we could alter the betatron phase advance toincrease the threshold up to over 5 mA. As an experiment
we also installed skew quads that changed a vertical kickinto a horizontal motion at the offending cavity [7]. With

TUCOS02

these magnets set correctly we could run at least 8 mA at
145 MeV (1.16 MW of beam) with no evidence of beam
breakup. In the future we will further characterize theBBU threshold dependence and study other ways to raise
the threshold.

Challenges in energy recovery
The magnets after the FEL must transport a beam withvery large energy spread to the dump with extremely low
losses. To do this, the energy vs. time distribution must
be properly matched to the decelerating gradient in the
linac. When this is done correctly the longitudinal phasespace is rotated 90 degrees by the time the electron beamreaches the beam dump. The matching is done to thirdorder in the energy offset using quadrupoles, sextupoles,
and octupoles. This system can, in principal, accept up to
15% energy spread [4]. Operating the accelerator close to
crest leads to a problem with this scheme. The highest
energy electrons in the distribution must be close totrough in order to decelerate all the electrons to the same
final energy. If this is done, the mean phase φdec must be
φ dec = ∆E Vlinac or more where ∆E is the full energy
spread and Vlinac is the total linac voltage. If we have a
distribution with 15% energy spread we must have a mean
phase of at least 22.5 degrees. One would like todecelerate the beam 180° out of phase with theaccelerating beam since no extra RF power is required as
the current is increased. If one accelerates 10 degrees off
crest this will not be possible due to the loss of the higher
energy electrons at the dump. We have discovered that itis still possible to recover the electron beam with very low
loss by decelerating less than 180° from the accelerated
beam at the mean phase derived above. A minor
drawback of this setup is that some RF is required toaccelerate the beam since it ends up at a higher energy
than at injection. The FEL power must come fromsomewhere. In the IR Demo it came from the injector. In
the IR Upgrade it comes from the linac. When longer
injector micropulses were used, the off crest phase waslimited to 10° to keep the energy spread below the
wiggler acceptance. We found that it was necessary to
run about 4 degrees further from trough to energy recover
during high power lasing. This configuration was stable
and the electron losses were minimal.
A new challenge in the IR Upgrade was CSR-induced
high-energy tails on the electron beam due to the shorterbunches and higher charge. If the bunches are fullybunched by the transport up to the wiggler, they willproduce copious coherent synchrotron radiation. This
leads to the growth of a high-energy tail on the beam in
the energy recovery section of the beam. We have foundthat, by setting the transport to the wiggler to slightly
underbunch the beam, the CSR can be greatly reduced
and the bunch length is only slightly longer than theminimum. The FEL performance is actually better when
this is done due to the smaller energy spread.
The final challenge is to correct for chromaticaberration. This can produce large growth in the beam
size as the energy spread increases. This was found to be

S. V. Benson et al. / Proceedings of the 2004 FEL Conference, 229-232

a major cause of beam loss in the linac. We have foundthat having matched betatron phase advances in thelattices before and after the second arc can suppress the
spot size growth due to chromatic aberration and lead towell-contained beams during energy recovery.
The machine is now essentially complete. Except for
the average current and the longitudinal emittance themachine matches the design values. A current of 9 mA
has been demonstrated at 88 MeV and we do not see any
fundamental reason why we will not be able to run at 10
mA, 160 MeV this fall. With two families of sextupolesin the first arc we found that the FEL efficiency closely
matched predictions made by pulse propagation codes.
We are now working on stability and reproducibility inthe lattice and are developing methods to ease setup of thetransverse match around the machine.

OPTICAL CHALLENGES
Optical challenges fall into two categories: 1. Getting
mirror losses down to acceptable levels, and 2. handlingthe circulating and outcoupled power. We graduallylearned how to accomplish both of these.

Reducing mirror losses
Previous work has shown that there is a limit to howmuch power the mirrors can absorb before the power
saturates [6]. For example a zinc selenide output coupler
can absorb 5W/µm*λ of power before the FEL power will
saturate. In practice one can slightly exceed this number
but it is a good design point. With the first set of 10 µm
mirrors we found a large amount of mirror heating foreven low power. Mirror losses were found to be 0.74%
and 0.3% for the output coupler (OC) and the highreflector (HR) respectively. We replaced the OC with amirror with 0.4% loss. This allowed us to achieve up to
700 W of CW power but it was clear that 10 kW was outof reach unless the losses could be reduced to under 500
parts per million (PPM). Discussion with mirror vendors
indicated that this was highly unlikely.
From our experience on the IR Demo we knew thatlower loss coatings were available in the 6 micron range.
We remounted our 97.3% reflectivity OC used for the
first light operation in a water-cooled mount and foundthat we could produce up to 2.3 kW from the laser. This
exceeded the IR Demo power record and produced acirculating power of 84 kW.
Using an OC with an even lower loss and a reflectivityof 92% we were able to push the power up to 4.1 kW. At
this power level the FEL itself becomes a good diagnostic
for measuring mirror absorption. This allowed us to tune
the wavelength for minimum loss. We found that the loss
for the output coupler at 5.75 microns was only 250 parts
per million (PPM). The high reflector had a loss of 400
PPM including an estimated 100 PPM of transmission.
One hypothesis for the high losses in the downstream
mirror was that THz edge emission from the dipole just
upstream of the mirror might dominate the OC heating.
Measurements with an electron-beam energy of 80 MeV

231

indicated that this was not the case. At an electron beamenergy of 145 MeV the absorbed THz power went up
dramatically, ranging from 50–85 W at 5 mA. The
maximum allowed power in the output coupler at 6
microns is 30 W. The absorbed THz power would notallow us to run at 10 kW CW, though we could run 10
kW with up to a 30% duty cycle and could run CW withover 6 kW of power output.
In order to avoid THz heating of the output coupler wereversed the optical cavity so that the backplane-cooledhigh reflector, which can absorb over 200 W of power
before limiting laser power, was downstream. The power
absorbed in the output coupler was now just thefundamental power. The power absorbed in the highreflector consisted of three sources: the absorbed
fundamental power, coherent second harmonic power,
and THz edge radiation. This configuration allowed us to
run 10 kW with a duty cycle of over 50% and to run CWwith up to 8.5 kW of laser output power.
Since the time constant for mirror distortion is quite
long it proved possible to run for periods of up to 1
second with power exceeding 10 kW. The power during
the laser pulse vs. time for a run on July 21, 2004 isshown in figure 2. The power during 1 second pulses was
as large as 10.6 kW. When shorter pulses were run the
power was as high as 11 kW during 0.25 second pulses.
The macropulse power vs. pulse length is shown infigure 3.

Figure 2. Power during 1 second pulses during time on
July 21, 2004. The power could be repeatedly raised tohigher than 10 kW. Dropouts are due to accelerator trips
or mirror mis-steering.

Handling the power
When the power output of an FEL is several kilowatts
in the mid-infrared even measuring the power is achallenge. We found that calcium fluoride windows
could not handle transmitted power exceeding 1500 W at
6 microns. We therefore moved to an in vacuo power
meter designed and built at Jefferson Lab capable ofhandling up to 50 kW of laser power. The power isabsorbed in a black copper coating in a water-cooled
cone. The rise in the water temperature of the coolingwater and the flow are monitored and used to calculate theabsorbed power. It is possible that power is also lost due
to backscatter and conduction so the power numbers

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S. V. Benson et al. / Proceedings of the 2004 FEL Conference, 229-232

quoted here are lower limits. Comparison at low powerwith a commercial power meter indicated that the power
reading might be as much as 10% low, though theuncertainty was large in this calibration.

wiggler with a higher gain-efficiency product. This willallow us to increase the output coupling and reduce
circulating power. It will also allow us to access shorter
wavelengths where mirror losses are very low. We expect
to be able to reach 10 kW CW with this setup. It should
also allow operation at over 10 kW in the 6 micron range.
Due to the lack of good mirrors we do not expect morethan about 5 kW at 10 µm. We plan to explore broadband
cavities to see what the average power limit is for a holeor scraper outcoupler system.
All these experiments dumped the laser power in theaccelerator vault. We are in the process of installing an
optical transport that will allow transport of the highpower beam up to users. Note that we can produce over
300 µJ/micropulse with this laser in a subpicosecond
pulse. It is not just a high average power laser but also ahigh peak power laser. This will be of great importanceto users of the laser.

Figure 3. Macropulse averaged power as a function ofpulse length. The point at 0.5 seconds was not fully
optimized.
The power was calculated assuming
negligible turn-on time. The rise in power with pulse
length is partly due to this and partly due to the fact thatthe high reflector radius of curvature was optimized forthe longer pulses.

This work supported by The Office of Naval Research
the Joint Technology Office, NAVSEA PMS-405, the Air
Force Research Laboratory, U.S. Army Night Vision Lab,
the Commonwealth of Virginia, and by DOE Contract
DE-AC05-84ER40150.

When lasing at 5.75 microns and 10 kW the output
coupling was 8%. This means that the circulating power
exceeded 125 kW. Even scatter of parts per thousand canlead to major problems in the cavity. We found that therings holding the mirrors tended to heat after a timerunning at high power. This caused changes in the mirroralignment and cavity length. We had planned to use ahelium-neon laser to track the mirror angle. Scattered
light absorbed in the windows for this system distorted
them sufficiently so that this was not possible. When we
tried to shield the windows with metal screens we foundthat the scattered light melted holes in them. THz lightalso heated beamline elements and led to vacuum rises
and optical distortion. Clearly, high power laser systems
have to account for all power losses in the system andmust be shielded from spurious light of all wavelengths.
Our optical cavities are being modified to account for thisreality.

[1] C. Behre et al., Nucl. Inst. And Meth. 528 (2004) 19–
22.
[2] J. Karn, G. Biallas, A. Guerra, and L. Harwood,“Magnetic Measurements Of The Prototype Dipole
For The IR-FEL At The Thomas Jefferson National
Accelerator Facility”, Proceedings of the 1997 PAC
conference (1997) 3334.
[3] C. Hernandez-Garcia et al., “Performance andModeling of the JLab IR FEL Upgrade Injector”,
these proceedings.
[4] “The Jefferson Lab 1 kW IRFEL”, Presented at the
Linac 2000 conference, Aug. 2000, Monterey CA,
http://www.slac.stanford.edu/econf/C000821/TH204.
pdf[5] C. Hernandez-Garcia et al., “Longitudinal Space
Charge Effects in the JLAB IR FEL SRF Linac”,
these proceedings.
[6] S. V. Benson, “Design details of the IR 10 kW
Upgrade Free-electron Laser Resonator”, Jefferson
Lab
Technical
note
TN-02-014,
http://tnweb.jlab.org/tn/2002/02-014.pdf.
[7] C. Tennant, D. Douglas, L. Merminga, E. Pozdeyev,
and T. Smith, "Suppression of Multipass, Multibunch
Beam Breakup in Two pass Recirculating
Accelerators", these proceedings.

ACKNOWLEDGMENTS

CONCLUSIONSThe IR Upgrade has been a learning experience.
Lessons learned from this machine can be used to both
upgrade the present machine and better design the next
generation machine. For example, in the future we plan toinstall a small chicane close to the wiggler that debunches
the electron beam and reduces the THz edge emission totolerable levels. We also plan to install a shorter period

TUCOS02

REFERENCES

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St. Guenster et al. / Proceedings of the 2004 FEL Conference, 233-236

VUV OPTICS DEVELOPMENT FOR THE ELETTRA STORAGE RING FEL
St. Günster, D. Ristau, Laser Zentrum Hannover e.V., Hannover, Germany,
A. Gatto, N. Kaiser, Fraunhofer-Institut für Angewandte Optik und Feinmechanik, Jena, Germany,
M. Trovò, M.B.Danailov, Sincrotrone Trieste, Trieste, Italy
F. Sarto, ENEA-Casaccia, Italy
Abstract
Vacuum ultraviolet optical components for the storage
ring FEL at Elettra are under continuous development in
the European research consortium EUFELE. Target of the
project is the progress to shorter lasing wavelengths in the
VUV spectral range. The current status allows lasing withoxide mirror systems down to 190 nm. The main
obstacles for the development of optical coatings for
shorter wavelengths is the high energetic background of
the synchrotron radiation impinging onto the front mirror
in the laser cavity. Investigations in single layer systems
and multilayer stacks of oxide or fluoride materials
demonstrate that fluoride mirrors reach highest
reflectivity values down to 140 nm, and oxide coatings
possess a satisfactory resistance against the high energetic
background irradiation. However, pure oxide multilayer
stacks exhibit significant absorption below 190 nm, andpure fluoride stacks suffer from strong degradation effects
under synchrotron radiation. Possible solutions could bebased on hybrid systems, combining fluoride stacks withoxide protection layers to provide high reflectivity and arobust behaviour under synchrotron radiation load.

INTRODUCTION
Dielectric mirror coatings for the vacuum ultraviolet(VUV , 120 – 195 nm) spectral range are deposited withphysical vapour deposition methods from oxide andfluoride compounds. Their optical properties in respect toreflectivity, losses and stability are acceptable forapplications in metrology systems, material processing
and lithography applications. [4] Mirror coatings for theFree Electron Laser (FEL) were produced from oxide
compounds which allowed a FEL lasing at the shortest
wavelength of 189,9 nm at Elettra. [2,3] However, themirror coating deposition for FEL lasing in the spectral
range between 150 and 190 nm has to overcome severe
obstacles. In this contribution the mirror development for
the FEL at Elettra is summarised from the viewpoint of
optical coating production. The work was performed in
the framework of the European research project“Development of the European Free-Electron Laser at
ELETTRA as a VUV Research Facility” (EUFELE).

PROBLEM
Mirrors for the Elettra FEL running in the VUV range
below 190 nm should be provided. The laser cavity isembedded in the Elettra storage ring. Enclosed in thecavity a wiggler accelerates the electron, which generates
finally photons for the FEL (Fig.1). The lasing
wavelength is determined by the electron energy and the

Available online at http://www.JACoW.org

wiggler parameters (period and gap). The front mirror
suffers the load of spontaneous synchrotron radiation that,besides the laser wavelength, contains also photons withenergy up to the MeV range. Therefore the front mirror
must be able to reflect the fundamental wavelength and totolerate these high energy background photons.
E-beamWiggler
Laserbeamn s n s n s n s n s n

BackMirrorn s n s n s n s n s nFront
MirrorFig. 1 : Configuration of a free electron laser resonator.
Laser action can be reached only if the amplification
exceeds the optical losses, which in the case of FEL
cavity are determined by the reflectivity of the twomirrors. While in the visible region losses due toabsorption and scattering in the coating can be kept very
low and are practically negligible, in the VUV range they
have to be carefully considered and minimized. The
tolerable minimum reflectivity for the SR-FEL at Elettra
can be estimated to a value of 90 % for the front mirror, if
the back mirror reflects above 95 %.
FEL systems are embedded in a vacuum environment(UHV). Residual molecules, especially hydrocarbon
compounds, may lead to a surface contamination of
optical components followed by a decrease of mirror
reflectivity. In combination with VUV radiation and thechemical sensitivity of the coating material, thisdegradation effect can be amplified strongly.

DEVELOPMENT CONCEPT
Summarising the demands outlined before, suitablemirrors for the FEL laser system must provide areflectivity above 95 %, they have to be able to withstandthe high energetic background radiation, and they must be
insensitive in respect to contamination effects. In thedevelopment phase suitable mirror materials wereidentified, different multilayer designs were developed,
andcomplementarydeposition
methods
were
investigated. After coating deposition, the opticalcomponents were characterised in respect to their opticalparameters. Then, the mirror coatings were irradiated at
SR-FEL at Elettra. Finally, the components were
inspected again and compared to the data gathered before

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St. Guenster et al. / Proceedings of the 2004 FEL Conference, 233-236

irradiation. Single layer coatings were investigated in asimilar procedure. Results were reported elsewhere [4].

EXPERIMENTAL
Deposition of optical coatings
Coating properties are determined by material selection
and the employed deposition technique. For mirror
systems down to the wavelength 190 nm, pure oxide or
fluoride systems can be used. However, the material
selection for the VUV spectral range is restricted by theband gap of most common deposition materials. Amongthe oxide materials, only SiO2 with its low refractive
index exhibits a negligible absorption down to 160 nm.
Al2O3 as the potential high index material can be
employed down to 190 nm. For shorter wavelengths only
fluoride compounds are applicable. In this study SiO2 andAl2O3 as oxide materials and MgF2 as low refractive
index material in conjunction with
LaF3 as highrefractive index compound from the fluoride class were
investigated.
Deposition techniques strongly influence the physicalproperties of the thin film. The aggregation of thin films
depends strongly on the kinetic energy of the particles
impinging on the substrate surface or an additional ion
assistance. In order to provide a broad spectrum of film
properties, deposition techniques with low kinetic energyof the aggregating particles and with high kinetic energyof the aggregating particles were employed: Thermal
evaporation methods (E-Beam and boat evaporation), ion
assisted deposition (IAD), plasma ion assisted deposition(PIAD) and ion beam sputter deposition (IBS).
Mirror designs were developed for the central
wavelength 180 nm with maximum reflectivity as main
target parameter. (See table 1) A standard fluoride

quarterwave stack was used as reference system. Thissystem was deposited by thermal evaporation, ion assisted
deposition (IAD) and ion beam sputtering (IBS)
deposition for comparison purposes. From the single layer
investigations it was concluded that LaF3 exhibits thestrongest degradation in the FEL environment. Thus, a socalled bi-stack system, with reduced LaF3 content was
deposited as a pure fluoride system also. Protected
mirrors were designed using a SiO2 top layer on a fluoride
stack. For the SiO2 protection layer E-Beam films and
IBS films were compared. In addition, protection systems
using a combination of Al2O3 and SiO2 were deposited.
Besides the fluoride stacks, a pure bi-stack oxide system,
which was designed for the central wavelengths 187 nm,
was deposited by IBS. For this mirror the Al2O3 layer
thickness was minimised to reduce the effect ofabsorption.
All coatings were deposited on CaF2 substrates.

Characterisation
Optical characterisation was performed before and after
the irradiation experiment. VUV, VIS, and IR optical
spectra were recorded for all samples. A VUVspectrometer developed at the Laser Zentrum Hannoverhas been employed for the measurement of the spectral
behaviour in the VUV-range [5]. Spectra in the uv-visible
range and the MIR range were measured employing
commercial spectrophotometers (λ900 and F1600 [Perkin
Elmer]). Also, spatially resolving techniques wereadapted and applied [6] for all spectrophotometricmethods. Microscopic surface inspection was performed
for the untreated substrates as well as for the irradiatedsamples. The samples were tested in irradiation
experiments at SR-FEL at Elettra.

Table 1 : Overview of the deposited optical coatings.
Multilayer model coatings HR@180 nm

Multilayer design

Boat

Oxide Compounds
Al2O3 / SiO2 HR@187 nm

Employed deposition techniqueIAD(0.65 H 1.35 L)20 0.65 H

PIAD

IBS
x

Fluoride Compounds
MgF2 / LaF3

HR@180 nm

MgF2 / LaF3 Bi-Stack HR@180 nm(H L)20 H

x

20

x

(0.7 H 1.3 L) 0.7 Hxx

Hybrid mirrors: Oxide and Fluoride
MgF2 [L1]/ LaF3 [H2]
SiO2 [L2-E-Beam]
MgF2 [L1]/ LaF3 [H1]
Al2O3 [H2-IBS] / SIO2 [L2-IBS]
MgF2 [L1]/ LaF3 [H1]
SIO2 [L2-E-Beam] / SIO2 [L3-IBS]

TUCOS03(H1 L1) 20 H1+ 6 L2 (SiO2 Protection)(H1 L1) 20+ H2 L2 H2 (Oxide Protection)(H1 L1) 20 H1+ 1 L2 + 5 L3 (SiO2 Protection)

x
x

x

x

x

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St. Guenster et al. / Proceedings of the 2004 FEL Conference, 233-236

80

60
50
40

20
10

80
70

R [%]

60

HR @ 185 nm

50

LZH

160

170

180

190

200

210

220

230

Lambda / nm

100
90

LZH

After Deposition

R1
R2

IAD Fluoride(HL)20H80
7060(6,0211) IAD-HR1.opj

Fig. 3 : Reflectivity of fluoride bi-stack deposited bythermal evaporation before and after irradiation at SRElettra.

After Irradiation

50
40
30
20

40

10

30

0
150

20

160

170

180

190

200

210

220

230

Wavelength / nm

10
0
150

0
150

R [%]

HR @ 193 nm

HR @ 190 nm(6,0211) TH1203-HR@18x-AOOI0°-Schief-01.opj VGL-IBS-OIC

Measurements on bi-stacks of the material pair Al2O3
and SiO2 show that, even with an extreme thin Al2O3
layer thickness, the absorption of aluminium oxides isdominating the mirror performance. An adequate
reflectivity can not be reached below 190 nm due to theabsorption of Al2O3. Figure 3 illustrates this with thereflectivity spectra of three different coating runs targetedto three different central wavelengths. The reflectivity ofthe produced HR@187 nm was below 90 % at 180 nm.
90After Lasing Attempt30

Pure Oxide Coatings

TH0103E1v01
TH11032V02
TH12031V01

20

Sub / (0.7H1.3L) 0.7H
H : LaF3 L : MgF2

70

RESULTS100

LZH

Fresh Sample

90(6,0211) OIC03.opj E37-E1-Irrad-VUV-PubOIC

100

[%]

In the free electron laser mode, Elettra runs in 4-bunch
filling mode at relatively low energies (0.75-1.5 GeV),
however, these specific FEL conditions are restricted to afew shifts per year. The number of tests would be
insignificant. To increase the number of irradiation
experiments, a configuration routinely adopted for user
operation (multi-bunch, 2 GeV) was used as standard test
condition. To reduce the high energetic backgroundradiation, the synchrotron radiation load was restricted tobending magnet contributions. For the evaluation of theexperimental results it has to be considered, that theirradiation stress under standard conditions is more severe
than in the FEL mode.

strongest reflectivity degradation after irradiation. From
additional measurements in the IR an intense hydrocarbon contamination on the optics surface can be stated.
The reflectance can be restored to approximately 90 % of
the initial value of reflectivity with UV cleaning methods.
A surface damage can not be observed by optical
microscopy.

R

Synchrotron and FEL Radiation Characteristics

160

170

180

190

200

210

220

230

Wavelength / nm

Fig. 2: Reflectivity of oxide Al2O3/SiO2 deposited as
bi-stack system [(0.65 H 1.35 L)20 0.65 H ] for threedifferent central wavelengths.

Pure Fluoride Coatings
Mirror system for the central wavelength 180 nm were
deposited with different techniques. Multilayers producedby thermal evaporation and IAD deposition reachreflectivity values above 90 %. First results for IBS
fluoride mirrors show, that a further process optimisation
is essential. The results of the irradiation experiments on
the conventional and the IAD mirror at Elettra display astrong degradation of reflectivity. Figure 3 and 4 present
the behaviour for a bi-stack fluoride mirror deposited bythermal evaporation and for a standard mirror design
produced by IAD, respectively. Both systems show

Fig. 4 : Reflectivity of a fluoride mirror deposited by ion
assisted deposition (IAD) before and after irradiation at
SR-Elettra.

Fluoride Coatings with Oxide Protection
Fluoride stacks, protected with SiO2 single layers,
could be produced with high reflectivity at 180 nm.
However, the process concept has to be optimised to
combine the fluoride and SiO2 deposition. In particular,
SiO2 has to be deposited in a reactive O2 atmospherewhich may lead to an unwanted oxidation of the fluoride
material. In addition, high energetic ions could create
defects in the fluoride stack during the IBS process. After
process optimisation, protected stacks with reflectivities
above 95 % can now be realised.
The characterisation after SR-FEL irradiation reveals
significant differences between the stacks protected with
E-Beam SiO2 and IBS SiO2. Similar to the pure fluoride
systems, the stack with E-Beam SiO2 protection layer is

FEL Oscillators

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St. Guenster et al. / Proceedings of the 2004 FEL Conference, 233-236

LZH

90

Fresh Sample

80(6,0211) OIC03.opj

100

an appropriate deposition of a dense SiO2 layer on a
fluoride stack. The structure of the sputtered SiO2 layer
seems to be much more effective for the protection of thefluoride surface, than the porous E-Beam SiO2 layer. With
optimised deposition cycle a reflectivity close to 99 % has
been recently reached (Fig. 7). The FEL lasing test has tobe performed.
100
LZH

20

Sub / (HL) HL+6λ/4 SiO2
H : LaF3 L : MgF2

70

90
80

40

60

After irradiation(2 GeV, no undulator)

30

40
30

10

20

0
150

10

160

170

180

190

200

210

220

230

Lambda / nm

ROC Front - Mirror
Fluoride + SiO2 [E-Beam]+ SiO2 [IBS]
After Run 71 : 0,75 GeV 12,9 mAh

LZH

Fresh sample

80

After irradiation

70(6,0211) BA2704-HR180+SiO2.opj

90(HL) 20 H+ 1 l/4 SiO2[E-BEam]+ 5 l/4 SiO2 [IBS]

60
50

30
20
10
160

170

180

190

200

210

220

230

Wavelength / nm

Fig. 6 : Reflectivity of a fluoride stack with IBS SiO2
protection layer before and after irradiation at SR-Elettra.
Fluoride stacks protected with combinations of SiO2
and Al2O3 did not achieve reflectivity values above 90 %at 180 nm. Further optimisation for this approach wasterminated.

CONCLUSIONSIn the framework of this study optical materials for the
production of VUV coatings were identified, adapted
coating designs were developed and tested. Furthermore,
the characteristics of selected deposition technique werestudied. In the present stage, the protection of highreflecting fluoride stacks is considered as the major
problem. Fluoride mirrors exhibit a high sensitivity for ahydro carbon contamination which causes a subsequentdegradation of reflectivity in the FEL system. A clear
improvement of robustness using ion assisted deposition
technique, which produce film system with higher
packing density, could not be observed until now. An
adequate protection layer combination can be realised by

TUCOS03

160

170

180

190

200

210

220

230

Fig. 7 : Reflectivity of an optimised fluoride stack withIBS SiO2 protection layer after production.
The authors gratefully acknowledge the support of the European
Commission (EUFELE-Project). “Development of the European FreeElectron Laser at ELETTRA as a VUV Research Facility“, a Project
funded by the European Commission under FP5 Contract No. HPRICT-2001-50025.

REFERENCES

40

0
150

0
150

Wavelength / nm

Fig. 5 : Reflectivity of a fluoride stack with E-Beam SiO2
protection layer before and after irradiation at SR-Elettra.

R [%]

50

20

100

Front - Mirror
Fluoride stack (HL)20+ SiO2 [E-Beam]+ SiO2 [IBS]

70

R [%]

[%]

50

R

60

(6,0211) BG1304+TGXX04-Si+Temp+TH1204.opj

strongly degrading in respect to its reflectivity (Fig. 5). In
contrast, the stack with the IBS SiO2 protection layershows only a small decrease of reflectivity of about
2 - 4 %. (Fig. 6). With a mirror of this type stored
emission in the FEL cavity was observed.

[1] J. Ullmann et al “Substrates and optical coatings for
157 nm applications”, Conference Inorganic Optical
Materials II. Proceedings of SPIE Vol. 4102, 2000
[2] A. Gatto et al, “High-performance deep-ultraviolet
optics for free electron lasers”, Applied Optics, 41(16), 3236-3241, (2002).
[3] M. Marsi, et al, “Operation and Performance of freeelectron laser oscillator down to 190 nm ”, Appl.
Phys. Lett. 80, 2852 (2002)[4] St. Günster et al, “Radiation resistance of single andmultilayer coatings against synchrotron radiation”,
Proc. SPIE 5250 , 146-157, (2004)[5] P. Kadkhoda et al, " Investigations of transmission
and reflectance in the DUV/VUV spectral range" ,Proc. SPIE 4099, 311-318,(2001).
[6] H. Blaschke et al, “DUV/VUV spectrophotometry forhigh precision spectral characterization” , Boulder
Damage Symposium XXXIV, (BD02) Proc. SPIE
4932, 536 , (2003)

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gdn. De Ninno et al. / Proceedings of the 2004 FEL Conference, 237-240

COHERENT HARMONIC GENERATION USING THE ELETTRA
STORAGE-RING OPTICAL KLYSTRON
G. De Ninno∗ , M. B. Danailov, B. Diviacco, M. Ferianis, M. Trovò, Sincrotrone Trieste, Italy
L. Giannessi, ENEA, Frascati, Italy
Abstract

Seeding laser

Dispersive section
Modulator

Radiatore- beam

Coherent harmonic generation using single-pass devices
or oscillators is based on the frequency up-conversion of ahigh-power laser focused into the first undulator of an optical klystron. The seeding signal, which is necessary to
produce the modulation of the electron density and hence
to induce the coherent emission, may be provided by an
external laser or, in the case of storage-ring oscillators, by
the FEL itself. The latter possibility has been recently explored at Elettra allowing to generate radiation at 220 nm,
i.e. the third harmonic of an intra-cavity signal at 660 nm.
As for seeding using an external laser, a detailed campaignof simulations shows that the Elettra storage-ring optical
klystron is also well suited for the realization of this configuration. These results make the Elettra FEL an attractive
test-facility in view of coherent harmonic generation experiments planned on dedicated next-generation devices.

INTRODUCTION
The standard process leading to the generation of coherent harmonics (CHG) using single-pass devices or storagerings is based on the up-frequency conversion of a highpower seeding signal focused into an undulator, which canbe the first one of an optical klystron, and synchronizedwith an upcoming electron bunch [1, 3]. In the optical
klystron configuration (see Fig. 1), the seed-electron beaminteraction leads to a modulation of the electrons energy
inside the first undulator (Modulator). When the beamcrosses the dispersive section, such a modulation is converted into a spatial partition of the electrons in microbunches separated by the seed wavelength. Therefore, aFourier analysis of the bunch density shows, at the endof the dispersive section, a series of lines at the laser frequency and its harmonics. Finally, in the second undulator(Radiator), the light emission at the harmonics of the seedwavelength is enhanced by this coherent bunching and becomes proportional to the square of the number of electrons.
When installed on storage rings, an optical klystrongenerally serves as interaction region for oscillator freeelectron lasers (FELs). In this case, electrons amplify thelight stored in the optical cavity during successive interactions, till the achievement of the laser effect. The obtained
intra-cavity signal, which is naturally synchronized at eachpass with the electron bunch(es) at each pass, may provide
the seeding power necessary to initiate CHG [4]. As an∗ giovanni.deninno@elettra.trieste.it

Available online at http://www.JACoW.org

Energy modulation

Micro-bunching

Coherent emission

Coherent emission

Figure 1: Schematic layout of CHG using an optical
klystron.
alternative, CHG can be obtained by removing the cavity
mirrors and by coupling the electron bunch(es) with an external laser [5, 6]. It is worth stressing that in both casesa major difference with respect to the single-pass configuration is due to the fact the electrons are re-circulated and,
therefore, they can keep track of previous interactions.
FEL-induced CHG has been recently realized at Elettra,
allowing to generate the third harmonic of an intra-cavity
signal at 660 nm. In the first part of this paper, we reportabout the set of measurements that have been performed
with the aim of characterizing the energy as well as the
spectral and temporal features of the harmonic radiation.
As for seeding using an external laser, a detailed campaignof simulations, partially reported in the second part of thepaper, shows that the Elettra optical klystron is also well
suited for the realization of this configuration.

THEORETICAL FRAMEWORKThe light-electron beam interaction inside each undulator can be studied by solving the coupled pendulummaxwell equations (see, e.g., [7]):

dζj


 dτ = νj






dνj
(1)
= |an | cos (ζj + φn )

dτ







 dan = −2πg0,n exp (−inζ).
dτ
Here ζj is the phase of the jth electron in the combined“ponderomotive” (radiation + undulator) field; νj , the relative energy of the jth with respect to the resonance condition, is the variable conjugated to ζj ; τ is the distance along
the undulator (normalized to the undulator length); an and
φn are, respectively, the nth harmonic component and thephase of the complex optical field; g0,n is the small signal
gain and exp (−inζ) stands for the bunching coefficient
relative to the nth harmonic. The extracted power at a given

FEL Oscillators

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gdn. De Ninno et al. / Proceedings of the 2004 FEL Conference, 237-240

harmonic is maximized optimizing its bunching coefficient.
This can be done by means of a proper adjustment of boththe electron beam energy and dispersive section strength.
When the case of CHG on a storage ring is considered, thesystem (1) has to be “closed” by two further equations. The
first accounts for the laser evolution inside the optical cavity [8]:(2)(an )new = (an )old 1 − Tn + (an )0
where (an )old is optical field at the exit of the Radiator and(an )new its value at the beginning of the Modulator after adouble reflection on the optical cavity mirrors. In practice,(an )new provides, turn after turn, the initial seeding value
for Eqs. (1); Tn is the mirrors transmission (dependingon the harmonic number) and (an )0 stands for the spontaneous emission of the optical klystron.
The second equation, which is necessary for closing theloop, takes into account the damping of the electron-beamenergy spread, σν , when, along the ring, electrons do notinteract with the seed [8]:(σν )2new = (σν )2old −2T (σν )2old − (σν )20 .
τs(3)Here (σν )old is energy spread at the exit of the Radiator and(σν )new its value after one turn of the ring; (σν )new provides, turn by turn, the initial r.m.s. value of the vj distribution (assumed, in first approximation, to be a Gaussian)in Eqs. (1). T and τs stand, respectively, for the bounching
period of the laser in the optical cavity and the synchrotron
damping time; (σν )0 is the initial (laser-off) value of theenergy spread. Note that Eq. (2) is no longer necessary
when the optical cavity is removed and use is made of an
external seed.

fixes the maximum repetition rate at which the system canbe operated. When the gain has recovered its maximum
value, the perfect light-electron beam synchronism is reestablished and maintained for the time (order of few hundreds of microseconds) necessary for a single giant pulse
to be generated. Then, the system is detuned again andthe entire cycle repeated. The obtained signal, which isfound to be relatively stable and reproducible, is characterized by an increase of the peak intensity of about a factor
50 with respect to standard “cw” operation mode. In Table
1 are listed the experimental conditions for which results
reported in the following have been obtained.
Table 1: Experimental conditions for CHG using the Elettra
FEL as seed. The Elettra storage-ring optical klystron ismade up of two identical undulators having 18 periods, 10cm long. The mirrors of the optical cavity have total losses
of about 0.2% at the fundamental wavelength.
Beam energy
900 MeV
Beam current (4 bunches)
25 mA (max)Fundamental wavelength
660 nmIntra-cavity peak power (fund) 100 MW
Third harmonic wavelength
220 nmRepetition rate
2-10 HzThe correlated temporal evolution of the fundamental
and harmonic macro-pulses is shown in Fig. 2.

CHG INDUCED BY THE FELINTRA-CAVITY SIGNAL
Let’s start considering the case of CHG self-induced by
the FEL light stored in the optical cavity.

Harmonic macro-pulse characterization
As demonstrated theoretically by Dattoli et al. [9] andexperimentally on the Duke storage-ring FEL [4], the only
way to generate enough intra-cavity power so to get a detectable harmonic signal is to run the FEL in giant-pulse
regime. This can be done by means of different techniques.
The one employed at Elettra [10] for Q-switching is basedon a periodic variation of the radio-frequency so to inducea modulation of the temporal overlapping between the electron beam and the light stored in the optical cavity. Whenthe system is completely detuned, the laser is switched off.
If such a condition is kept for a time long enough (order offew synchrotron damping times), the electron beam cools
down and the gain recovers its initial (laser-off) maximum
value. The minimum duration of such a period of time

TUCOS04

Figure 2: Correlated evolution of the fundamental (upper
trace) and harmonic (lower trace) macro-pulses.
The harmonic pulse is characterized by a shorter risetime than the fundamental one (about a factor 3 difference); moreover, it reaches the saturation and decays faster.
Measuring the ratio between the maximum intensity of theharmonic signal and its background (corresponding to thespontaneous emission of the optical klystron at 220 nm)
allows one to give an estimation of the energy carried by
the most intense harmonic micro-pulse, i.e. about 0.2 nJ
for the case of Fig. 2. The intensity of the fundamental
and harmonic signals has been studied also as a function of
the dispersive section strength. The obtained result, shownin Fig. 3, is a clear signature of the nonlinearity of the239

gdn. De Ninno et al. / Proceedings of the 2004 FEL Conference, 237-240

Intensity (arb. units)b)

FWHM = 5 nm

Intensity (arb. units)
221.0

500

a)

FWHM=0.26 nm

Intensity (arb. units)

process. Indeed, the dispersive section strength at which
the harmonic intensity becomes maximum does not correspond to that maximizing the fundamental. The decreaseof the harmonic signal above a given threshold is to be attributed to the concurrent decrease of the fundamental andnot to an induced over-bunching (which never occurs in thisregime).

222.0

223.0

Wavelength (nm)

200

210

220

230

240

250

Wavelength (nm)400

Figure 5: Specrum profiles at 220 nm of the coherent signal (Fig. a) and of the spontaneous emission of the optical
klystron (Fig. b).

300
200

Harmonic (x 2·104)
Fundamental

100
0
0

10

20

30

40

50

60

70

Dispersive section strength

Figure 3: Evolution of the fundamental and harmonic intensities as a function of the dispersive section strength.

Temporal and spectral characterization of theharmonic micro-pulse
Measurements performed using a double-sweep streak
camera (see Fig. 4) show that the duration of the harmonic
micro-pulse is shorter than the fundamental one (about 6 ps
r.m.s.). The measured value, i.e. 3 ps r.m.s, is at the limitof the instrument resolution [11]).

ing that the micro-pulse duration is 3 ps r.m.s, that is what
has been measured using the streak camera (see Fig. 4).
Table 2: Experimental and simulated micro-pulse peak
power relative to the fundamental and harmonic signals.
Fundamental (W) Harmonic (W)Experimental
8.6 · 105
17.1
Simulated
6.7 · 105
16.4

It is worth noting that the obtained value for the harmonic micro-pulse peak power (less than 20 W) is much
weaker than the one reported by the Duke FEL group (i.e.
tens of kW [4]).

CHG INDUCED BY AN EXTERNAL SEED

Figure 4: Streak camera images of the fundamental a) andharmonic b) macro-pulses. The insets represent the respective micro-pulse profiles.
As for the spectral domain, the pulse width has beenfound to be of the same order of the fundamental one (i.e.
∆λ/λ  10−3 and about a factor 20 narrower than the
spontaneous emission of the optical klystron (see Fig. 5).

Comparison with theory
Eqs. (2) and (3) have been implemented into the numerical code PERSEO [12]. Simulations give results in good
agreement with experiments. In particular, as reported inTable 2, the theoretical value of the micro-pulse peak powerat the fundamental wavelength is close to the measured one.
As for the harmonic, a good agreement is obtained assum-

In the following are summarized the results of a campaign of time-dependent simulations performed, again using PERSEO, in order to investigate the possibility of CHG
using the Elettra storage-ring optical klystron in combination with an external seed.
The seeding system that has been considered is a Ti:Sa
delivering, after third harmonic generation, an optical pulse
at 260 nm characterized by a duration of 100 fs and by apeak power of 2.5 GW. Figs. 6a and 6b show the seeding effect on the electron-beam phase space at the end of
the modulator and of the dispersive section, respectively.
The correspondent bunching coefficients for the third, fifthand seventh harmonics are reported in the Figure’s caption. After the end of the dispersive section, the microbunched electron beam enters the radiator, which is tuned
at the third harmonic of the seed wavelength. Fig. 7 showsthe evolution of the harmonic signal along the undulator.
The expected output power at 90 nm is about 1 MW. The
power is reduced, respectively, by a factor 10 and a factor
100 (see Table 3) when the Radiator is tuned at the fifth( 50 nm) and seventh ( 40 nm) harmonics of the seeding laser wavelength. Time-dependent simulations havebeen performed in order to get the output micro-pulse andspectrum profiles (see Fig. 8). As expected, the harmonic

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gdn. De Ninno et al. / Proceedings of the 2004 FEL Conference, 237-240

904

904

902
900
898

902
900
898

896

896

894

894

0

50

100

150

200

the spectral range to the vacuum ultra-violet. As for CHG
using an external Ti:Sa system, simulations performed using PERSEO in time-dependent mode (and partially benchmarked using GENESIS [13]) give the very promising results reported in Table 3.

b)
906

Energy (MeV)

Energy (MeV)

a)
906

0

250

50

100

150

200

250

z(nm)

z (nm)

Figure 6: Effect of the seeding laser on the electron-beamphase space at the end of the Modulator, Fig. a), and at
the end of the dispersive section, Fig. b). The bunchingcoefficients for the third, fifth and seventh harmonics (b3 ,b5 , b7 ) are in the two cases (0.15, 0.04, 0.01) and (0.34,
0.17, 0.07), respectively.
10Power (W)

10

10

10

10

6

5

Such a results indicate the Elettra storage-ring optical
klystron as an attractive, ready-to-use, test facility in viewof CHG experiments planned on dedicated next-generation
devices.

4

3

2

0.0

0.5

1.0

1.5

ACKNOWLEDGMENTS

1.8

Distance along the radiator (m)Figure 7: Evolution of the harmonic signal along the Modulator tuned at the third harmonic (about 90 nm) of theTi:Sa seeding signal.
pulse duration is slightly shorter than the one of the seeding pulse (86 fs) and the spectrum profile is very clean(∆λ/λ  1.2 · 10−3 ).

CONCLUSIONS AND PERSPECTIVES
We have demonstrated the possibility of CHG using the
Elettra storage-ring FEL as seeding signal. The temporal
dynamics of the radiation at 220 nm has been studied andthe harmonic micro-pulse characterized in terms of energy,
duration and spectral width. Experiments are well reproduced by a simple 1D model developed exploiting the numerical code PERSEO. As a next step, we intend to extend
1.0Power spectrum (arb. units)b)Power (arb. units)

0.8

0.6

0.4

0.2

0.0
0

z ( µm )100

200[1] L. H. Yu, Phys. Rev. A 44, 51178 (1991).
[2] L. H. Yu et al., Phys. Rev. Lett. 91, 074801 (2003).
[3] B. Girard et al., Phys. Rev. Lett. 53, 2405 (1984).
[4] V. Litvinenko, Nucl. Instr. and Meth. A 507, 265 (2003).
[5] P.L. Csonka, Part. Accele. 8, 225 (1978).
[6] R. Coisson and F. De Martini, Phys. Quantum Electronics 9,939 (1982).

[9] G. Dattoli et al. Journ. of Appl. Phys. 83, 5034 (1998).

0.6[10] G. De Ninno et al., Nucl. Instr. and Meth. A 528, 278 (2004).

0.4

0.2

89.0

89.5

90.0

90.5x10-9Wavelength (nm)Figure 8: Simulated output micro-pulse and spectrum profiles (Figs a) and b), respectively).

TUCOS04

REFERENCES[8] M. Billardon et al. Phys. Rev. Lett. 69, 2368 (1992).

0.8

0.0
-100

We are thankful to the Elettra accelerator group for technical support. We also acknowledge useful discussions
with G. Dattoli that helped us in the development of thetheoretical model. Thanks to M. Coreno, M.E. Couprie, G.
Lambert and E. Longhi for participating to our shifts. This
work has been partially supported by EUFELE, a Project
funded by the European Commission under FP5 Contract
No. HPRI-CT-2001-50025.

[7] G. Dattoli et al., Free Electron Laser theory and related topics (World Scientific, Singapore, 1993).

1.0

a)

-200

Table 3: Expected performance of CHG using the Elettra
storage-ring optical klystron in combination with an external Ti:Sa laser system delivering an optical pulse at 260
nm, characterized by a duration of 100 fs and a peak powerof 2.5 GW.
Wavelength (nm)90, 50, 40
Peak power (W)106 , 105 , 104
Pulse duration (fs)
 90 fs
Repetition rate (Hz)10-100Spectral width
Same as seed pulse[11] M. Ferianis and M. Danailov, AIP Conference Proceedings/
648 (2002), Gary A. Smith and Thomas Russo editors, BNL,
Upton, NY, USA.
[12] L.
Giannessi,
PerseoFEL-cad
http://www.afs.enea.it/gianness/perseo.

library,[13] S. Reiche, Nucl. Instr. and Meth. A 429, 242 (1999).

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W. B. Colson et al. / Proceedings of the 2004 FEL Conference, 241-242

SHORT RAYLEIGH LENGTH FREE ELECTRON LASERS
W. B. Colson, J. Blau, R. L. Armstead, and P. P. Crooker
Physics Department, Naval Postgraduate School
Monterey, CA 93943
Abstract
Conventional free electron laser (FEL) oscillators minimize the optical mode volume around the electron beamin the undulator by making the resonator Rayleigh length
about one third of the undulator length. This maximizes
gain and beam-mode coupling. In compact configurationsof high-power infrared FELs or moderate power UV FELs,
the resulting optical intensity can damage the resonatormirrors. To increase the spot size and thereby reduce theoptical intensity at the mirrors below the damage threshold, a shorter Rayleigh length can be used, but the FEL interaction is significantly altered. A new FEL interaction is
described and analyzed with a Rayleigh length that is only
one tenth of the undulator length, or less.

INTRODUCTION
For several decades, it has been suggested that a freeelectron laser (FEL) oscillator can optimize the electronoptical coupling by minimizing the optical mode volume
around the smaller relativistic electron beam. The origin of
the idea was stated in Madey’s initial paper inventing the
FEL concept [1], and has lead to the common practice ofdesigning the FEL’s optical resonator so that its Rayleighlength Z0 is about half of the undulator length L. That assumption is studied in this paper and it is found that there
are several possible advantages to much shorter Rayleighlengths including increased gain.
In Madey’s original paper, the FEL gain was estimatedusing a “Filling factor” F in order to describe how thesmaller electron beam exchanged energy with the slightly
larger optical mode. The filling factor is defined as the ratio of the electron beam area to the optical mode area withboth assumed to be constant along the interaction length
L. FEL gain G is then estimated as proportional to thefilling factor, and the usual practice was to minimize theoptical mode volume around the smaller electron beam.
Since that time, it has been common practice to design
an FEL oscillator with minimum optical mode area along
the undulator length L. A further refinement is to average
the filling factor over L so that G ∝ (z0 + 1/(12z0 ))−1 .
The normalized Rayleigh length is defined as z0 = Z0 /L
and the actual Rayleigh length is Z0 = πw02 /λ, λ is the
optical wavelength, and w0 is the optical mode waist radius. The optimum weak field gain is then found by minimizing the mode volume over the undulator length L forz0 = 12−1/2 ≈ 0.29 [2]. Common practice uses values
z0 ≈ 0.3 → 0.5.

Available online at http://www.JACoW.org

The short Rayleigh length FEL design is an alternativethat makes use of a resonator cavity with a short Rayleighlength resulting in a larger laser spot at the mirrors [3].
Scientific, industrial, and military applications of FEL oscillators benefit from a more compact design. Laboratory
space is always valuable. When the application also requires moderate to high power at infrared or shorter optical
wavelengths, the conventional FEL oscillator design leads
to high intensity at the mirrors and possible mirror damage.
A couple of examples illustrate how this common practice (z0 ≈ 0.3 → 0.5) can limit an FEL performance. Take
the mirror separation of the resonator to be S = 12 m with
10% output coupling. Typical mirrors can be damaged by
2
a high laser intensity ∼ 10 kW/cm in the infrared and2∼ 1 kW/cm in the UV. Taking the electron beam and optical mode to be about 1mm in diameter in the undulator,
the commonly used design criteria would lead to a limitation in output power of 150 W in the infrared and only 3 W
in the UV. The UV FEL is a particular problem since thelonger Rayleigh length Z0 associated with the shorter UV
wavelength λ increases mirror intensity further by decreasing the mirror spot size. Both FELs would benefit from ashorter Rayleigh length resonator in order to reduce the intensity on the mirrors and keep the system compact. The
conventional estimate for gain would lead to G ∝ z0 for
small Rayleigh length z0  1. The research presented here
shows that this is incorrect, and that there is little or no loss
in gain for small z0  1. The design option is illustrated
in Figure 1 below.

Figure 1: Schematic comparison of the conventional andshort Rayleigh length FEL designs.
The FEL interaction is altered in the short Rayleighlength FEL because the optical field amplitude and phasechange significantly along the undulator [4]. The field amplitude a(τ ) and phase φ(τ ) at the mode center r = 0 are
shown in Figure 2 and are given bya(τ ) = a0 (1 + (τ − τw )2 /z02 )−1/2(1)

φ(τ ) = − arctan((τ − τw )/z0 )(2)where τ = ct/L is the dimensionless time of interaction
along the undulator length L, c is the speed of light, a0 is

FEL Oscillators

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W. B. Colson et al. / Proceedings of the 2004 FEL Conference, 241-242

the dimensionless optical field amplitude at the mode focus, and τw is the location of the mode focus along the undulator. When z0 is small, the field amplitude and phasechange rapidly along the undulator. While the rapidlychanging field would appear to be detrimental to the bunching process, it may improve coupling by focusing laser
light to a small waist to intensify the field strength.

shape plotted in (x, y) as they are slightly distorted fromtheir Gaussian fundamental shape. The distortion is notlarge, but sufficient to significantly increase the gain when
the Rayleigh length is small. In these cases, the electron
beam has been focused to a waist size of rb ≈ 0.06 mm sothat it remains inside the focused optical mode waist. The
normalized emittance required for this case is n = 3 mmmrad, but larger emittances have been explored finding thesame trend: there is no significant decrease in gain at small
Rayleigh length when mode distortion is allowed. Also, thelocation of the optical mode focus is found to be optimumfor τw = 0.5, in the middle of the undulator.

Figure 2: Optical field amplitude a(τ ) and phase φ(τ ) as
functions of dimensionless time τ = ct/L.

SIMULATION RESULTS

Figure 3: FEL gain as a function of Rayleigh length z0 .

As an example consider an FEL having an undulator of
N = 22 periods with total length L = 52 cm, rms undulator parameter K = 1, and period λ0 = 2.36 cm. The FEL
with a shorter Rayleigh length requires a shorter undulator
length so that the expanding mode does not scrape the undulator magnets. In this case the undulator gap is g = 1 cm
and there is no significant scraping of the focused electron
beam or optical mode. At the end of the undulator the opti−1/2
mm
cal mode radius is wu ≈ (λL/4πz0 )1/2 ≈ 0.2z0
in this case. In order to keep wu < 0.2g = 2 mm toavoid even the slightest scraping, we keep z0 > 0.01.
An electron micropulse of I = 400 A peak current andenergy of 80 MeV is focused to a small waist radius of
rb = 0.06 mm. The FEL resonance condition defines the
optical wavelength as λ ≈ λ0 (1 + K 2 )/2γ 2 = 1 µm ina resonator with mirror separation S = 12 m and 25%
output coupling. FEL gain is evaluated from simulations
following the electron beam dynamics and optical mode
self-consistently [2].
Figure 3 is the result for this FEL, varying the dimensionless Rayleigh length over the range z0 = 0.1 → 1.
The most dramatic result is that gain does not decrease likeG ∝ z0 for small z0 , but remains roughly constant aroundz0 ≈ 0.01. This is due to optical mode distortion that is allowed to occur self-consistently in the simulations, but notin the simple estimate using the filling factor F . The single pass gain is large for this example (nearly 400%), but
the trend shown here has been confirmed for much smaller
gain as well. To the right are examples of the optical mode

If the electron beam focal radius rb is made too large,
some of the electron beam is outside of the optical mode
waist, decreasing coupling and gain. If the electron beam
focal radius is made too small, the larger angular spread resulting from fixed emittance n results in some of the electron beam drifting outside of the optical mode at the endsof the undulator, so that again gain decreases. There is typically an optimum electron beam focal radius rb ∼ 0.1 mm
for the short Rayleigh length designs examined.
The effects of mirror vibration and positioning are morecritical in the short Rayleigh length design, but we find thatthey are still within normal design tolerances [5].

TUCOS05

ACKNOWLEDGMENTS
The authors are grateful for the support from NAVSEA,
ONR, and the JTO.

REFERENCES[1] J. M. J. Madey, J. Appl. Phys., 42, 1906 (1971).
[2] W. B. Colson, Free Electron Laser Handbook, NorthHolland, 1990, Ch. 5, pp. 115-194.
[3] D. W. Small, R. K. Wong, W. B. Colson, R. L. Armstead,
Nucl. Instr. and Meth. A393 (1997) 262.
[4] W. B. Colson, J. Blau, and R. L. Armstead, Nucl. Instr. andMeth. A507 (2003) 48.
[5] P. P. Crooker, T. Campbell, W. Ossenfort, S. Miller, J. Blau,
and W. B. Colson, Nucl. Instr. and Meth. A507 (2003) 52.

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M.T. Trovò et al. / Proceedings of the 2004 FEL Conference, 243-246

ELECTRON-BEAM STABILIZATION FOR THE EUROPEAN
STORAGE-RING FREE-ELECTRON LASER AT ELETTRA∗
M. Trovò† , D. Bulfone, M. Danailov, G. De Ninno, B. Diviacco, V. Forchı̀, M. Lonza,
Sincrotrone Trieste, Trieste, Italy
L. Giannessi, ENEA, Frascati, Italy

INTRODUCTION
Instabilities of different nature may affect electron
beams accumulated in a Storage Ring (SR) and degrade
the performance of synchrotron light sources by leading
to increased beam emittance, energy spread and transverse/longitudinal vibrations of the center of mass of thebunches. The origin of such instabilities can be traced backeither to external perturbations (e.g. mains induced modulations, mechanical vibrations, etc.) or to the electromagnetic wake fields, which are generated by the interaction of
the electron bunches with the surrounding vacuum chamber and other cavity-like structures. In general, such fields
re-act on the bunches and perturb their motion.
Beam instabilities may affect the dynamics of a SR freeelectron laser and, if strong enough, even prevent its onset. In this respect, beam perturbations which normally do
not affect the performance of normal synchrotron radiation
beamlines may instead have a strong effect on the FEL intensity. This is mainly due to the tight requirements on
temporal synchronization and transverse overlap between
electron bunches and light pulses stored in the optical cavity at each pass inside the interaction region [1].
We have observed that a longitudinal coupled-bunch instability (LCBI) of only few degrees in amplitude can spoil
the laser synchronization and prevent it from starting. In
order to damp LCBIs, a bunch-by-bunch digital feedback
system [2] has been activated at Elettra during some FEL
shifts.
A different effect is observed when a beam-orbit perturbation of only few microns in the FEL straight section imposes a temporal structure to the laser intensity, changing
the natural behavior of the system. The use of a local orbit
stabilization feedback (LOF) [3], recently installed in cor∗ Partially funded by EC contract HPRI-CT-2001-50025† mauro.trovo@elettra.trieste.it

Available online at http://www.JACoW.org

OPERATIVE FEEDBACKS
Without the use of any feedback system, the Elettra FEL
is generally characterized by a macrotemporal structure
showing a disturbed behavior and a high sensitivity to different kinds of electron beam instabilities. Figure 1 showsa measured FEL structure acquired with a photodiode together with its Fourier transform. The spectrum shows astrong 50 Hz component and harmonics.
Amplitude (arb. units)

The temporal structure of the storage-ring free-electron
laser at Elettra shows high sensitivity to electron-beam instabilities. In fact, even small beam perturbations may affect the FEL dynamics and periodically switch off the laser.
In order to improve the FEL operation and performance,
different and complementary feedback systems have been
activated. This paper reports on their beneficial effect.
Plans for future improvements are also briefly outlined.

respondence of the Elettra FEL section, has significantly
reduced this low-frequency noise.
A further feedback system, complementary to the previous
ones, has been developed in order to prevent the onset ofa “naturally” pulsed FEL regime when the light-electron
beam detuning is increased (e.g. by an external perturbation) above a given threshold.
In the following we summarize the results obtained so far
using these different systems and we present a plan to develop a new feedback acting on the longitudinal bunch motion in the low frequency regime.

0.00

0.05

0

100

0.10
Time (s)

0.15

0.20

Amplitude (arb. units)

Abstract

200
300
Frequency (Hz)400

Figure 1: Typical temporal pulsed behavior of the FEL intensity (acquired with a photodiode) and its spectrum.
Since its first operation in February 2000 a lot of effort
has been made in order to identify the major photon noise
sources and to implement systems for their compensation.

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M.T. Trovò et al. / Proceedings of the 2004 FEL Conference, 243-246

Longitudinal Multi-Bunch Feedback1√
π τ0 τs(1)

Amplitude (arb. units)

where τs is the synchrotron oscillation damping time andτ0 = T0 /(G − P ) is the laser rise-time, with T0 the opticalcavity round-trip period, P the optical cavity losses and G
the amplification gain at the laser start-up. Using the Elettra parameters, the expression above predicts a frequencyof 180-340 Hz depending on the beam current and on thespecific mirrors. The observed FEL behavior, see Figure 1,
is not that of a free oscillator at its own frequency, but appears to be regularly perturbed at 50 Hz.
With the goal of understanding if and how much the FEL
pulsed behavior is sensitive to transverse beam orbit instability, the synchrotron light emitted by the electron beam
has been observed making use of a Position Sensitive Detector (PSD). As clearly shown in Figure 2 (continuouslines), a 50 Hz component and its harmonics are present
in both planes.
5

Horizontal
4

Off

On

3
2
1
0
0

100

200

300

400

Frequency (Hz)Amplitude (arb. units)

When there are many bunches in a storage ring and theelectron-beam induced wake fields are strong and persistent enough to act back on successive ones, a coherent oscillation may grow up [4]. This oscillation can affect thebunch motion in the transverse plane and in the longitudinal direction. Both transverse and longitudinal instabilities
are undesired for FEL operation, but the longitudinal one
is the most dangerous for the laser onset.
During FEL operation, Elettra is run in 4-bunch fillingmode at relatively low energies (0.75-1.5 GeV). This configuration is completely different from the one routinely
adopted for user operation (96 % multi-bunch continuous
filling, 2-2.4 GeV). In the 4-bunch mode, LCBIs can bedamped by acting on the temperatures of the four radiofrequency cavities, finding a suitable higher-order mode
combination [5]. However, the stability intervals are narrow and current dependent, so the operating temperatures
have to be continuously adjusted following the natural current decay.
With the goal of improving the longitudinal beam stability
and simplifying the operator task of keeping the beam stable, a longitudinal multi-bunch feedback has been recently
activated. This feedback system acts on each individual
bunch, which is considered an independent oscillator at thesynchrotron frequency. A digital processing system is used
to calculate the correction signal to be applied to the bunch
through a dedicated kicker. Due to a limitation of the system bandwidth, the feedback is not effective in the lowfrequency spectrum range.
This system has shown to be able to provide a perfect beam
LCBI free, also without any specific adjustment of cavity
temperatures. Moreover, its damping efficiency does notdepend on the storage-ring filling pattern: we have alreadytested the case with eight bunches arranged in the ring infour pairs of two successive buckets and no LCBI was observed on the beam with the feedback on, whereas strong
oscillations appeared without it.
This feature allows us to plan exotic fillings of the Elettra
SR, e.g. four symmetric trains of bunches, which would increase the FEL average output power, being the latter proportional to the average beam current.

fr =

5

Vertical
4

Off

On

3
2
1
0
0

100

200

300

400

Frequency (Hz)

Local Orbit Feedback

Figure 2: Photon beam transverse position spectra measured in the experimental area by a photon PSD with (dotted line) and without the orbit feedback. In this case, theoperational bandwidth is limited up to 200 Hz.

SR-FEL theory predicts a pulsed time structure of thelaser intensity on a millisecond temporal scale when thesystem is not close to synchronization, while a continuous
wave (CW) mode of laser operation is expected around theperfect tuning condition. For Elettra, the CW region aroundthe perfect synchronism is very narrow [7] and never experimentally observed. Due to that and to the 50 Hz (and harmonics) instability, the pulsed regime is the standard one
for the Elettra SR-FEL. The natural frequency of the pulsed
regime is given by the following relation [6]:Thanks to the recent implementation of a Local Orbit Feedback (LOF) on the SR section hosting the FEL,
the transverse micron-range orbit instability has been measured and compensated up to frequencies of a few hundred
Hz, see Figure 2 (dotted lines).
This feedback system detects the electron beam position
and angle at the Insertion Device (ID) center and stabilizes
it without affecting the rest of the orbit. Two Elettra Beam
Position Monitors, located on both sides of the ID, are used
to measure the beam position and angle, while four cor-

THPOS09

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0

0

10

10

20

20

30

30

40

40

50

50

c)

a)

60
0

5

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25

-4

60
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Intensity (arb. units)Time (ms)Time (ms)M.T. Trovò et al. / Proceedings of the 2004 FEL Conference, 243-246

0

2

4

Position (ps)

0

0

10

10

20

20

30

30

40

40

50

50

60

a)
0

60

c)
5

10

15

20

25

Intensity (arb. units)-4Time (ms)Time (ms)Figure 3: Streak camera image (b) of the FEL light without LOF. Along the vertical axis one can follow the time evolutionof the laser on ms scale. Figure a) shows the intensity behavior along the slow time scale as obtained by an analysis of theimages, while in Figure c) the phase stability with respect to RF is presented.

-2

0

2

4

Position (ps)Figure 4: Streak camera image of the FEL light with LOF. Figures a) and c) as the previous figure.
rector magnets apply the closed local bump compensation.
The feedback algorithm combines a PID (Proportional, Integral and Derivative) controller, which compensates theslow orbit drifts and lower frequency components of thebeam noise spectrum, and a number of so called “Harmonic
Suppressors” [3], which remove specific periodic components induced by the mains.
The LOF effect has been studied by means of a streak camera. Collected data (see Figures 3 and 4) show that theorbit stabilization due to the LOF reduces the fluctuationsof the FEL intensity (a). Moreover, the FEL phase oscillation with respect to the radio-frequency (c) is halved
when the feedback is on. Such oscillations, characterized
by a frequency of 100 Hz, are probably induced by a lowfrequency longitudinal noise source and, for this reason,
they are not completely damped by the two feedback systems.

lution period is modulated making use of a signal proportional to the derivative of the laser intensity.
Preliminary results (see Figure 5) show a damping of
the laser oscillations and the achievement of a quasicontinuous regime.

Figure 5: Stabilizing effect of the derivative feedback on
the laser intensity.

Derivative Feedback
A further feedback system has been developed as a result of a deeper theoretical understanding of the mechanism leading the system from the continuous to the pulsed
behavior when the electron-photon synchronism is increased [8, 9]. When the system is active, the bunch revo-

PLANNED FEEDBACK
The combined action of the previous systems has been
recently tested and it has shown to be beneficial for thelaser performance. However, such a test has also pointed
out that, in order to fully counteract the 50 Hz (+ harmon-

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M.T. Trovò et al. / Proceedings of the 2004 FEL Conference, 243-246

ics) instability affecting the bunch motion (see Figure 6)
a further system is needed for the control of longitudinal,
low-frequency, perturbations.

10

Time (ms)

30
40
b)
50
-10

-5

0

5

10

Centroid position (ps)Figure 6: (a): streak camera image of the electron beam
(6 mA). A longitudinal instability of the bunch centroid isvisible. (b): evolution of the beam center of mass obtainedby the image analysis.
We plan to implement a new system to detect the longitudinal low-frequency bunch instability by exploiting theexisting LOF Beam Position Monitors. Such devices areequipped with an analog front-end for the demodulation of
the RF signal [3] plus a digital receiver. A suitable correction of the Elettra RF will be applied by means of a phasemodulation.

CONCLUSION
The performance of a SR-FEL in terms of light stability
and extracted power depends on the possibility of simultaneously controlling the electron-beam and laser dynamics.
To this purpose, three feedback systems have been recently
activated during FEL operation, one acting on longitudinal
multibunch instabilities, another on transverse orbit vibrations and a third one directly on the pulsed regime of the
FEL intensity. As we have shown, their action significantly
improves the beam stability and thus laser performance.
Efforts are, however, still required to reach a regular andreproducible CW regime. For that, we plan to design alow-frequency longitudinal feedback which should lead toa further, hopefully decisive improvement of the FEL temporal structure.

REFERENCES[1] M. Billardon et al., “Saturation mechanism for a storage-ringfree-electron laser”, Phys. Rev. Letters, Vol. 69, 2368 (1992).
[2] D. Bulfone et al., “Operation of the Digital Multi-Bunch
Feedback Systems at ELETTRA”, PAC’03, Portland, May
2003.
[3] D. Bulfone et al., “Fast Orbit Feedback Developments at
ELETTRA”, EPAC’04, Lucerne, July 2004.
[4] A. W. Chao, “Physics of collective Beam instabilities in HighEnergy Accelerators”, Wiley, New York (1993).

THPOS09[6] P. Elleaume, J. Phys., Vol. 45, 997 (1984).
[7] G. De Ninno and D. Fanelli, “Controlled Hopf Bifurcation of
a Storage-Ring Free-Electron Laser”, Phys. Rev. Letters, Vol.
92, 094801 (2004).

020[5] M. Swandrlik et al., “The cure of Multibunch Instabilities in
ELETTRA”, PAC’95, Dallas, May 1995.

[8] G. De Ninno and D. Fanelli, “Analytical theory and controlof the longitudinal dynamics of a storage-ring free-electron
laser”, Phys. Rev. E., Vol. 70, 016503 (2004).
[9] C. Bruni et al., “Stabilization of the Pulsed Regimes on a
Storage Ring Free Electron Laser: The Case of Super-ACO
and ELETTRA”, EPAC’04, Lucerne, July 2004.

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T. Tanaka et al. / Proceedings of the 2004 FEL Conference, 247-250

TUNABILITY AND POWER CHARACTERISTICS OF THE LEBRAINFRARED FEL
T. Tanaka*, K. Hayakawa, Y. Hayakawa, A. Mori, K. Nogami, I. Sato, K. Yokoyama+, LEBRA,
Institute of Quantum Science, Nihon University, 7-24-1 Narashinodai, Funabashi, 274-8501 Japan
K. Ishiwata, K. Kanno, K. Nakao, T. Sakai, Graduate School of Science and Technology,
Nihon University, 7-24-1 Narashinodai, Funabashi, 274-8501 Japan
Abstract
The use of the infrared (IR) Free-Electron Laser (FEL)
in medical science and material science started in October2003 at the Laboratory for Electron Beam Research andApplication (LEBRA) of Nihon University. The FEL
resonator which consists of silver-coated copper mirrors
has demonstrated a wavelength tunability ranging from
0.9 to 6.5 µm as a function of the electron energy and theundulator K-value. The wavelength dependence of the
FEL output power has been measured in terms of different
electron energies and different undulator K-values. At
about 2 µm, an FEL energy of roughly 25 mJ/macropulse
has been obtained at the FEL monitor port, whichcorresponds to the peak power of 1 to 2 MW, provided
that the FEL pulse length is less than 0.5 ps that resulted
from the measurement by the autocorrelation method. A
power decrease observed in the long-wavelength range
has resulted from the wavelength dependence of thecoupling coefficient of the FEL resonator mirror and thetransport efficiency of the FEL guiding optics.

INTRODUCTION
Since the first lasing at 1.5 µm by the LEBRA FEL
system in 2001 [1], efforts have been made to achieve thesaturation of the FEL power, and to stabilize the pulse-topulse power level.
In the early lasing experiment in the infrared region, theFEL resonator consisted of dielectric multilayer mirrors
optimised for lasing at a narrow wavelength range ofaround 1.5 µm. The mirrors were easily damaged by ahigh optical power. However, this suggested that theproperty of the LEBRA FEL system including theelectron beam is sufficient for intense lasing.
The resonator mirrors were changed to silver-coatedcopper mirrors in August 2003, which was intended tobring about an early beginning of user’s experiments by awide-range variability of the FEL wavelength and a highmirror tolerance for an intense FEL power. The FEL beam
has been extracted from the mirror placed upstream fromthe undulator through a small coupling hole, and the FEL
beam has been successfully transported to user’s
experimental rooms by the optical guiding system. The
user’s experiments in medical science and materialscience began in October 2003.
This paper reports on the improvement of the LEBRAFEL system, the result of the experiments on the

wavelength variability and the power characteristics. The
current specifications and arrangement of the FEL systemare expressed elsewhere [2].

IMPROVEMENT OF THE FEL SYSTEM
Lasing by dielectric multilayer mirrors
Improvement of the FEL power stability has been an
important problem for user’s experiments. The uniformityof the electron beam energy and current in macropulse
duration was improved by the reduction of the phasefluctuation of the accelerating rf in the linac [3]. Although
it contributed to the increase of the FEL power, theimprovement did not show a significant effect on thestability. Use of the dielectric multilayer mirrors withinsufficient tolerance for high power FEL resulted indamage to the mirrors by the FEL before its saturation,
which led to difficulty in the investigation of the stability.
In a series of lasing experiments using the dielectric
mirrors, the 1.5 µm FEL was observed by detecting thelight transmitted through one of the mirrors, where only afraction of the light beam stored in the resonator was
detected using the transmission property of the mirrors.

Vibration and drift of the mirrors
Besides the tolerance for the optical power, there were
problems of the vibration of the mirrors and the drift ofthe mirror separation, which was found from theobservation of the interference pattern by the alignment
laser lights that reflected on the two mirrors in theresonator [4]. The drift of the mirror separation resulted
from a change in room temperature. However, thebehaviour of the temperature dependence has not yet been
well understood. The slow drift of the mirror separation
has been compensated for by adjusting a piezo device
manually. The vibration of the mirrors resulted from thevibration of the mirror chambers, which was caused by
the water flow for cooling of the bending magnets in the
beam transport line, which suggested a lack of flexural
rigidity of the mirror chamber’s frame bases. The
amplitude of the vibration in the bases, measured with alaser displacement gauge, was suppressed from several
hundred nm to within 20 nm (limit of measurement) by
the reinforcement of the frames, which was made with 6mm thick steel plates attached to the side faces of thebases.

___________________________________________*E-mail address: tanaka@lebra.nihon-u.ac.jp+
Present address: KEK, 1-1 Oho, Tsukuba, 305-0801 Japan

Available online at http://www.JACoW.org

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Lasing by silver-coated copper mirrors
The FEL guiding optics system for user’s experiments
was constructed in June 2003. This system was designed
to use an external-coupling mirror which has a small
coupling hole. Since August 2003 the silver-coated copper
mirrors have been used for the lasing experiments
corresponding to the new optical guiding system. The
nominal reflectance for the mirrors is greater than 99.3 %in the wavelength range longer than 0.9 µm. The FEL has
been extracted from the mirror placed upstream from theundulator through a coupling hole of 0.15 mm in radius.
The silver-coated copper mirrors demonstrated a highperformance. The saturation of the FEL power has been
observed for the wavelength range from 0.9 to 6.5 µm.
There has been no evidence of damage so far by thesaturated FEL power.
Provided that the FEL in the resonator is a Gaussianbeam, the coupling coefficient κ of the coupling hole isgiven by [5]κ = 1 − exp( −2a 2 / w 2 ) ,(1)
where a is the radius of the coupling hole, w the FEL
beam radius on the surface of the resonator mirror that isgiven as a function of the FEL wavelength λL, theRayleigh length LR in the resonator and the separation D
between the two resonator mirrors by

w=

λL LR
{1 + ( D / 2 LR ) 2 } .
π(2)Using the parameters for the LEBRA FEL system, D =6.718 m and LR = 1.47 m, the wavelength dependence ofthe coupling coefficient is approximated asκ = 0.687

a2

λL

,

(3)

where the units of a and λL are mm and µm, respectively.
For instance the coupling coefficient of the 1.5 µm FEL is0.0103.
The divergent FEL beam extracted from the resonatorthrough the coupling hole has been converted to a parallel
beam in the expander system which consists of anellipsoidal mirror and the parabolic mirrors. Then, theoptical size of the collimated beam is determined by thediffraction pattern on the surface of the ellipsoidal mirror.

EXPERIMENTAL SETUP
Fig. 1 shows a schematic layout of the FEL system andthe guiding optics system from the accelerator room to thelarge experimental hall. Also, the experimental setup is
shown in Fig. 1. All the measuring devices for monitoringof the FEL have been installed in the large experimental
hall.
The macropulse waveform of the FEL and thespontaneous emission were observed with an LN2-cooled
InSb detector in combination with a focusing lens or
neutral density filters depending on the intensity of thelight. The light was picked up with a CaF2 beam sampler
or an aluminium total reflection mirror in the first FEL
monitor chamber.
The light picked up from the second FEL monitor
chamber can be divided into the infrared components andthe visible components with a cold mirror as shown in Fig.
1. A simultaneous measurement is possible for the spectraof the higher harmonics in the near infrared to the visible
region and the fundamental FEL power, if the FEL
wavelength lies in the range where the absorption of thefundamental FEL in the cold mirror is negligibly small.
The optical power of the FEL in a wavelength range
longer than 2 µm was measured by placing the power
meter on the upstream side of the cold mirror. Then, theFEL power and the spectra of the higher harmonics were
measured alternately. The FEL power was measured as anintegrated energy over the macropulse duration of 20 µs
by using a pyroelectric element.

Fig. 1. Schematic layout of the FEL system, the FEL guiding optics system, and the experimental setup. The
macropulse waveform, the power and the spectrum of the FEL have been measured in the large experimental hall inorder to monitor the FEL during user’s experiment. The intense FEL has been picked up with a CaF2 beam sampler ineach FEL monitor chamber.

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B0 = 2 Br {1 − exp( −2πh / λU )}× exp( −2πg / λU )Fig. 2. An example of the macropulse waveform of
the FEL lased at 5.75 µm (a). Also shown is theelectron beam macropulse current (b).
Fig. 2 shows an example of the macropulse waveformof the FEL measured at a wavelength of 5.75 µm, where
the FEL power was saturated in 8 µs from the beginningof the electron beam injection into the FEL system.
The macropulse energy of the FEL was measured usinga pyroelectric element with an injection window of 24×24mm2, where no focusing device was placed in front of theelement. In the experiment, the measured macropulse
energy was calibrated only to the fraction contained inabove square region in the FEL monitor chamber. It is
assumed that the optical beam profile at the pyroelectricelement has approximately the same size and shape as in
the FEL monitor chamber. Then, the macropulse energyof 2 mJ for the case of Fig.2 was deduced from themeasurement.
The electron beam from the linac has been bunchedevery period of the 2856 MHz RF. From the FWHM of
the FEL macropulse in Fig.2, the average energy in eachsaturated FEL micropulse is estimated to be 0.064 µJ. An
FEL micropulse length was deduced to be less than 0.5 ps
for the wavelength of 1.5 µm from a measurement withthe autocorrelation method [6]. As a result, the micropulse
energy of 0.064 µJ corresponds to a peak power greaterthan 0.1 MW. The maximum FEL energy obtained in thelasing experiment was 25 mJ at a wavelength around 2µm, which corresponds to the micropulse peak power ofnearly 2 MW.

TUNABILITY OF THE WAVELENGTH
The result of the experiment on the FEL wavelength
tunability is shown in Fig. 3, where the rhombus-shaped
data points show the wavelengths measured in terms ofthe various undulator gap widths for the fixed electronenergy Ee. The 2D analytical expression for thefundamental sinusoidal component of the undulator peakfield B0 is given as [7]sin(π / 4) ,
π /4

(4)

where Br (= 1.2 T) is the remanent field of the permanent
magnet, λU (= 48 mm) the undulator period, g theundulator half gap width, h (= 35 mm) the block height ofthe magnet [7]. The dependence of the wavelength on theundulator gap width was calculated from the magnetic
field given by Eq. (4) as shown by the curves in Fig. 3.
The electron energy has an ambiguity within ±1 % due tothe momentum acceptance of the electron beam analysing
system. Therefore, the curves were fitted to theexperimental results by a small correction for the electronenergy. The good agreement with the experimental result
suggests that the undulator magnetic field is welldescribed by Eq. (4).
The FEL lasing is possible over the range of g from 12
to 18 mm, which makes change of the K-value from 1.99
to 0.91. Thus, the FEL wavelength can be varied
continuously to 1/2 of the wavelength at the minimum
gap width for fixed electron energy.

Fig. 3. The FEL wavelength measured as a functionof the undulator half-gap width for fixed electronenergies. The curved lines show predicted wavelength
dependences on the gap width.

POWER AT THE FEL MONITOR PORT
Fig. 4 shows the dependence of relative FEL power on
the electron energy and the FEL wavelength, which wasmeasured as the macropulse energy using the pyroelectricelement. The wavelength was changed by the adjustmentof the undulator gap width with the electron energy fixed.
The experiment for the same electron energy was run in
one machine shift, therefore the relative change of thepower dependent on the wavelength was obtained withapproximately the same electron beam condition. On theother hand, the relative power between the different
electron energies involves the difference of the electron
beam condition due to the difference of the beamemittance, the energy spread, and the beam focusing

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where d (= 2.5 m) is the distance between the couplinghole in the resonator mirror and the ellipsoidal mirror in
the expander system, and the area of the power injection
window was approximated by a circle with the radius A( = 13.5 mm).
From Eqs. (3) and (5), the micropulse peak FEL powerin the resonator can be estimated by applying a factork=Fig. 4. Relative FEL power obtained with different
electron beam energies.
parameters. Also, the absolute value and stability of the
FEL macropulse energy has been strongly dependent on
the beam handling and the alignment of the resonatormirror. However, the result shown in Fig. 4 gives a good
indication of the power available at the user’s port.

ESTIMATION OF THE POWER IN THE
RESONATOR
The macropulse energy measured at the FEL monitor
port represents the energy contained in the power meter
injection window area of 24×24 mm2. By a simple
assumption that the profile of the parallel beam obtainedat the output of the expander system is conserved at the
FEL monitor chamber, the detection efficiency εd of thepower meter for the total extracted energy is given by [8]ε d = 1 − J 02 ( 2πaA / dλL ) − J 12 ( 2πaA / dλL ) , (5)1TRF

ε dκτ L TM

(6)

to the macropulse energy measured at the FEL monitor
port, where τL is the FEL micropulse length, TRF theperiod of the micropulse, TM the FEL macropulse length.
The effect of corrections for εd and κ on the FEL
power measured at Ee = 52 MeV is shown in Fig. 5,
where the open circles are the raw data divided by TM, thestars corrected for εd (the same vertical scale as raw data),
the black circles corrected for εd and κ (corresponding to
the power in the resonator). The FEL macropulse length
was measured for each wavelength. Fig. 4 shows adecrease of the power in the wavelength region longer
than 3 µm at the FEL monitor port. However, the result ofcorrections for εd and κ suggests that the power in theresonator was not necessarily decreased in this region.

SUMMARY
Saturation of the FEL power was achieved in the
wavelength range from 1.0 to 6.5 µm by use of silvercoated copper mirrors in the FEL resonator. The propertyof the wavelength variability is in agreement with thetheoretical prediction. The FEL power measured at the
FEL monitor port has shown a decrease of saturated
power in the wavelength region longer than 3 µm.
However, the power in the FEL resonator has not beennecessarily decreased, considering the detection
efficiency and the coupling coefficient of the externalcoupling mirror.

REFERENCES

Fig. 5. The FEL power obtained at Ee = 52 MeV.
Open circles: raw data divided by TM, stars: correctedfor εd, black circles: corrected for εd and κ. The error
bars represent the fluctuation of the macropulse
energy and the macropulse length in the experiment.

THPOS15[1] Y.Hayakawa et al., Nucl. Instr. and Meth. A 483(2002) 29.
[2] T.Tanaka et al., “Guiding optics system for LEBRAFEL user facility”, FEL2004, Trieste, Italy, Aug.
2004.
[3] K.Yokoyama et al., Nucl. Instr. and Meth. A 507(2003) 357.
[4] K.Nakao et al., Proc. of the 28th Linear Accelerator
Meeting in Japan, (2003) 396 (in Japanese).
[5] H.Kogelnik and T.Li, Applied Optics 5, No.10(1966) 1550.
[6] K.Hayakawa et al., Proc. of LINAC2004, XXIIInternational Linear Accelerator Conference, Lubeck,Germany, Aug. 2004 (to be published).
[7] K.Halbach, Nucl. Instr. and Meth. 187 (1981) 109.
[8] M.Born and E.wolf, Principles of Optics, Cambridge
University Press (1999).

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H. Horiike et al. / Proceedings of the 2004 FEL Conference, 251-254

STATUS OF INSTITUTE OF FREE ELECTRON LASER, OSAKAUNIVERSITY
H. Horiike, N. Tsubouchi, K. Awazu, M. Asakawa, M. Heya, Y. Naito, H. Kondo and S. Suzuki
Institute of Free Electron Laser, 2-9-5 Tsudayamate, Hirakata, Osaka 573-0128 Japan
Abstract
Institute of Free Electron Laser at Osaka University is
FEL research facility, where beam physics and lightapplication studies are being carried out. Owing to huge
research field and to scientists or students of theuniversity, various scientific studies have been initiatedunder collaborations with schools and institutes in theuniversity, national institutes and industrial companies.
The main research field in the institute concerns beamphysics towards high quality longer wave length,
semiconductor application, environmental chemistry andbio-medical applications, which are supported by thebeam quality assurance of the beam physics study.

INTRODUCTION
Since the establishment in April 2000, Institute of Free
Electron Laser Osaka university (iFEL) [1] has supplied
the laser beam for about 5000 hours as well as the beam
study. While the first year was spent for the test run of
the accelerator, beam operation time reaches 1500-2000
hours per year afterwards. The research field mainly lies
in Bio-Medical application, semiconductor research andPhoto-chemistry, where 60%, 24% and 8% of the totalmachine time were dedicated, respectively. These
application studies were carried out within collaborations
with research groups in universities, national laboratories
and industries. Many users in the research programs used
the far-infrared radiation in the wavelength range from 5
to 20 µm, and requested for the longer wavelength up to
100 µm. Therefore the physics research aims to stabilize
the infrared FEL system and extend the wavelength
region towards longer wavelengths.
In this paper, we will present the achievements and thefuture plan of our institute. The accelerators and FEL
systems will be described in the next section, and then thestatus of the application programs will be reported in thefollowing section. The future plan will be also presented.

FEL SYSTEMSTwo S-band (2.856GHz) linear-accelerators are housed
at iFEL. One has a maximum energy of 180 MeV, andthe other an energy of 20 MeV. With these accelerator,
the FEL system covers the wavelength range from 0.28 to
60 µm. Details of the FEL systems are described in thefollowings.

Main Linac
The main linac consists of seven S-band standingwave accelerating tubes and boosts the electron energy up
to 180 MeV. The electron bunches are injected into the

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accelerator at a frequency of 22.3 MHz, 1/128 of the Sband frequency, from a thermionic electron gun driven bya grid pulser. A sub-harmonic buncher compresses theelectron beam of 500 ps into a 10 ps bunch to increase thepeak current before injection into the accelerating sections.
The 24 µs-long macropulse contains 550 electron bunches.
The charge of single bunch is 0.25 nC. This macropulse
is produced at a repetition rate of 10 Hz, and thecorresponding average current is 2 µA. A small fractionof the charge, 5%, is lost as the bunch passes through thesections. The peak current is about 80 A at the 180 MeV
beam line.
Three wigglers are installed on this linac and cover
the ultraviolet to mid-infrared part of the spectrum, 0.28 20 µm. The MIR wiggler is fed by 25 MeV electrons andlases in the range of 5 - 20 µm, the NIR wiggler 80 MeV
and 1 - 6 µm, the UVV (ultraviolet-visible) wiggler 180
MeV and 0.28 - 1.3 µm. The wiggler periods of MIR,NIR and UVV are 3.4, 3.8 and 4.0 cm, respectively.
Almost the same period, but they are driven by different
energy electron. The FIR system is installed to cover the
wavelength range from 20 – 60 µm and is now underdevelopment. The wiggler has a 9 cm period and is fed
by 25 MeV electrons which have passed through the MIR
wiggler. We are aiming for the simultaneous operation of
MIR and FIR systems to deliver “two color FEL beams”.
All the resonators have a length of 6.72 m so that one
radiation micropulse is restored in them. A coupling hole(1.5 mm in diameter) is bored on the center of the Aucoated metallic mirror installed on the upstream side. The
FEL light passes through this hole and is then converted
into the parallel beam with a diameter of 200 mm in orderto reduce the diffraction loss in the 50 m long transport tothe user's room. The transport tubes for MIR and NIR are
evacuated to reduce the absorption loss by air.
Figure 1 shows the average power vs. wavelength on
the MIR system. The MIR system covers the 5-20 µm
range with an average power of 20-45 mW. The power
falls off in the vicinity of 6.1 mm probably because ofabsorption by residual water in the transport tube. The
decrease in power for the longer wavelength range is due
to electron transport loss in the accelerator and magnetic
chicane. In the case of 17 µm operation, the average
current drops to 1.7 µA. The wavelength is changed in
two ways: the strength of wiggler field and the electron
beam energy. The wiggler parameter, or the K-parameter,
ranges from 1.0 to 1.5 with a gap spacing from 25 to 17
mm, respectively. (Although the wiggler itself can vary
the K-parameter from 0.5 to 1.5, the FEL power is too
small with K less than unity.) The tuning range by

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H. Horiike et al. / Proceedings of the 2004 FEL Conference, 251-254

30

28.5MeV

PhotocathodeRF-gun23MeV

average power (mW)25α-magnet

20.1MeV
24.3MeV

20

19.5MeV

Accelerating
tube

15

27.5MeV
1017.8MeV
5

0

4

6

8

10

12

14

16

18

wavelength ( µm)

Figure 1. Tunabilty of the iFEL mid-infrared FEL
system.

8m

Undulator
λu=2 cm

0.8
0.6
120

0.4
80

0.2

40
9.8

10.0

10.2

10.4

0
10.6

time (min.)wavelength (µm)

Figure 2. Spectral stability of the iFEL mid-infrared
FEL system.
varying the K-parameter is then about 20%, for example,
the wavelength can be varied from 8 to 10 mm with afixed electron energy. In this way, the wavelength can becontinuously varied in a minute.
For wider scanning, the electron energy is changed.
The electron energy is varied by changing the rf-power tothe accelerator. The energy is varied from 22 MeV to 26
MeV to cover the 5 - 20 µm range. Once the electronenergy is changed, it takes about 10 minutes to adjust theaccelerator components such as bending magnets,
quadrupole lenses, phasing of the rf field, and so on.
The spectral width is varied by 0.8-1.6% according to
the wavelength: for longer wavelength, the spectral
purity tends to degrade. This ranges is limited by thedevice parameter (the number of wiggler periods is 58)
and FEL physics (the spiking nature of the FEL
micropulse).
For stable operation of the FEL, temperature control of
the accelerator is the critical issue. The accelerator iscooled by water, which is controlled at a temperature of
40 degree centigrade with an accuracy of 0.1 degree.
With this technique, we achieve long-period ( -2-3 hours)
stable operation. Figure 2 shows the spectral stability.
The central wavelength fluctuates only 0.1 % during 2
hour long operation. This fluctuation is much smaller
than the spectral width and does not make any practicalproblem so far. On the other hand, the average powerstability is 1.9 %. Most of application programs call for
better stability in the power. We are investigating the

THPOS17

Figure 3. Compact FEL system for Bio-medical
application programs
origin of the power fluctuation [2] and developing a morestable machine.

Compact FEL system for Bio research
In order to meet the growing request on the beam time,
we are developing new far-infrared, 5-10 µm,FEL system
fed by a compact 20 MeV accelerator. This system can be
operated independently of the main accelerator and aims
to drive the mass spectrometer for the Bio-Medical
application programs. The accelerator consists of an RFgun, the alpha-magnet and an accelerating tube. With a
LaB6 thermionic cathode, the accelerator outputs anelectron beam with a peak current of 10 A and pulse widthof 3 ps during 5 µs macropulse-duration. This accelerator
can also be operated as the photo-injector by irradiating
the LaB6 cathode with a frequency-tripled mode-locked
YLF laser running at 89.25 MHz which corresponds to
1/32 of the S-band RF frequency. In this case, the peakcurrent reaches 60 A.
A hybrid planar undulator with a period of 2 cm and 50
total periods is installed in the magnetic chicane. With agap spacing of 1 cm, the undulator achieves a K value of
0.5. The resonator consists of a pair of Au-coated mirrors
with a spacing of 5.7 m. We expect 500kW peak power
FEL output of and 20 mW average power.

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H. Horiike et al. / Proceedings of the 2004 FEL Conference, 251-254

1800

800

(b)

1600

700

1400

600

(c)

1200

500

calculation of FEL output

For this FEL system, the pulse-picking system isdeveloped to investigate the dynamics of photo-ionizationand photo-dissociation. Also it is possible to use themode-locked laser synchronized to the accelerator for thepump-probe experiments and MALDI experiment.

1000

Figure 4 shows the detuning curve of the mid-infrared
FEL system installed on the main linac and the time
traces of the FEL macro pulse for various resonator
lengths. It is seen that the stability of the FEL output is afunction of the resonator. A detailed study has indicatedthat the power fluctuation was correlated with thefluctuation in the electron beam pulsewidth: the FEL
power started to drop when the pulsewidth of the electron
beam elongated while the power started to increase whenthe electron beam pulsewidth shortened. Numericalsimulation reproduced these experimental result andrevealed that the fluctuation in the FEL power arose fromthe non-linear evolution of the FEL micro pulse which
was governed by the resonator length. The fluctuation in
the electron beam pulse width has origin in the jitter
between the grid pulse of the electron gun and rf of the
sub-harmonic buncher. We are developing a feed backcircuit to synchronize the grid pulse and the rf source ofthe sub-harmonic buncher.

Development of the light sources
In order to meet the resent growing interests ofmaterial science in the THz spectral range, we aredeveloping a cyclotron laser [3]. This light source isinstalled on an 180 MeV beam-line of the main linac andproduces radiation with a broadband continuous spectrum
similar to the THz light source fed by femto-second laser.
The peak power, however, is expected to be 1 MW, which
is much more intense than the conventional light source inthis spectral range. Also a millimeter range compact FEL
using a micro-wiggler [4] and a tiny cherenkov FEL in the
far-infrared range are under development. These small
FEL systems are aiming at applications in practicalsituations.
Research in the photo-chemistry calls for a strong
radiation source in the wavelength range from 2 µm to 4
µm. A near-infrared FEL system which can cover 1-5 µm
is being developed using the 80 MeV beam-line of themain linac. For this wavelength range, we furnished a
OPA light source fed by a femto-second Ti:Sapphire laser.
This OPA system generates intense short-pulse light witha peak power of 1GW and a pulsewidth of 150 fs.
Comparison of the response to FEL and OPA will be
useful to study the nonlinear phenomena because of thelarge difference between the pulsewidth of these lasers.

APPLICATION PROGRAMS
So far, 40 application studies are performed withincollaborations with research groups belonging touniversities, national laboratories and private companies.
The representative themes are listed in Table 1. Research

800

300
200

400

100
0

(d)

600

200

10

20

30

40

50

0

signal(mV)Research on the stability of FEL [2]

400

0.50

(e)

0.25
0.00

0

10
20
time(µs)

30

detuning(µm)

Figure 4. Detuning curve of the mid-infrared
FEL system (a) and the time trace of the FEL
macro pulse (b)-(e) φορ 9, 13, 26, ανδ 32 µm
detuning, respectively.
Table 1. List of application programs
Theme
Semiconductor carrier dynamics
under the mid-infrared radiation
Far-infrared absorption and photoconduction of Semiconductors
Ion-injection into the shallow
junction formation using infrared
FEL
Infrared sensor study
THz semiconductor laser
Thin-film deposition assisted by
mid-infrared FEL
Molecular 18O concentration
Domain Change of Columnar
Liquid Crystal by FEL
UV/FEL-MALDI
mass
spectroscopy for analysis of
insoluble protein
Photonic Intervention Processes
for innovative Therapeutics
Biomimetic lipped bilayers as
matrix substances in MALDI-MS
Infrared
spectrographic
distinguishing method for aphosphate group andthe FEL irradiation effects against
a phosphorylated peptide
Laser surgery in blood vessel for
removal of cholesterol
Modification of dental tissue by
infrared lasers for caries therapy
Monitoring of soft tissue cutting
using acoustic waves
Measurement of bio-regenerative
material and modifications by FEL

Collaborator
Department
ofElectronics
Department of Physics
Mitsubishi
Electric
Corporation,
Ion
Engineering ResearchInstitute Corporation
Mitsubishi
Electric
Corporation
Department of Physics
Osaka
National
Research InstituteHitachi corporation
National Institute ofAdvanced Industrial
ScienceandTechnology (AIST)
the Intellectual Cluster
Project
the Intellectual Cluster
Project
National Institute ofAdvanced Industrial
ScienceandTechnology (AIST)
Nara
InstituteofScienceandTechnology
School of Medicine
Kinki
university,
Osaka
dentaluniversity
Kansai university
Kyoto university

FEL Oscillators

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H. Horiike et al. / Proceedings of the 2004 FEL Conference, 251-254

themes cover various fields: material science [5],chemistry [6], bio-medial research [7], and contain both
fundamental and practical research.
Some of these programs of 18O concentration, MALDI
and semiconductor dynamics research, were proceededwith use of both the FEL and external lasers such as CO2
laser, mode-locked YLF laser and N2 laser. A
synchronized OPA system which covers the 3-5 µm is
operational.

FUTURE PLAN
The present operation project will be concluded at
the end of March 2007. Beyond this period, a new projectof application research that fully uses the present
capability of the facility is being proposed. Developmentof medical applications is expected in the near future,including laser surgery and protein analysis with using the
MALDI mass spectroscopy. Several years after 2007, it ishoped that advanced quantum semiconductors will be
developed and widely used. These could not be performed
or invented without using FEL grade lights, and such highquality light spectra can not be re-produced easily by
conventional lasers.
The other application field of FELs would be inlonger wave spectrum. So called radiation in terahertz
region is difficult to be emitted by a conventional vacuum
tube or by light crystals. Even though the accelerator
based light source is large, it can generate much stronger
radiation than existing sources. High quality light can beeasily produced by FELs, and the present institute isstrongly expected to supply light in this spectral range.
For the purpose of analysis, FEL stabilization is the
key issue. Application projects that are based on steadyphysics research is the key issue of the institute, and ourinstitute is expecting and welcomes innovative proposalsof FEL itself and its application studies from all over theworld.

THPOS17

CONCLUSION
Sine its establishment in 2000, iFEL Osaka university
has supplied the FEL for 5000 hours during the operation
period from 2001 to 2004. The users, belonging to theuniversity, national laboratory and industrial company,
utilized the facility for research in the various fields.
Though the FEL system can potentially cover the spectral
range from ultraviolet to fir-infrared, most of application
programs were carried out with mid-infrared FEL system
which can produce the mid-infrared from 5 to 18 µm.
These programs call for the stability and the terahertz
radiation.
We are studying FEL physics and theaccelerator physics for the stabilization. Proposals of thelight source are also being developed to expand thewavelength range that our facility can deriver. The
accelerator based radiation source is believed to be able toopen a new scientific field in near future.

REFERENCES[1] http://www.fel.eng.osaka-u.ac.jp/[2] H. Nishiyama, M.Asakawa, et al, Nucl. Instr. andMeth. A507 (2003) 74.
[3] M. R. Asakawa, et. al., Nucl. Instr. and Meth. A 528(2004) 152.
[4] N. Ohigashi, et al, Nucl. Instr. and Meth. A507 (2003)
250[5] N. Mori, et al, Physica B 314 (2002) 431[6] M. Yasumoto, et al, Nucl. Instr. and Meth. A475
(2001) 640[7] K. Awazu, et al, Nucl. Instr. and Meth. A507 (2003)
547

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R. Nagai et al. / Proceedings of the 2004 FEL Conference, 255-257

MISALINGMENT TOLERANCE OF A HOLE-COUPLING OPTICALRESONATOR FOR JAERI ERL-FEL
R. Nagai, R. Hajima, N. Kikuzawa, E. Minehara, N. Nishimori, M. Sawamura,
JAERI, Tokai, Ibaraki, Japan
Abstract
The misalignment tolerance of a hole-coupling opticalresonator for the JAERI ERL-FEL is estimated with awavelength of 22 µm by a Fox-Li procedure simulation
code. To ensure the high-power and stable FEL operation,
the misalignment tolerance has to be clear, because the
FEL power depends on the misalignment of the opticalresonator. It is found that the misalignment tolerance ofthe hole-coupling mirror is less than the non-coupling
mirror and the offset effect of the non-coupling mirror iscompensable the mirror tilting.
The misalignment
tolerance is sufficiently large for the FEL powerfluctuation of 1%.

INTRODUCTION
An R&D program aimed at a 10-kW class free-electron
laser based on a superconducting energy recovery linac(ERL-FEL) is in progress at the Japan Atomic Energy
Research Institute (JAERI) [1]. To use the FEL light forvarious applications, the FEL power should be stable.
The FEL power stability is depends on the electron beamstability and the misalignment tolerance of the opticalresonator. To be stabilized the electron beam, the RF
system and electron gun of the JAERI ERL was improved[2, 3]. In this paper, the misalignment tolerance of the
optical resonator of the JAERI ERL-FEL is presented.
The optical resonator of the JAERI ERL-FEL consistsof gold-coated end mirrors and a center-hole output
coupler [4]. This allows wide broadband operation [5]and ultrashort optical pulse generation [6]. To ensurehigh-power and stable FEL operation, the misalignment
tolerance should be larger than the setting error of the
optical resonator and the vibration of the floor. The
misalignment tolerance with a wavelength of 22 µm is
estimated using a Fox-Li procedure simulation code [4].

MISALIGNEMT TOLERANCEThe FEL extraction efficiency is inversely proportional
to the square root of round-trip loss and the square root ofinteraction mode volume of the optical resonator [7]. The
output efficiency of the optical resonator is defined asηout=αout/αloss, where αout is the output ratio, αloss is theround-trip loss. The FEL power is then represented by thefollowing equation:

Pfel ∝

α out

α loss 3 / 2 ⋅ V 1 / 2,(1)

where V is the interaction mode volume. The round-trip
loss includes the output ratio, the reflective loss at the end
mirrors, and the additional diffractive loss. Because themisalignment of the optical resonator introduces

Available online at http://www.JACoW.org

additional diffractive loss and expansion of the interaction
mode volume, the FEL power is fluctuated by themisalignment. The FEL power is calculated by the FoxLi simulation code. The FEL power is normalized by the
FEL power of perfect aligned optical resonator. The
misalignment tolerance for the FEL power fluctuation of
1% is estimated by calculation the normalized FEL powerof the misaligned optical resonator.

Model of the Optical Resonator
The estimation model of the optical resonator consistsof two end mirrors, four apertures, and a center-hole
output coupler as shown in Fig. 1. The end mirror
reflectivity is 99.4 %. The four apertures represent theundulator duct and bending magnet ducts. The opticalguide and gain guide effect of the electron beam are nottaken into account. The parameters of the estimation
model are listed in Table 1.
Aperture of the bending magnet duct (74×34mm)
End mirror
Aperture of the undulator duct
60 mm

15 mm

R=3.877 m

56 mm
End mirror
Center-hole coupler
Aperture of the bendingZ
magnet duct (44×32.5mm)

YX

7.198 mFig. 1: Model of the optical resonator
Table 1: Parameters of the optical resonator
Length of the resonator
Length of the undulator duct
Rayleigh range
Radius of the end mirror
Reflectivity of the end mirror
Radius of the center-hole coupler

7.198 m2m
1m
60 mm
99.4 %
1 mm

Tilt Tolerance of the Misalignment
To estimate tilt tolerance of the misalignment, theoutput ratio, the additional diffractive loss, and theinteraction mode volume are calculated with the tilt
misaligned optical resonator. The additional diffractive
loss and the output ratio are shown in Fig. 2. The tilting
directions are in yz and zx plane (see Fig. 1). M1 andM2 represent the hole-coupling mirror and the noncoupling mirror, respectively. The output ratio decreases
with an increase of the tilt misalignment. In the tilt of lessthan 190 µrad, the additional diffractive loss decreases
with an increase in the tilt misalignment due to the

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R. Nagai et al. / Proceedings of the 2004 FEL Conference, 255-257

1.8
1.6

M2-yz
M2-zx
M1-yz
M1-zx

1.4
1.2
1.0
2.2

Output ratio (%)

2.0
1.8
1.6

M2-yz
M2-zx
M1-yz
M1-zx

1.4
1.2
0

50

100
150
Tilt (µrad)

200

250

Fig. 2: Additional diffractive loss (upper) and output ratio(lower) for the tilt misaligned optical resonator
The normalized FEL power with the tilt misalignmentis shown in Fig. 3. The tilt tolerance for the FEL powerfluctuation of 1% is about 100 µrad for both end mirrors.

where λ is the wavelength, d is the optical resonator
length, and g=1-d/R (R is the curvature radius of the end
mirror) is the stability parameter [8]. For JAERI ERLFEL, the tilt tolerance is ∆ΘM<<378µrad. This value isconsistent with the estimation of the tilt tolerance.

2.2
2.0
1.8
1.6
1.4
1.2

100

1.0
2.2
2.0

95

1.8
1.6

Output ratio (%)

Normalized FEL power (%)

105

M2-yz
M2-zx
M1-yz
M1-zx

90
85
0

50

100
150
Tilt (µrad)

200

250

Fig.3: Normalized FEL power for the tilt misaligned
optical resonator
The tilt tolerance of a symmetrical optical resonator isgiven byTHPOS22(2)

To estimate offset tolerance of the misalignment, theoutput ratio, the additional diffractive loss, and theinteraction mode volume are calculated with the offset
misaligned optical resonator. The additional diffractive
loss and the output ratio are shown in Fig. 4. The offset
directions are in x and y direction (see Fig. 1). The
output ratio decreases with an increase of the offset
misalignment. In the offset of less than 0.8 mm, theadditional diffractive loss decreases with an increase in
the tilt misalignment due to the decrease of the scattering
at the edge of the center-hole coupler. In the offset oflarger than 0.8 mm, the additional diffractive loss
increases with an increase in the tilt misalignment due tothe increase of the scattering at the aperture of theundulator duct.
The interaction mode volume isapproximately flat in this range of tilt misalignment. The
mode degeneracy due to the tilt misalignment is therefore
sufficiently small for the FEL interaction.

2.0

80

(1 − g )1 4 (1 + g )3 4 ,Offset Tolerance of the Misalignment

2.2

1.0

12

 2λ 
∆Θ M << π d 

Additional diffractive loss (%)

Additional diffractive loss (%)

decrease of the scattering at the edge of the center-hole
coupler. In the tilt of larger than 190 µrad, the additional
diffractive loss increases with an increase in the tilt
misalignment due to the increase of the scattering at theaperture of the undulator duct. The interaction mode
volume is approximately flat in this range of tilt
misalignment. The mode degeneracy due to the tilt
misalignment is therefore sufficiently small for the FEL
interaction.

1.4
1.2
1.0
0.8
0.6
0.0

M2-x
M2-y
M1-x
M1-y

M2-x
M2-y
M1-x
M1-y
0.2

0.4

0.6
0.8
Offset (mm)

1.0

1.2

Fig. 4: Additional diffractive loss (upper) and output ratio(lower) for the offset misaligned optical resonator
The normalized FEL power with the offset
misalignment is shown in Fig. 5. The offset tolerance for
the FEL power fluctuation of 1% is about 0.1 mm and 0.4
mm for M1 and M2, respectively. In the tilt misalignment

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R. Nagai et al. / Proceedings of the 2004 FEL Conference, 255-257

and the offset misalignment of the M2, the center-hole
coupler is aligned with the resonator axis. In the offset
misalignment of M1, the center-hole is offset from theresonator axis. M1 is therefore more sensitive than M2 forthe offset misalignment.

100
95

115

M2-x
M2-y
M1-x
M1-y

90
85
80
0.0

0.2

0.4

0.6
0.8
Offset (mm)

1.0

1.2

Fig. 5: Normalized FEL power for the offset misaligned
optical resonator
Because the optical resonator of the JAERI ERL-FEL isnear-concentric configuration, the relationship of the tilt
tolerance and the offset tolerance is given by∆ M ≈ R ⋅ ∆Θ M .
(3)
In the case of M2, the offset tolerance of 0.4 mm
corresponds to the tilt tolerance of 100 µrad.

Offset Effect Compensation by the Mirror Tilting
As mentioned above, the offset misalignment is similar
to the tilt misalignment in the near-concentric opticalresonator. Therefore, the offset effect compensation by the
mirror tilting is possible. To estimate offset effectcompensation of M2, the normalized FEL power iscalculated with the offset and tile misaligned opticalresonator. As shown in Fig. 6, the offset effect of M2 iscompensable tilting the mirror with the offset of up to 1
mm.
Normalized FEL power (%)

115

105
100
95
90
85
80
-500

-400

-300

-200 -100
Tilt (µrad)

0

100

110
105

y-offset 0.1mm
y-offset 0.2mm
y-offset 0.4mm
y-offset 0.6mm
y-offset 0.8mm
y-offset 1.0mm

100
95
90
85
80
-500

-400

-300

-200 -100
Tilt (µrad)

0

100

200

Fig. 7: Offset effect compensation by mirror tilting for thehole-coupling mirror

CONCLUSION
The misalignment tolerance of a hole-coupling opticalresonator for the JAERI ERL-FEL is estimated with awavelength of 22 µm by a Fox-Li procedure simulation
code. The offset and tilt tolerance for the FEL powerfluctuation of 1% are 0.1 mm and 40 µrad, respectively.
The vibration of the floor is less than 1 µm. The accuracyof the He-Ne alignment system of the optical resonator isless than 20 µrad. The offset and tilt tolerance of the
optical resonator is therefore sufficiently large for the FEL
power fluctuation of less than 1%.

REFERENCES

y-offset 0.2mm
y-offset 0.4mm
y-offset 0.6mm
y-offset 0.8mm
y-offset 1.0mm

110

Normalized FEL power (%)

Normalized FEL power (%)

105

offset effect compensation is not expected. To investigate
offset and tile misalignment effect of M1, the normalized
FEL power is calculated with the offset and tilt
misaligned optical resonator. The normalized FEL poweris enhanced by the suitable offset and tilt misalignment asshown in Fig. 7. The flat top range of the normalized
FEL power decreases with an increase of the offset
misalignment. The offset and tile tolerance for the FEL
power fluctuation of 1% are 0.1 mm and 40 µrad,respectively.

200

Fig. 6: Offset effect compensation by the mirror tilting forthe non-coupling mirror
Because the offset effect of M1 is irregular due to theoffset effect of the center-hole as shown in Fig. 5, the[1] R. Hajima, et al., these proceedings.
[2] R. Nagai, et al., Proc. of the 1st Annual Meeting ofParticle Accelerator Society of Japan, (2004) 293295.
[3] N. Nishimori, et al., Nucl. Instr. and Meth. A445
(2000) 432-436.
[4] R. Nagai, et al., Nucl. Instr. and Meth. A528 (2004)
231-234.
[5] R. Nagai, et al., Proc. of the 13th Symposium on
Accelerator Science and Technology (2001) 455-457.
[6] R. Hajima, R. Nagai, Phys. Rev. Lett. 91 (2003)
024801.
[7] N. Piovella, et al., Phys. Rev. Lett. E52 (1995) 54705486.
[8] C. A. Brau, “Free-Electron Laser”, Academic Press
Inc. (1990) pp.326

FEL Oscillators

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H. O. Ogawa et al. / Proceedings of the 2004 FEL Conference, 258-261

OPTIMIZATION OF THE NIJI-IV FEL SYSTEM FOR THE COHERENTHARMONIC GENERATION IN A Q-SWITCHED REGIME
H.Ogawa#, K. Yamada, N. Sei, M. Yasumoto
National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba,
Ibaraki 305-8568, Japan
Abstract
The Coherent Harmonic Generation (CHG) in the VUVregion at the storage ring NIJI-IV has been numericallyinvestigated. The harmonic radiation is produced in an
FEL oscillator with a hole-coupled resonator including a
6.3-m optical klystron ETLOK-II. The evolution of lightpulses through Q-switched FEL process is simulatedusing the code GENESIS1.3 and its extended version. The
parameters of the NIJI-IV FEL system were optimized forelectron-beam energy and optical cavity configurations.

was used for the calculation. The reflected field aref(r, z)
exp(-iksz) can be expressed in the incident field ainc(r,z)exp(iksz) in approximation of ksR≫1 as
ird r rd r
aref ( r , z 0 ) = ainc ( r , z 0 ) −ainc (r , z 0 )2 k s RMINTORODUCTION
Several works on harmonic generation in storage ring
FELs (SRFELs) have been experimentally andtheoretically performed [1-9]. In the previous work [9],we have made simulation code for investigation theharmonic generation with a hole-coupled resonator
combined with a 6.3-m optical klystron ETLOK-II [10].
In this paper the optimization of the NIJI-IV FEL systemis studied by means of the code.

OUTLINE OF SIMULTAION
The detail of simulation procedure was described in
Ref.[9] and this section presents the outline: The FEL
process in an optical klystron ETLOK-II is simulatedusing the code GENESIS1.3 [11]. In SRFELs the electronenergy spread induced by the FEL interaction
accumulates from turn to turn. This code includes theenergy spread growth which was calculated by
GENESIS1.3. The optical field emitted from ETLOK-II isreflected by a hole-coupled resonator. The paraxial wave
equation∂  iφ ∆ ⊥ + 2ik s  a s e = 0
∂z 


(1)

r 3d
r2
ainc ( r , z 0 ) − 2 r ainc ( r , z 0 )
2
RM
RM

+


ik s r 4
ainc (r , z0 )  exp( 2ik s z M )
RM3


(2)

Here the surface of a spherical mirror with radius ofcurvature RM was parameterized as zM = z0 – r2/2RM, as
shown in Fig. 1, and the last four terms in Eq.(2) can beneglected for NIJI-IV. In this simulation, the reflection ofa hole on the mirror axis was assumed a smooth-edge
function as R(r)=2(r/Ra)4-(r/Ra)8. The effective radius of
the hole, Reff =0.74Ra, is defined as the radial position
where the reflection R becomes 0.5 [12].
The coherent emission from the number of electron Ne
in the straightforward direction at the harmonic n [7,8]was evaluated by

d 2In
d 2I0
1
= N e2 an2dωdΩ 2
dωdΩ

(3)

where


∆γ m 
 fn
an = 2 J n  4πnN dγ is the enhancement factor of nth coherent harmonic
emission and d2I0/dωdΩ is the emission from a single
electron and Jn is Bessel function of the order n and fn themodulation factor. The energy modulation ∆γm wasestimated by GENESIS1.3.

(r,z M )RM

OPTIMIZATION OF THE NIJI-IV FELSYSTEMrz
Figure1: Definition of mirror geometry

THPOS27−

Electron beam energy
The NIJI-IV is a compact storage ring whose
circumference is 29.6m and is usually operated at thebeam energy of ~310MeV for UV/VUV FEL experiments.

Available online at http://www.JACoW.org

259

H. O. Ogawa et al. / Proceedings of the 2004 FEL Conference, 258-261

2 3
22π E  f s  σ lP −σ l 0σ lPI=(Z / n)eff .
eαR3  f rev (4)Here fs and frev are synchrotron oscillation frequency andring revolution frequency, α and R are momentum
compaction factor and ring average radius, σl0 and (Z/n)eff
are natural bunch length and the effective longitudinal
coupling impedance, η is the phase-slip factor defined as
η=α−1/γ2. The bunch lengthening due to microwave
instability occurs above the threshold current

I

th

=

(2π )3 / 2ηf revσ l E  σ γ 
ec Z / n bb

2

 γ  .



(5)

The bunch length σlM is described as

1/ 3


ηR3 I Z / n bb
σ lM =  2π ( E / e)( f s / f rev ) 2 



(6)

where |Z/n|bb and σγ/ γ are longitudinal broad-band
impedance and relative energy spread, respectively. The
natural energy spread and emittance are proportional to E
and E2, respectively, which causes the decreases of FEL
gain and power of harmonics at high energies. The
emittance growth via intra-beam scattering (IBS) was
estimated using the code ZAP of which the influence isremarkable at low energies.
The simulation has been performed at the energy of 310,
350, 380, 400 and 450MeV in a single-bunch operation at
30mA.The electron-beam parameters at 310MeV are
listed in Table 1. In this study, the designed values ofnatural energy spread and emittance were used for
simulation. The optical resonator parameters are listed inTable 2. The fundamental at 300nm was calculated at
RM=8m with an effective hole diameter of 0.2mm in a
Table 1: Parameters of NIJI-IV at the electron-beamenergy of 310MeV
Natural relative energy spread
2.4×10-4
Natural emittance
5.6×10-8
Revolution frequency
10.1MHz
Momentum compaction factor
0.0884Beam current
30 mA

Table 2: Parameters for ETLOK-II and optical resonator
Magnetic period
Undulator section
Dispersive section
Total length
Number of period
Cavity length
Cavity loss

72mm
216mm
6.288m
42×2
14.8m
1.0%

Q-switched regime. In this condition, the intra-cavity
peak power of third harmonic at 100nm was obtained as
maximum intensity when the beam energy was 380MeV.

Asymmetric resonator
In the previous section, the calculation was performed
with symmetric resonator, while there are someadvantages of making use of asymmetric resonator: i) the
spot size on the downstream mirror can be larger so thatthe cavity loss becomes smaller. ii) the beam waist
position can be near the center of the upstream undulator
so that the energy modulation ∆γm could be larger. Hence,in this section, asymmetric resonator is considered at thebeam energy of 380MeV.
The intra-cavity power of third harmonic at 100nm wascalculated by changing the radius of curvature ofdownstream mirror Rd with a 0.2mm effective holediameter as shown in Fig.2. (The radius of curvature of
upstream mirror Ru was fixed at 8m.) The third harmonic
power of asymmetric resonator with Rd =9 and 10m is
larger than that of symmetric resonator with Rd =8m. The
value of Rd is optimized at 10m and the power decreases
more than Rd =11m.
In order to understand the tendency in Fig.2, spot size
on upstream wu and downstream mirror wd were
calculated, as shown in Fig.3, by

1/ 4

w =
d


λs Rd Lc ( Ru − Lc )π  ( Rd − Lc )(Ru + Rd − Lc ) .
4

P ow er (m W )There is a possibility to increase harmonic radiation
power in the higher electron-beam energy operation, since
the average power of an undulator FEL is proportional toγ4. Therefore the beam energy dependence of third
harmonic radiation power was investigated.
The electron-beam parameters for different energies
were estimated as follows: The bunch length was
calculated by σl=(σlp2+σlM2)1/2. The bunch lengthening
under the influence of the potential well distortion σlp was
evaluated by

3

2

Ru=8m
1

8

9

10

11

12

R d (m )Figure2: Dependence of intra-cavity peak power for
third harmonic on the radius of curvature ofdownstream mirror Rd with Ru=8m.

FEL Oscillators

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H. O. Ogawa et al. / Proceedings of the 2004 FEL Conference, 258-261

2.0

1.0

0.5

wu
wd

Ru=8m
8

9

10

11

12

R d (m )1/ 4

Lc ( Rd − Lc )λ R w = s uuπ  ( Ru − Lc )(Ru + Rd − Lc ) 

where Lc is cavity length. The value of wd is almost
constant against Rd and that of wu decreases withincreasing Rd. The beam waist position was also
calculated by

L ( R − Lc )l = c du Ru + Rd − 2Lc.

The waist position for Rd =11 and 12m locates between
the center and entrance of the upstream undulator.
Therefore the filling factor for Rd =11 and 12m becomes
small so that the power of third harmonic for Rd =11 and
12m is smaller than that for Rd≤10m. And the waist
position for Rd =10m is found to be nearest the center ofthe upstream undulator. Hence the power of third
harmonic for Rd =10m becomes maximum because theenergy modulation ∆γm is largest.

1.5
1.0
0.5

Rd=10m
5

6

7

8

9

Figure5: Spot size on upstream wu and downstream
mirror wd with Rd=10m.
The calculations have been also performed bychanging Ru with Rd =10m. Figures 4 and 5 show
dependence of power for third harmonic at 100nm andspot size on Ru, respectively. The optimized Ru was foundto be 6m and the power of third harmonic was obtained as~10mW which was much larger than the former one.

CONCLUSION
The generation of third harmonic in a Q-switchedregime for the NIJI-IV FEL has been simulated usingcode GENESIS1.3 and its extended version. Optimizationof asymmetric resonator has been performed by varying
the radius of curvature for upstream and downstream
mirror. The calculated intra-cavity peak power of third
harmonic at 100nm was ~10mW with a hole-coupledresonator at the electron-beam energy of 380MeV.

ACKNOWLEDGEMENT
This study was financially supported by the Budget
for Nuclear Research of the Ministry of Education,
Culture, Sports, Science and Technology, based on thescreening and counseling by the Atomic Energy
Commission, Japan.

REFERENCES

10

8

P ow er (m W )2.0

R u (m )Figure3: Spot size on upstream wu and downstream
mirror wd with Ru=8m.

64

Rd=10m5

6

7

R u (m )8

9Figure4: Dependence of intra-cavity peak power for
third harmonic on the radius of curvature of upstream
mirror Ru with Rd=10m.

THPOS27

2.5

0.0

0.0

2

wu
wd

3.0

1.5

W aist size (m m )W aist size (m m )3.5[1] J.M. Ortega et al., IEEE J. Quantum Electron. QE-21(1985) 909.
[2] R. Prazeres et al., Europhys. Lett. 4 (1987) 817.
[3] K. Yamada et al., Nucl. Instr. and Meth. A407 (1998)
193.
[4] V.N. Litvinenko, Nucl. Instr. and Meth. A507 (2003)
265.
[5] E.C. Longhi et al., Proceedings of the 25th Free
Electron Laser Conference, Tsukuba, Japan, Sep. 812, 2003, to be published.
[6] R. Prazeres et al., Nucl. Instr. and Meth. A304 (1991)
72.
[7] P. Elleaume, Nucl. Instr. and Meth. A250 (1986) 220.
[8] J.M. Ortega, Nucl. Instr. and Meth. A250 (1986) 203.

H. O. Ogawa et al. / Proceedings of the 2004 FEL Conference, 258-261[9] H. Ogawa et al., Nucl. Instr. and Meth. A528 (2004)
301.
[10] T. Yamazaki et al., Nucl. Instr. and Meth. A331
(1993) 27.
[11] S. Reiche, Nucl. Instr. and Meth. A429 (1999) 243

261[12] B. Fattz et al., J. Phys. D: Appl. Phys. 26 (1993)
1023.

FEL Oscillators

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W.K. Lau et al. / Proceedings of the 2004 FEL Conference, 262-265

PRELIMINARY DESIGN OF A SYNCHRONIZED NARROW BANDWIDTHFEL FOR TAIWAN LIGHT SOURCE
W.K. Lau, J.R. Chen, T.C. Fan, F.Z. Hsiao, K.T. Hsu, C.S. Hwang, C.C. Kuo, G.H. Luo, D.J. Wang,
J.P. Wang, M.H. Wang, NSRRC, Hsinchu, Taiwan
C.W. Chen, H.Y. Chen, NTHU, Hsinchu, Taiwan
Abstract
Design study for a narrow bandwidth, high power IRFEL has been carried out at NSRRC. This device will be
synchronized with the Taiwan Light Source (TLS) storage
ring for two-colour experiments. Instead of using lower
gradient super-conducting linacs at UHF frequency, it has
been proposed to use a high gradient 1300 MHz TESLA
super-conducting linac to accelerate a high average
current electron beam up to 60 MeV to drive this FEL
oscillator. To obtain narrow bandwidth, the beam isstretched in bunch length by using a chicane decompressor before it passes through the U5 undulator of
the FEL. Operating this linac in energy recovery mode isbeneficial to improve system stability, wall-plug
efficiency and to reduce neutron generation at beam dump.
This device will be equipped with a low emittanceinjector for future upgrade towards shorter wavelengths.
The ideas of the TESLA linac plus bunch stretcher
scheme as well as a new type of low emittance highaverage current thermionic DC gun will be introduced inthis report.

described in the later sections, we have a different
approach. Figure 1 is a cartoon of the IR-FEL facility.
Since the revolution frequency of the TLS storage ring is2.4983 MHz, assuming that the storage ring is evenly
filled with two electron bunches, the bunch crossing
frequency is will be two times of the revolution frequency.
Whereas the total number of rf buckets is 200.
Continuous 4.9967 MHz IR pulses from the FEL
oscillator will be synchronized with the synchrotron
radiation from the U9 undulator in the TLS storage ring
also at the same pulse repetition rate.

INTRODUCTION
Many high power THz and IR, FEL facilities that basedon energy recovery linac (ERL) technology have been
constructed [1-3]. Similar devices have been proposedand some are under construction [4-5]. Applications aremainly on photo-chemistry, isotope separation andmaterial processing [6] etc.
TLS is a 1.5 GeV third generation storage ring
synchrotron radiation source. It has been operating stably
in the pass few years with high availability. The feasibilityof building a high power IR FEL facility that will be
synchronized with the synchrotron radiation from TLS
beam-line is being discussed. It is believed that thisfacility will be a very valuable tool for local photochemistry and condensed matter research community.
Some basic performance requirements as suggested bypotential users are summarized as follows:• Wavelength range: 2.5 ~ 10 µm• Resolution: < 1 cm-1
• Wavelength Stability: < 0.1 cm-1
• High peak power• Macro-pulse energy > 1 J/pulse• Synchronize with TLS storage ring
Note that these requirements are actually quite similar
to the FEL proposed for Chemical Dynamics ResearchLaboratory (CDRL) in 1992 at Berkeley [4]. However, as

THPOS36

Figure 1: A cartoon showing the proposed IR-FEL insynchronization with the U9 radiation from the TLS
storage ringBASIC CONSIDERATIONS
Since the bandwidth of a linac-based FEL oscillator isjust the Fourier transform of the electron bunch length [7],the choice of bunch length has to be consistent with the
bandwidth requirement. To produce coherent infrared
radiation at very narrow band-width, long bunch length ispreferred. In our case, at 10 µm wavelength for example,
the bandwidth according to users’ wish list is better than
0.1%. Therefore, the required bunch length should be
longer than 33 ps. Other means such as putting a gratingin the optical cavity can be considered as further
reduction in bandwidth. On the other hand, the injector
should have significant peak beam current to getreasonable single pass gain to overcome total round trip
loss in the optical cavity, but available bunch current islimited by total bunch charge provided the injector. For a
fixed amount of bunch charge, as the bunch length
become longer, the achievable peak current would belowered. Therefore, an injector for high bunch charge is

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W.K. Lau et al. / Proceedings of the 2004 FEL Conference, 262-265

necessary. Although the emittance requirement of an IRFEL is not too stringent, we would also like to have alower emittance injector so that upgrade for shorter
wavelengths will be possible.
For high power operation, the choice of using superconducting is natural. Furthermore, it also provides goodstability because of its slow response time to external
perturbations. To avoid the effect of Lorentz detuning, it
is advantageous to employ the energy recovery concept
and operate the super-conducting linac at CW mode (i.e.
Energy Recovery Linac, ERL). ERL also helps toimprove wall-plug efficiency and reduce neutron
production at the beam dump. Since we are pursuing a
relatively long bunch, it seems straight forward to use
lower frequency linac (e.g. 500 MHz) to accelerate thebeam to nominal beam energy without much degradationin energy spread. However, the gradient for such linacs
are much lower than that for higher frequency linacs. For
example, the TESLA linac has a record gradient of 35
MV/m [8] whereas a typical gradient of a few hundreds
MHz linac is ~5 MV/m. But to accelerate such a longbunch with higher frequency linac, larger beam energy
spread is expected due to the rf curvature. An alternative
solution is to accelerate a short bunch electron beam tonominal energy with higher frequency linac and followed
by a bunch de-compressor to elongate the bunch to
specified beam length. Such scheme is in principle
feasible except the beam current in the linac will be muchhigher. Longitudinal phase space manipulation and beam
instability that may be excited in the ERL has to betreated carefully.

Table 1: Basic Design Parameters for the NSRRC IR-FEL
Wavelength [µm]Bandwidth
Micro-pulse peak power [MW]Micro-pulse duration [ps]Micro-pulse rep. rate [MHz]Minimum Macro-pulse [ms]CW mode operation

2.5~10
0.1 % @ 10 µm(transform limited)
16
33
4.996
> 10
yes

Tuning of the laser wavelength is of critical importanceto users. Interruptions to the users during tuning should be
minimized. As depicted in Figure 2, wavelength tuningfrom 2.5 to 10 µm is unavoidably required a change indriver accelerator operation state. However, change ofaccelerator system energy and optimize all parameters for
FEL lasing without much disturbance to the users is notan easy task. This is especially true for ERL.

THE FEL OSCILLATORAs an initial study, a single undulator FEL oscillator
configuration is considered. And the parameters of the U5
undulator as described in the Berkeley CDRL IR-FEL
design report [4]. It is a 40-period undulator with period
length of 5 cm. The peak magnetic field is 0.45 T. The
gap is adjustable from 23 mm to 36.5 mm. It provides a
deflection parameter setting ranging from 0.9 to 2.1. The
electron beam energy is set at 60 MeV based on the FEL
resonant condition for planar undulator. An undulator
with shorter period length helps to reduce beam energy.
However, a narrow undulator gap (e.g. 12 mm) is
required for operation in wavelength range from 2.5 to 10µm. In the U3 case, operation at wavelength longer than
10 µm will be limited by the interception between the
optical beam and narrow vacuum chamber. The opticalcavity is a 30 m confocal configuration with a hole on one
mirror for outcoupling of laser power. The choice ofcavity length is determined by the micropulse repetition
rate. The Rayleigh length of this optical cavity is chosen
at half of the undulator length and a total round trip lossof 10% is assumed.
To meet those performance requirements as stated in
the last section, some basic design parameters for the IRFEL are listed in the following table and the electron
beam parameters are listed in next section:

Figure 2: Wavelength tuning of the IR-FEL oscillator
using U5 undulator
The use of a planar in-vacuo super-conducting
elliptically polarized undulators with period length of 5
cm (SEPU5) is being study. At 100 MeV, the undulator iscontinuously tuneable from 1 to 10 µm without changing
the electron beam energy. And the polarization of thelaser field is also tuneable [9].

ACCELERATOR SYSTEM
In designing the accelerator system as a driver for the
FEL, the 1300 MHz TTF SC linac is used as an example
simply because it has a record high gradient of 35 MV/m.
However, the linac is decided to operate at 15 MV/m forreasonably low cryo-load. Since the revolution frequency
for TLS storage ring is 2.49833 MHz, the linac cavity
frequency has to be multiples of the revolution frequency.
The closest multiple to the TESLA linac cavity is 520.
That is, the desired cavity frequency is 1299.13 MHz. The
resonant frequencies of the cavities have to be adjusted tothis value during fabrication [10]. The TESLA cryo-

FEL Oscillators

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W.K. Lau et al. / Proceedings of the 2004 FEL Conference, 262-265

Figure 3: Layout of the ERL with bunch de-compressor before undulator
module consists of eight cavities and each cavity has 9
cells [11]. We hope we will have one such module in thesystem provide an energy gain of 120 MeV. The above
FEL design parameters are based on a beam withfollowing properties:
Table 2: Expected Electron Beam Parameters
Maximum beam energy [MeV]
Bunch current [A]Beam average current [mA]
Bunch charge [nC]
Bunch length [ps]Bunch rep. rate [MHz]
FWHM energy spread
RMS normalized emittance [mm-mrad]

60
30-60
11
>2
> 33
4.9967< 0.5%< 25

A possible layout of the driver accelerator for the FEL
oscillator is depicted in Figure 3. The beam injector
provides a ~5 MeV beam with bunch charge of 2 nC. And
bunch length is adjusted to about 8 ps before injection to
the main linac. Since bunch repetition rate of the beam isabout 5 MHz (two symmetrical filled bunches). Hence,
the average current of the beam provided by the injector
will be 11 mA. After the main linac, the beam isaccelerated to 60 MeV. The expected energy spreadinduced by the linac is about 0.2 %. It is much lower than
the allowable beam energy spread for the FEL interaction.
The bunch de-compressor will be designed to expand thebunch by four times. In the first stage of the proposed
project, the FEL will be operated at low macro-pulse
repetition rate without energy recovery. Design of the
return arc in the ERL that will remains as a challenge for
future CW operation.

THPOS36

Two types of cathode technologies are being studied.
That is, the photo-cathode DC gun and the CeB6 cathodeDC gun. For the photo-cathode dc gun which operates
routinely at JLab’s IR-FEL, the repetition rate is high but
it provides only 135 pC bunch charge. Also, the GaAs
cathode has to work in ultra-high vacuum environment of
10-12 torr. A high power mode-lock laser and special
technique in treating the cathode are also required. The
CeB6 crystal cathode in the electron gun developed at
Spring8 for the SCSS project is pulsed at -500 kV for 3 µs.
And the repetition rate is at 60 Hz. In spite of its low duty
factor, it has the advantages of low emittance, long
lifetime and ultra-high vacuum is not essential. The
measured normalized emittance of this gun is 1.1 π mmmrad at 1 A beam current [12]. It has been discussed
whether this type of electron gun can be built for highaverage current operation. Operation at lower cathodevoltage for DC mode operation without causing
breakdown is possible. For example, the cathode voltage
can be set at -100 kV. A control grid can be added topulse the beam at 5 MHz repetition rate (Figure 4). It
allows an average beam current of 11 mA [13].
Preliminary EGUN simulation results showed that bychanging the control grid voltage, emittance degradation
due to space charge can be compensated by the focusing
field near the grid.
It has been discussed in house that some users may findapplications in the UV range with wavelength less than
200 nm. In such wavelength range, single pass high gain
FEL can be used. The high gradient SC linac plus bunch
de-compressor scheme allows easy beam energy upgrade
just by adding more cryo-modules into the system. The
de-compressor can be converted into compressor for

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W.K. Lau et al. / Proceedings of the 2004 FEL Conference, 262-265

single pass high gain FEL operation. At such beamenergy, ERL is of essential importance in relaxing rf
power requirement.

ACKNOWLEDGEMENT
The authors would like to thank Dr. George Neil, Dr.
Tsumoru Shintake, Dr. Dieter Proch and Dr. Peter Michel
for many stimulating discussions and provide very helpful
information.

REFERENCES

Figure 4: A CeB6 cathode DC gun with control grid

SUMMARY
The feasibility of using the TESLA high gradient field
super-conducting linac plus a bunch de-compressor todrive IR-FEL oscillator for a narrow bandwidth is being
investigated. Further studies includes: the design of a low
emittance high average current injector that based on
CeB6 cathode technology and beam transport system forenergy recovery.

[1] G.R. Neil et al., Phys. Rev. Lett., 84, p. 662-665(2000).
[2] R. Hajima et al., Nucl. Instrum. Methods Phys. Res.,
A507, p. 115-119 (2003).
[3] E.A. Antokhin et al., Nucl. Instrum. Methods Phys.
Res., A528, p. 15-16 (2004).
[4] Design Report of “An Infrared Free-Electron Laser for
the Chemical Dynamics Research Laboratory”, LBL
PUB-5335 (1992).
[5] B.C. Lee et al., Nucl. Instrum. Methods Phys. Res.,
A528, p. 106-109 (2004).
[6] G.R. Neil, “Industrial Applications of Free Electron
Lasers”, in Workshop on Advanced Free Electron
Lasers and Their Applications, Hsinchu (2004).
[7] K.J. Kim, Phys. Rev. Lett., 66, p. 2746-2749 (1991).
[8] L. Lilje et al., TESLA report no. 2004-05 (2004).
[9] C.S. Hwang et al., in these proceedings.
[10] D. Proch, private communication.
[11] B. Aune et al., PRST-AB, 3, 092001 (2000).
[12] K. Togawa et al., PAC2003 proceedings, p. 33323334 (2003); K. Togawa et al., in APAC2004
proceedings.
[13] T. Shintake, private discussion.

FEL Oscillators

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O.A. Shevchenko et al. / Proceedings of the 2004 FEL Conference, 266-269

NUMERICAL MODELING OF THE NOVOSIBIRSK TERAHERTZ FELAND COMPARISON WITH EXPERIMENTAL RESULTS
O.A. Shevchenko #, A.V. Kuzmin, N.A. Vinokurov,
Budker Institute of Nuclear Physics, 11 Acad. Lavrentyev Prosp., 630090, Novosibirsk, Russia
Abstract
Recently a new high-power terahertz FEL has been put
in operation at the Siberian Center for Photochemical
Research in Novosibirsk. The first lasing at the
wavelength near 140 micrometer was achieved in April
2003. Since then some experimental data were obtained
which required theoretical explanation. In this paper weuse a simple 1-D model for numerical simulations of the
FEL operation. The model is based on the excitation ofmultiple longitudinal radiation modes of the opticalresonator by the charged discs. We restrict ourconsideration to the transverse fundamental mode only.
This approximation is valid in the case of long-wave
FELs. We compare the results of numerical simulations
with some analytical estimates and experimental data.

INTRODUCTION
The Novosibirsk high power FEL started operation
recently [1]. It operates in CW mode at terahertz bandusing simple two-mirror optical resonator. The computercode was created to provide simulations for all measured
data. As the beam transverse sizes are significantly lessthan the radiation eigenmode size, it is enough to use a
one-dimensional code.

Electron beam in our model is presented as a set of thin
rigid disks with Gaussian transverse distribution of
charge, which is supposed to be the same for each disk.
The total charge of a disk is equal to the total charge ofthe bunch, divided by the number of disks and the chargeto-mass ratio is the same as for a single electron. We
neglect the influence of the radiation field on thetransverse motion of a disk. It means that transverse
trajectory is definitely determined by the undulator field
and the disk has only the longitudinal degree of freedom.
We also neglect betatron oscillations and include theircontribution to the longitudinal velocity as an additionalenergy spread. It is convenient to use the longitudinal
spatial coordinate z as an independent variable. In thiscase the system of equations for the longitudinal motion
can be written asd∆ne
E x x ′(z )=dz γ 0 me c 2

velocity,τnis the time delay with respect to thereference particle with energy γ 0 ,energy deviation,Ex∆n is the relativeis radiation electrical field,

averaged over disk charge distribution. x ′(z ) is thetransverse trajectory angle in x-z plane, in our
approximation it depends only on z coordinate, and in thecase of planar undulator x ′(z ) = −K

γ0sin (k w z ) , where

K is the undulator deflection parameter,k w is theundulator wave number.
The radiation field inside the optical resonator may be
represented as the linear combination of the resonator
eigenmodes. Taking into account small transverse size ofelectron beam and relatively high damping rate for highorder transverse modes, one can restrict the consideration
to the fundamental transverse mode only. Then the onaxis radiation electric field may be represented as
E x (0, 0, z, t ) = 2 Re  ∑ ak ( z )e ik ( z −ct ) 
 k


(2)

For the numeric calculations it is convenient to consider
the discrete spectrum wave packet with the carrier wave

MODEL DESCRIPTION AND BASIC
EQUATIONS

dτ n
1
1
=
−
dz Vz (∆n ) Vz (0)where n is the disk number, Vz (∆ ) is the longitudinal(1)

number k0: k m =2πm+ k 0 , m is integer, and T0 is thecT0envelope period. T0 have to be chosen much more, thanthe packet duration (typically, of the order of the electron
bunch length). Using this field expansion, one can derive
the FEL equations for a single pass of the wave packet
and particles (charged disks) through the undulatordbk= ∑ De i [θδ k +ϕ n (1+δ k ) ]
dθ
n
d∆ n
= − Re ∑ bk e −i [θδ k +ϕ n (1+δ k ) ]
dθ
k
dϕ n
= −2∆ ndθ(3)Here we introduced the following set of dimensionlessvariables and constants: ϕ n = k 0 cτ n , θ = k w z ,δk =k − k0eK (JJ )0 i
, bk = −ak ,me c 2 γ 02 k w
k0___________________________________________#

O.A.Shevchenko@inp.nsk.su

THPOS46

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O.A. Shevchenko et al. / Proceedings of the 2004 FEL Conference, 266-269

 K (JJ )0 Q
D =π
, where3 
T0 S 0 I 0γ 0  k w 
2(JJ )0 is thestandard combination of Bessel functions, I 0 =me c 3ethe Alfven current, S0 is an effective area of radiation (the
power
over
the
on-axisintensity),andk 0 = 2γ 02 k w (1 + K 2 2 ) is chosen.

One can easily check that the system Eq. (3) conserves
the total energy

delayed by the optical resonator length L detuning δT =1/f0-2L/c (f0 is the bunch repetition rate). We used
Gaussian distribution for energy ∆n and uniform,
parabolic or Gaussian distributions for coordinate ϕn. The
typical number of radiation modes is 800 and the numberof particles is 1000.
Accuracy of the code was checked for the small-signal
low-gain calculations. The obtained dependences for thegain showed a very good agreement with the theoreticalexpressions. The results of simulation with the real FEL
parameters are presented below.

2

SIMULATION RESULTS(4)

It also worth noting that this system can be derived
from the Hamiltonian

2 DI ksin[θδ k + ϕ n (1 + δ k ) − Ψk ] ,
1+δk
(5)

H = − ∑ ∆2n + ∑∑
n

n

k

2

bk
,Ψ k = arg (bk ) ; Ψ k , ϕ n andwhere I k =
2 D (1 + δ k )I k , ∆n are canonical coordinates and momenta
respectively. Then the existence of the integral Eq. (4)follows from the invariance of Eq. (5) with respect to thetransformation
ϕ n → ϕ n + δs , Ψ k → Ψ k + (1 + δ k )δs .

NUMERIC APPROXIMATION ANDCOMPUTER CODE DESCRIPTION
To obtain the numeric solution of Eq.(3) we used thefollowing difference schemebkj +1 = bkj + hD ∑ e i [θδ k +ϕ n (1+δ k ) ]j∆b j +1 + bkj −i [θδ k +ϕ nj (1+δ k ) ], (6)= ∆ − h Re ∑ ke2kϕ nj +1 = ϕ nj − 2h∆ jn+1
where j is the step number, h is the step size. This scheme
implements a canonical transformation of the phasespace. It also conserves the following value
2∑ 2 D + ∑ ∆ = const ,
k

j
n

12

δf/f0=010
8-5

δf/f0=1.43x10

6
4
2

-5

δf/f0=2.68x10
0

j
n

bkj

14

0

n
j +1
n

Simulations were carried out with the Novosibirsk FEL
parameters [1]. The dependence of the average radiation
power inside the optical resonator on the pass number fordifferent detunings is presented at Fig. 1. One can see thatthe radiation power reaches saturation after few hundredsof electron bunch passes through the undulator. For somedetunings there was no constant saturation level and thepower was non-stationary.

Average power, kWbd( ∑ k + ∑ ∆n ) = 0 .
dz k 2 Dn(7)nwhich corresponds to the energy integral (4).
The computational algorithm, which directly followedfrom Eq.(6), was realized in a simple computer code. The
code simulates reiterated passes of the radiation wave
packet and the electron beam through the undulator. At
the beginning of each pass a new particle initial
distribution is formed, and all amplitudes of the radiation
field modes bk are reduced with accordance to the lossesof the optical resonator. The center of a new bunch is

200

400

600

800

1000

Pass number
Figure 1: Dependence of average radiation power inside
the optical resonator on pass number for different
detunings δf/f0=-cδT/(2L).
The maximum level of average power inside the opticalresonator at zero detuning is about 12 kW, which is in agood agreement with the value obtained in theexperiment.
Spectral density of radiation in the case of zerodetuning is shown in Fig. 2. The presence of several
bands in spectrum apparently indicates the developmentof side-band instability.

FEL Oscillators

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O.A. Shevchenko et al. / Proceedings of the 2004 FEL Conference, 266-269

1,0Spectral density, a.u.

Spectral density, a.u.

1,0
0,8
0,6
0,4
0,2

0,6
0,4
0,2

0,0
-0,08

-0,06

-0,04

-0,02

0,00

δλ/λ0

The corresponding power distribution in time domain ispresented at Fig. 3. It can be seen, that the radiation wave
packet in this case consists of three short pulses. The
distance between adjacent pulses is slightly shorter thentotal slippage at the undulator length. The mechanism ofsuch short pulse generation was described analytically in
[2].
1,0

0,0
-0,03

0,02

Figure 2: Spectral density distribution for zero detuning.

0,00

δλ/λ0

0,01

0,02

Power distribution in time domain for nonzero detuning
is presented at Fig. 5. The wave packet length in this caseis much longer then in the previous one.
1,0

current profile

0,8
0,6
0,4

0,4

0,2

0,2

0,0
-10

-5

0

5

10

z, cm

0,0
-2

-1

0

1

2

z, cm
Figure 3: Power distribution over the wave packet lengthfor zero detuning. The dot line corresponds to the beam
current profile.
For large enough nonzero detuning the spectrum ofradiation is narrow as it shown on Fig. 4. Similar
spectrum with FWHM ~ 0.3% has also been observed in
the experiment for some regimes.

THPOS46-0,01

δf f 0 = 2.65 × 10 −5 .

Power, a.u.

0,6

-0,02

Figure 4: Spectral density distribution for the detuning

current profile

0,8Power, a.u.

0,8Figure 5: Power distribution for the detuning

δf f 0 = 2.65 × 10 −5
In Fig. 6 one can see so-called detuning curve.
Dependence, presented at this figure, shows, that there isa narrow peak near the zero detuning. The similar results
were reported in [3].

O.A. Shevchenko et al. / Proceedings of the 2004 FEL Conference, 266-269

1,0

Average power, a.u.

0,8

269

CONCLUSION
The results of calculations demonstrate a good
agreement with the measured ones. The lack of
information about the particle distribution in the realelectron beam is, probably, the main limiting factor forthe comparison of the experimental data and thesimulation results. Calculations for more advanced FEL
magnetic systems (multisection and tapered undulators,
optical klystron, electron outcoupling, etc.) are planned.

Simulations
Experiment

0,6

0,4

REFERENCES
0,2

0,0
-5
-5
-5
-5
-6,0x10 -4,5x10 -3,0x10 -1,5x10

0,0

Detuning δf/f0[1] E. A. Antokhin et al. NIM A528 (2004) p.15-18.
[2] N. Piovella, P. Chaix, G. Shvets and D.A.
Jaroszynski, Phys. Rev. E 52, 5470 (1995)[3] R. Hajima, N. Nishimory, R. Nagai, E.J. Minehara,
NIM A483 (2002) p.113-118.

Figure 6: The average power vs. the detuning.

FEL Oscillators

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Ch. Gerth et al. / Proceedings of the 2004 FEL Conference, 270-273

START-TO-END SIMULATIONS OF THE ENERGY RECOVERY LINAC
PROTOTYPE FEL
C. Gerth∗ , M. Bowler, B. Muratori, H.L. Owen, N.R. Thompson,
ASTeC, Daresbury Laboratory, Warrington WA4 4AD, UK
B. Faatz, DESY, Notkestraße 85, D-22603 Hamburg, Germany
B.W.J. McNeil, University of Strathclyde, Glasgow, G2 0NG, Scotland
INJECTOR

Abstract

The performance of a free-electron laser (FEL) depends
crucially on the electron beam parameters. While analytical calculations can give an estimate of the expected performance, numerical start-to-end (S2E) simulations are required to account for various aspects of beam dynamics
during the generation, transport and compression of thebeam [1, 2, 3]. FELs based on the Energy Recovery Linac(ERL) concept have a distinct advantage in terms of rf
power and beam dump requirements. However, another aspect becomes important for S2E simulations: the electron
beam, which may have a large energy spread induced by
the FEL process, needs to be recirculated for decelerationand then transported into the beam dump [4].
Daresbury Laboratory are currently building an ERL
Prototype [5] which will operate at a beam energy of
35 MeV and drive an infra-red oscillator FEL. In this paper we present the results of the first S2E simulations for
the ERLP including the FEL. To account for space charge
effects, ASTRA [6] was used for the modelling of the low
energy part (350 keV) of the injector from the cathode to
the booster. The beam was tracked with elegant [7] fromthe booster (8.35 MeV) to the main linac (35 MeV) andthen to the FEL. The FEL interaction was modelled with
GENESIS, and elegant was used to transport the beamback to the linac for energy recovery and then to the beam
dump.
∗ c.gerth@dl.ac.uk

THPOS47

CathodeSolenoid

Solenoid

Buncher

0.5

1

Booster6
beam size [mm]INTRODUCTION

The injector consists of a high-average current DC photocathode gun, a booster and a transfer line to the main
linac. The DC photocathode gun is a replica of the 500 kV
Jefferson Lab gun [8] and will operate at a nominal accelerating voltage of 350 kV and bunch charge of 80 pC.
Electrons will be generated at a GaAs photocathode by
the frequency-doubled light (532 nm) of a mode-locked
Nd:YVO4 laser with an oscillator frequency of 81.25 MHz.
Two solenoids will be used for transverse focusing andemittance compensation, and a normal-conducting singlecell buncher cavity will be utilised to decrease the bunch
length from the GaAs cathode. The buncher cavity will be
operated at 1.3 GHz and is based on the buncher design employed at the ELBE facility [9]. Electrons are accelerated
to an energy of 8.35 MeV in the booster, which consists of
two super-conducting 9-cell TESLA-type cavities operated
at 1.3 GHz. The cryo-module design is based on the designof the ELBE linac [10]. The layout of the ERLP injector
is shown in Fig. 1 and a detailed description of the injector
design can be found in Ref. [11].

bunch length [mm] norm. emittance [µm]Daresbury Laboratory is currently building an Energy
Recovery Linac Prototype (ERLP) that serves as a testbed
for the study of beam dynamics and accelerator technology
important for the design and construction of the proposed
4th Generation Light Source project. Two major objectivesof the ERLP are the demonstration of energy recovery andof energy recovery from a beam disrupted by an FEL interaction as supplied by an infrared oscillator system. In
this paper we present start-to-end simulations of the ERLP
including such an FEL interaction. The beam dynamics in
the high-brightness injector, which consists of a DC photocathode gun and a super-conducting booster, have beenmodelled using the particle tracking code ASTRA. Afterthe booster, particles have been tracked with the code elegant. The 3D code GENESIS 1.3 was used to model the
FEL interaction with the electron beam.

4
2
0
3
2
1
0
6
4
2
0

0

1.5

2

2.5
3
z [m]

3.5

4

4.5

5

Figure 1: Layout of the ERLP injector and evolution of thebeam size, norm. emittance and bunch length (all rms).

Available online at http://www.JACoW.org

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Ch. Gerth et al. / Proceedings of the 2004 FEL Conference, 270-273

Figure 2: The layout of the ERL Prototype.
Cof 0.28 m
gler. The compression chicane has a static R56(positive in our sign convention) [14]. For optimum bunch
compression, the main linac needs to be operated at an offcrest phase of about ϕrf  9◦ . The TBA arcs are able toprovide a large negative R56 . In nominal setup, the firstA1= 0 whereas the second arc is tuned toarc is set to R56
A2C
R56 = −R56 in order to decompress the bunch. The sextupoles in the first arc can be used to linearise the lowestorder curvature induced by the sinusoidal rf during acceleration by varying T566 . The effect of the sextupoles on thelongitudinal phase space is demonstrated in Figure 3. Twocases are compared: all sextupoles turned off and all sextupoles excited to 100 m−3 . The sextupoles in the second
arc can be used to minimise the energy spread after deceleration for optimised energy recovery and extraction to thebeam dump.

1
sextupoles off
0.5∆ p / p [%]To account for space charge effects in the injector theparticle tracking code ASTRA has been used for the modelling of the beam dynamics. The transverse properties ofthe electron bunch at the cathode are determined by thecathode laser parameters whereas the longitudinal profile
is dominated by the GaAs cathode for short laser pulses
due to the rather long response time of GaAs. For themodelling, a longitudinal Gaussian distribution with an rms
length of 20 ps has been assumed. The transverse distribution was chosen to be Gaussian with an rms beam size σr= 1.25 mm truncated at ±2σr . Results for the evolution of
the rms values of the beam size, normalised emittance andbunch length are shown in Fig. 1 for a simulation with 250k
macro-particles.
The booster is followed by a transfer line which transports the beam to the straight of the main linac where itis merged with the full energy (35 MeV) single-pass recirculated beam. The transfer line employs four quadrupoles
to match the beam into a double-bend achromat which isfollowed by a 2-dipole achromatic dog-leg. Tracking thebeam from the booster to the main linac was carried out by
the code elegant. This code does not include space charge
effects and so the resulting emittance degradation, as studied in [12], have been simulated further upstream by using
appropriate rf phase and sextupole settings.

0−0.5
sextupoles on−1300

BEAM TRANSPORT SYSTEM

250
200
I [A]

The layout of the ERLP is shown in Fig. 2. Electrons
from the injector are accelerated to 35 MeV in the superconducting main linac, which is identical to the booster andcomposed of two 9-cell TESLA-type cavities. Two 180◦
triple-bend achromat (TBA) arcs [13] are used to recirculate the beam to the main linac where the electrons are decelerated to their injection energy. The electrons are separated from the full energy beam (35 MeV) by an extraction
chicane and then dumped in the beam dump. A 4-dipole
chicane provides bunch compression upstream of the wiggler and bypasses one of the FEL mirrors.
The minimum bunch length is required within the wig-

σ = 197µms
σs = 68µm

150
100
50
0
−0.8

−0.6

−0.4

−0.2
0
s [mm]

0.2

0.4

Figure 3: Comparison of longitudinal phase space after thecompressor chicane with sextupoles turned on and off.

FEL Oscillators

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Ch. Gerth et al. / Proceedings of the 2004 FEL Conference, 270-273

2 (a)
1

before FEL

after FEL

2 (b)1after deceleration

2 (c)
1

2 (d)
1

0

0

0

0

−1

−1

−1

−1

−2

−2

−2

−2

8

150

150

100

100

50

50

I [A]

∆ p / p [%]after acceleration

10

6
4
2
0

−2

0
s [mm]

20−20s [mm]

2

0

5

−2

0
s [mm]

2

0
−10

−5

0

5

s [mm]

Figure 4: Longitudinal phase space and bunch profile at different locations in the ERLP: (a) after off-crest acceleration
by ϕrf = 7.8◦ in the main linac; (b) after the compressor chicane with the sextupoles set to 120 m−3 ; (c) after FEL
interaction; (d) after energy recovery in the main linac.
Results of the S2E simulations for the longitudinal phasespace and bunch profile at 4 different locations in the ERLP
are shown in Fig. 4: (a) after acceleration in the main linac,(b) after the compression chicane, (c) after the FEL, and (d)after deceleration. The ASTRA particle distribution fromthe injector modelling was used as an input for elegant, andthe beam was tracked from the exit of the booster to thewiggler; the program MAD8 was used to match the latticefunctions. The bunch was not fully compressed in the S2E
simulation (Fig. 4(b)). The rf phase ϕrf and sextupole settings have been chosen to approximate the expected beam
parameters at the wiggler enterance, thus simulating the effects of the neglected space charge in the injector to linac
beamline. The FEL interaction, which induces a large energy spread as can be seen in Fig. 4(c), was modelled with
GENESIS 1.3 and is described in more detail in the next
section. The particle distribution was then converted backto elegant and tracked to the beam dump. When the secA2
C= −R56, the deceleration phase is
ond arc is set to R56
given by ϕrf + π. In order to achieve exactly the injectionenergy during deceleration, the deceleration phase needs tobe reduced slightly to account for the mean energy loss ofabout 0.8% in the FEL process. Apertures were included in
the elegant tracking, which were chosen to be 10% smaller
than the envisaged vacuum chamber dimensions to approximately account for the effect of misalignment. No particles were lost during the recirculation even with the sextupoles turned off in the second arc.

FEL
The wiggler has been supplied on loan from Jefferson
Laboratory, and is a planar device with 40 periods of length
27 mm. The magnet arrays are vertical giving focussingin the horizontal plane. The matched beam conditions in

THPOS47transverse phase space are therefore a waist in the horizontal plane at the entrance to the wiggler and a waist in thevertical plane at the centre of the wiggler. The desired βfunction at the wiggler entrance in the horizontal plane is
0.5 m. In the vertical plane the α and β values are set togive a waist in the centre of the wiggler with the minimalvertical beam radius averaged along the wiggler. The optimum matched beam parameters at the wiggler entrance
were found to be αy = 1.75 and βy = 1.25 m.
The shortest possible length of the optical cavity, definedby the bunch repetition frequency and layout constraints, is
D = 9.22 m. The wiggler is positioned slightly off-centre
within the cavity, and the mirror radii of curvature R1 andR2 are chosen to give a near-concentric cavity with an optical waist in the centre of the wiggler. The Rayleigh lengthis 0.75 m compared to a wiggler length of 1.08 m – the optimum Rayleigh length for FEL coupling would be less than
this but would drive the cavity towards instability. The cavity stability is given by g1 · g2 = 0.9, with g1 = 1 − D/R1
and g2 = 1 − D/R2 .
The FEL process was modelled with GENESIS as follows: first, the projected rms values of the tracked particle
distribution were calculated, and the predicted performanceof the FEL was estimated with analytical formulae and
GENESIS in steady-state mode (FEL wavelength, intracavity power, etc.). These results and the SDDS toolkit
program elegant2genesis were then used to generate theinput files for GENESIS, which was run in time-dependent
mode with a seed power given by the analytic estimate of
the intra-cavity peak power at saturation of ≈80 MW. This
seed power is approximated by a uniform intensity overthe entire electron bunch. Although this is not an exact
representation of the pulse structure in a cavity it should
approximate reasonably well the energy spread induced by
the FEL interaction.

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Ch. Gerth et al. / Proceedings of the 2004 FEL Conference, 270-273

SUMMARY AND OUTLOOK

10
9
before FEL

8Intensity [arb. units]

7
6

after FEL

5
4
3
2
1
0

−3

−2.5

−2

−1.5

−1
−0.5
∆E/E [%]

0

0.5

1

1.5

Figure 5: Results of GENESIS simulation: energy spreadinduced by the FEL interaction with 80 MW seed beam(data taken from Figs. 4(b) and (c)).
The utility code elegant2genesis discretises the elegant
supplied macro-particle distribution into radiation wavelength slices (here 4.4 µm) and calculates the relevant
GENESIS input parameters. The charge of each slice is
proportional to the number of macro particles it contains.
These parameters are then applied to form a GENESIS
macro-particle distribution with a constant number of particles for each slice (typically 8192). To convert the GENESIS output file back to an elegant input file, the numberof particles in each slice should again be made proportional
to the slice charge. This is achieved by randomly sampling
the GENESIS particles to give the required number of elegant macro particles.
Care should be taken when converting complex particle
distributions using elegant2genesis. Inhomogeneous distributions may be inadvertently simplified as elegant2genesis
only calculates the mean and rms values for each slice. For
instance, in the ‘sextupoles-off’ particle distribution of Fig.
3, the tail of the distribution comprises two energy bands
each of which has a relatively small energy spread. The
calculation of the slice values by elegant2genesis results
in a mean energy in the centre with a rather large energy
spread. This situation does not arise for the ‘sextupoleson’ particle distribution used here in the S2E simulation.
The energy profiles of the electron bunch before and after the FEL process are compared in Fig. 5 for a seed powerof 80 MW. The mean energy loss in the simulation is 0.8%
which is in good agreement with analytical predictions.
The return arc must have an energy acceptance sufficient
to transport all the electrons. Assuming a Gaussian distribution, a range of ±3σE represents 99.7% of the electrons, so an estimate of the full FEL exhaust energy spreadis given by 6σE . A full energy spread of ≈ 4% is predicted by one-dimensional steady-state codes for the given
parameters which is in good agreement with the GENESIS
result shown in Fig. 5.

First S2E simulations of an ERL including both an FEL
interaction and energy recovery have been performed. The
particle tracking codes ASTRA and elegant were used forparticle transport. The FEL oscillator was modelled asa seeded single pass amplifier configuration with a seed
power equivalent to the estimated intra-cavity peak powerat saturation.
There is ongoing work to improve the S2E simulations.
Space charge effects will be included in the modellingof the transfer line from the booster to the main linac at
8.35 MeV. To improve the modelling of the FEL process,a Gaussian seed pulse of variable length will be implemented. The implementation of cavity feedback effects byfeeding the output radiation back into the wiggler and including cavity parameters and slippage effects are also envisaged.

REFERENCES[1] S. Reiche et al., “Start-to-end Simulations for the LCLS
Xray-FEL”, PAC’01, Chicago, June 2001.
[2] M. Biagini et al., “Start to End Simulations for the SPARX
Proposal”, PAC’03, Portland, May 2003.
[3] M. Dohlus et al., “Start-To-End Simulations of SASE FEL
at the TESLA Test Facility, Phase I: comparison with experimental results”, Nucl. Instr. and Meth. A 528, 448, 2004.
[4] P. Piot et al., “Longitudinal phase space manipulation in energy recovering linac-driven free-electron lasers”, Phys. Rev.
ST-AB 6, 030702, 2003.
[5] M.W. Poole, E.A. Seddon, “4GLS and the Prototype Energy
Recovery Linac Project at Daresbury”, EPAC’04, Lucerne,
July 2004.
[6] K. Flöttmann, “ASTRA User Manual”, September 18, 2000.
http//www.desy.de/~mpyflo.
[7] M. Borland, “elegant: A Flexible SDDS-Compliant Code forAccelerator Simulation ”, APS LS-287, September 2000.
[8] T. Siggins et al., “Performance of a DC GaAs photocathodegun for the Jefferson lab FEL”, Nucl. Instr. and Meth. A 475(2001) 549.
[9] E. Wooldridge et al., “Comparison of different Buncher Cavity Designs for the 4GLS ERLP”, EPAC’04, Lucerne, July
2004.
[10] A. Büchner et al., “The ELBE-Project at DresdenRossendorf”, EPAC’00, Vienna, June 2000.
[11] C. Gerth, F.E. Hannon, “Injector Design for the 4GLS Energy Recovery Linac Prototype”, EPAC’04, Lucerne, July
2004.
[12] B. Muratori et al., “Space Charge effects for the ERL Prototype”, EPAC’04, Lucerne, July 2004.
[13] H.L. Owen, B. Muratori, “Choice of Arc Design for the ERL
Prototype at Daresbury Laboratory”, EPAC’04, Lucerne, July
2004.
[14] B. Muratori et al., “Optics Layout for the ERL Prototype at
Daresbury Laboratory ”, EPAC’04, Lucerne, July 2004.

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P. P. Crooker et al. / Proceedings of the 2004 FEL Conference, 274-277

STABILITY OF A SHORT RAYLEIGH RANGE LASER RESONATORWITH MISALIGNED OR DISTORTED MIRRORS
P.P. Crooker ∗ , J. Blau, and W.B. Colson
Naval Postgraduate School, Monterey, CA 93943 USA
Abstract

SIMULATION TECHNIQUES

Motivated by the prospect of constructing an FEL withshort Rayleigh length in a high-vibration environment, wehave studied the effect of mirror vibration and distortion
on the behavior of the fundamental optical mode of a coldcavity resonator. A tilt or transverse shift of a mirror causes
the optical mode to rock sinusoidally about the original resonator axis. A longitudinal mirror shift or a change in the
mirror’s radius of curvature causes the beam diameter at a
mirror to dilate and contract with successive impacts. Results from both ray-tracing techniques and wavefront propagation simulations are in excellent agreement.

We start by assuming a resonator with two identical mirrors of radius of curvature R (focal length f = R/2) separated by distance S and enclosing a Gaussian beam which
is an eigenmode of the resonator with Rayleigh length z 0(Fig. 1). If we normalize all longitudinal distances by S,
all transverse distances by (λS/π) 1/2 and all angles by(λ/πS)1/2 , then f = z02 + 1/4, and the 1/e radius of thebeam at any z is w(z) = (z0 + z 2 /z0 )1/2 . In particular, the
1/2
waist radius is w0 = z0 [5]. For a 10 m long resonatorwith λ = 1µm, the transverse scaling length is 1.8 mm andthe scaling angle is 0.18 mrad.
y

INTRODUCTION
Some designs for a high-power free electron laser (FEL)call for a short Rayleigh length optical resonator in orderto reduce the system size while minimizing heat damage tothe mirrors [1, 2]. An additional advantage of this design isimproved optical beam quality, due to the small interaction
region in the center of the resonator [3]. However, this design raises concerns about mode stability, in particular thesensitivity to motions of the mirrors. This paper presents
a study of the effect on beam behavior of mirror motion
and mirror radius change, particularly as they affect shortRayleigh length resonators.
We study the results of several cavity distortions: mirror
tilt, transverse and longitudinal shifts in mirror position,and changes in mirror focal length. In order to isolate resonator effects, our results are for a resonator alone withno gain. Since mirror motions are relatively slow (∼ms)
compared with the optical round trip time (∼ns), the motions are assumed to be fixed over many passes of the beamthrough the resonator.
In general, the optical beam in a laser resonator retraces
itself — it is an eigenmode of the resonator. If a mirror
is misaligned or distorted, however, the resonator eigenmode will be redefined and the existing optical beam willtend to walk around the mirrors [4]. For sufficiently large
misalignment, the beam radius may increase indefinitely— i.e., the resonator may become unstable. These effects
are most pronounced for short Rayleigh length resonators,
which are already near the stability limit. In practical terms,
the mirror misalignment and distortion will cause the beamdisplacement to exceed the size of the mirrors, thereby creating beam loss and lowering the resonator Q.
∗ ppcrooke@nps.edu

THPOS59

w

w0
-z0

h

T0
z0

Tm
z

'S

S

Figure 1: Resonator with Gaussian mode characterized byRayleigh length z 0 . Distortions of the right-hand mirror
include tilt θm , transverse shift h, longitudinal shift ∆S,
and focal length change ∆f (not shown).
The beam is simulated using two techniques. In the
ray tracing technique, a Gaussian beam is simulated bya random collection of rays, Gaussian distributed in bothtransverse position y and angle θ and set up at the beam
waist [6]. For a beam whose amplitude in the y-plane is
A exp(−y 2 /w02 ), the joint probability density is given by
1/2
f (y, θ). Setting the distribution widths to δy = w 0 = z0
−1/2
and δθ = θ0 = z0,
f (y, θ) =1 −(y2 +z02 θ2 )/z0
e
.
π

(1)

Here θ0 is the angular spread of the beam at z  z 0 as
shown in Fig. 1. Each ray is then propagated numericallywith the usual ABCD ray matrices and the evolving ray
density and direction is found to closely emulate the actual
behavior of a Gaussian beam .
In the wave propagation technique [1], the spatial part of
the Gaussian beam a(x, y, z)is set up at the beam waist andthen propagated numerically by the paraxial wave equation∂z a = (−i/4)∇2⊥ a .
Both simulation methods can accommodate tilted,

Available online at http://www.JACoW.org

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P. P. Crooker et al. / Proceedings of the 2004 FEL Conference, 274-277

Figure 2: Evolution of an optical beam in a resonator withz0 = 0.1 and θm = 0.05. Each vertical line corresponds
to a mirror, with the successive reflections unfolded to see
the overall behavior. The shaded area shows the trajectories of 1000 random rays; the center line is the center ofthe optical beam; and the top and bottom lines, calculated
from beam theory, correspond to the radius w(z) for theGaussian mode.
shifted, and distorted mirrors, while the latter method canalso incorporate laser gain.
In a third analytical method [5], the Gaussian beam isrepresented by complex beam radius q(z) = z + iz 0 . Propagation is then accomplished using the ABCD matrix elements in the form q 2 = (Aq1 + B)/(Cq1 + D) and extracting the beam front curvature R(z) and beam radiusw(z)from 1/q = 1/R−i/w 2. This method will accommodate longitudinal mirror shift and focal length change only.
However, when coupled with ray tracing, can also describe
the effects of tilt and transverse shift of the mirrors.

MIRROR TILT AND SHIFT
We now let the right-hand mirror undergo tilt θ m and/ortransverse shift h and investigate the subsequent behaviorof the Gaussian beam. The immediate effect is that thereflection angle of any ray incident on the mirror will be
increased by 2θ m + h/f . The resonator will remain stable,
but a new resonator axis will be defined which tilts withrespect to the old axis by amount φ, whereφ = −[(1 + 4z02 )θm + 2h]/(8z02).

(2)

The optical beam, which initially was an eigenmode of theold resonator, now becomes tilted with respect to the newaxis and is no longer an eigenmode of the realigned resonator. Consequently, with each reflection, its angle withrespect to the old axis will change in a rocking fashion, depending on the value of z 0 .
The effect of the rocking over many passes n is to makethe beam position on the mirror walk sinusoidally up anddown. If y n is the beam position on the mirror after n reflections [5],yn = C1 [1 − cos(αn)] + C2 sin(αn)

(3)

where
α =

cos−1



2f 2 − 4f + 1
2f 2


,

(4)

Figure 3: z0 dependence of the maximum excursion y c of
the beam center from the original cavity axis when a mirror
tilts by θm or undergoes transverse shift h. Tilt and shift areplotted separately. The lines are beam theory; the points arefrom wave simulations. For an FEL with S = 10 m and λ =1 µm, yc = 10 corresponds to 1.8 cm.

C1

=

C2

=


2f − 1(h + 2f θm ) ,4f − 1−(h + 2f θm )√.
4f − 1(5)(6)

Figure 2 shows the result of mirror tilt. The beam isstarted on axis with the right mirror tilted. Successive reflections of the beam are unfolded, so that the horizontal
axis is time. The beam angle changes continually, depending on z0 and, for this figure, θ m . In general, the maximum
deflection of the beam center y c is proportional to θ m andh, as calculated from Eq.(3):yc =(4z02 + 1)θm + 2h
.
8z02

(7)

The rocking period n 0 can also be calculated: n 0 = 2π/α.
For the small z0 case we are concerned with here, y c isa strong function of z 0 . We show this dependence in Fig. 3
where yc /θm and yc /h are plotted separately against z 0 .
As z0 becomes smaller, the transverse excursions becomecomparable to the mirror diameter and the beam will walk
off the mirrors.

LONGITUDINAL MIRROR SHIFTLet the resonator contain a Gaussian beam which is aresonator eigenmode with Rayleigh length z 0 . Since z0
is small, the mirror focal lengths f = z 02 + 1/4 are already only slightly larger than the resonator stability limit
fmin = 1/4. Let the right-hand mirror shift by (normalized) amount ∆S in the z-direction. Successive reflectionsof the beam will remain on axis, but the Rayleigh lengthsof the beam and the resonator eigenmode will no longer be
equal. If ∆S is positive (cavity length increases), the focal
lengths decrease to f  = f /(1 + ∆S), and if f  < 1/4,

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P. P. Crooker et al. / Proceedings of the 2004 FEL Conference, 274-277

Figure 4: Evolution of an optical beam in a resonator withz0 = 0.1 and right mirror shift ∆S/S = 0.031. The vertical lines represent mirrors, with successive reflections unfolded to see the overall behavior. The gray areas are thetrajectories of 1000 random rays; the dotted lines, calculated from beam theory, correspond to the radius w(z) of
the Gaussian mode. The beam remains on axis, but expands
and contracts with successive reflections.

the resonator will become unstable and the beam will expand without limit. The maximum allowable value for ∆S
is therefore ∆Smax = 4f − 1 = 4z02 .
If ∆S < ∆Smax , the resonator remains stable but thebeam will no longer retrace itself in succeeding passes, as
shown in Fig. 4. With each pass, the beam width at themirrors will expand and contract, depending on both ∆S
and z0 . Figure 5 shows the effect of varying ∆S for several z0 . For ∆S < ∆Smax , the effect on y max is small.
However, as ∆S approaches ∆S max , ymax increases andfinally diverges at ∆S max .

Figure 6: Evolution of an optical beam in a resonator withz0 = 0.1 and right mirror shift ∆f /f = −0.05.

MIRROR DISTORTION
Now let the focal length f of the right-hand mirror in thepreviously undistorted resonator change by amount ∆f /f .
Since the mirror focal lengths are unequal, the mode waistof the resonator eigenmode will move away from the resonator center. The effect is to change the resonator eigenmode so that it no longer corresponds to the original beam.
Consequently the beam radius on the mirror will expand
and contract with each subsequent reflection, as shown in
Fig. 6. In addition, if ∆f /f is negative (a decrease in the
mirror focal length) and made too large, the resonator will
no longer be stable and the beam will diverge indefinitely.
The stability criterion is ∆f > −8z 02 /(1 + 4z02 ).
Figure 7 shows the results from our simulations. The
beam radius at the mirror is y max , as before. As ∆f ismade increasingly negative, y max increases slowly as thethreshold for resonator instability (vertical dashed lines) isapproached, and then diverges sharply at the threshold.

For ∆S < 0 (resonator length decreases), the resonatorremains stable but the beam width again expands dramatically as the difference between the Rayleigh lengths of thebeam and the resonator eigenmode becomes large.

We have shown that for a short Rayleigh length resonatorwith no gain, the effects of mirror tilt, shift, and focal length

Figure 5: Maximum beam radius y max for right-hand mirror shift ∆S at several values of z 0 . The vertical dashedlines show the limits of resonator stability at ∆S max =4z02 . The data points are taken from ray and beam simulations; the solid lines are guides to the eye. For an FEL with
S = 10 m and λ = 1 µm, y max = 10 corresponds to 1.8 cm.

Figure 7: Maximum beam radius y max for focal lengthchange ∆f /f of the right-hand mirror at several valuesof z0 . The minus sign in front of ∆f indicates the focal
length is decreasing. The points are taken from ray simulations and beam calculations; the solid lines are guides
to the eye; and the vertical dashed lines show the limits ofresonator stability at ∆f = −8z 02/(1 + 4z02 ).

THPOS59DISCUSSION

P. P. Crooker et al. / Proceedings of the 2004 FEL Conference, 274-277

277change can produce dramatic changes in the beam direction
and width. In the cases of mirror tilt and transverse shift,
the effect is to cause the beam to rock up and down on the
mirrors and, if the rocking amplitude is sufficiently large, tocause the beam position to exceed the mirror radius. In thecases of longitudinal mirror shift and focal length change,
the beam will remain on axis but the beam radius at themirror will expand and contract with successive reflections.
If the beam radius becomes too large, portions of the beam
may exceed the mirror radius. In either case beam power
can be lost, or, equivalently, the cavity Q will be reduced.
For comparison with actual mirrors, the y-axes in Fig. 3,
5, and 6 can be converted to real values by multiplying by
the transverse scaling length (λS/π) 1/2 . For a laser with
S = 10 m and λ = 1 µm, y = 10 corresponds to an actual
y of 1.8 cm.

ACKNOWLEDGEMENT
The authors are grateful for support from NAVSEA,
ONR, and the JTO.

REFERENCES[1] W.B. Colson, J. Blau, and R.L. Armstead, “The Free Electron Laser Interaction with a Short-Rayleigh Length Optical
Mode”, Nucl. Instr. and Meth. A 507 (2003) 48.
[2] P.P. Crooker, et al., “A Study of a High-Power Free Electron
Laser Utilizing a Short Rayleigh Length”, Nucl. Instr. andMeth. A 507 (2003) 52.
[3] W. Colson, “Short Rayleigh Length Free Electron Lasers”,
Proc. FEL2004[4] D. Herriott, H. Kogelnik, and R. Kompfner, “Off-Axis Paths
in Spherical Mirror Interferometers”, Appl. Opt. 3 (1964)
523.
[5] A. Siegman, “Lasers” (University Science Books, 1986).
[6] J.B. Rosenzweig, “Fundamentals of Beam Physics”, (Oxford
University Press, 2003).

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C. A. Brau et al. / Proceedings of the 2004 FEL Conference, 278-281

GAIN AND COHERENT RADIATION FROM A
SMITH-PURCELL FREE-ELECTRON LASER*
H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D. Jarvis
Department of Physics, Vanderbilt University, Nashville, TN 37235, USA
Abstract
It has been shown recently that the electron beam in a
Smith-Purcell free-electron laser interacts with anevanescent wave for which the phase velocity is
synchronous with the electron velocity. However, thegroup velocity of this wave may be either positive or
negative, and when the group velocity vanishes, the gain
diverges. In addition, the bunching of the electrons by theinteraction with the evanescent wave enhances theordinary Smith-Purcell radiation due to coherent effects.
In particular, the spacing of the bunches causes the SmithPurcell radiation to peak at the harmonics (andcorresponding Smith-Purcell angles) of the evanescentwave frequency. The high gain achievable near zerogroup velocity makes it possible to design high-power cw
Smith-Purcell free-electron lasers. An experiment isbeing assembled to observe these effects.

with velocity β c that fills the region y > 0 above thegrating. The electrons in the beam interact with anevanescent wave that travels along the surface of thegrating in synchronism with the electron beam. To
describe the evanescent wave, Floquet’s theorem is used
and the periodic function is expanded in a Fourier series.
In the grooves of the grating the fields are expanded in a
Fourier series, but numerical computations show that it issufficient to keep just the zeroth term in this series.
Across the interface between the grating and the electron
beam, the tangential component of the electric field andthe tangential component of the magnetic field must becontinuous. When this expansion is substituted into theMaxwell equations, we get the dispersion relation
R00 − 1 + χ 0 S00 = 0
where

(2)

κ 0 A cos ( k + pK ) A − 1
2
p =−∞ α p L( k + pK ) A2

(3)

κ 0 A cos [ kA] − 1
α 0 L k 2 A2

(4)∞

INTRODUCTION
Smith-Purcell (SP) radiation is emitted when an
electron passes close to the surface of a grating [1]. The
virtual photons of the electron field are scattered by thegrating, and the wavelength λSP of the radiation observedat the angle θ from the direction of the electron beam is
λSP 1= − cos θ(1)Lβwhere L is the grating period, β c the electron velocity,and c the speed of light. The angular and spectral
intensity of SP radiation is described by the theory of vanden Berg and Tan [2,3,4]. When the current in theelectron beam is sufficiently high, the interaction between
the electrons and the fields above the grating becomes
nonlinear. This causes bunching of the electrons in thebeam, which enhances the SP radiation. Recently, atabletop SP-FEL has been demonstrated at Dartmouth [5].
This device operated near threshold in the spectral region
from 300-900 µm. To improve on this performance, it isnecessary to understand how these devices operate.

GAIN
A theoretical description of the small-signal gain in a
Smith-Purcell free-electron laser (SP-FEL) is discussed indetail elsewhere [6]. The electron beam is represented bya uniform plasma traveling in the positive x direction*Supported by the Medical Free Electron Laser Programof the Department of Defense under grant number
F49620-01-1-0429.

THPOS60

R00 = 2 tanh (κ 0 H ) ∑and

S00 = 2 tanh (κ 0 H )in which A is the width of the grooves and H the depth,
K = 2π / L the grating wave number, k the x component of the wave vector of the evanescent wave,
and2
ω2 ω '
2
α p2 = ( k + pK ) − 2 + 2p
(5)cc
κ 02 = −ω 2 / c 2(6)where ω is the frequency of the evanescent wave andω ' p is the plasma frequency of the electron beam in therest frame of the beam.

Table I. Parameters for the planned experiments.
Grating period
Groove width
Groove depth
Grating length
Electron energy
Electron-beam current
Electron-beam diameter

200 µm
100 µm
175 µm12.7 mm
45-65 keV
1 mA
50 µm

In the absence of the electron beam, the last term in (2)vanishes, and we are left with the dispersion relation for
the empty grating. Some simple computations carried out

Available online at http://www.JACoW.org

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C. A. Brau et al. / Proceedings of the 2004 FEL Conference, 278-281

2
S00 (ω0 , k0 )
3 ωp
µ=
3 2 2
2 γ β c R '00 (ω0 , k0 )

1/ 3

(7)

where γ = 1/ 1 − β 2 . The growth rate for the power is
twice this. The total power gain per pass is theng = e2µ Z(8)Normalized frequency

where Z is the overall length of the grating.
0.5
0.4

Beam line

0.3

Grating dispersion

0.2
0.1
0
0

0.2

0.4

0.6

0.8

1

Normalized wave number

Figure 1. Dispersion diagram for a SP-FEL; beam line
drawn for a 56-kV beam.

Amplitude growth rate (1/m)

As shown in Figure 2, the gain has a strong peak near
56 kV, and actually diverges where the group velocity
vanishes. In a fundamental sense, the net gain for theevanescent wave is a balance between the energy
absorbed from the electron beam and that lost by energy
flow along the grating. But the energy in the evanescentwave travels at the group velocity, d ω / dk , and thisdepends on the wave number of the wave, as indicated in
Figure 1.

Present theory
3

10

Schaechter and Ron
Kim and Song

10
40

45

50

55

60

Operating Voltage (kV)

Figure 2. The gain of a SP-FEL.

65

COHERENT RADIATION
The frequency of the synchronous evanescent wave isfound from the dispersion relation (2).
Somecomputations for the parameters of Table I are shown in
Figure 3. As shown there, the free-space wavelength ofthe evanescent wave is always longer than that of the SPradiation. Since it does not radiate, the evanescent wave
is coupled out from the SP FEL only at the ends of thegrating. When the group velocity vanishes, this radiation
disappears. The evanescent wave was not observed in theDartmouth experiments.
1 10

3

Evanescent mode

800
600

Smith-Purcell wavelengths
400
200
0
40

45

50

55

60

65

70

Operating voltage (kV)

Figure 3. Wavelengths emitted from a SP-FEL.
For the grating parameters in Table I, the conventional
SP radiation is emitted over a range of wavelengths from
λ / L = (1 − β ) / β to λ / L = (1 + β ) / β , as indicated by(1) and shown in Figure 3. When the electron beaminteracts with the evanescent wave, it is bunched at thefrequency of the evanescent wave. This bunchingenhances the SP radiation at the harmonics of theevanescent wave. This can be seen in the following way.
When a single electron passes over the grating, theangular spectral intensity S SP of the SP radiation is

4

10

100

Other theories have been proposed to describe theoperation of a SP-FEL [7,8,9]. Schaechter and Ron
analyze the interaction of an electron beam with a wave
traveling along the grating, and include waves that are
emitted by the beam and reflected off the grating [8].
Kim and Song consider an electron beam that interacts
with a Floquet wave traveling along the surface of thegrating, somewhat like the present theory [9]. However,they assume that at least one of the Fourier components of
the Floquet wave is radiative, rather than evanescent.
That is, at least one component of the wave is notexponentially decreasing away from the grating surface.
The results of computations using these alternative
theories are shown for comparison in Figure 2. In thepresent theory, the gain peaks near 56 kV due to thedispersion of the grating, which is not explicitly includedin the other theories.

Emitted wavelength (microns)

using MathCad are shown in Figure 1 for the grating
parameters summarized in Table I. In Figure 1, theoperating point of the laser is the point where the beamline, β k intersects the dispersion curve. As shown there,for 56-keV electrons the intersection occurs at a pointk / K ≈ 0.5 , where d ω / dk ≈ 0 . Below this point thegroup velocity is positive, and above this point the groupvelocity is negative, in the manner of a BWO.
When the effect of the electron beam is nonvanishingbut small, the solution to (2) can be expanded about the
no-beam case. Since the susceptibility diverges near thesynchronous point, the gain is largest there and theamplitude growth rate is found to be70

proportional to q 2 , where q is the electronic charge, andthe total radiation from ne electrons is proportional tone q 2 . When the ne electrons are formed into a bunch of
charge ne q whose dimensions are small compared to awavelength, the SP radiation is proportional to ( ne q ) ,2

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C. A. Brau et al. / Proceedings of the 2004 FEL Conference, 278-281

which represents a coherent enhancement of the radiationby the factor ne over the entire band of SP radiation.
However, when the electrons appear in periodicallyspaced bunches, there is yet another effect. As shown in
Figure 4, the bunches interfere constructively at
wavelengths that satisfy the relation
λb + β nh L cos θ = nh L
(9)where nh > 0 is an integer, λb = βλ∞ is the spacing
between the bunches, and λ∞ is the free-space wavelengthof the evanescent wave. But if we use the SP relation (1)we find that
1

(10)
λ∞ = nh L  − cos θ  = nh λSPβ
so the coherent SP radiation is enhanced at the harmonics
of the evanescent wave. Relative to the intensity from thesame number of electrons in randomly spaced bunches,
the angular intensity of the radiation at the harmonic nh isenhanced by the number N g / nh of bunches that radiate inphase with the wave over the length of the grating, whereN g is the total number of grooves in the grating.
However, the angular width of the harmonic is on theorder of 1/ N g , the angular resolution of a grating with

N g grooves, so the coherent radiation is compressed intoa narrow angular width but the total power is conserved.
These effects are indicated schematically in Figure 5.

where I e is the total current in the electron-beam. For

λ∞ = 920 µ m this gives ne ≈ 2 × 104 , so if the electrons
are perfectly bunched, the SP radiation is enhanced bythis factor. Of course, even at saturation the bunching isless than perfect and the actual enhancement will be lessthan this. The number of periods in the grating is
N g = 64 , so the angular spectral intensity at the peak of
the second harmonic ( λSP ≈ 460 µ m ) will be enhancedby the additional factor N g / nh ≈ 32 . But from the theoryof van den Berg, the total power of the incoherent SP
radiation emitted by this beam is on the order of ahundred nanowatts, so the coherent radiation should be on
the order of a milliwatt at saturation. However, even withcoherent enhancement, the SP radiation is still small
compared with the power in the evanescent wave itself.
We can estimate the power in the evanescent wave atsaturation by the following argument. The electronscontinue to lose energy to the evanescent wave until theylose enough energy to drop out of synchronism. For smallchanges in energy, the change in the velocity of anelectron is∆β = ∆γ / βγ 3(12)and the phase shift in one gain length is
2π∆β
2π∆β
(13)
∆φ =
=
2

µβλb

µβ λ∞

The total power lost by the beam is thenmc 2
P=I e β 3γ 3 µλ∞ ∆φ
2π q

(14)

Saturation corresponds to ∆φ = O (1) . For the parameters

Figure 4. Coherent SP radiation is formed whensuccessive bunches radiate in phase, where ∆t is the time
for a wave to catch up to the previous bunch.

in Table 1, the saturated power at 56 kV is on the order ofa watt, which is much larger than the coherent SP
radiation on the second harmonic of the evanescent wave.
When the group velocity is large, this power comes out
from the evanescent wave at the ends of the grating.
However, when the group velocity is sufficiently small,the power put into the evanescent wave by the electrons islost by scattering from imperfections in the grating and by
dissipation in the grating surface.

EXPERIMENT

Figure 5. Incoherent and coherent SP radiation from abunched electron beam.
For a numerical estimate of these effects we can use theparameters of Table I. The number of electrons in abunch is on the order of
ne = I e λ∞ / qc
(11)

THPOS60

At the present time, an experiment is being assembled
to test these predictions.
The parameters of theexperiment are summarized in Table I, and a schematic
diagram of the experiment is shown in Figure 6. The
electron beam is emitted from the tip of a blunt needle
illuminated by 3-ns pulses from the fifth harmonic of a
Nd:YAG laser pulsed at 20 Hz [10,11]. The electron
beam is focused by a solenoidal lens and aligned above
the surface of the grating by two pairs of steering coils.

C. A. Brau et al. / Proceedings of the 2004 FEL Conference, 278-281

281

REFERENCES

Figure 6. Schematic diagram of the experiment
The wavelength range of greatest interest is 400-1000µm, as indicated in Figure 3, so a quartz window close to
the surface of the grating can be used to provide a large
collection solid angle. The radiation is detected using aliquid-He-cooled InSb bolometer, which is sensitive(above the noise level) to signals as small as nanowatts.
Therefore, it should be possible to observe both theincoherent and coherent SP radiation. Measurements will
be performed at voltages ranging from 45 to 65 kV, whichspans the region of zero group velocity. It should bepossible to observe the peak in the output power at thezero-group-velocity point, as well as the wavelength ofthe evanescent wave (about 930 µm) and the enhanced
coherent emission at the second harmonic (around 420µm).

1 S. J. Smith and E. M. Purcell, Phys. Rev. 92, 1069
(1953).
2 P. M. van den Berg, J. Opt. Soc. Am. 63, 689 (1973).
3 P. M. van den Berg, J. Opt. Soc. Am. 63, 1588 (1973).
4 P. M. van den Berg and T. H. Tan, J. Opt. Soc. Am. 64,
325 (1974).
5 J. Urata, M. Goldstein, M. F. Kimmitt, A. Naumov, C.
Platt, and J. E. Walsh, Phys. Rev. Lett. 80, 516(1998).
6 H. L. Andrews and C. A. Brau, Phys. Rev. ST-AB 7,070701 (2004).
7 A. Gover and P. Sprangle, IEEE J. Quantum Electron.
QE-17, 1196 (1981).
8 L. Schaechter and A. Ron, Phys. Rev. A 40, 876 (1989).
9 K.-J. Kim and S.-B. Song, Nucl. Instr. Meth. A 475, 159(2001).
10 C. Hernandez Garcia and C. A. Brau, Nucl. Instr.
Meth. A 475, 559 (2001).
11 C. H. Boulware and C. A. Brau, “Photo-Field
Emission from Needle Cathodes,” proceedings of the24th International Free-Electron Laser Conference,
Argonne, Il, September 9-13, 2002.

CONCLUSIONS
The detailed theory of gain in a SP-FEL shows theimportance of taking into account the dispersion relation
for the evanescent wave. It has long been recognized thatthe electron velocity must be synchronous with the phasevelocity in slow-wave devices, but in a SP-FEL the gain
has a maximum near the condition where the groupvelocity vanishes. In a BWO, the output vanishes for thiscondition since the energy flows at the group velocity.
However, in a SP-FEL an alternative source of output isprovided by the coherent SP radiation at the harmonics ofthe evanescent frequency. Although this is radiated atlower power, the high gain makes it possible to envision
low-current devices operating in cw mode with significant
average power. In addition, if the group velocity is not
too small, power from the evanescent wave can bedirectly coupled out from the ends of the grating. This
would produce watts of average power from the device.

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T. Shaftan et al. / Proceedings of the 2004 FEL Conference, 282-284

EXPERIMENTAL DEMONSTRATION OF WAVELENGTH TUNING IN
HIGH-GAIN HARMONIC GENERATION FREE ELECTRON LASER
T. Shaftan*, E. Johnson, S. Krinsky, H. Loos, J.B. Murphy, G. Rakowsky, J. Rose, B. Sheehy,
J. Skaritka, X.J. Wang, Z.Wu, L.H. Yu, NSLS, BNL, Upton, NY 11973, USA
Abstract
Tunability is one of the key aspects of any laser
system. In High-Gain Harmonic Generation Free Electron
Laser (HGHG FEL) the seed laser determines the output
wavelength. Conventional scheme of tunable HGHG FEL
requires tunable seed laser. The alternative scheme [1] isbased on compression of the electron bunch with energytime correlation (chirped bunch) in the FEL dispersive
section. The chirped energy modulation, induced by theseed laser with constant wavelength, is compressed as thewhole bunch undergoes compression. In this paper we
discuss experimental verification of the proposed
approach at the DUV FEL [3,4] and compare
experimental results with analytical estimates.

INTRODUCTION
High-gain FELs have been proposed as highpeak power light sources for the short-wavelength range[5,6]. Ultrashort and powerful radiation pulses from VUV
to X-ray provide a unique possibility for studying fast
processes in a large variety of scientific applications.
Output radiation coherence, stability and tunability areimportant measures of the FEL performance.
For an initially prebunched beam, i.e. when the
beam density contains a coherent bunching at the FEL
resonant frequency, the FEL radiation output preserves
full longitudinal coherence. In this case FEL acts as anamplifier of the external seed. Due to the nonlinearity of
the FEL process, not only the fundamental harmonic canbe amplified, but the higher harmonics too. This allows
for frequency multiplication and generation of radiation in
VUV and X-ray wavelength regions [7,8].
Seeding by an external source offers an
opportunity to control the output pulse properties bycontrolling the shape of the input seed pulse. State-of-theart conventional lasers are capable of providing ultra-shortpulses with high peak power. Using the Harmonic
Generation (HG) approach, one can shift and amplify theseed laser pulse in the short-wavelength region,
preserving the flexible temporal format of the seed andgenerating short radiation output. Important benefits ofseeded HG scheme are high stability, control of thecentral wavelength and small energy fluctuations due tostable input from the seed laser.
In HGHG scheme (Fig. 1), a coherent seed at a
subharmonic wavelength of the desired output radiationinteracts with the electron beam in an energy-modulating
section. The energy modulation is then converted into

spatial bunching as it traverses a dispersive section. In thesecond undulator (the radiator), which is tuned to a higher
harmonic of the seed radiation, the microbunched electron
beam first emits coherent radiation and then amplifies it
exponentially until reaching saturation.

Fig.1: High Gain Harmonic Generation scheme
The seed laser determines the central wavelengthof HGHG FEL. Therefore, as generally understood, totune the wavelength of the seeded FEL, the seed laser
should be tunable. An alternative technique for the
tunable HGHG FEL [2,1] utilizes a seed with fixedwavelength. The essence of this technique is in thecompression of the chirped electron bunch in the HGHG
dispersive section. Since the whole beam undergoes
compression, the laser-induced modulation along thebunch also must be compressed with the same
compression factor. Therefore prebunched electron beam
enters the radiator with a new bunching wavelength.
Changing the value of the energy chirp allows for asmooth tuning of the FEL output wavelength.
In this paper we present and discuss theexperimental verification of this technique. In theexperiment at the Deep Ultra Violet Free Electron Laser(DUV FEL, BNL) we have demonstrated tuning of the
HGHG output around wavelength of 265 nm.

EXPERIMENTIn order to test new approach we performed anexperiment at the DUV FEL (Fig. 2). The DUV FEL
parameters are listed in Table 1.
For a phase offset ∆ϕch the energy chirp h isgiven by the following expression [5]:h=Ech sin (∆φ ch )
1 ∂E
2π
=−
,
E ∂z
λ RF E0 + E ch cos(∆φch )(1)

where E is the energy, z is longitudinal coordinate, λRF is
RF wavelength, Ech is amplitude of the chirping tank andE0 is energy of the beam entering chirping tank.
The compression ratio for a chirped beam is:

C=

σ out
≈ 1 − R56 h,
σ in

(2)

The wavelength detuning due to compression is
given by (3) [1].

Corresponding author: shaftan@bnl.gov∆λ λC − λ0=
= R56 ⋅ h,λλ0

WEAIS01

Available online at http://www.JACoW.org________________*(3)

T. Shaftan et al. / Proceedings of the 2004 FEL Conference, 282-284

283

Fig. 2: The DUVFEL layout. 1 – gun and seed laser system, 2 – RF gun, 3 – linac tanks, 4 – focusing triplets, 5 –magnetic chicane, 6 – spectrometers dipoles, 7 – seed laser mirror, 8 – modulator, 9 – dispersive section, 10 – radiator,
11 – beam dumps, 12 – FEL radiation measurements area.

Beam energy, MeV

175

Seed laser wavelength, nm

800

Seed laser Raleigh range, m

2.4

Harmonic number

3

Radiator period, m

0.0389Radiator length, m

10

Modulator length, m

0.8

Modulator period, m

0.08

Maximum R56 of DS, mm-0.34

Bunch length (RMS), ps

0.5

HGHG pulse length (RMS), ps

0.5

from the Figure, there is obvious disagreement between
measured data and the fit. For a second linear fit (dashedline) we included dispersion in the radiator (R56=-0.162mm) into expression 3. In this case measurement is in agood agreement with calculation. This implies that theadditional wavelength compression takes place in theradiator. The error bars in Fig. 4 correspond to the HGHG
line width determined from the measured spectra.

Table 1: DUV FEL parameters
Using parameters from Table 1 together withexpressions 1 and 3 we obtain the detuning of 0.37% for
the phase offset of 33 degrees in the chirping tank.
Changing sign of the chirp causes decompression of theenergy modulation in the electron beam (C>1 in (2)) and,in turn, detuning towards longer wavelengths. Thus, for asymmetric chirp tuning range from +33° to -33° we
calculate the DUV FEL tunability range of 0.74% or 2 nm
around the nominal wavelength of 266 nm.
At the beginning of the experiment weminimized the projected energy spread in the beamcanceling the energy chirp. The energy chirp has beenmeasured by an energy spectrometer. The dispersion
section current has been set to a maximum value,corresponding to the R56 value of -0.34 mm.
In the experiment we varied the phase of the last
linac tank (tank 4 on Fig. 2), measuring HGHG spectrum
for each value of the tank RF phase. The measured singleshot spectra are shown in Fig. 3. The nominal value ofcentral wavelength for the beam without chirp has beenmeasured as 265 nm. The overall wavelength tuning range
is measured of about 1% (from 263.4 nm for -45° to 266.1
nm for 25° in RF phase).
Fig. 4 shows the dependence of the HGHG
central wavelength versus energy chirp h. The first linear
fit (solid line) is based on the expression 3, taking into
account the R56 of the dispersion section. As it follows

Fig. 3: Measured single-shot spectra for different valuesof energy chirp (phase offset from left to right: -45°, -30°,-10°, 0°, +10°, +25°).
At the DUV FEL the seed radiation is stretchedout of approximately 100 fs long pulse with a bandwidthof 5.6 nm at 800 nm (Ti:Sapphire laser). The frequencytripled seed pulse is 3 ps (RMS) long and contains
wavelength chirp of 0.31 nm/ps at 266 nm. In Fig. 5 wecompare the wavelength chirp in the DUV FEL seed laser
with the energy chirp in the electron beam. For
comparison we plot the chirped electron beam (bunch
length of 1 ps, chirp is 11 m-1) on the same figure,assuming that electron beam energy corresponds to theplot ordinate via expression for the FEL resonant
wavelength. As follows from the plot, another way toachieve the wavelength detuning in our experiment would
be by using the wavelength chirp in the seed laser pulse.
In this case the electron bunch can be delayed (orexpedited) in time and, therefore, would interact with adifferent local wavelength of the seed pulse. As the plotshows, measured tunability range of 1 % exceeds the seedlaser bandwidth. Besides, in order to achieve the observed

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maximum detuning range, electron beam must be shiftedby more than 3 ps (Fig. 5). We note that laser-to-beamsynchronization has been kept constant during our
experiment. Thus, observed wavelength detuning is due tothe compression of the chirped electron bunch in the FEL
dispersive section.

Fig. 4: Measured dependence of the HGHG central
wavelength on the normalized energy chirp. Error bars
represent measured single-shot HGHG linewidth.
Tunability range of one percent lies between horizontal
lines. First fit (dashed line) is calculated based on the DS
calibration. Second fit (solid line) takes into accountdispersion in the radiator.

bandwidth. This shows that we can tune the output photon
energy with a high accuracy.
We performed wavelength tuning by changing
only two parameters, linac section amplitude and phase.
In contrast, when changing the seed laser wavelength, one
has to change the seed laser set-up followed by
optimization of the FEL set-up for new photon energy.
The described method brings a simplification of the FELtuning.
Demonstrated tuning range of one percent isbelow capabilities of modern lasers that can be used as aseed in HGHG FEL. In our experiment we were limitedby the available dispersive section strength.
Straightforward upgrade of the DUV FEL dispersive
section is in progress. In this case we expect to increase
the tuning range up to about 3 percent (it depends on thevalue of sliced energy spread that is not well known yet).
However, this is still not a limit. A special
modification of the DUV FEL magnetic system [1] would
increase the tunability range to ~20 %. The optimized
HGHG scheme includes the secondary RF system locatedbefore and after FEL dispersive section. First RF section
imparts a chirp in the beam, which, being compressed inDS, gets unchirped in the second RF section. Therefore
chirp is provided only locally and, since it does not affectan FEL dynamics, can be made very large. In turn, thiswill provide a large wavelength tuning range.
Since the developed method can be used around
any of HGHG harmonics (e.g. 4th, 5th, etc.), DUV FEL
can be made tunable over a large wavelength range,
having seed laser wavelength fixed.

ACKNOWLEDGEMENTS
We would like to thank M. Lehecka, V.
Litvinenko, S. Mihailov, I.Pinayev and Y. Wu for their
help with OK-4 dispersive section. The work was
performed under DOE contract DE-AC02-98CH10886.

REFERENCES

Fig. 5: Representation of the seed laser (dashed ellipse)
and electron beam (solid) in wavelength (ordinate) – time
(abscissa) coordinates. Tunability range of one percent
lies between horizontal dotted lines. Measured tunability
range exceeds the seed laser bandwidth.

CONCLUSION
In the experiment described in this paper wedemonstrated control over HGHG FEL central
wavelength. The precision of the positioning the central
wavelength is, in general, a small fraction of the FELWEAIS01[1] T. Shaftan and L.H. Yu, BNL-720-34-2004-JA, Feb.
2004 and submitted in Phys. Rev. E.
[2] S. Biedron, H. Freund and S. Milton, Nucl. Instrum.
Methods Phys. Res. A 475, p. 401[3] L.H. Yu, A. Douyran, L. Di Mauro, et al., Phys. Rev.
Lett. 91, No. 7, 074801-1, (2003).
[4] L. Di Mauro, A. Doyuran, E. Johnson, et al., Nucl.
Instrum. Methods Phys. Res. A 507, 15 (2003).
[5] SLAC Report No. SLAC-R-593, edited by J,
Galayda, 2002
[6] V. Ayvazyan et al., Phys. Rev. Lett. 88, 104802(2002).
[7] L.H. Yu et al., Phys. Rev. A 44, 8178 (1991)[8] I. Ben-Zvi et al., Nucl. Instrum. Methods Phys. Res.,
Sect. A 304, 181 (1991).

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SPECTRAL PHASE MODULATION AND CHIRPED PULSEAMPLIFICATION IN HIGH GAIN HARMONIC GENERATION
Z. Wu, H. Loos, Y. Shen, B. Sheehy, E. D. Johnson, S. Krinsky, J. B. Murphy, J. Rose, T. Shaftan, ,X.-J. Wang, L. H. Yu, NSLS, Brookhaven National Laboratory, Upton NY, USA 11973
Abstract
Amplitude and phase measurements are conducted on
the 266 nm output of the DUVFEL laser at the National
Synchrotron Light Source (NSLS) at Brookhaven
National Laboratory. With the FEL operating in High
Gain Harmonic Generation (HGHG) mode, we havestudied narrow-bandwidth HGHG output, and observe
pulses near the transform limit. We have also chirped
both the electron bunch energy and the seed pulse
wavelength, and successfully imposed a linear chirp on
the HGHG output.
These results demonstrate thepotential to generate short harmonic pulses throughchirped pulse amplification [1] or coherently shape FEL
output.

output, a dispersive line could compress it to pulse widths
much shorter than the electron bunch length.
A
theoretical study of this process predicts achievable pulse
widths of 4 fsec in X-ray FELs [1]. We demonstrate
amplitude and phase measurements of HGHG, using
spectral phase interferometry for direct electric fieldreconstruction (SPIDER) [5]. This is the first time that
SPIDER has been reported for wavelengths this short. We
examine first the narrow bandwidth emission produced by
HGHG using an unchirped electron bunch, and a nearlymonochromatic seed. We then chirp both the frequencyof the seed pulse and the energy of the electron bunch,and measure the chirp imposed on the HGHG output.
Finally we discuss the implication for effective pulse
compression.

INTRODUCTION
In High Gain Harmonic Generation [2] operation of an
FEL, a coherent optical seed pulse at a subharmonic of theresonant FEL output wavelength is used to impose a
coherent microbunching of the electron bunch before it
enters the radiator. This permits rapid saturation of theharmonic output over short distances, and the possibilityof reaching X-ray wavelengths by cascading the process
through a relatively small number of stages [3].
An important advantage of this scheme is thelongitudinal coherence of the harmonic output.
Longitudinal coherence in itself is important for many
experimental applications of short pulse X-rays, but it alsopresents the possibility of achieving femtosecond pulses
through chirped pulse amplification (CPA) [1], andshaping short-wavelength pulses on ultrafast time scales.
Pulse-shaping techniques developed for ultrafast laser
systems allow complex modulations limited essentiallyonly by the available bandwidth of the pulse.
Manipulating optical interactions with such pulses yields
unprecedented control over dynamics, and such ‘quantum
control’ been demonstrated in a multitude of systems [4].
In principle, such techniques could be extended all theway down to X-ray wavelengths by seeding an HGHG
cascade with a shaped seed pulse. The question thenbecomes what role noise or distortion introduced by
HGHG will have on the shaping capabilities. For thisreason, it is useful to consider the full “HGHG transfer
function”, and measure both the amplitude and phase of
the output pulse as a function of the modulation of theseed pulse. This should also have an added benefit as an
FEL diagnostic, since modulations introduced by HGHG
are likely to be sensitive functions of electron bunchcharacteristics and radiator dynamics.
In this work, we study the simplest pulse shape: a linear
frequency chirp. This is an important test of the feasibilityof CPA. If a linear chirp can be imposed on the HGHG

Available online at http://www.JACoW.org

EXPERIMENTAL SETUPSPIDERThe SPIDER technique, developed by Walmsley andcoworkers [5], is an interferometric technique forrecovering the amplitude and phase of an ultrafast pulse.
Its principal advantages in FEL applications are that awell-characterized reference pulse is not needed, and a
rapid inversion algorithm that makes shot to shotmeasurements possible. We use a variant here known as
down-conversion SPIDER [6]. A diagram of our
implementation of the technique is shown in Fig. 1. Light
from the seed pulse at 800 nm is separated from the 266
nm HGHG output and stretched in a grating compressor
to a pulse width of 55 psec FWHM, to serve as theshearing pulse. The 266 nm pulse passes through aMichelson interferometer, which splits it into two

Fig 1. SPIDER implementation for measurement of
266 nm HGHG pulses. GC, grating compressor; DL,delay line; MI, Michelson interferometer, BBO,
crystal for down-conversion; F, filter, S, spectrometer.
For calibration, the 800 nm beam is blocked and filter
F is removed.

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Fig. 2 SPIDER trace from a chirped HGHG pulse.
identical replicas with a delay of τ = 3.5 psec between
them. Both 266 nm replicas are mixed with the chirped
shearing pulse in a 250 µm thick BBO crystal, which isphase-matched for down-conversion to 400 nm(θ=44.7 deg. Type I).
They each see a nearlymonochromatic slice of the long shearing pulse, with afrequency
differenceΩ = τβref = 0.2 THz,
where
βref = 0.06 THz/psec is the frequency chirp of theshearing pulse. The two 400 nm replicas produced in the
down-conversion are thus shifted in frequency by Ω and,as phase is preserved in the down-conversion, a frequency
component ω in one of the replicas carries the same phase
information from the parent pulse as the ω+Ω component
in the other replica. Hence by interfering the two pulses,
the phase difference between (ω,ω+Ω ) frequency pairs
may be measured and the spectral phase variation over theentire pulse determined.
Fig. 2 shows a SPIDER interferogram trace. In theabsence of the spectral shear (Ω=0), the fringe spacing
would be just 1/τ. The phase variation across the pulse
spectrum is manifested in variations from this spacing.
Abstracting this “carrier phase” from the measurement isa recurring problem in spectral interferometry, of which
SPIDER is a special case. Dorrer [7] notes that suchmeasurements are very sensitive to calibration errors inthe spectrometer, and that this problem is often avoided in
SPIDER by generating a calibration with Ω=0, while
maintaining a spectrometer configuration identical to thatused in the measurement. The effect of the spectrometer
error is then largely canceled by subtraction of thecalibration from the measurement. He also notes, and it
has been experimentally demonstrated [6] that, if the ratioof parent and converted pulse wavelengths is an integer,then an identical spectrometer configuration can be
maintained by using different grating orders for the

WEAOS02

calibration and the measurement. In fact, a slightly lessrestrictive condition holds: if these wavelengths are both
harmonics of a third wavelength, the same can be done.
Thus, here we set the spectrometer (a 320 mm focal
length Jobin-Yvon TRIAX, using a 2400 line/mm grating)to a center wavelength of 800 nm, and measure the 400
nm SPIDER trace in second order. The calibration ismade by interfering the 266 nm parent pulses directly, andmeasuring in third order.
For the inversion, we follow the procedure of Iaconis
and Walmsley [8] to obtain the phase. The spider trace isfourier-transformed, filtered with a fourth-ordersupergaussian centered at t = τ, with a 1/e half-width of
1.5 psec, and back-transformed to the frequency domain.
This phase is unwrapped, the calibration phase subtracted,
and the result concatenated to obtain the spectral phase of
the test pulse. The amplitude is obtained from a similar
procedure [9], using the t = 0 component of thetransformed SPIDER trace. With the field fully specified
in the frequency domain, the temporal profile, frequency
chirp, etc, can be obtained after transforming into the time
domain.

Fig. 3 Spectral and temporal characteristics of an
unchirped HGHG pulse, retrieved from SPIDER.
Intensity profiles are plotted in arbitrary units. (a)Spectral intensity (dashed), spectral phase (solid). (b)instantaneous frequency (dashed) , 3 times theresidual frequency chirp of the 6 psec seed laser (dashdot), intensity (solid), transform limited intensity(phases set to zero, dotted line)

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Z. Wu et al. / Proceedings of the 2004 FEL Conference, 285-288

HGHG

RESULTS AND DISCUSSION

(a)

(b)

Fig. 4 Spectral and temporal characteristics of achirped HGHG pulse, retrieved from SPIDER. (a)Spectral intensity (dash-dot), spectral phase (solid), 2ndorder polynomial fit to spectral phase (dashed),
spectral phase with quadratic component subtracted(dotted). (b) intensity profile (solid) , intensity withquadratic phase component subtracted (dashed),transform-limited intensity (dotted)
photoinjector followed by a 4-stage linear accelerator. A
magnetic chicane compressor after the first two linac
stages permits the compression of the electron bunch
down to ~1 psec FWHM. Varying the phase of the thirdand fourth linac stages permits the imposition of anenergy chirp on the bunch. Following the linac, theelectron bunch energy is modulated using a synchronized
optical seed pulse in a 1-meter undulator, which isresonant at the seed pulse wavelength of 800 nm. The
seed pulse is derived from the same laser that drives thephotoinjector, and its chirp is adjusted by varying its
length in a grating compressor. Following a dispersive
section, the coherently microbunched beam enters the 10m NISUS wiggler, which is resonant at the third harmonicof the seed. Both the 266 nm third-harmonic HGHG
output and the 800 nm seed propagate to the SPIDER setup shown in Fig 1.

We first examine narrow bandwidth HGHG (0.12%
relative bandwidth rms), with no chirp. For this, the seedpulse was stretched to 6 psec in length (FWHM), and theelectron beam parameters were optimized to minimize the
HGHG bandwidth. Fig. 3 shows typical data, obtained
from SPIDER from a single HGHG shot. In the firstpanel the spectrum and spectral phase variation are
shown. The second panel shows the temporal profile ofthe pulse obtained by Fourier-transforming the data in thefirst panel, as well the instantaneous frequency of thepulse as a function of time. The center frequency issubtracted for clarity. The frequency is essentially flatover the length of the pulse, with some distortion towards
the trailing end and in the wings. The chirp of the seedpulse, multiplied by the harmonic number n=3 of the
HGHG process, is shown for reference. Because theelectron beam is not chirped, we do not expect to see thechirp reflected in the HGHG output.
The flat phase profile indicates that the pulse is nearlytransform-limited. The pulse shape does deviatesignificantly from a Gaussian though.
The time
bandwidth product is σωσ τ = 0.9, or 1.8 times thetransform limit for a Gaussian pulse. However, if we set
the spectral phase identically to zero, and take thecalculated temporal profile as the transform limit, then thewidth (rms) of the measured profile is only 20 % larger
than the transform-limited width, στ/σ TL = 1.2. For a 50
shot sample, we obtain σωσ τ = 1.15 ± 0.15 andστ/σ TL = 1.4 ± 0.1.
In order to obtain a chirped HGHG pulse, it isnecessary to chirp the energy of the electron bunch so thatthe resonant frequency at each point along the bunch isequal to the third harmonic of the instantaneous seedfrequency, i.e, the resonant frequency chirp must be 3
times that of the seed pulse. This is done by running theFrequency (THz)

The Brookhaven DUVFEL operation in HGHG mode is
fully described elsewhere [10]. A 170 MeV, 300 pC
electron bunch is generated using a
BNL GUN-IV

Time (psec)

Fig. 5 Time-dependent frequency for several chirped
HGHG pulses. The data in the first panel are for the
shot represented in Fig 4. The curves are instantaneous
frequency (solid), theoretical chirp (dashed, see text),
and the intensity profile (dotted)

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Z. Wu et al. / Proceedings of the 2004 FEL Conference, 285-288

third and fourth linac tanks off-crest, and incompletely
compensating the chirp imposed for bunch compression

Fig. 6 Distribution of frequency chirp values
measured in a 200 fsec window around the center of aset of 136 HGHG pulses. The dashed line indicatesthe chirp expected to be imposed by the chirped seedpulse
(using both tanks reduces the effect of rf curvature).
Due to technical problems during the experimental run,we were only able to match the electron and seed chirps towithin 40%. The 800 nm seed pulse is 2 psec long
FWHM, with a bandwidth of 5.4 nm FWHM, and a chirpof 1.27 THz/psec. The corresponding chirp to be imposedon the HGHG output is then β266= 3.8 THz/psec, but theenergy chirp imposed on the electron bunch corresponded
to a resonant frequency chirp of only 2.7 THz/psec. We
find however, that the seed chirp is still clearly observablein the HGHG output.
Fig. 4 shows the recovered spectrum, phase andtemporal information for a single shot. A parabolic
spectral phase indicates a linear frequency chirp. Panel (a)shows the spectrum, the spectral phase, a parabolic fit to
the phase, and the resultant phase when the quadraticcomponent of the phase is subtracted off. Panel (b) shows
the temporal profile as measured, the transform-limited
profile (obtained by setting the spectral phase identicallyto zero), and the temporal profile that would obtain if thequadratic part of the phase were removed. The latter is tosimulate the temporal profile expected after putting thepulse through the appropriate compressor. We define thecompression ratio as the ratio of the as-measured rms
pulse width to the rms pulse width of this distribution.
The instantaneous frequency may be defined as the first
derivative of the temporal phase, and the chirp is then thesecond derivative. Both may be obtained from the data,
and the frequency vs time is displayed for several shots,
along with their respective temporal profiles, in Fig. 5.
The center frequency is subtracted for clarity, and thetheoretical curve represents a constant chirp of 3 times theseed pulse chirp. The first shot displayed in Fig. 5 is forthe same shot represented in Fig. 4., and shows a nearconstant chirp over the length of the pulse. The
compression ratio for this pulse is 3.2, and, as is clear

WEAOS02

from Fig. 4(b), the compressed pulse would be close to
the transform limit. More typical shots are shown in thesubsequent panels. The strong phase variation in thewings destroys the compressibility for most of the pulses,
but a chirp near the expected value is usually observed
near the peak of the pulse. If we simulate a single
compressor for all pulses by extracting the same quadraticcomponent from the phase as for the shot in Fig 4, we findthat, for 136 pulses measured, 20, or 15%, would show
some compression. However, if we fit the chirp in a 200
fsec window about the peak of the pulse we find that the
distribution of chirp values (Fig. 6) is peaked about the
expected value β266 .
The shot-to-shot fluctuations in compressibility
probably arise from a combination of the mismatch ofelectron bunch and optical seed chirps, the 150 fsec (rms)synchronization jitter between the electron bunch andseed pulse, and fluctuations in the electron bunch
compression that were due to technical problems during
the experiment. The latter two, coupled with thenonlinearity of the electron bunch chirp due to rf
curvature, can lead to emission effectively occurring over
only a fraction of the electron bunch. Supporting thisinterpretation is a strong positive correlation observed
between the pulse width of the HGHG pulse and thecompression ratio.
While the control of these factors will be necessary fora practical implementation of chirped pulse amplificationin high gain harmonic generation FEL systems, theobservation of compressible pulses in the present work,
does demonstrate the viability of the technique, and thepotential for more complex shaping at short wavelengths.

ACKNOWLEDGEMENTS
The work was performed under DOE contract DEAC02-98CH10886.

REFERENCES[1] L. H. Yu, E. Johnson, D. Li, and D. Umstadter
Phys. Rev. E 49, 4480-4486 (1994)[2] L. H. Yu Phys. Rev. A 44, 5178-5193 (1991); L. H.
Yu et al. Phys. Rev. Lett. 91, 074801 (2003);[3] L. H. Yu, in Proceedings of the X-Ray FEL Theory
and Simulation Codes Workshop SLAC Stanford
University Sep 23-24, (1999)[4] For a recent review, see D. Goswami, Phys. Rep. 374,
385–481 (2003)[5] C. Iaconis and I. A. Walmsley, Opt. Lett. 23, 792–794(1998).
[6] P. Londero et al J. Mod. Opt. 50, 179 (2003)[7] C. Dorrer. J. Opt. Soc. Am B 16, 1160–1168 (1999).
[8] C. Iaconis and I. A. Walmsley, IEEE J. Quant. Elect..
35, 501 (1999)[9] A. Muller and M. Laubscher, Opt. Lett. 26, 1915
(2001).
[10] A. Doyuran et al Phys Rev ST AB 7, 050701, (2004)

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STUDY OF COHERENCE LIMITS AND CHIRP CONTROL IN LONGPULSE FEL OSCILLATOR
Y. Socol, A. Gover, A. Eliran, M. Volshonok
Dept. of Physical Electronics – Faculty of Engineering, Tel Aviv University, Tel-Aviv, Israel
Y. Pinhasi, B. Kapilevich, A. Yahalom, Y. Lurie, M. Kanter, M. Einat, B. Litvak
Dept. of Electrical and Electronic Engineering – The College of Judea and Samaria, Ariel, Israel
Abstract
Electrostatic Accelerator FELs (EA-FELs) have thecapacity to generate long pulses of tens microseconds andmore, that in principle can be elongated indefinitely (CW
operation). Since a cold beam FEL is by nature a"homogeneously broadened laser", EA-FEL can operate,unlike other kinds of FELs, at a single longitudinal mode
(single frequency). This allows the generation of very
coherent radiation. The current status of the Israeli
Tandem Electrostatic Accelerator FEL (EA-FEL), which
is based on an electrostatic Van de Graaff accelerator,
allows the generation of pulses of tens microseconds
duration. It has been operated recently past saturation, andproduced single mode coherent radiation of record narrowinherent relative line width ~∆f/f =10-6 at frequencies near
100 GHz. A clear frequency chirp is observed during
pulses of tens of microseconds (0.3-0.5 MHz/µs). This isessentially a drifting frequency pulling effect associatedwith the accelerator voltage drop during the pulse. We
report experimental studies of the spectral line width andchirp characteristics of the radiation, along with theory
and numerical simulations, carried out using spacefrequency model, matching the experimental data.

Figure 1(a)INTRODUCTION
The Israeli Electrostatic Accelerator FEL was relocatedto Ariel and returned to operation a year ago. Peak powerof 150W usable radiation was previously reported [1].

RADIATION MEASUREMENTS
The mm-wave radiation is transported to the user's
rooms by means of a corrugated over-moded waveguide.
The measurements were performed by two means: a)using W-band detector Millitech –DXP-10; b) using
heterodyne mixer of Hughes-47496H-100 with local
oscillator (LO) from a HP-8797D Network Analyzer. In
both cases, Tektronix –TDS-784A oscilloscope was used
to monitor the output. The input signal was attenuated inorder to cope with the dynamic range of the detectors.
The maximal peak power at the user location wasmeasured to be 1200W.

SINGLE MODE OPERATION AND CHIRP
In most measurements single mode lasing was observed
after a short mode competition period. This is expected
because of the "homogeneous broadening" nature of FEL
in the cold beam regime. The detector, operating at

Available online at http://www.JACoW.org

Figure 1 (b)Figure 1: Typical oscillograms of the radiation. Middle
line: heterodyne (IF) output. Lower line: W-band detector
output. The local oscillator (LO) frequency fLO is set very
close to laser frequency: a) fLO=86,400MHz – the IF
frequency decreases with time; b) fLO=86,402MHz – IF
increases with time.

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square-law detection scheme produces on the scope thedifference (beat) intermediate frequency:(1)f IF = f − f LO
there is no distinction in the measurement between
negative and positive frequencies, and what is seen on thescope is a signal of frequency f IF .
In all measurements the IF signal exhibited either
negative or positive chirp (Fig. 1). To determine the chirp
direction of the laser signal, one should notice that if thelaser signal has negative chirp (f drops down with time)
the IF signal would also exhibit negative chirp only whenf>fLO and would exhibit positive chirp when f<fLO.
Fig. 1 shows typical oscillograms of the radiation. The
heterodyne mixer frequency was set at two close
frequencies: (a) 86,400MHz and (b) 86,402MHz,
enabling the accurate determination of the single mode
radiation frequency ( f m = 86.401± 1MHz) , and confirming
negative direction of the laser chirp.
At heterodyne (local oscillator – LO) frequency
86,400MHz, the intermediate frequency (IF) decreases
with time. At 86,402MHz – increases with time.
This behaviour of the IF signal indicates that the laser
radiation exhibits a down shift frequency chirp. Thiseffect is associated with the drift of the gain curve due tothe beam energy drop during the pulse, and can be
explained as time varying "frequency pulling" effect of
the laser oscillator. A theoretical analysis of this effect
was provided in on earlier publication [2].

CHIRP ANALYSISIn order to analyze the chirp, we performed the socalled I/Q analysis (Fig. 3). The obtained oscilloscope
signal (Fig 2.a) was multiplied by sin(ω0t) and cos(ω0t),with ω0 corresponding to an arbitrary chosen frequency(169.0MHz at Fig. 2a). These multiplied signals I and Q
were subjected to slow-pass filters (LPF) of 15MHz
bandwidth. Then, amplitude I2 +Q2 (Fig 2,b) and phasedeviation were extracted, and the frequency deviation∆f(t)=f-f0 Eq. (2) was obtained as the deviation time
derivative of the phase deviation:
 Q(t ) 1 d
(2)∆f (t ) =arctg 
2π dt
 I (t ) To obtain the inherent spectrum width of the laser
radiation (which we define as the linewidth of the wave
when the spectral broadening due to the chirp is
eliminated), we performed time-stretching. Namely, as
the signal was approximated as sin((ωo+ω1 t)t), the time
was transformed as t’=t(1+tf1/f0), with the chirp rate
f1=0.35MHz/µs as follows from the data (Fig 2.d). The
Fourier spectrum of the transformed signal is shown in
Fig 2.c, exhibiting inherent spectral linewidth (FWHM) of
0.2MHz (in comparison with 2.0MHz FWHM of theoriginal chirped signal spectrum).

FIGURE. 2

Figure 2a

Figure 2b

Figure 2c

Figure 2d

Figure. 2: I/Q analysis of the oscilloscope signal – low-pass filter is set to 15 MHz band width. Fig. 2a:original oscillogram. Fig. 2b: mode amplitude (blue line-experimental data, red line FEL 3D calculations). The
mode frequency is 83,669.0 MHz. Fig. 2c: inherent spectral width, nearly pulse-time-limited (the limit is 0.1
MHz). Since the actual chirp is non-linear in time, the spectrum is wider (0.2 MHz). Fig. 2d: frequency
deviation obtained as phase deviation time derivative (blue line-experimental data, red line FEL 3D
calculations). The chirp rate is approximately 0.35 MHz/µs

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A. Gover et al. / Proceedings of the 2004 FEL Conference, 289-292

LPF

This value is in excellent correspondence with theexperimental data, taking into account accuracy of theparameters involved in the calculation.

I(t)+cos(ω0t)

arctg(Q/I)

Y(t)

291

θ(t)

1

d

2π dt

∆f(t)

LPF
Q(t)

-sin(ω0t)

Figure. 3: I/Q analysis block-scheme of the intermediate
frequency oscillograms.
Since the actual chirp is a little non-linear in time in theends of the pulse, the spectrum width is somewhat higher
than the pulse-duration-limited value (0.1MHz).
We analyze here the chirp effect in terms of the basic
theory of frequency-pulling in laser oscillators [3]. In ourcase this frequency pulling shift varies with time (chirps)
due to the drift of the gain curve associated with theaccelerator voltage drop during the pulse. Namely, forresonator eigenmode frequency fm, resonator mode
linewidth (FWHM) ∆f1/2, maximum gain frequency fmax
and gain bandwidth ∆f the pulled oscillation frequency f
is [3]:(3)f − f m = ( f max − f m ) ⋅ ∆f 1 / 2 / ∆f

The experimentally measured chirp behaviour (Fig.
2d) also agrees well with results of simulation of FEL3D.
The chirped instantaneous frequency is calculated byevaluating the rate of change of the computed phaseaccumulation in each round-trip traversal of theoscillation build-up[2].
We then eliminated the chirp mathematically and useda window of 10µs to obtain the Fig. 4b. In this case,bandwidth is window limited to 0.1MHz, enabling thedetermination of the inherent mode linewidth as 0.27
MHz.

Figure 4(a)During the pulse, f0 drifts towards lower frequencies (dueto the accelerating voltage drop) with the rate
df max
dV
=C
dt
dt

(4)

where:

e df max ∆f 1 / 2(5)
mc 2 dγ ∆fis the maximum gain frequency sensitivity to voltage drop(see e.g. [4]).
γ2 β c θ max ⋅
f 0 = z 0 z 0 ⋅  k w +
Lw 
2π

(6)
C=



(2πf co )2⋅ 1 + β z20 −2
γ z 0 k w + θ max Lw c 

[ (

)]

where:

θ max - the maximal gain of detuning parameterf co - the cut off frequency of the resonator waveguideFor
ouroperatingregimeweevaluated
C=156MHz/kV. Synchronism width ∆f (FWHM of the
FEL gain) was calculated using FEL3D software [5] andyielded ∆f = 6.0GHz. The resonator eigenmode linewidth∆f1/2 was measured (in “cold” resonator) to be∆f1/2=16MHz (Q-factor of 5·103 at 86GHz). The voltage
drop rate was measured to be 0.7kV/µs. The chirp rate
df/dt is therefore df/dt = 0.3MHz/µs.

Figure 4(b)Figure. 4: Spectrum (Fig.4a) and inherent spectral width(Fig.4b) of 85,022MHz RF mode. Time window is 1 µs
(Fig.4a) and 10µs (Fig.4b).
In Fig. 4a we show different processing of the IF data. A
spectrogram in ω-t phase space was computed by
employing a running window Fourier-Transform [2] of
1µs width. This window makes it possible to observe thespectrum chirp, which agrees well with the 0.35MHz/µs
estimate, but limits the measurable bandwidth to
1MHz=1µs-1.

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MODE HOPPING AND OSCILATORRELAXATION OSCILATION
Mode hopping was observed in many cases, and isassociated with accelerating voltage drop, which wasmeasured to be in the range of 7 – 30kV (depending
primarily on pulse duration) during the observed pulses.
A typical case is shown in Fig. 5 (arranged like Fig. 2).
The mode frequencies were uniquely identified by taking
several oscillograms with different heterodyne
frequencies (usually by steps of 100MHz). One can seethat the first mode (85,021.5 MHz) decays when thesecond (83,676.5MHz) rises.

One can also see a clear trend (both modes at Fig. 5,
also the mode at Fig. 1): chirp rate is significantly higher
at the rising stage of each mode, and this rate is larger as
the corresponding mode rise is steeper. This phenomenon
is probably connected to damped relaxation oscillations
and is well reproduced by the FEL3D [5].
The chirp direction in both modes is the same
(frequency decreases with time). The opposite chirp signof the IF signal of the 83,676.5MHz mode (Fig 5c) is
because fm, the mode frequency, is below that of the local
oscillator fLO, and therefore the IF frequency fIF=fm-fLO is
negative (aliasing effect).

REFERENCES[1] A. Gover et al. NIM A 528(2004) 23-27.
[2] A. Abramovich, et al, Phys. Rev. Lett. 82, (1999),5257-5260[3] A. Yariv. Optical Electronics, 3-rd ed. CBS College
Publishing, 1985; see 6.2-5[4] E. Jerby A. Gover IEEE QE-21 No.7 (1985) 10411057[5] Y.Pinhasi et al. Int. J. of Elect. 78 (1995) 581.

Figure 5(a)Figure 5(b)Figure 5(c)Figure. 5: Demonstrating of mode hopping apposite withthe accelerating voltage drop: (a) IF signal (b) signal
growth and decay of the numerically filtered modes (c)isolated IF frequency chirp measurement of the twomodes.

WEAOS04

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CHARACTERIZATION OF LASER-ELECTRON INTERACTION AT THE
BESSY FEMTOSLICING FACILITY ∗K. Holldack, T. Kachel, S. Khan† , R. Mitzner, T. Quast, F. Senf
BESSY, 12489 Berlin, Germany

Abstract
A ”femtoslicing” facility to generate ultrashort x-ray
pulses by laser-electron interaction is being commissioned
at the BESSY II storage ring. The energy modulation ofelectrons by femtosecond laser pulses is a good test casefor FEL seeding schemes. The dependence of the interaction efficiency on various parameters is discussed.

INTRODUCTION
A laser pulse co-propagating with an electron bunch inan undulator modulates the electron energy if the resonancecondition
λU
K2
λL = 2 1 +(1)2γ
2
is fulfilled. Here, λL is the laser wavelength, λU is theundulator period, γ is the Lorentz factor of the electrons,
and K is the undulator field parameter. The oscillatory energy modulation has a period length equal to λL and an
envelope corresponding to the laser pulse shape enlarged
by λL NU , the slippage of the electrons relative to the laser
field over NU undulator periods.
Laser-induced energy modulation has a number ofpromising applications, among them seeding of a freeelectron laser (FEL), either by high-gain harmonic generation (HGHG) [1] or by sideband seeding [2]. Energy modulation is the basic mechanism for ”femtoslicing” [3, 4]
and various proposals for sub-femtosecond pulse generation, e.g. [5]. Another idea is to generate coherent-light
replica of electron bunches for diagnostics purposes [6].
Periodic energy modulation of electrons by a femtosecond
laser pulse leads to:– transverse displacement due to dispersion, which isthe desired effect in the context of femtoslicing,– the formation of microbunches for small differences (below λL /2) of the energy-dependent electron path
length, emitting coherent radiation at a fraction of λL , particularly at higher harmonics of the laser, as in HGHG,– a dip in the longitudinal electron distribution for path
length differences exceeding the laser pulse length, giving
rise to coherent radiation in the THz regime.
At the BESSY II storage ring, a femtoslicing source togenerate x-ray pulses of 50 fs (fwhm) duration is currently∗ Funded by the Bundesministerium für Bildung und Forschung and by
the Land Berlin.
† email: shaukat.khan@bessy.de

Available online at http://www.JACoW.org

being commissioned [7, 8]. Its purpose is to study ultrafast structural and magnetic changes in matter, and to gain
experience in view of BESSY’s soft-x-ray FEL project [9].
As a test case for FEL seeding schemes, femtoslicing allows to study the dependence of the energy modulation
efficiency on various parameters. Relevant electron beam
parameters are the electron energy (or Lorentz factor), thebeam size given by emittance, beta functions and dispersion, and the energy spread. The laser properties of interest are the laser wavelength, bandwidth, chirp, polarisation,pulse energy and duration, as well as beam size and divergence, which in turn depend on λL and the quality parameter M 2 . The undulator is specified by the period length, thenumber of periods, and to first order by the magnetic fieldparameter K, but higher harmonics of the field may also be
relevant. The interaction efficiency depends critically on
the overlap of laser and electrons in all phase space dimensions, i.e. horizontal and vertical position and angle, longitudinal coordinate (timing) and spectral overlap according
to eq. 1.
The amplitude of the energy modulation ∆E is in principle given by [3]K 2 /2 ∆ωL,(2)
1 + K 2 /2 ∆ωUwhere α is the fine structure constant, AL is the pulse
energy, EL is the photon energy, and K is the undulator
parameter. The bandwidth ratio ∆ωL /∆ωU of laser andundulator radiation is roughly given by NU /NL ≤ 1, theratio of undulator periods and optical cycles in the laser
pulse (if NU > NL , the electron slippage exceeds the laser
pulse length and there is no further gain). There are corrections for matching laser and undulator spectra, and for thefinite electron beam size [4], but the dependence on otherparameters has to be studied by numerical simulation or
experimentally, as discussed below.
(∆E)2 = 4παAL EL

FEMTOSLICING – PRINCIPLE AND
IMPLEMENTATION AT BESSY II
The principle of femtoslicing involves energy modulation of electrons in an undulator (”modulator”) by a shortlaser pulse, followed by transverse displacement in order toextract the short-pulse component of radiation emitted in a
subsequent undulator. At BESSY II, the modulator U-139(a planar wiggler with λU = 139 mm, NU = 10) and radiator UE-56 (an elliptical undulator with λU = 56 mm,
NU = 30) are both placed in the same straight section to

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minimize pulse lengthening. The energy-modulated electrons are displaced by angles upto 1 mrad such that their radiation does not overlap with the radiation from the bunchcore, which can be blocked by an aperture without using
imaging elements, which would cause a large backgrounddue to non-specular scattering. A liquid-nitrogen cooled
Ti:sapphire laser system [10] provides pulses at a wavelength of λL = 800 nm with a pulse energy up to 2.8 mJ
at 1 kHz (alternatively 1.8 mJ at 2 kHz). Further detailsof the technical implementation at BESSY are given in thecaption of fig. 1 and elsewhere [7].

pulse duration and M 2 ), to study the effects of imperfectelectron-laser overlap and other deviations from an ideal
situation, and to devise a suitable separation scheme forthe short-pulse x-ray component. The generation of a realistic distribution of energy-modulated electrons allows to
predict the shape of the dip causing THz radiation emission as well as properties of the short x-ray pulses such as
photon rate, background, spatial distribution and spectral
characteristics.
The laser-induced energy deviation ∆E is modelled byintegrating the product of the horizontally transverse electron velocity x and the electric field E over the length
L = NU λU of the modulator∆E = −e

 L/2
−L/2

x (s) E(x, y, z) ds(3)

for an ensemble of randomly generated ”macroelectrons”. The electric field of the laser pulse is given by2ρ(x, y, z)/ε◦ sin [2πz/λL − ϕG (z)] .
(4)Here, ε◦ is the permittivity of free space, ϕG is the Guoyphase shift [11], and (x, y, z) is the electron position relative to the laser pulse, where z changes by one laser wavelength λL for each undulator period. The laser pulse is assumed to be Gaussian with an energy density ρ. While thepulse length is constant, the transverse rms size depends
on the position sL of the laser pulse relative to the waist
position s◦ and on the beam quality factor M 2 :E(x, y, z) =
σx,y (sL ) =Figure 1: Overview of the femtoslicing facility. A laser
hutch outside the storage ring tunnel houses a Ti:sapphireoscillator and amplifier (red) with respective pump lasers(green). The main pulse is focussed by a telescope (T)and enters the storage ring vacuum, while a small fraction
will be sent as a pump pulse to the experiment. Modulator(U-139) and radiator (UE-56) are within a chicane formedby three bending magnets B1 (3.32◦ ), B2 (6.40◦ ) and B3(3.08◦ ). Laser and U-139 radiation are directed to a diagnostics station (D) above the storage ring tunnel.

NUMERICAL SIMULATIONS
Prior to the construction of the femtoslicing facility
at BESSY II, numerical simulations were employed todetermine the laser requirements (such as pulse energy,

THPOS04
2 (s ) +σx,y◦M 2 λL
4πσx,y (s◦ )2(sL − s◦ )2 .

(5)
Modifications of the laser field in this low-gain process
are assumed to be small and are not included in the model.
The result of the simulation is the amount of energy acquired by each macro-electron in the interaction process
and the energy-modulation ”profile”, i.e. the electron distribution along the ∆E-axis. The endpoint of that distribution is the modulation amplitude, which – for a realistic
simulation – is systematically lower than given by eq. 1.
Another useful quantity is the number of electrons exceeding a certain energy offset. For femtoslicing at BESSY II,
for example, radiation from electrons with ∆E/E > 0.7%
is assumed to be separable.

EXPERIMENTAL METHODS
Successful electron energy modulation at a femtoslicing
facility can be verified by various means, including(1) cross-correlation of visible synchrotron radiationfrom transversely displaced electrons with laser pulses,(2) measurement of the spectral dependence of the laser
gain as a function of K, i.e. the single-pass FEL gain,

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S. Khan et al. / Proceedings of the 2004 FEL Conference, 293-296

THz Diagnostics
The radiation power emitted by an electron distribution(z) for a given photon wave number 1/λ isP (1/λ) = N p1/λ + f1/λ N (N − 1) p1/λ ,(6)where p1/λ is the power emitted by a single electron, N
is the number of electrons, and f1/λ is a form factor linked
to the electron distribution via Fourier transform:

2


i2πz/λ(z) dz  .
f1/λ =  eFigure 2: Square root of the THz signal, locked to the laser
repetition frequency of 998 Hz, as function of (a) the undulator gap, (b) the orientation of a half-wave plate, where
the dashed line indicates a sin2 -dependence, (c) the longitudinal laser position and (d) horizontal misaligment with
0.33 mm corresponding to the rms electron beam size.

(3) detection of THz radiation from a dip in the longitudinal bunch profile,(4) scraping transversely displaced electrons and measuring the electron loss rate,(5) observation of synchrotron radiation from transversely displaced electrons,(6) observation of enhanced radiation due to microbunching.
Methods (1) and (2), employed at the pioneering experiments described in [4], were not yet applied to the BESSY
case, because method (3) offers very sensitive and simple on-line diagnostics, once THz detection is available.
At BESSY II, a dedicated THz beamline with a fast infrared bolometer was constructed [12], and examples arepresented below. THz diagnostics indicates the occurrenceof energy modulation and allows to optimize its efficiency,
but does not directly measure the modulation amplitude.
The transverse displacement of electrons is proportional
to their energy modulation and can be measured by methods (4) and (5), where (4) is very simple but destructive,
whereas (5) involves the rather complex synchrotron radiation emission characteristics. Method (6), finally, is noteasily realized in a storage ring and has not yet been attempted.

(7)

When path length differences of energy-modulated electrons exceed the laser pulse length, a hole is created in
the longitudinal electron distribution, giving rise to a large
form factor around 1/λ ∼ 100 cm−1 , i.e. coherent radiation in the THz regime.
At BESSY II, THz radiation from a dipole magnet isroutinely employed to detect laser-induced energy modulation and to optimize the spatial, temporal and spectral
laser-electron overlap. The dependence of the THz signal,
locked to the laser repetition rate of 998 Hz, on several critical parameters is shown in figure 2.
In part (c) of the figure, the square root of the signal is
directly proportional to the electron density. Otherwise,quantitative conclusions regarding the energy modulation
are not easily drawn from the THz spectrum. A modeldependent comparison would include the electron dynamics between modulator and the location of the THz beamline, application of eq. 7 to the resulting electron distribution, and consideration of the detector bandwidth.

Scraper Measurements
The energy modulation ∆E/E at a position with optical functions βx , αx , γx , dispersion D and D = dD/ds
excites a horizontal betatron oscillation. With a scraper positioned at a distance ∆x from the beam center, electrons
contribute to the loss rate (i.e. the inverse beam lifetime) if∆x ≤ ∆E/E



βxS



γx D2 + 2αx DD + βx D2 ,(8)

where the horizontal beta function is βxS and the dispersion is zero at the location of the scraper. The top part offigure 3 shows the beam lifetime while the scraper is moved
towards the beam and the laser is blocked periodically. The
scraper position relative to the beam center is deduced fromthe position at which the quantum lifetime becomes dominant, as shown in the bottom part of figure 3. The solidline is derived from a simulated energy-modulation profile,where ideal overlap was assumed and the laser pulse energy was varied to match the data. The resulting pulse energy was about half the value measured at the laser exit,
indicating power losses or insufficient overlap at the timeof the experiment.

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Figure 4: Angular distribution of undulator radiation at 707
eV recorded with a GaAs photodiode while the laser isblocked periodically. With laser (black symbols), the photocurrent is enhanced even though the laser repetition rateis only 1 kHz, while the electron bunch rate is 1.25 MHz.
Experiments to this end are in preparation. Until then,quantitative conclusions rely on scraper measurements during dedicated shifts, while THz diagnostics remains thebest everyday tool for optimization.
Figure 3: Top – beam lifetime versus time while a scraper
is moved towards the beam and the laser is blocked periodically. Bottom – loss rate versus scraper position. The
dashed line indicates the quantum lifetime limit, the solidline is a simulation result.

Synchrotron Radiation from Displaced Electrons
The purpose of femtoslicing is to generate short radiation
pulses from electrons transversely displaced in the radiator.
Figure 4 shows the photocurrent from a GaAs diode behindthe exit slit of a monochromator, which was recorded while
an aperture in the frontend was moved across the radiation
distribution of the UE-56 radiator and the laser was blocked
periodically. With laser-induced energy modulation, theaverage photocurrent is enhanced even though the singlebunch rate is 1250 times larger than the laser repetion rate.
This is due to the fact, that the transverse displacementof an energy-modulated electron is maintained over manyturns, given by the longitudinal and transverse damping
time, and radiation from the same electron is detected manytimes, depending on the energy-modulation profile and theobservation angle. The time-integrated measurement is a
simple method to detect the presence of energy modulation, while a quantitative measurement requires:– selection of a fast detector signal at the interaction
time to exclude radiation from successive turns or fromother electron bunches,– pulse height analysis to detemine the number of simultaneously arriving photons,– interaction with the same bunch only after one or two
radiation damping times to exclude radiation from electrons excited at previous interactions.

THPOS04

ACKNOWLEDGEMENTS
We would like to express our gratitude to all BESSY colleagues contributing to the femtoslicing project. Helpful
discussions with P. Heimann, R. Schoenlein, A. Zholents(LBNL, Berkeley), R. Abela, G. Ingold, A. Streun (SLS,
Villigen) and hardware support by T. Lohse (HU, Berlin)
are gratefully acknowledged.

REFERENCES[1] L.-H. Yu, Phys.Rev. A44 (1991), 5178.
[2] W. Brefeld et al., NIM A 483 (2002), 62.
[3] A. A. Zholents, M. S. Zoloterev, PRL 76 (1996), 912.
[4] R. W. Schoenlein et al., Science 287 (2000), 2237.
[5] A. Zholents et al., EPAC’04, Lucerne (2004), MOPKF072.
[6] E. L. Saldin, et al., DESY 04-126 (2004).
[7] S. Khan et al., PAC’03, Portland (2003), 836.
[8] S. Khan et al., EPAC’04, Lucerne (2004), THPKF014.
[9] The BESSY Soft X-Ray Free Electron Laser, Technical Design Report, March 2004, www.bessy.de.
[10] Kapteyn-Murnane Laboratories Inc. MTS oscillator and
HAP-AMP amplifier, Coherent Verdi V5, Quantronix
527DQE-S.
[11] A. E. Siegman, Lasers, University Science Books, Sausalito(1986).
[12] K. Holldack et al., EPAC’04, Lucerne (2004), THPKF013.

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MEASUREMENT AND CALCULATION OF THE ‘ELECTRONEFFICIENCY’ ON THE ‘CLIO’ FREE-ELECTRON LASER
R. Prazeres, F. Glotin, J.M. Ortega : LURE, bat 209D, BP34, 91898 ORSAY CEDEX, FRANCE
Abstract
This paper describes the recent measurements of‘Electron efficiency’ which has been done with the‘CLIO’ Free-electron laser (FEL). The ‘Electron
efficiency’ is the relative energy loss of the electron beamin the undulator during the FEL interaction. It gives anabsolute measurement of the optical power produced by
the FEL, which is then compared to the direct
measurement using a power meter at the exit of the FEL.
An analytical expression of the ‘Electron efficiency’ isgiven here, and it is compared to the measurements.

THE CLIO FREE ELECTRON LASER
The ‘CLIO’ Free Electron Laser (FEL) is an infrared
tuneable laser source [1]. It uses a linear accelerator,
which produces an electron beam of adjustable energy
from 13MeV to 50MeV. The laser spectral range istuneable from 5µm to about 120µm. Such a wide
broadband is achieved by using, for λ >100µm, a special
set of toroidal mirrors. Also, in order to reduce the cavity
losses at large wavelength, a waveguide is installed inplace of the vacuum chamber in the undulator section.
The laser extraction of the cavity is achieved by hole
coupling in the front mirror.
The best configuration of radius of curvature for thecavity mirrors has been obtained with a numerical code[2] [3]. This code calculates the propagation of the laser
wave front A(x,y) in the optical cavity. It uses an iterative
process of wave propagation in the cavity, whichconverges to a steady state laser mode As(x,y)
corresponding to the FEL saturation regime. It takes into
account the design of the cavity (mirrors, vacuum
chamber,…) including the waveguide effect in theundulator section, and the hole coupling in the front
mirror. This code gives the amplitude distribution As(x,y)
of the laser mode at saturation, in any point of the cavity,and it gives all related parameters : the cavity losses L,
the ‘extraction rate’ Tx of hole coupling, the optical modecross-section Σo,…

‘ELECTRON EFFICIENCY’, AND FEL
POWER
In order to measure the energy distribution of theelectrons after FEL interaction, an electron spectrometer[1] is installed at the exit of the undulator. It gives anexperimental value of the ‘Electron efficiency’ η, whichcorresponds to the percentage of energy of the electron
beam which is transferred to the laser optical mode,
during the FEL interaction :(1)
η=∆We/We
where We=Q.(γmc2/e) is the electron bunch energy, with
Q the charge of each electron bunch, and ∆We is the

Available online at http://www.JACoW.org

amount of energy produced in FEL interaction by eachelectron micro-bunch. The average extracted power(energy per second) of the FEL can be deduced from η byT
〈Px 〉 ≅ We .η.∆Tsat . x .fµ .fM(2)
L
where fM and fµ are respectively the repetition rates ofmacro-pulses and micro-pulses, and ∆Tsat is the time
duration of the FEL saturation in the macro-pulse. The
ratio Tx/L is the ‘extraction ratio’ between the losses byhole coupling Tx and the total losses L of the laser cavity.
It depends on the intracavity laser mode, and it is obtained
here by numerical simulation. The power <Px>, deduced
from expression (2), is compared here to the direct
measurement using a detector at the exit of the FEL.
In order to fit the measurements of ‘Electron
efficiency’ with the theory, we have written an analyticalexpression [4] for η, which is based on the analyticalexpression [5] [6] of the FEL intensity at saturation:η≈ Σ ⋅∆t 
1⋅ α +0.22⋅goα2 +4.85⋅10−3 ⋅go2α3 ⋅ 1−e−h ⋅Ff  o o 4Nu Σe ⋅∆te 

(

)(

)

(3)

where go is the gain coefficient for linearly polarized
undulators :
J N2
16 π
2
go =
λ R Lu e u 4 ξ [J 0 (ξ ) − J1 (ξ )](4)γ
1.7 ⋅10K2
1
where ξ =and K is the undulator parameter,
4 1+ K 2 /2
Nu and Lu are respectively the number of periods andlength of the undulator, λR is the resonance wavelength
and Je is the density current of electrons. The coefficient
α=Finh.FS in expression (3) is an attenuation factor for thegain coefficient go. It depends on the inhomogeneous
broadening factor Finh [5] :1
1Finh =⋅(5)
1+1.7 ⋅ µ e2 1+ µ y2(

with µ e = 4N u σ γ γ) depending on the relative RMS

energy spread (σγ/γ) of the electron beam, andKN 2µy = u⋅ εnor corresponding [7] to theλu 1 + K 2 / 2
normalized emittance εnor=4πγσσ’ along vertical axis (y).
The longitudinal mode coupling factor FS is [6] :
1
Fs =
(6)
1 + µc / 3
where µ c = N u λ R /cσ e is the ratio between slippage
length NuλR and electron bunch length cσe, with σe theRMS time duration of electron bunch. The last part ofexpression (3) involves the size of the laser pulse :Σo=πσoxσoy and ∆t o = πσ o , which are respectively thecross-section and time duration of intensity, with σo the

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RMS time duration of the laser mode amplitude. The sizeof the electron bunch is : Σe=2πσexσey for the crosssection and ∆t e = 2πσ e for the time duration with σethe RMS time duration. The ‘filling factor’, used in
expression (3), is depending on the transverse crosssections:
Ff≅ 1/(1+Σo/Σe).
The
coefficient
h=[1.8/(1+G*p)].[(1-L)G*p-L]/L in expression (3) depends
on the ‘Small Signal Gain’ of power G*p, and on the
optical losses L. The ‘Small Signal Gain’ of power is :G* = F ⋅ 0.85⋅ g α + 0.19⋅ g α 2 + 4.12⋅10− 3 ⋅ g α 3 (7)
p
f 
o
o
o 
where α=Finh.FS. Note that this expression includes thenon linear components which are present for large valuesof the gain [5]. The expression (3) of ‘Electron efficiency’
also takes into account the non linear behaviour.
In first approximation, for small values of gain
coefficient go, the expression (3) of η is close to 1/4Nu
multiplied by the attenuation factor α which lies generally
in the range 0.5 to 1. The factor [1-exp(-h)] becomes
important when the ‘small signal gain’ G*p is close to thelosses L. The last two terms of (3) are dependant on thevolume of optical and electron bunches. Now, in highgain regime, i.e. for large values of gain coefficient go, thenon linear behaviour of the gain G*p may increasestrongly the ‘Electron efficiency’. Note that, the thirdorder correction in (7) works [5] in a large range of govalues (go≤20) ; and this always keeps the ‘Electron
efficiency’ η<1.

( )

( )

( )

MEASUREMENTS
An example of electron spectra is shown in figure 1,
with γmc2=15.2MeV and laser wavelength λ=72µm. The
horizontal axis of electron spectra is the time scale, andthe vertical axis is the variation, in %, of the electronenergy γmc2 during the macro-pulse. Two spectra aredisplayed here: for ‘laser OFF’ and for laser ‘ON’. The
time evolution of electron energy centroid <γmc2>(t) isrepresented by a curve on each spectrum. The two curves
on bottom of figure 1 represent a Y-cut of the energy
distribution. The dashed vertical lines represent thecentroid of electron energy <γmc2>. The difference(<γmc2>OFF−<γmc2>ON),
betweenthecentroids,
corresponds to the ‘Electron efficiency’ η(t)=∆We/We.
At low electron beam energy (about 15MeV), the whole
series of measured spectra show, as observed in figure 1,
an important slope of electron energy versus time atmacro-pulse time scale : about 1.5% of energy variationin 10µs. Indeed, the electron beam at low energy is much
more sensitive to all perturbations than at high energy (>40MeV). The slope of electron energy reduces the powerat laser saturation, because the wavelength centroid iscontinuously shifted along the macro-pulse, by about∆λ/λ =3% (twice of electron energy shift), whereas the
FEL gain line width is only about δλ/λ=1/2Nu=1.3%.
Therefore, the laser saturation is not fully obtained during
the macro-pulse.

THPOS06

Figure 1: Electron energy spectrum at theundulator exit, with laser OFF and laser ON, atlaser wavelength λ=72µm.
The loss of energy of the electrons during the FEL
interaction is well represented by a subtraction between
density spectra of figure 1 : ‘laser ON’-‘laser OFF’. This
subtraction is represented in figure 2 by a series of Y-cut,
performed in the middle of the electron macro-pulse.
Each curve displays the subtraction of electron density(laser ON-laser OFF) as a function of the relative electronenergy (in %). Each curve corresponds to a different
undulator gap, from 18mm to 27mm, corresponding tolaser wavelengths from λ=49µm to 92µm. The hollow
which is observed here corresponds to a lack of electronsof nominal energy γomc2 (energy at undulator entrance).
The bump corresponds to an accumulation of electrons
which have lost energy during the FEL interaction. The
whole set of curves in figure 2 exhibit a variation of
amplitude, but they are keeping the same shape and same
position of the peaks. This last feature means that theenergy loss ∆γmc2/γomc2 of the electrons, during the FEL
interaction, is independent on wavelength: it is close to
2% in any case. Note that this parameter ∆γmc2/γomc2 is
not equivalent to the ‘Electron efficiency’ η, which values
are always less than 2% (see figure 3). Indeed, ηrepresents an average over the whole number of electrons,
and it corresponds to the difference of centroid of theenergy distributions.
At first sight, the similitude of the curves in figure 2
would lead to the conclusion that the ‘Electron efficiency’η is also independent on wavelength. However, as it will
be shown below (in figure 3), it is not the case. Indeed,
the variations of η, according to wavelength, are well
represented in figure 2 by a variation of amplitude of thecurves of electron density. These amplitude variations
correspond to a difference in the number of electrons

R. Prazeres et al. / Proceedings of the 2004 FEL Conference, 297-300

299

Figure 3: ‘Electron efficiency’ η versus laser
wavelength. The dots are experimental data, and the grayarea is theoretical from the analytical expression (3).

Figure 2 : Subtraction of electron density (laser ONlaser OFF) versus electron energy (in %). Each curve
corresponds to a different undulator gap, and a different
laser wavelength.
which are involved in the FEL interaction and which arelosing energy. As a conclusion, a variation of η
corresponds to a variation in the number of electrons
involved in the FEL interaction, and not to a variation in
the energy loss of the electrons. This conclusion is ingood agreement with the fundamental theory [5] of theelectron trapping in FEL interaction, which shows that theenergy loss of the electrons is governed by the line widthof the gain distribution, which only depends on 1/Nu andnot on the laser wavelength.
The figure 3 represents the ‘Electron efficiency’ η as afunction of the laser wavelength. The black dots represent
an experimental estimation of the 'Electron efficiency’ ηwhich is deduced from the electron energy spectra (suchas of figure 1). The estimation of the electron energy
centroid <γmc2>, from the electron spectra, is rather
sensitive to the noise background of these spectra. This
represents the main source of error in the estimation ofthe ‘Electron efficiency’ η, because this parameter isobtained by a small difference between large andThe
imprecisequantities<γmc2>OFF-<γmc2>ON.
experimental data in figure 3 are compared to atheoretical model, using the analytical expression (3).
This expression is dependant on the electron beam crosssection Σe, which is not known with a good precision.
Therefore, two theoretical curves are represented infigure 3. The line curve on the top of the grey area has
been calculated with σex=1.5mm and σey=1mm ; and theline curve on the bottom of area has been calculated with
σex=2mm and σey=1.5mm. The optical losses L, the‘Filling factor’ Ff and the cross-section Σo of the opticalmode are calculated by the numerical code [2] [3]. The
optical pulse length ∆tο of the FEL is deduced from thespectrum line width ∆λ/λ of the laser. Taking into accountthe various sources of error for both theory andexperiment, the figure 3 shows that the measurement ofthe ‘Electron efficiency’ is in rather good agreement withthe analytical expression (3). In addition, this means thatthe numerical simulation, which gives L, Ff and Σo, israther reliable.
The average extracted power <Px> of the FEL can becalculated from the value of ‘Electron efficiency’ η, using
the expression (2). Three curves <Px>=f(λ) are displayedin figure 4 : (A) a purely experimental measurement of<Px>=f(λ) using a power meter at the exit of the FEL ;(B) a semi-experimental estimation of <Px> using theexperimental values of η displayed in figure 3 ; (C) atheoretical estimation of <Px> using the theoretical valuesof η displayed in figure 3. The behaviour is similar for thethree plots. The theoretical curve C fits rather well thecurve B. Both of these curves are using the expression (2)for <Px>. The fit between these two curves B and C, in
log scale here, corresponds to the fit of η (theoretical andexperimental) in figure 3. The ‘extraction ratio’ Tx/L has
no influence in the comparison between B and C because
it is used in both curves. Now, a comparison between B orC, and A, shows a larger discrepancy: this means that the‘extraction ratio’ Tx/L, obtained by numerical simulation,
does not correspond to the experiment and is responsibleof the rather bad fit of curve A. The figure 5 corresponds
to the numerical simulation, and it shows L and Tx as afunction of wavelength. Taking into account the above
conclusion about the reliability of the numericalsimulation for L, we can suppose that Tx is the parameter
which gives the most important error. This conclusion iseasy to understand, because Tx must be very sensitive tothe alignment of the cavity mirrors and to the transverse

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Figure 4: Average extracted laser power <Px> versus
wavelength. The curve A is purely experimental: obtainedwith a power meter at exit of the FEL. The curve B issemi-experimental, using the measurement for η and thenumerical simulation for Tx/L. The curve C is purely
theoretical: η is obtained by analytical expression (3), and
Tx/L is obtained by numerical simulation
profile of the laser mode. A small error of theseparameters may change strongly the coefficient Tx. Notethat the figure 5 exhibits, at λ=50µm, a strong decreasingof the laser extraction Tx and an increasing of the cavity
losses L. This has already been commented in the past[8], and it is due to a special transverse distribution of thelaser mode in the cavity, which has zero intensity on
longitudinal axis. This effect can be observed in theexperimental curve (A) in figure 4, which shows adecreasing of the power <Px> by a factor 5 between λ=
54µm and 50µm.
As a summary, the estimation of <Px> is less accurate
than η because of the uncertainty on Tx. Nevertheless, thethree curves of <Px> in figure 4 exhibit the same
behaviour and they fit the same order of magnitude.
Taking into account the various sources of error, both inmeasurements and simulation, we can consider that theestimation of laser power from the direct power
measurement, from the analysis of electron beam spectra,
and from the analytical expression, are in rather good
agreement.

CONCLUSION
The electron energy spectra show the scattering due tothe FEL interaction between the electron bunch and thelaser pulse. This gives a measurement of the ‘Electron
efficiency’ η of the FEL, corresponding to the ratio
between the energy produced by the FEL and the input
energy of the electron beam. The measurements of η arein rather good agreement with the analytical expression of‘Electron efficiency’ which is written here. This
expression involves the electron beam parameters, whichsome of them are only imprecisely estimated, and theoptical cavity parameters, which are obtained bynumerical simulation.

THPOS06

Figure 5: Numerical simulation : cavity losses L and‘extraction rate’ Tx versus wavelength
The extracted laser power <Px> is deduced from thevalues obtained for η. We have made a comparison
between the power <Px> and the direct measurement
using a power meter at the exit of the FEL. These data are
in rather good agreement, and the remaining error ismainly due to the error in the calculation of the‘extraction rate’ Tx of hole coupling in the optical cavity.
The calculation of the FEL power is less reliable than thecalculation of the ‘Electron efficiency’, but both of them
are still sufficiently reliable to give the right order ofmagnitude. The perfect knowledge of electron beamcharacteristics would give a much better result.

REFERENCES[1] R. Prazeres, F. Glotin, JM. Ortega, C. Rippon, R.
Andouart, JM. Berset, E. Arnaud, R. Chaput :Nucl.Instr.&Methods A445, n°1-3; (2000), p.204-207[2] R. Prazeres, M. Billardon : Nucl. Istr. & Meth. A318
(1992) 889-894[3] R. Prazeres : Eur. Phys. J AP 16, 209-215 (2001).
[4] “Measurement and calculation of the ‘Electron
efficiency’ of an F.E.L.” : submitted to Eur. Phys.
Jou. Appl. Phys.
[5] “Insertion devices for synchrotron radiation and freeelectron laser”, by F. Ciocci, G. Dattoli, A. Torre &A. Renieri (ENEA INN-FIS, Frascati, Rome, Italy)
ISBN 981-02-3832-0.
[6] G. Dattoli, Jou. of Appl. Physics, vol.84, (1998)
p2393-2398[7] G. Dattoli, T. Letardi, JMJ. Madey, A. Renieri, Nucl.
Instr.& Methods A237 (1985) 326-334[8] R. Prazeres, F. Glotin, JM. Ortega, Nucl. Instr. &Methods A528 (2004) 83-87

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RECENT RESULTS OF THE JAERI ENERGY-RECOVERY LINAC FEL
R. Hajima∗ , M. Sawamura, R. Nagai, N. Kikuzawa, N. Nishimori,
H. Iijima, T. Nishitani, E.J. Minehara
JAERI, Tokai, Ibaraki 319-1195, Japan
Abstract

Gun Grid Pulser

In Japan Atomic Energy Research Institute (JAERI), weare developing an energy-recovery linac (ERL) for a highpower free-electron laser (FEL). The ERL was completed
in 2002 by remodeling the original superconducting accelerator. In this paper, we summerize recent research activities at JAERI-ERL.

The electron gun is equipped with a thermionic cathodeand operated at 230 kV DC voltage. A train of electron
bunch is generated by grid pulser. In the original configuration, the gun was designed to produce 0.5 nC electron
bunches at 10.4 MHz repetition, that is 5 mA. We installeda new grid pulser working at 20.8 MHz, doubled repetitionof the original one, and a 10 mA beam is now available [5].
The new grid pulser is designed at Budker Institute of Nuclear Physics and can be operated in CW-mode as well as
pulse-mode.
We measured electron beam properties with the new grid
pulser and confirmed that it keeps similar performance tothe original one. The pulse width and the normalized rms
emittance at the gun are 590 ps (FWHM) and 20 πmmmrad, respectively.
As presented above, the injection cavities are ready for
40 mA beam, which requires 83 MHz operation of the grid
pulser. Design of a grid pulser for the higher repetition rate,
41.5 MHz and 83 MHz, is under investigation.

INTRODUCTION
A research program towards a high-power free-electron
laser (FEL) has been conducted at Japan Atomic Energy
Research Institute (JAERI) since 1987. The initial target ofthe program, FEL lasing in kilowatt level, was achieved in
2000[1], and the research program is now stepping forward
to the next stage, demonstration of a 5-10 kW FEL.
It is considered that same-cell energy-recovery in a superconducting linac is the only practical solution to put
such a high-power FEL in work efficiently[2]. Hence,
we decided to remodel the superconducting accelerator
into an energy-recovery linac (ERL)[3]. The original
linac was shut down in the spring of 2001, and the ERL
was completed after a half-year construction period. We
demonstrated first energy-recovery operation at 19 February, 2002, and first FEL lasing at 14 August, 2002 [4].
In this paper, we present recent research activities
at JAERI-ERL FEL: upgrading major components ofthe superconducting accelerator, investigation of longmacropulse operation, beam dynamics studies and others.

COMPONENTS UPGRADE
Injector RF Sources
Increasing the injector beam current is a straightforward
approach to enlarge the FEL power by taking full advantageof the energy-recovery. In the original JAERI-FEL without
energy-recovery was operated at 5 mA injector beam current. Two single-cell cavities of the injector were driven
by 6 kW solid state amplifier for each, enough capacity for
5 mA operation. The solid state amplifier has been replacedby an IOT-klystrode of 50 kW, which enables one to injecta 40 mA beam into the ERL. The IOT is designed for CW
operation as well as pulsed operation, while the original
amplifier allowed only pulsed operation with small dutycycle such as 1 ms × 10Hz. We also plan to replace RF
amplifiers for 5-cell main modules by the same IOT systems for future long-pulse operation.
∗ e-mail: hajima@popsvr.tokai.jaeri.go.jp

Available online at http://www.JACoW.org

RF low-level controllers
Stable operation of an FEL relies much on the stability of an accelerator. In a superconducting accelerator,
an RF low-level controller is one of the key components
for achieving good stability. The original JAERI-FEL wasequipped with a low-level controller, which kept phase flatness at ±1 degree within a 1 ms macropulse. This controller had been contributed to the 10-year operation of
JAERI-FEL. After the remodeling into the ERL, however,
we found that the stability of the low-level controller was
insufficient to extract the full performance of the ERL.
Since the controller had no special function to compensate
temperature drift, we could hardly obtain long-time stability against the change of room temperature.
The low-level controller was replaced by new one. The
new system is based on phase and amplitude control of thecavity RF field coupled with a tuner controller, which issame as the original system. In the design of the new lowlevel controller, we introduced the following functions forthe better stability: the feedback gain and bandwidth canbe varied during operation to obtain good flatness of RFphase and amplitude within a macropulse, all the circuits
are contained in boxes with temperature stabilization.
The original controller was placed at the operation room,and the feedback loop involved 50-m cables to connect thecontroller and the RF cavity. We found that large temperature drift was caused by this long cables. The new con-

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1-cell SCA

Undulator
2nd Arc

Half Chicane
1st Arc
Beam Dump

SHB

Electron Gun

Injection Merger

Main 5-cell SCA

Figure 1: The layout of JAERI Energy-Recovery Linac. An electron bunch generated by 230 kV electron gun is accelerated to 2.5 MeV and injected into the energy-recovery loop. The electron bunch is accelerated to 17 MeV by mainsuperconducting cavities and transported to the FEL undulator. The electron bunch is, then, reinjected to the main cavities and decelerated down to 2.5 MeV and collected by a beam dump. All the superconducting cavities are driven at499.8 MHz.
troller is installed just beside the cavity to make the cable length as short as possible. Furthermore the cables
between the controller and the cavities are contained ina temperature-controlled pipe to suppress the temperaturedrift.
After these upgrade, the accuracy and stability of accelerating RF has been greatly improved. The flatness of
RF phase and amplitude within a 1 ms macropulse are
0.20 deg. and 0.013% for the old system, 0.06 deg. and0.013% for the new system, where all the values are RMS.
Phase and amplitude fluctuation for 5 minutes in the new
system are measured as 0.15 deg. and 0.015%, respectively. In this measurement, mechanical vibration of thecavity due to the refrigerator is the dominant source of thefluctuation.

Operation Control System
The operation control system of JAERI-ERL has also
been upgraded. The old system based on CAMAC and PC9801 with Windows-95 became obsolete and difficult tomaintain and make further extension. We have developed
a new system consisting of CAMAC and local controllers
working with µ-ITRON [6], which are robust hardware
without mechanical component such as hard-disc drives.
Console applications for the operation are written by JAVA
and CORBA, modern software independent of platform.
We have also prepared data-logging and database services
using WEB and MySQL.

FEL Transport LineA laser-beam transport line has been built to deliver FEL
pulses to an experiment room. We have installed an opticalbeam expander, which consists of two elliptic mirrors, atthe end of FEL optical cavity to convert a diverging beamfrom a center-hole at a FEL cavity mirror into a parallel
beam. The expanded beam is transported to the experimental room through a 24 m-long evacuated pipe.

THPOS21

LONG-MACROPULSE OPERATIONThe superconducting accelerator of JAERI-ERL FEL
has been operated in a pulse-mode, 1 ms (flat top) × 10 Hz,
which is restricted by refrigerator capacity. For the demonstration of a high-power FEL in industrial applications,however, the longer macro pulses are preferable. In the upgrade of JAERI-ERL FEL, we designed all the new components to meet CW operation. The grid-pulser and the
IOT’s are CW-ready. Since the refrigerator has capacity for
3% duty cycle, long-pulse operation is only available withkeeping this duty cycle such as a 1 second macro pulse every 30 seconds.
Several technical issues should be resolved for the longpulse operation of the superconducting cavities, whichwere originally designed for 1 ms pulses. One is pressure
rising of the cryostat during a macro pulse due to the heat
unbalance between the dissipated RF power and the refrigerator power. This pressure rising causes detuning in thecavity resonance frequency. In the JAERI cryostat, a refrigerator is directly installed at the top of cryomodule. Mechanical vibration of the refrigerator is, therefore, anothersource of the cavity frequency detuning. We investigatedthe effect of pressure rising and mechanical vibration, andconfirmed that long-pulse operation of 1-5 seconds is possible after minor modification of the existing piezo tuner[7].

BEAM DYNAMICS STUDIESInjector Optimization by Simulated Annealing
It is known that spontaneous frequency-chirping is induced in a high-gain FEL oscillator. Such chirped pulses
can be used to excite unharmonic potential ladder of molecular systems, one of coherent chemical processes. We
demonstrated 14.3% frequency chirping in a FEL pulse at
JAERI-FEL before the ERL modification[8].
To construct an ERL, the injector beam line was modified from a straight path into a 2-step staircase. This modification made it difficult to generate an electron bunch

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as short as before, 5 ps (FWHM), which is important forthe chirped-pulse generation. In the ERL design, we obtained the bunch length as 15 ps (FWHM) from particle
simulations[9], and the measurement during the ERL operation almost agrees with this simulation result.
The bunch length is determined by electrons motion in
the longitudinal phase space. In the JAERI-ERL injector, we have six parameters to manipulate electrons motion in the longitudinal phase space, which are amplitude
and phase of the subharmonic buncher and two 1-cell cavities. We considered that these parameters can be further
optimized to generate the shorter bunch, and applied simulated annealing algorithm[10] to the optimization. From
the optimization using simulated annealing, we have founda parameter set of the injector, which gives 5.6 ps (FWHM)
electron bunch[11]. The ERL operation with these new parameters will be tried soon.

(SCC), which is a critical problem in nuclear reactors inJapan[17].

Emittance Growth in the Merger[2] G.R. Neil and L. Merminga, Rev. Mod. Phys. 74, 685(2002).

Energy redistribution in an electron bunch caused by longitudinal space charge force or coherent synchrotron radiation (CSR) along a dispersive path induces transverse emittance growth. The emittance growth by CSR in the constant wake regime, where the bunch keeps constant temporal profile, can be analyzed by linear matrix approach[12].
The linear analysis shows that the emittance growth can be
minimized by matching the beam ellipse to the direction of
displacement of bunch slices in the (x, x ) phase space.
In the JAERI injection merger, longitudinal space charge
force causes the emittance growth through the energy redistribution. We are studying the emittance growth during
the merger by particle tracking simulations instead of thelinear analysis, because the bunch length is not constant,
20 ps (FWHM) at the entrance and 10 ps at the exit ofmerger in typical operation. From PARMELA [13] simulation, it has been found that the emittance can be minimized
by using appropriate beam envelope along the merger. As
the best result, we obtain normalized RMS emittance and
FWHM bunch length at the merger exit, εx = 35πmmmrad, εy = 26πmm-mrad, and 9.4 ps.

OTHER R&D’S
An electron gun with low-emittance and high averagecurrent is a key component for a high-power FEL and afuture light sources based on the ERL technology. A DC
photocathode gun with a NEA cathode is considered as themost promising device for high average-current ERLs, 10100 mA [14]. We, therefore, started research activity on a
DC photocathode gun. A test bench to study a DC photocathode gun is under development with components from a
200 kV gun [15] and an old MBE system. A mode-locked
Ti:Sap. laser of 83.3 MHz is also prepared. Details arepresented in an accompanying paper[16].
For FEL applications, we are proposing laser pealingof stainless steal surface to suppress stress-corrosion crack

SUMMARY
An energy-recovery linac has been developed for a highpower free-electron laser at JAERI. An R&D program towards a 5-10kW FEL and future ERL light sources is inprogress. We have upgraded major components of the
ERL, RF low-level controller, injector RF sources, operation control system, a gun grid pulser, for stable operationof the ERL and high-power FEL demonstration. The upgrade has been almost completed, and we restart the ERL
soon.

REFERENCES[1] N. Nishimori et al., Nucl. Instr. Meth. A475 (2001) 266–
269.

[3] R. Hajima et al., Nucl. Instr. and Meth. A445 (2000) 384–
388; T. Shizuma et al., Nucl. Instr. and Meth. A475 (2001)
569–573; R. Hajima et al., Proc. EPAC-2000, 1033–1035;
T. Shizuma et al., Proc. EPAC-2000, 1074–1076.
[4] R. Hajima et al., Nucl. Instr. and Meth. A507 (2003) 115–
119.
[5] N. Nishimori et al., “20.8MHz Electron Gun System for an
Energy Recovery Linac FEL at JAERI”, Proc. APAC-2004.
[6] N. Kikuzawa, “Control system upgrade of JAERI ERLFEL”, Proc. FEL-2003.
[7] M. Sawamura et al., “RF Properties of the JAERI ERL-FEL
for Long-Pulse Operation”, Proc. 1st Annual Meeting ofParticle Acc. Society of Japan, (2004) 305–307.
[8] R. Hajima and R. Nagai, Phys. Rev. Lett. 91 (2003) 024801.
[9] T. Shizuma et al., Proc. EPAC-2000, 1074–1076.
[10] W.H. Press et al., “Numerical Recipes in C, second ed.”,Cambridge Univ. Press, (1992) p.444.
[11] R. Nagai et al., “Parameter Optimization of JAERI ERLInjector by Simulated Annealing”, Proc. 1st Annual Meeting of Particle Acc. Society of Japan, (2004) 420–422 (inJapanese).
[12] R. Hajima, Jpn. J. Appl. Phys. 42 (2003) L974–L976.
[13] PARMELA ver. 3.34; L.M. Young, LA-UR-96-1835.
[14] C.K. Sinclair, Proc. PAC-2003 (2003) 76–80.
[15] E.J. Minehara and K. Whitham, Proc. EPAC-98 (1998)
1474–1476.
[16] T. Nishitani et al., “The Development of the JAERI 200keV
Electron Gun with an NEA-GaAs Photocathode”, Proc.
FEL-2004.
[17] E.J. Minehara et al., “Femtosecond Laser Prevention for the
Cold-Worked Stress Corrosion Crackings on Reactor Grade
Low Carbon Stainless Steal”, Proc. FEL-2004.

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JAERI 200kV ELECTRON GUN WITH AN NEA-GaAs PHOTOCATHODE
T. Nishitani #, E. J. Minehara, R. Hajima, R. Nagai, M. Sawamura, N. Nishimori, N. Kikuzawa,T. Yamauchi
FEL Lab., Advanced Photon Research Center, Kansai Research Establishment, Japan Atomic
Energy Research Institute, 2-4 Shirakata shirane, Tokai, Naka, Ibaraki 319-1195 JAPAN
Abstract
The photocathode DC-gun with high average current,
low beam emittance and long operational lifetime isconsidered to be indispensable for ERL-FEL. We havestarted the developmental program of a 200keV electron
gun with the NEA-GaAs photocathode for the first time in
JAERI. In order to long an NEA surface lifetime, JAERI
200kV electron gun system consists of a 200kV DC-gunchamber on extreme high vacuum condition and an NEA
activation chamber with load-lock system. We report thegoal of photocathode DC-gun R&D and the schedule of adevelopmental program.

INTRODUCTION
ERL-FEL and 4th generation ERL-LS with higher
output and higher luminosity than the existing technology
can be realized by the extraordinary high injector
performance. Especially, electron source with higher
current and lower beam emittance than existing is
indispensable in order to improve the injector
performance.
As such an electron source, it is thought that the GaAs
type semiconductor photocathode with negative electron
affinity surface (NEA-GaAs) is a strong candidate.
It is because maximum quantum efficiency of NEAGaAs photocathode is 10% or more of quantum efficiency
and NEA-GaAs photocathode has the advantage that
initial emittance can be made small by choosing the
wavelength near a band gap for excitation laser [1].
We started development of the NEA-GaAs
photocathode electron gun which generates the electron
beam with the structure of 1.3GHz of repetitions and
77pC/bunch (the average current of 100mA).

NEA SURFACE
Since the surface of NEA-GaAs photocathode forms a
NEA state by Cs and O2 of angstrom order of thickness(or NF3), the surface before NEA activation must be pureand NEA surface is also very weak.
Therefore, the countermeasure to clean-surface before
NEA activation and long life time of NEA surface is
indispensable to the design of an NEA photocathodeelectron gun.
The surface of the photocathode exposed into theatmosphere before the introduction to a vacuum chamber
is being worn with impurities, such as an oxide andcarbide.

When the photocathode electron gun introduces
photocathode out of the atmosphere, it needs surface
cleaning such as annealing, atomic hydrogen cleaning [2]in order to remove impurities in the surface.
The following cause can be considered for degradationof NEA surface; the adsorption phenomenon to thesurface of remains gas in vacuum chamber, and ion backbombardment due to field emission dark current between
anode- and cathode-electrode.
The former degradation phenomenon can be suppressedby extra high vacuum chamber in order to suppression of
the adsorption phenomenon.
It is thought that the field emission dark current isdependent not only on the fall of electrode work function
due to the adsorption of caesium, but also thecharacteristic of the electrode material.
The following conditions are needed for good NEA
surface.
• The photocathode surface before NEA surface
activation is clean.
• The vacuum of chamber should be extra highvacuum in order to suppress the remains gas inchamber.
• In order to suppress of field dark current, it ischoosing the electrode with the sufficientcharacteristic, and prevent caesium adsorption to theelectrode.

DESIGN AND COMPONENTS OF JAERIPHOTOCATHODE GUN
As an electron gun which realizes the NEA surface of along lifetime, development of the electron gun which
combined MBE apparatus with NEA activation systemand 200kV electron gun chamber under extreme highvacuum by the load-lock system was started.
JAERI photocathode gun has the performance offabrication of photocathode in vacuum chamber by using
MBE apparatus. That is, it means that surface cleaning
process (such as anneal and atomic hydrogen cleaning)
and the exchange of photocathode become unnecessary. It
is the first photocathode gun which has the photocathodeproduction system in the world.
Figure 1 show the design of JAERI photocathode gun
which consists of three components (MBE chamber, gunchamber and mode-lock laser system).
The following describes a design and parts about eachcomponent.

___________________________________________#

nisitani@popx.tokai.jaeri.go.jp

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MBE apparatus with NEA activation system
JAERI photocathode gun use MBE apparatus (EV-10:
eiko-engineering co.) as an NEA activation chamber.
This main chamber can realize ultra high vacuum of a
10-8Pa order by using an ion pump (500 l/s) and titanium
sublimation pump (400 l/s) after 200 degree baking of
100 hours by a rotary pump and a turbo pump. Thisdegree of vacuum fulfils the necessary condition for NEA
surface formation. In the main chamber, it has the liquid
nitrogen shroud, and a still better vacuum can be expectedby introducing liquid nitrogen.
The semiconductor substrate on which is carried out
photocathode growth is inserted from gate-bulb-A in
Figure 1, and it introduces to a main chamber after apreliminary pump. In a main chamber, photocathodegrowth and NEA surface activation by vacuum
evaporation of caesium and oxygen is carried out.
The photocathode with NEA-activated surface istransported to gun chamber with a transfer rod, and it
equips with it from behind cathode electrode.

The design of gun chamber
In order to realize extreme high vacuum, it is necessary
to make gun chamber capacity small. For this reason,
cathode- and anode- electrode are designed small, a sizeof photocathode is made into the sufficiently larger
diameter of 5mm than the excitation laser diameter of

2mm, and the gap between cathode- and anode- electrodeis 30-50mm, and anode hole-size is 20mm.
About the vacuum of gun chamber, after baking of 200
degrees, the combination of an nonevaporating type getterpump and an ion pump aims at realization of a extra highvacuum (10-10Pa order).
Anode- and cathode-electrode are under design using
beam simulation codes, such as EGUN, PARMERA. As
the material of electrode, Ti and Mo are used. It is thoughtthat these materials have the advantage which suppresses
the field emission dark current from SUS or Cu in recent
years [3].
A high-voltage power supply uses 200kV power supply(PK200N18: GLASSMAN HIGH VOLTAGE INC.) withthe maximum voltage of 200kV and the maximum currentof 18mA.

Mode-lock laser
As excitation laser for photocathode, the mode lock Ti:
Sapphire laser (TSUNAMI: Spectra Physics) of 83MHzof repetitions is used. Laser is irradiated from anode backto photocathode through an anode hole.
TSUNAMI has a maximum of 500mW output on the
wavelength of 790nm. When it is 10% of quantum
efficiency of photocathode, a maximum current of 16mA
will be obtained by laser excitation with a wavelength of
790nm.

Gun Chamber

CathodeElectrode(under design)-200kVtem
MBE Chamber with NEA Activation System

e-

Laser

NEA Activation
Epitaxial Growth

GaAs Substrate
Installation

Anode
Electrode

Photocathode
Transporter

Transfer Rod

A

B

C

Modelock Laser(TSUNAMI)
Cs dispencer

Turbo Pump
Rotary Pump

O2 flow

Ion Pump,TSP

Laser

Upper side view

Figure 1: The design of JAERI photocathode gun.

FEL Experimental Results

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T. Nishitani et al. / Proceedings of the 2004 FEL Conference, 304-306

The present condition and a work schedule
We consider the present target of JAERI photocathodegun as 200keV electron beam generation of 77 pC/bunch(average current of 6.2mA) and 83MHz repetition, andshow the schedule of a developmental program in Table 1.
We are performing the design of photocathode holder,electrode (anode and cathode) and gun chamber, and thevacuum examination of MBE apparatus.
We are considering development of the beam
evaluation system such as measurement of the bunch
width and emittance as a next subject. Furthermore, byusing MBE apparatus, development of the new typephotocathode which has high quantum efficiency and thestrong NEA surface compared with the conventional NEA
photocathode is also planned.

REFERENCES[1] S. M. Gruner and M. Tigner, eds., “Study for a
proposed Phase I Energy Recovery Linac
Synchrotron Light Source at Cornell University,
CHESS Technical Memo 02-003, JLAB-ACT-01-04,
2001[2] M. Yamamoto, et al., “Proceedings of the 28th Linear
Accelerator Meeting in Japan, Tokai, July. 30-Aug.
3, 2003, P99-101[3] F. Furuta, et al., “Proceedings of the 28th Linear
Accelerator Meeting in Japan, Tokai, July. 30-Aug.
3, 2003, P111-113
Table 1: The schedule of a developmental program

THPOS23

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N. S. Sei et al. / Proceedings of the 2004 FEL Conference, 307-310

PERFORMANCE OF THE OPTICAL KLYSTRON ETLOK-III FOR
DEVELOPING INFRARED STORAGE RING FREE ELECTRON LASERS*
N. Sei#, K. Yamada, H. Ogawa, M. Yasumoto, Research Institute of Instrumentation Frontier,
National Institute of Advanced Industrial Science and Technology, 1-1-1 Umezono, Tsukuba,
Ibaraki 305-8568, Japan
Abstract
Oscillations of free electron lasers (FELs) with thecompact storage ring NIJI-IV in a wade wavelength
region of 1-12 µm are planned in National Institute ofAdvanced Industrial Science and Technology (AIST).
The optical klystron ETLOK-III for developing infrared
FELs has been installed in a long straight section of the
NIJI-IV. The ETLOK-III has two undulator sections of 7
periods and one 75 cm dispersive section. The maximum
K value was estimated to be about 10.4 from ameasurement of magnetic field. Fundamental and higher
harmonics of spontaneous emission from the ETLOK-III
were observed with large gaps. The modulation of thespectra of the spontaneous emission suggested that the
maximum FEL gain would be about 2% in the visible andnear-infrared regions.

INTRODUCTION
Oscillations of broad-band free electron lasers (FELs)
have been studied with the storage ring NIJI-IV at
National Institute of Advanced Industrial Science andTechnology (AIST). Although the NIJI-IV is a compact
storage ring with a 29.6 m circumference, it has two 7.25
m straight sections. The optical klystron ETLOK-II has
been installed in one of the straight sections so as torealize FEL oscillations in a shorter wavelength region [1].
The NIJI-IV FEL system advanced the record of theshortest FEL wavelength down to 212 nm in 1998 [2]. It
achieved the FEL oscillations at the wavelength of 198
nm in 2003, and became the third device which realized
storage ring FELs in the VUV region [3]. Output powerof an FEL at a wavelength around 200 nm was increased
to 0.5 mW by using cavity-mirrors with higher
transmission. Preliminary experiments of photoelectron
emission microscopy were carried out, and the good
spatial resolution was obtained with video-rate time
resolution.
A new optical klystron ETLOK-III for FEL oscillationsin the infrared region was installed in the other straightsection in this February. Although many infrared FEL
facilities based on linear accelerators are operating, nostorage ring FEL has been achieved in the wide infrared
region. However, the storage ring FEL has the advantage
of a narrow line width and stability of the lasing
wavelength compare with the linear accelerator FEL. It
can be used as well as synchrotron radiation that passed a
monochromator. Then, we have planed FEL oscillations
with the ETLOK-III in a wavelength region of 1-12 µm[4]. The infrared storage ring FEL will be applied for not
only a light source of photoelectron emission microscopy

Available online at http://www.JACoW.org

but also generation of a hard X-ray beam by the Compton
backscattering process [5]. In this article, we explain thefeature of the optical klystron ETLOK-III, and reportresults obtained from the spontaneous emissions of the
ETLOK-III.

OPTICAL KLYSTRON ETLOK-III
DesignA planar undulator with bump magnets was remodelled
into the ETLOK-III [4]. The 3 m undulator had magnets
with 20 cm period. The magnet material was SEREMN38H with a remanent field higher than 1.24 T. Magnetsof undulator sections of the ETLOK-III reuse those of theold undulator. Then, number of the periods in one
undulator section is 7. The gap of the undulator sections
can be changed between 36 and 150 mm. The dispersive
section of the ETLOK-III was designed so that Nd, which
is a number of periods of the FEL wavelength passing
over an electron in the dispersive section, became about
90 due to the then electron-beam qualities. In order toobtain the large Nd, the length of the dispersive section is
set to be 72 cm and free spaces of 1.5 cm are installed
between the dispersive section and the undulator sections.
The gap of the dispersive sections can be changed
between 36 and 188 mm. However, the magnets in thedispersive section are inserted between tables which fix
the magnets of the undulator sections, so that the gap of
the dispersive section must be smaller than addition of thegap of the undulator section and 38 mm.
. Figure 1 shows the outline of the ETLOK-III. The
magnetic field on the center axis of the ETLOK-III under
the some gap conditions was measured before theinstallation. The measured value of the magnetic field isabout 4% larger than the designed one, and the maximum
K value is 10.4.
Because the dispersive section is long, the NIJI-IV
electron beam with comparatively low energy meanders
greatly in it. When the uniformity of the magnetic field isinsufficient horizontally in the dispersive section, theelectron beam is kicked in it and comes off the center axisof the ETLOK-III. The calculated horizontal distributionof the magnetic field in the dispersive section under theminimum gap condition is shown in Fig. 2. Width of themagnet is small with 88 mm, so that the magnetic field
weakens by 7.6 % at the point of 20 mm away from thecenter axis. Therefore, it is necessary to move an axis of
the electron-beam orbit from the center axis of the
ETLOK-III or to change the magnetic field in thedispersive section. Because the shift of the electron beamin the dispersive section is large, the latter idea would be

FEL Experimental Results

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N. S. Sei et al. / Proceedings of the 2004 FEL Conference, 307-310

(a)

30
βx
βy

βx , βy , 10ηx

25

ETLOK-IIIETLOK-II

10ηx

20
15
10
5
0
0

5

10

15

20

25

30

Length [m](b)Fig. 1. Outline of the optical klystron ETLOK-III.

35
βx
βy

βx , βy , 10ηx

30

0.582
gap of the dispesive section: 36 mm

Magnetic field [T]

0.581

0.580

ETLOK-IIIETLOK-II

10ηx

25
20
15
10
5
0

0.579

0

5

10

15

20

25

30

Length [m]
0.578

0.577
-30

-20

-10

0

10

20

30

Distance in the horizontal direction [mm]Fig. 2. Calculated magnetic field at the center of thedispersive section of the ETLOK-III. The gap is set to be
the minimum of 36 mm.
more practicable. We plan an improvement that themagnetic field of the both end magnets of the dispersive
section is shunted by iron plates and a steering coil is
attached to a vacuum chamber in the dispersive section.
At present, a small steering coil which can compensate
for the magnetic field of ~2×10-3 T are attached, and thegap of the dispersive section can be set down to 120 mm.

Influence for the electron beam parameters
The ETLOK-III arranges the magnets horizontally, sothat it has a vertical focusing effect. This effect causes
vertical tune shift and distorts the vertical betatronfunction due to asymmetrical arrangement of the ETLOKIII in the straight section. Present betatron tunes of the
NIJI-IV electron beam are 2.291 in the horizontal
direction and 1.394 in the vertical direction, and themagnetic field of quadrupole magnets is adjusted with thegap of the ETLOK-III to keep the tunes. Figure 3 shows
calculated betatron functions and dispersion functions
with and without the ETLOK-III at the same betatrontunes. As this figure shows, vertical betatron function in
the long straight sections decreases due to the strong
vertical force with the ETLOK-III. Natural emittance also

THPOS28

Fig. 3. Calculated betatron functions (horizontal βx andvertical βy) and dispersion function (ηx) without (a) andwith (b) the ETLOK-III.
decreases by about 5%. Therefore the vertical beam size
would become small about 10% at the center of the
ETLOK-III. When the gaps are minimum, total radiation
power from the NIJI-IV is about 6% stronger than thatwithout the ETLOK-III. We can expect that the power ofthe short-wavelength FEL from the ETLOK-II enhances.

OBSERVATION OF THE SPONTANEOUS
EMISSION
The optical klystron ETLOK-III has been installed in
the NIJI-IV in this February, and the electron-beamcurrent has been over 200 mA with the undulator gap of
125 mm. The electron-beam energy is set to be 340 MeV.
Because the electron beam is kicked at the exit of thedispersive section, the undulator gap is set to be over 95
mm and the spontaneous emission is observed in thevisible and near-infrared regions. Uniform area of themagnetic field in the ETLOK-III is narrow horizontally,so that the electron beam must be passed in parallel tocentral axis of the ETLOK-III in order to obtainsymmetry spontaneous emission. A photograph of the
spontaneous emission observed with the undulator gap of
140 mm is shown in Fig. 4.
Spectra of the spontaneous emission were measured bya photodiode array with a monochromator which had theresolution of 0.2 nm. Because the dispersive section has aparabolic distribution of magnetic field in the horizontal

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N. S. Sei et al. / Proceedings of the 2004 FEL Conference, 307-310

1.0Single-bunch operation
E = 340 [MeV]I = 1.7 [mA]

Intensity [a.u.]

0.8

0.6

0.4

∆ λ m = 0.2 nm

0.2

0.0
285

290

295

300

305

310

315

320

325

Wavelength [nm]Fig. 4. Photograph of the spontaneous emission fromthe ETLOK-III. The gaps of the undulator section andthe dispersive section are 140 and 150 mm,
respectively.

Intensity [a.u.]

(a)

1.0
0.8

Single-bunch operation
E = 340 [MeV]I = 1.1 mA

0.6
0.4
0.2
0.0
600

Intensity [a.u.]

(b)

610

620

630

640

Wavelength [nm]1.0Single-bunch operation
E = 340 [MeV]I = 1.1 mA

0.8
0.6
0.4
0.2
0.0
740

750

760

770

780

Wavelength [nm]Fig. 5. Spectrum of the spontaneous emission from the
ETLOK-III: (a) the end of the short wavelength and (b)the end of the long wavelength. The gaps of theundulator section and the dispersive section are 125
and 160 mm, respectively.
direction, precise adjustment of the electron-beam orbit isnecessary so as to obtain a large modulation factor for the
spontaneous emission. Figure 5 shows a spectrum of
spontaneous emission with the undulator gap of 125 mm

Fig. 6. Spectrum of the third harmonic emission fromthe ETLOK-III. The gaps of the undulator section andthe dispersive section are 115 and 150 mm,
respectively.

and the dispersive gap of 160 mm. The resonant
wavelength measured in this condition was about 690 nm,
and it was agreement with the wavelength estimated fromthe measurement of magnetic field in the ETLOK-III. The
value of Nd estimated from intervals of the modulation of
the fundamental was about 140. The value calculated
from the magnetic field in the dispersive section was
about 150. The difference between the measurement andthe calculation would suggest that the adjustment of theelectron-beam orbit was insufficient. Moreover, energy
spread of an electron bunch can be estimated by using themodulation factor [6]. The energy spread measured withthe undulator gap of 125 mm was 2.7±.0.2×10-4, which
was close to the natural energy spread of 2.6×10-4.
The spectra of the higher harmonic emission were also
investigated in the ultraviolet and the visible regions.
Further precise adjustment of the electron-beam orbit isdemanded for the higher harmonics. Figure 6 shows aspectrum of the third harmonic emission with theundulator gap of 115 mm and the dispersive gap of 150
mm. Relative width of the spectrum of the third harmonic
emission was about 19 in Fig. 6. Because the theoreticalone was 21, the spectrum was a little broader. The
measured interval of the modulation of the third harmonic
emission at the resonant wavelength was about 0.75 nm,
and it was slightly narrower than the theoretical one of
0.72 nm. The modulation factor for the third harmonic
emission which was removed an influence of themeasurement system was smaller than that estimated fromthe modulation for the fundamental emission. We havenot ascertained the whether these results were caused by
misalignment of the electron-beam orbit or distortion of
the magnetic field in the ETLOK-III yet. However, Nd canbe decreased by closing the undulator gap. Because themodulation factor become over 0.6 with the narrow
undulator gap, it will be possible to obtain FEL
oscillations which amplify the third harmonic emission in
the infrared region.

FEL Experimental Results

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N. S. Sei et al. / Proceedings of the 2004 FEL Conference, 307-310

0.030

FEL gain

0.025

E = 340 [MeV]I = 15 [mA]
gd = gu + 35 [mm]

0.020

0.015

0.010
500

1000

1500

2000

Wavelength [nm]Fig. 7. Relationship between the wavelength and theestimated FEL gain at the electron-beam current of 15
mA. The gap of the dispersive section is set to be 35
mm wider than the gap of the undulator section.

We can estimate the maximum FEL gain from theobserved spectra of the spontaneous emission. Figure 7
shows a relationship between the wavelength and theestimated FEL gain in the visible and the near-infrared
regions. Though the K value is comparatively small (<3.5)in those regions, the maximum FEL gain is expected to beabout 2% at the electron-beam current of 15 mA [3].
Because high-reflection mirrors of 99.8% or more areavailable in those regions, the FEL oscillations will be
realized with the ETLOK-III. However, we have notoperated the NIJI-IV with the undulator gap under 95 mm
due to the bend of the electron-beam orbit in thedispersive section yet. It is impossible to evaluate themaximum FEL gain in the longer wavelength region forthe present. We will improve the dispersive section tocompensate non-uniformity of the magnetic field, so that
it will allow us to observe the spontaneous emission with
the narrower undulator gap.

CONCLUSIONS
We have installed the optical klystron ETLOK-III fordeveloping infrared FEL oscillations in the long straightsection of the storage ring NIJI-IV. The number of the 20

THPOS28

cm magnetic period in an undulator section of the
ETLOK-III is 7, and the length of the dispersive section
with two 1.5 cm free spaces is 75 cm. The maximum K
value was designed to be about 10, and it was estimatedto be 10.4 from the measurement of the magnetic field.
We have also observed the spontaneous emission from the
ETLOK-III in the visible and near-infrared regions. It wasnoted that the maximum K value which was estimatedfrom the fundamental wavelength of the spontaneousemission on the axis of the electron-beam orbit was about
10.4. Value of Nd estimated from the measurements of themagnetic field in the dispersive section was also in accord
with that obtained from the spectra of the spontaneousemission. The maximum FEL gain which was evaluatedwith the NIJI-IV electron-beam qualities and theperformance of the ETLOK-III was about 2% in thevisible and near-infrared regions. Then, it will be possible
to realize FEL oscillations with the fundamental andhigher harmonics in the regions.
Now an improvement of the dispersive section isplaned in order to store the electron beam with thenarrower gap of the ETLOK-III. In the mid-infrared
region, the maximum FEL gain would be higher due tothe higher K value. Because Nd becomes smaller, it would
be easy to oscillate the FELs with higher harmonics. We
will investigate the performance of the optical klystron
ETLOK-III in the higher K value region.

ACKNOWLEDGEMENTS
This work was supported by the Budget for Nuclear
Research of the Ministry of Education, Culture, Sports,
Science and Technology of Japan.

REFERENCES[1] T. Yamazaki et al., Nucl. Inst. and Meth. A331
(1993) 27.
[2] K. Yamada et al., Nucl. Inst. and Meth. A445 (2000)
173.
[3] K. Yamada et al., Nucl. Inst. and Meth. A528 (2004)
268.
[4] N. Sei et al., Jpn. J. Appl. Phys. 41 (2002) 1595.
[5] N. Sei et al., Nucl. Inst. and Meth. A483 (2001) 429.
[6] D. A. G. Deacon et al., App. Phys. B34 (1984) 207.

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K. Y. Yamada et al. / Proceedings of the 2004 FEL Conference, 311-313

IMPROVED PERFORMANCE OF THE NIJI-IV COMPACT VUV/IR FEL
AND ITS APPLICATION TO THE SURFACE OBSERVATION*
K.Yamada, N.Sei, H.Ogawa, K.Watanabe, M.Yasumoto, Research Institute of Instrumentation
Frontier, AIST, Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki, 305-8568 Japan
Increase of the transmittance of the out coupling mirror
as well as e-beam energy brought a sufficient freeelectron laser (FEL) power around 200 nm for a real-time
surface observation. By irradiating surfaces of transitionmetals, such as Chromium and Palladium, with deepultraviolet (DUV) FEL, fine structure and surface
chemical reaction were successfully observed with spatial
and temporal resolutions of ~ 300 nm and 33 ms,
respectively.
Every efforts to shorten the lasing
wavelength below 190 nm are being made continuously
by correcting magnetic-field errors in the optical klystronand developing cavity mirrors with a smaller optical loss.
A new optical klystron for use in the infrared (IR) region
was installed into the north straight section of the NIJI-IV
to extend the lasing range up to ~ 10 µm.

INTRODUCTION
At AIST, an FEL with ultra-wide wavelength range
from the vacuum ultraviolet (VUV) to the far infrared(FIR) is being developed based on a compact storage ring
NIJI-IV. Though its shortest lasing wavelength is still
limited to 198 nm because of an unexpected gain smaller
than that estimated by the analytical calculation [1], asufficient margin of the gain enabled us to obtain oneorder larger FEL power than before, by adopting an
output-coupler with a higher transmittance as well as
increasing the stored beam energy in the ring.
Since the work function of transition-metals lies around
5 eV, DUV FELs with a wavelength of ~ 200 nm aresuitable as a intense light source to observe surface finestructure or surface chemical reactions on such transitionmetals with high spatial and temporal resolutions in
combination with the photoelectron emission microscopy(PEEM).
The intensity of NIJI-IV FEL recently
obtained is large enough to extract sufficient amount ofphotoelectrons for sub-micron scale and video-rate realtime observation from transition-metal surfaces.
Unexpectedly small FEL gain is probably caused bysome demagnetization of magnet blocks in the 6.3-m
optical klystron, which may deflect the beam and reduce
the overlapping between electron beam and optical mode.
We are preparing high performance dielectric multilayer
mirrors optimized around 190 nm to compensate such an
insufficient gain. We also plan to replace or remagnetize
such degraded magnet blocks.
A 3.6-m optical klystron for lasing in the IR wasrecently installed into the north straight section of the

NIJI-IV to extend the lasing wavelength range up to ~ 10
microns. One of our interests in the IR-FEL application is
the microscopic Raman spectroscopy which can examine
adsorbed molecules and their bonding conditions on themetal surfaces. Establishment of a total surface analysis
system using NIJI-IV compact VUV/IR FEL combinedwith characteristic surface analysis techniques is one ofour goals in the near future.

PERFORMANCE OF THE NIJI-IV FEL
We have been modifying the NIJI-IV FEL system toextend its lasing range. As shown in our previous paper[2,3], replacement of the NIJI-IV vacuum chambers to
low-impedance-type ones as well as installation of thin
sextupole magnets into the ring brought a higher peakcurrent of the stored beam and a resultant higher FEL gain.
This led to easy FEL lasing around 200 nm even with ourcompact system. To utilize such a DUV FEL, we tried toenhance the laser output power by increasing thetransmittance of the output coupler of the optical cavity
from 0.05 to 0.5 %. The beam energy was also increasedby 10 % from 310 up to 340 MeV. As a result, theaverage output FEL power at 202 nm was successfullyincreased up to 0.5 mW per one laser port with a beam
current of 15 mA, which is larger by an order ofmagnitude than before [2]. A higher power is expected
through further increase of the beam energy as well as
multi-bunch operation of the ring. Fig.1 shows thedependence of average output power on the beam energy.

1.6

AVERAGE OUTPUT POWER (arb.units)

Abstract

1.4

1.2

1.0

0.8
300

310

320

330

340

350

ELECTRON ENERGY (MeV)

Fig.1. Dependence of average output power on the
beam energy. Solid circles and solid curve indicate theobserved power and an expected curve proportional to
the 4th power of the beam energy.

____________________________________________*This work is supported by peaceful utilization technology of nuclear
energy from the ministry of education, culture, sports, science andtechnology of Japan.

Available online at http://www.JACoW.org

FEL Experimental Results

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K. Y. Yamada et al. / Proceedings of the 2004 FEL Conference, 311-313

Solid circles and curve respectively indicate the observed
FEL power at 202 nm
and an expected energy
dependence of the laser power which can be proportional
to the 4th power of the beam energy. In this figure, theobserved average power was estimated from the peakheight of the lasing line spectrum detected with aphotodiode array attached to a 25-cm monochromator.
Here, the peak height was corrected for the beam current.
Absolute power was measured with a highly sensitive andstable CW power meter (Gentec TPM-310) with a windblock. It is found in Fig.1 that the observed output power
was enhanced by at least 30 % during 10-% increase of
the beam energy, which does not largely deviate from theexpected curve. Now we plan to increase the beamenergy from 0.31 up to at least 0.4 GeV which will bring
three times power enhancement. A few-mW power in the
DUV to the VUV range is in a sufficient level for PEEM
measurement.

Degraded loss
Exposure: 58 mA*h

1.8

14
12

1.5

10

1.3

8

1.0

6

0.8

4

0.5
Original loss

0.3
185

190

195

CAVITY LOSS (%)

SPECTRAL INTENSITY (arb. units)

2.0

A new optical klystron for lasing in the IR was installedin the north straight section of the NIJI-IV.
Its
performance is being checked spectroscopically [4].

APPLICATION OF NIJI-IV DUVFEL TO
SURFACE OBSERVATION
NIJI-IV DUVFEL was applied to surface observation,in combination with a PEEM system (STAIB Instrumente,
type 350). This PEEM system has three sets ofelectrostatic electron lenses and a micro channel plate(MCP) equipped with a fluorescent screen. By viewing
the focused images on the fluorescent screen with a CCD
camera, transient phenomena, such as chemical reactions
on transition-metal surfaces, can be monitored withvideo-rate time resolution. Since the spatial resolution ofthis system is 80 nm and our FEL intensity is large
enough to extract sufficient amount of photoelectrons torecognize the surface contrasts within 33.3 msec, we can
examine real-time physical and chemical information ontransition-metal surfaces in a sub-micron scale. Fig.3
shows the experimental setup for FEL-PEEM
measurement. The FEL with a wavelength of 202 nm
comes from left-hand side through a long focus lens andis reflected by a flat aluminium mirror to focus onto thesample surface. The FEL intensity on the sample surface
is roughly estimated to be 500 mW/cm2.

2
0
200

WAVELENGTH (nm)Fig. 2. Cavity-loss as a function of wavelength. A
spectrum of the spontaneous emission resonating
inside the optical cavity is also indicated.
Lasing around 190 nm and below is also being tried
using a low-loss optical cavity composed of two
Al2O3/SiO2 mirrors. Though the original loss of thiscavity was 2.8 % at 193 nm, it rapidly increased up to
3.7 % with 58 mA-h exposure to the undulator radiation.
Due to an unexpectedly smaller FEL gain, probably
caused by some demagnetization of the undulator
magnets, we have not obtained lasing around 190 nm yet.
Now we are preparing robust mirrors with an optical loss
smaller than 1 % and also planning to replace thedegraded magnet blocks in the optical klystron. Fig.2
shows the loss curve for the above mentioned cavity as afunction of wavelength. A spectrum of the spontaneousemission resonating inside the optical cavity, observed ata beam current of ~ 7 mA, is also indicated in the figure.
Though the spectrum is strongly distorted by intense
long-wavelength off-axis components and lightabsorption by the Schumann-Runge system of Oxygen
molecules around 193.8 nm, spectral modulation peculiar
to an optical klystron is clearly seen. Since such aspectral modulation becomes much more obvious andeven spiky for a beam current more than ~ 14 mA, thelasing seems to be achieved soon.

THPOS29DUV FELPEEM

CCD

SamplechamberFig.3 Experimental setup for FEL-PEEM
measurement.
To examine the total resolution of our FEL-PEEM
system, we observed a standard reference sample forscanning electron microscope (SEM) which has a finestructure formed with 70-nm thick CrO2 on a Crovercoated SiO2 substrate. A typical example of thevideo-rate real-time imaging of the standard SEM sample
is shown in Fig.4 (a) and (b). It was found that the FEL
was intense enough to obtain video-rate moving images
on the Cr surface. From higher magnification image(Fig.4 (b)), the spatial resolution of our system isestimated to be ~ 300 nm at present. Suppression of
mechanical vibration from a vacuum pump will benecessary to realize the specification of the PEEM system.

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K. Y. Yamada et al. / Proceedings of the 2004 FEL Conference, 311-313

(a)

(b)

Fig. 4. Typical example of the video-rate real-time
imaging of the standard SEM sample for lower (a) andhigher (b) magnifications. The narrowest feature width is
1 µm in both images.
As a preliminary experiment for the FEL-PEEM
measurement, we observed a Palladium surface,
introducing CO and O2 gasses. In this case, CO2 iscreated from adsorbed CO and O2 molecules under thecatalysis of Palladium and desorbed from the Palladium
surface. Such a reaction process must be reflected in thecontrast of the PEEM image [5]. Fig.5 (a) – (d) shows
still shots for four deferent situations, sampled out from areal-time moving image. After cleaning with Argon
sputtering and annealing at 1,100 K in a high vacuum
below 5 x 10-7 Pa, pure surface of a Palladium standard
sample (from Mateck) was exposed to the CO gas to becovered with CO molecules. Then, Oxygen gas wasintroduced to be reacted with adsorbed CO molecules to
produce CO2 which will desorb immediately. Fig.5
corresponds to the FEL-PEEM images for pure surface
after cleaning (a), a CO-adsorbed surface (b), surface
reaction of CO and O2 (c), and the same surface reaction

at a different moment (d). In these images the full widthof the viewing field is 200 µm. During the measurement,
the FEL was lasing at 202 nm with a beam current
between 11 and 8.5 mA In Fig.5 (a), many crater-likestructures are scratches which remains on the polishedsurface originally. One can see in Fig.5 (b) that thebrightness of the image was reduced through theadsorption of CO molecules over the whole surface. On
the other hand, the images indicated clearly different
features after introducing Oxygen gases, Fig.5 (c) and (d),where a complicated black and white blindle appeared.
The black small patches seen around upper right area of(d) imply Oxygen-adsorbed regions, while several brightislands seen from upper left to lower right of (c) seems tobe the areas where the adsorbed CO molecules weredesorbed to form CO2 through chemical reaction with O2.
These patterns varied rapidly in a-few-second time scale
and were observed only during FEL lasing. More detailed
observation is being carried out under various conditions,such as different gas pressure and substrate temperature.

SUMMARY
Output power of the NIJI-IV FEL was enhanced by anorder of magnitude in the DUV region around 200 nm.
The DUV FEL was utilized to make real-time imaging offine structures and chemical reactions on transition-metal
surfaces in combination with a PEEM system. Moving
images of reactions by CO and O2 on a Palladium surface
were visualized with video-rate time resolution. Moredetailed FEL-PEEM experiment is being carried out atpresent. Efforts to obtain FEL lasing at a wavelength
shorter than 190 nm are being continued. Lasing in the
IR using our compact ring is also expected to be realized.
A total real-time analysis system based on the NIJI-IV
compact VUV/IR FEL will be established in combination
with characteristic surface analysis techniques in the near
future.

REFERENCES
[1]
(a)

(b)

(c)

(d)

K.Yamada, N.Sei, H.Ohgaki, T.Mikado,
T.Yamazaki, Nucl. Instr. and Meth. A475
(2001) 205.
[2] K.Yamada, N.Sei, H.Ogawa, M.Yasumoto,
T.Mikado, Nucl. Instr. and Meth. A528 (2004)
268.
[3] N.Sei, K.Yamada, H.Ohgaki, V.N.Litvinenko,
T.Mikado, T.Yamazaki, Nucl. Instr. and Meth.
A429 (1999) 185.
[4] N.Sei, K.Yamada, H.Ogawa, M.Yasumoto, in thisproceedings.
[5] H.H.Rotermund, Surface Science 283 (1993) 87.

Fig. 5. Still shots, sampled from a real-time moving
PEEM image, on a Palladium surface under deferent
conditions; after surface cleaning by both Argon
sputtering and annealing (a), with the surface covered
by CO molecules (b), and during reaction of CO withO2 (c)(d).

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A MM-WAVE, TABLE-TOP CERENKOV FREE-ELECTRON LASER*
I. de la Fuente#, P.J.M. van der Slot, K.J.Boller
University of Twente, Laser Physics & Non-Linear Optics Group, PO Box 217, 7500 AE Enschede,
The Netherlands
Abstract
A Cerenkov Free-Electron Laser (CFEL) has theadvantage that the operating frequency increases withdecreasing electron beam energy. The low beam energy
allows for the construction of compact devices. We havedesigned and constructed such a device with a footprintof 0.5 m x 1.5 m, an operating frequency of 50 GHz and adesign output power of 1 kW CW. We will present theoverall design and experimental set-up, and firstexperimental results.

INTRODUCTION
High frequency microwave radiation has shown to be
attractive for several applications such as wirelesscommunication, material processing or microwave
chemistry [1]. In some cases, also high output power isrequired, e.g., mm-wave radar applications that require
increasingly higher output powers at higher frequencies[1,2]. However, industrial applications seem to be limited
to the operating frequencies of the magnetron, thoughapplications have been studied at higher frequencies.
The CFEL may be a welcome addition to the family of
microwave sources as a cost-efficient, compact device
capable of delivering kW-level output power at
frequencies of up to 100 GHz. Compared to undulator
based FELs, they have the advantage of generating higher
frequencies at lower electron beam voltages and may beespecially interesting for millimetre wavelength
generation [3,4].
In order to test this potential of the CFEL and to research(industrial) applications as higher frequencies, a compact
CFEL with a footprint of about 0.5 m by 1.5 m(excluding a 19 inch rack for power supplies and control
electronics) producing an output power in access of 1 kW
CW has been constructed and is currently beingcommissioned. In the remaining part of this paper we willreport on the design and construction of this device andpresent some preliminary experimental results.

OVERVIEW OF THE SYSTEM
A general overview of the CFEL is presented in fig. 1.
The main parts of the system are the electron gun, theinteraction area, the outcoupler and the collector.
Electrons are accelerated from the electron gun towards
the lined cylindrical waveguide that forms the interaction
area. The electrons are transported through this section up___________________________________________* Research is funded by the EU, contract G5RD-CT-2001-00546#

i.delafuentevalentin@utwente.nl

THPOS33

to the collector by means of an axial magnetic field. An
outcoupler separates the generated radiation from theelectron beam, while at the same time it acts as the downstream mirror of the oscillator. Table 1 shows the generaldesign values of the CFEL at the University of Twente.
Electron gun

Post-accelerating gap
Lined section
Outcoupler

Vc

Cbuffer
10 kV
power
supplyR

B
upstream
mirrorVa

downstream
mirrorCollector

100 kV power supply

Figure 1. Overview of the CFEL. The depressed collector
is initially not installed and instead a buffer capacitor isused to supply the beam current in pulsed operation.
Nominal operational frequency
Electronic tuning range
Nominal peak output power
Nominal outcoupling
Accelerating voltage
Material
Liner
Dielectric constant, εr
Thickness, dε
Inner radius, Rd
Length, L
Magnetic field on axis
Beam diameter
Beam current
Max HV Power Supply current

50 GHz>10 %1 kW (10 µs-CW)
80-9 %
From 65 to 100 kV
fused GE quartz type 219
5.8
1.3 mm
1.5 mm
250 mm0.15 T
2 mm
800 mA
30 mA

Table 1: Design values of the tabletop Cerenkov FEL.

Electron gun and beam transport
In the CFEL, the electron beam is generated using acommercially available 10 kV, 800 mA, and gridded
thermionic electron gun. The beam is further accelerated
to a maximum of 100 kV using a post acceleration
section. The grid allows for flexible temporal control ofthe electron beam and thus also for the generated
radiation field. By keeping the acceleration and gridvoltage of the (10 kV) electron gun constant, and byvarying the post-acceleration voltage, an electron beam is
produced with constant current and varying beam
voltage.

Available online at http://www.JACoW.org

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M.I. de la Fuente et al. / Proceedings of the 2004 FEL Conference, 314-317

A combination of commercial air insulated HV power
supplies and home build supplies are used for theacceleration, respectively grid, and heater voltages of theelectron gun. Short isolating distances are obtained byusing SF6 as an insulating gas and the overall footprint of
the complete device could thus be limited to 0.5 by 1.5 m.
The design value for the electron beam is 800 mA,
whereas the HV power supplies are only able to supply 30
mA. In the final set-up a depressed collector will be
installed for cw operation, however, initially the system
will be operated in pulsed mode and a buffer capacitor isused to supply the beam current (see fig. 1). Using abuffer capacitor of 70 nF resulted in single pulses of up to
40 µs duration with a rise and fall time of about 0.1 µs,
and a train of 10 µs pulses at a few Hz repetition rate. The
capacitance, which essentially limits the pulse length, will
be increased stepwise to 2 µF, thereby increasing thepulse duration to about one millisecond with a duty cycleof almost 4 %.
First measurements on performance of the electron gun
show that the e-beam current varies linearly with theapplied grid voltage between 0 and 725 mA and it isindependent of the total accelerating voltage. Fig. 2 shows
the peak current delivered by the cathode as a function of
the grid voltage for a total acceleration of 69.45 kV and apulse of 10 µs duration.
750
700

Ic (mA)

650

Va-c=9.45 kV

600
550
500
450
400
80

100

120

140

160

180

Vg (V)

the end of the first solenoid and indicates nearly complete
beam transport from gun up to the end of the interaction
region. This is concluded from simulations with thesoftware package Trak 6.0 [5], which show that inabsence of the second solenoid, Faraday cup collects only
a fraction of the electrons within the beam.

Tuning and output characteristics
For sufficiently high frequency the electromagnetic wave
propagating through the lined waveguide attains a phasevelocity less than the speed of light in vacuum. Such awave is mainly propagating through the liner and has anevanescent part extending into the vacuum. If the electron
velocity is slightly higher than the phase velocity of thewave, the latter produces longitudinal bunches within theelectron beam and consequently the beam will coherently
amplify the wave, at least as long as it has a longitudinal
electric field component. The resonant frequency isdefined as the frequency for which the two velocities areequal. As the wave’s phase velocity is not only
determined by the value of the dielectric constant but also
by the geometry, i.e., inner liner radius and waveguide
radius, the tuning characteristics can be influenced byappropriate choices of these parameters. It should bepointed out here that variations in, e.g., the inner radius of
the liner result in variations of the phase velocity of the
wave along the liner and may thus degrade the gain of thedevice in a way similar to undulator errors in undulator
based FELs [6]. This may be especially important for
low-gain devices like the current CFEL.
The liner in the actual set-up is a tube made of fusedquartz type GE 219 with a specified dielectric constant of
5.8 and dielectric loss less than tan δ = 10–4. As the exact
value of the loss tangent is not known, a value of 1·10-5 isused in the simulations. The liner tube has an innerdiameter of 3 mm. At the outside of the tube a thin copper
coating is applied, which acts as the waveguide wall, toensure that no gap exists between the liner and thewaveguide.

Figure 2: Beam current as a function of grid voltage for a
first anode-cathode voltage Va-c of 9.45 kV.

55
Freq (GHz)

Characterization of the electron beam transport up to theend of the interaction region, with no liner present, isdone by measuring the collected current using a Faradaycup placed just after the first solenoid at the end of the
waveguide. The Faraday cup consists of an OFHC copper
plate. In addition, the Faraday cup contains a 50 µmdiameter tungsten wire, which can be swept verticallythrough the electron beam, in front of the plate. The latter
gives information about the transverse spatial distributionof the electron beam.
So far, the collected current is 73 % of the current emitted
by the cathode and the beam possesses a symmetric
distribution in the scan direction. This measured value isconsistent with the distance between the Faraday cup andThickness of the liner
1 mm
1.2 mm
1.3 mm
1.4 mm60

εr=5.850

Rd= 1.5 mm
Ib=0.8 A

45

40

65

70

75

80

85

90

95

100

Beam Voltage (kV)

Figure 3: Resonant frequency as a function of electron
beam accelerating voltage

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M.I. de la Fuente et al. / Proceedings of the 2004 FEL Conference, 314-317

2500

Pout, Pdis (W)2000

Output Power (W)1500

Vb=75 kVεr=5.8Rd=1.5 mm
dr=1.3 mm
L=25 cm

500

Dissipated Power (W)

0.2

0.4

0.6

0.8

1.0

R

Figure 4: Calculated output and dissipated power due todielectric losses for different reflection coefficients. The
frequency is 50 GHz and a liner length of 25 cm is used.
Fig. 5 summarises the calculated maximum output powerfrom the oscillator, the corresponding dissipated power
due to dielectric losses, and the total reflection coefficientnecessary to obtain that output power for different valuesof the liner length. The intra-cavity power should be small
to keep the dissipation in the liner and waveguide as low
as possible. Therefore, a relative small feedback with alarge single pass gain is more desirable than a lower
single pass gain and a higher feedback. However, fig. 5
shows that after an initial decrease in dissipated powerwith increasing interaction length (and thus withincreasing single pass gain) it levels off. Apparently, thelower dielectric loss due to a lower intra-cavity power iscompensated by the increase in liner length, which results
in a higher loss. From fig. 5 it follows that a 20 cm
interaction length would be sufficient, leading to a
maximum output power of almost 2.3 kW and a requiredreflection coefficient of about 24 %. The design of the

THPOS33

2300
40
36

2200

32
28

2150
reflection coefficient

24

28

20

dissipated power

26

16
12

24
22

44
Reflection coefficient (%)

max. power

2250

8
14

16

18

20

22

24

26

length (cm)Figure 5: Calculated maximum output power anddissipated power due to dielectric losses with thecorresponding reflection coefficient as a function of thelength of the liner. The beam voltage is 75 kV and otherparameters are as in Table 1.
outcoupler limited. Therefore the construction of the
CFEL allows for a maximum liner length of 25 cm.

RF Outcoupler

1000

0
0.0

outcoupler indicates that a somewhat lower reflectivity
was desirable, to keep mode conversion within theMax. Power
Dissipated Power (W)Figure 3 shows the calculated output frequency of the
CFEL as a function of the total electron accelerating
voltage, for several thicknesses of the liner. It can be seenthat the expected frequency range covers the interval from40 GHz to 60 GHz by varying the voltage from 65 to 100
kV, for a 1.2 mm or 1.3 mm thickness of the liner. Larger
and smaller values give a more limited tuning range. The
thickness of the liner has not only an influence on thetuning characteristics, but it also influences the couplingstrength between the electron beam and the copropagating EM wave. A thickness of 1.3 mm will bechosen for the experiment as with this we expect a higher
output power the CFEL (than with 1.2 mm).
The 800 mA current is not enough to provide saturation ina single pass within a reasonable distance, so that thesystem is configured as an oscillator. To determine therequired total reflectivity for a particular length of theliner, fig. 4 shows an example of the calculated output anddissipated power due to dielectric losses as a function of
the total reflection coefficient of the oscillator. The
reflection coefficient includes all losses except dielectriclosses in the liner.

To form an oscillator, the second anode (at ground
potential) is used as the upstream mirror while the RFoutcoupler forms the downstream mirror. The upstream
mirror contains a small aperture to pass the electron beamthrough. The aperture is below cut-off for the frequency
range of interest. The RF outcoupler, which is shown infig. 6, is designed to separate the electron beam from thegenerated radiation, to reflect part of that radiation and toconvert the cylindrical geometry into the standard WR19
waveguide geometry for the output waveguide system.
Both the radiation field and the electron beam reach theoutcoupler at input port 1. The diameter of the cylindricalinput waveguide is tapered down to a smaller value toPort 2 WR19
radiation
Port 3 Cylindricale-beammoveable shortwith aperture
Port 1 Cylindricale-beam plus radiation
Figure 6: Outcoupler with the corresponding port
denomination.

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M.I. de la Fuente et al. / Proceedings of the 2004 FEL Conference, 314-317

that all other higher order modes above the TM01 modeare below cut-off. The radiation is coupled into a standard
rectangular WR19 waveguide mounted at a right angle
with regard to the input cylindrical waveguide. The
amount of coupling, and thus the amount of reflectedradiation, can be controlled through the position of a
movable short that is connected to port 3. This shortcontains an aperture that is below cut-off for the
resonating frequencies and allows the e-beam to passstraight through to port 3 of the RF-outcoupler. Finally, a1.85 mm thickness high-density polyethylene vacuum
window is placed in the output port 2.
In order to characterize the reflection properties of the RF
outcoupler we have measured the S11 parameter of port 2
as a function of the position of the short using a Network
Analyser with a maximum frequency of 50 GHz.
Measurements of the other S-parameters are currently notpossible due to the non-standard geometries of port 1 andport 3. The results for a frequency of 50 GHz are shown
avoid excessive mode conversion from the TM01 mode ofthe laser into the TE11 mode. The final diameter is such in
Figure 7 for two cases, one with port 1 open and one
when a short is applied to port 1. The measurement data
do not change whether port 3 is opened or shorted. This
indicates that no measurable radiation is coupled fromport 1 or port 2 to port 3. When a short is applied to port 1
the measured S11 values indicate that the RF power isdissipated in the RF-outcoupler, which is mainly due tomode conversion. For the positional range of interest (3-6mm), the dissipated power is less than 7 %, except near
the 6 mm position where it increases to 26 %. For port 1
open, the S11 ranges from –2 dB to –8 dB when the short
is moved from 3 mm to 6 mm, indicating that the desiredreflection of 10-20 % is indeed obtained.
0.0

F=50 GHz-0.2(via increasing the buffer capacitance). The results will
provide the necessary data for designing the depressedcollector, to be installed subsequently.
Once the source will be fully operational, it will be used
to study several novel microwave applications.

REFERENCES[1] M. Thumm, Free-electron masers vs. gyrotrons:
prospects for high-power sources at millimetre andsubmillimetre wavelengths. Nuclear Instruments andMethods in Physics Research A 483 (2002) 186 –194.
[2] S. H. Gold et. al., Review of high-power microwave
source research, Rev. Sci. Instrum. 68, 11, November(1997).
[3] J.E.Walsh, T.C. Marshall and S.P. Schlesinger,
Generation of coherent Cerenkov radiation with anintense relativistic electron beam, The Physics of Fluids,
20, 4, (1977).
[4] E. Garate et. al., Cerenkov maser operation at lowermm wavelengths, J. Appl. Phys. 58, 2, (1985).
[5] Trak 6.0 from Field Precision, http://www.fieldp.com.
[6] I. de la Fuente, P.J.M. van der Slot K.-J. Boller, The
effect of liner induced phase fluctuations on the gain of a
Cerenkov FEL, in these Proceedings.

0
-2

-0.6

-4

-0.8

-6

-1.0
-8

-1.2
-1.4

S11 (db)

S11 (dB)

-0.4

0

1

2

3

4

5

6

7

8

Position stub (mm)

9

10

-10
11

Port 1: short
Port 1: open

Figure 7: Measured S11 parameter at port 2 of theoutcoupler for 50 GHz.

FUTURE PLANS
After the electron beam transport is optimised, the RF
outcoupler will be installed. Initially, operation andcharacterization of the laser will be done in pulsed mode,with a progressive increment of the length of the pulses

FEL Experimental Results

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A.K. Kaminsky et al. / Proceedings of the 2004 FEL Conference, 318-321

STATUS OF 30 GHZ FACILITY FOR EXPERIMENTAL INVESTIGATION
OF THE COPPER CAVITY LIFETIME (CLIC COLLIDER PROJECT)*
A.V. Elzhov, E.V. Gorbachev, A.K. Kaminsky+, V.V. Kosukhin, E.A. Perelstein, N.V. Pilyar,
T.V. Rukoyatkina, S.N. Sedykh, A.P. Sergeev, A.I. Sidorov, V.V. Tarasov
Joint Institute of Nuclear Research, Dubna, Russia
N.S. Ginzburg, S.V. Kuzikov, N.Yu. Peskov, M.I. Petelin, A.S. Sergeev, N.I. Zaitsev
RAS Institute of Applied Physics, Nizhny Novgorod, Russia

Abstract
The facility for experimental investigation of a copper
cavity lifetime under multiple action of 30 GHz
microwave power pulses is being created now by thecollaboration of CLIC (CERN), JINR (Dubna) and IAP
RAS (Nizhny Novgorod). A design of the test cavity, anestimation of the operating parameters of the FEM
oscillator and the RF power transmission line was alreadydiscussed at FEL’03. Last year was devoted to theachievement of the design parameters of all of theelements of the facility. We have developed theequipment and the method of RF transmission line
adjustment, improved the stability of the linac power
supplies, created the new system of data acquisition.
Effect of central mode splitting in Bragg resonators is oneof the problems under study. Start of the full-scale
experiments is planned to the end of 2004.

1 INTRODUCTION
One of the strict limits on the accelerating gradient in
future linear colliders is the fatigue of the copper wall ofhigh-gradient accelerating structure due to multiple actionof powerful RF pulses [1]. Experimental investigation ofthis limitation at the frequency of 11.4 GHz has been
carried out in SLAC for several recent years [2]. A similar
research at the frequency of 30 GHz is prepared now bycollaboration of CLIC team (CERN) [3], JINR (Dubna)
and IAP RAS (Nizhny Novgorod) groups. The nearest ourgoal is a wall temperature rise about 200 K with thestatistics of 106 pulses [4]. The source of RF power is
JINR–IAP FEM oscillator with Bragg resonator which
provides the 25 MW/150 ns pulses with spectrum width
not greater than 30 MHz [5, 6] at the operating mode
TE11. The breakdown-safe mode TE01 has been chosen as
the operating mode of the tunable copper test cavity
which simulates the CLIC accelerating structure.
A key element of the experimental facility is the RF
power transmission line. It should provide the highefficiency, elimination of the breakdown at the vacuum
windows, possibility for diagnostics of the incident,
reflected and transmitted RF power and radiation___________________________________________* This work is supported by grants №№ 04-02-17118, 03-02-16530,
02-02-17438 of Russian Foundation for Basic Research and by INTAS
grant №03-51-5319.
+ Corresponding author: Dr. A.Kaminsky, E-mail: alikk@sunse.jinr.ru

THPOS37

spectrum.
One of the effects under study is the mode splitting in
FEM Bragg resonators observed both in cold and hot
experiments. Possible reason of this undesirable effect is
discussed.

2 RF TRANSMISSION LINEThe scheme of the RF transmission line is presented inFig. 1. It contains FEM output horn with cylindricalinsertion, long oversized waveguide with vacuum window
inside it, a diagnostic film with detectors of incident andreflected power, two quasi-optic focusing mirrors, amovable reflector, long input waveguide with vacuum
window, accepting horn with cylindrical insertion, TE11 to
TE01 mode converter, a test cavity, an output horn withvacuum window and a detector of the transmitted power.
It is well known that a Gaussian wavebeam is the mostsuitable one for quasi-optic focusing mirrors. In our line
the Gaussian beam is formed at the FEM oscillator output
by the special horn with cylindrical insertion (Fig. 2)
which provides the optimal phase shift between the initial
TE11 mode (87% of power) and TM11 mode (13%) formedin the horn. The long output waveguide employs thephenomenon of wave-front self-reproduction in oversizedwaveguide (Talbot effect) [7]. The wavebeam in an
oversized waveguide may be considered as asuperposition of partial eigenmodes with different phasevelocities. So the phase relations between the partial
modes evolve spatially and become similar to the initial
one at a certain length (e.g. ~ 90 cm for the FEM output
waveguide we had used). While the Gaussian wavebeam
is reproduced at the end of the waveguide, it is possible tofind the cross-section with almost uniform amplitude of
the RF field to install the vacuum window and eliminate
the breakdown. It is also possible to reduce the influenceof the reflected wave on the FEM oscillator. Efficiency of
the Gaussian wavebeam reproduction is about 90% due tomismatching phases of high-order modes.
The thin film is installed between the FEM output
waveguide and the first mirror at the angle of 45° withrespect to the wavebeam. Small reflection from both sidesof the film provides possibility of non-destructive control
of both incident and reflected power pulses.
The distant-controlled movable reflector can be liftedfrom its conventional horizontal position to direct the

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A.K. Kaminsky et al. / Proceedings of the 2004 FEL Conference, 318-321

Figure 1: Overview of the quasi-optic RF transmission line.

radiation upward. It isolates the testing cavity fromradiation when the radiation parameters don’t matchthe requirements of the experiment.
The geometry of the transmission line is close tocentral-symmetrical one. The second oversizedwaveguide employing Talbot effect allows one tomatch the wave beam behind the second mirror and at
the accepting horn as well as eliminate breakdown at
the vacuum window of the test cavity. The position of
the input vacuum window closer to the input hornallows us to reduce the volume of the vacuum chamberof the test cavity. The input horn with cylindricalinsertion restores the pure TE11 mode at the input of themode converter. The calculated transverse profiles of
the RF field amplitude in several points of both
waveguides are demonstrated in Fig. 1. General layoutof the experimental facility is shown in Fig. 3.
A new system of optical laser alignment of thetransmission line has been introduced. According to theresults of cold measurements, we managed to reduce
loss of the power delivered to the test cavity. The
power transmission factor obtained in cold experiments

was close to the designed level of 70% including allmode conversions and resistive losses.
An image of the wavebeam cross-section obtained
behind the test cavity using the monitor of wavebeam
position and size [4] is illustrated in Fig. 4. The
intensity profile looks as well-expressed TE01-like
distribution.

Figure 2: Horn with cylindrical insertion.

FEL Experimental Results

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A.K. Kaminsky et al. / Proceedings of the 2004 FEL Conference, 318-321

Figure 3: General view of the experimental facility.
and hot experiments show two modes with typicalfrequency difference of 50–100 MHz (Fig. 5). This effectis very undesirable for narrow-band loads such as RF
pulse compressors or imitator of CLIC accelerating
structure in our experiment.

Figure 4: Cross-section image of the wavebeam behind
the test cavity.

3 PROBLEM OF CENTRAL MODESPLITTING IN BRAGG RESONATOR
According to the theory, Bragg resonators used in
FEM oscillator have only one central mode with high Qfactor. But precise spectrum measurements both in cold

THPOS37

Figure 5: Splitting of the central mode of the Bragg
resonator (cold measurements).

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A.K. Kaminsky et al. / Proceedings of the 2004 FEL Conference, 318-321

Reasons of this mode splitting are under study now.
One of the possibilities is the influence of TM11!TM11
resonance not far from the operating TE11!TM11
resonance. Numerical simulation shows that this influencecan be strong enough for our parameters of the resonator(Fig. 6).
Now we are developing a new type of Bragg resonator
operating in TE11!TE11 reflection zone and much larger
frequency distance from other possible resonances.

expanding capability due to the modularity principle andopen system architecture.
The system of data acquisition has been built realized
as several server programs and a single multi-client
program employing API sockets in asynchronous regime.
Much attention is paid to modernization of power
supplies both for accelerating voltages of the induction
linac and focusing magnetic fields. They are very
important elements of the facility in terms of providing
stable parameters of the experiment during the wholestatistics of 106 pulses.

5 CONCLUSIONS

Figure 6: Splitting of the central mode of the Bragg
resonator (numerical simulation).

4 DIAGNOSTIC EQUIPMENT AND DATAACQUISITION SYSTEM
The experimental facility is equipped with 3 detectorsof RF pulse which control the incident, reflected andtransmitted power. The RF power and spectrum of eachpulse from the required millions must be registered andstored in order to obtain correct value of the RF load at
the cavity wall. We use a heterodyne spectrum meter withon-line fast Fourier transformation realized by the
supplemental chip in the digital oscilloscope Tektronix
TDS3032. Built-in procedure of the oscilloscopemeasures the spectrum width of the radiation. The
oscilloscope also measures the pulse parameters ofincident power. The oscilloscope sends the results to thecomputer via Ethernet switch using HTTP protocol. RF
power of reflected and transmitted waves as well as
electron beam currents and pulses of accelerating voltages
are measured by the analog-to-digital converters withresolution time of 10 ns in CAMAC standard. We also
have slow ADC to control the magnetic fields in the linear
induction accelerator and FEM oscillator.
A distributed asynchronous object growing multichannel system for data acquisition from the experimental
facility has been built under client-server principle.
The system unites the servers of linac subsystems
capable of maintaining autonomous operability ofmanifold equipment with different operating speed andmaster client computer collecting information on thewhole system for subsequent processing and analysis.
Such an organization allows one to reach stability
relatively to faults of single servers, the flexibility,

A quasi-optic transmission line is designed forproviding the high efficiency, elimination of the
breakdown at the vacuum windows, possibility for full
diagnostics of the incident, reflected and transmitted RF
power and radiation spectrum. Multiple transformation of
the transverse distribution of the wavebeam is used in theline.
A new technique of optical laser alignment of thetransmission line has been introduced. According to theresults of cold measurements, we managed to reduce lossof the power delivered to the test cavity. The powertransmission factor obtained in cold experiments was
close to the designed level of 70%.
An undesirable effect of central mode splitting in FEM
Bragg resonator must be taken into account for providing
the effective power transmission to narrow-band test
cavity.
RF pulse diagnostic equipment and a distributed
asynchronous system for data acquisition from theexperimental facility built under client-server principle
make it possible to register parameters of each pulse fromrequired statistics of 106 pulses which is necessary toobtain correct value of the RF load at the cavity wall.

6 REFERENCES[1] O.A. Nezhevenko, Proc. of PAC’97, Vancouver,
Canada, May 1997, p. 3013.
[2] D.P. Pritzkau, Phys. Rev. Spec. Topics - Accel. &Beams, 2002, v. 5, 112002. 22 pp.
[3] J.-P. Delahaye et al., Proc. of EPAC'98, Stockholm,
June 1998, p. 58.
[4] A.V. Elzhov, N.S. Ginzburg, A.K. Kaminsky et al.,Nucl. Instr. and Methods, 2004, v. A528, p. 225.
[5] A.K.Kaminsky, N.S.Ginzburg, A.A.Kaminsky et al.,Nucl. Instr. and Methods, 1998, v. A407, p. 167.
[6] V.L.Bratman, G.G.Denisov, N.S.Ginzburg, M.I.
Petelin, IEEE J. of Quant. Electr., 1983, v. QE-19,№ 3, p. 282.
[7] G.G. Denisov, S.V. Kuzikov, Strong Microwaves in
Plasmas, Nizhny Novgorod, 2000, v. 2, p. 960.

FEL Experimental Results

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V. Pinayev et al. / Proceedings of the 2004 FEL Conference, 322-324

CHARACTERIZATION OF STORAGE RING FEL OPERATING IN THE
GIANT PULSE MODE
I. Pinayev, K. Chalut, Duke University, Durham, NC 27708, U.S.A., V.N. Litvinenko, BNL Upton,
NY 11973, U.S.A.
Somewhat unexpected use of the giant pulse mode of
Abstract
In this paper we present experimental results on thestorage ring free electron laser operating in giant pulse
mode with variable repetition rate. The experiments wereconducted through a wide range of electron beam energies
from 270 MeV to 600 MeV with the giant pulses
generated using a gain modulator. Dependence of thepeak and average power, and the other properties andparameters of giant pulses on the pulse repetition rate
were studied. In particular, it was found that the averagelasing power in the giant pulse mode can reach levels of
70-90% of that in the CW power mode. Applications ofsuch mode of operation are discussed.

operation came when OK-4/Duke FEL was generating-rays for HIGS users [3]. The optical power wasconcentrated in a series of short macropulses and small
filling factor (product of the macropulse length andrepetition rate) made possible to reduce a backgroundnoise by using a time gate [4].
The electron beam excitations, caused by the noise ofmagnetic system power supplies or RF system, canstrongly affect the stability of SRFEL output [5, 6]. In
order to suppress variation of the optical power the SuperACO group implemented a few feedback systems [7, 8].
Application of the giant pulse technique may be more
attractive in this case as well.

INTRODUCTION
The gain modulation technique [1] was initially designed
for storage ring free electron lasers (SRFEL) to satisfy
user experiments demanding high peak power. Later its
application was extended for generation of harmonic offundamental free electron laser wavelength. High peakintracavity power allowed expansion of the operational
range of SRFEL into the vacuum ultraviolet range [2].
270 MeV

THEORETICAL CONSIDERATION
Even a small modulation of the SRFEL gain can resultin significant variations of the output power. Suchphenomenon arises from the significant difference of twotime constants: the synchrotron damping time and FEL
optical power growth. It manifests itself usually in chaotic
behavior of the output power [5].

350 MeV450 MeV

530 MeV

600 MeVApproximation

0.5

1.0

1.5

2.0

2.5

1.0

Pav/Pcw

0.8

0.6

0.4

0.2

0.0
0.0

Duty factor

Figure 1. The dependence of the ratio of the average power in the giant pulse mode and CW power on the
duty factor (product of the pulse repetition rate and synchrotron damping time). The pulse repetion
frequency varies from 1 Hz at 270 MHz to 60 Hz at 600 MeV.

THPOS54

Available online at http://www.JACoW.org

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V. Pinayev et al. / Proceedings of the 2004 FEL Conference, 322-324

600 MeV

274 MeV450 MeV

530 MeV

350 MeVApproximation

1.1

G/Go

1.0

0.9

0.8

0.7
0

0.2

0.4

0.6

0.8

1

1.2

1.4

Duty factor

Figure 2. Dependence of the giant pulse' start-up gain on the duty factor. The gain is normalized withrespect to the low repetition rate value.

EXPERIMENTAL RESULTS
The experiments were conducted on the OK-4/Duke
SRFEL for which the parameters were publishedelsewhere [11]. The operational wavelength was definedby the installed mirror set and was 450 nm. Electron beamenergy varied from injection energy of 274 MeV to600 MeV where the wiggler current reached its
maximum. The synchrotron damping time changed from
416 milliseconds down to 40 milliseconds. The buncher
was set at low level (ND<7) providing maximal peak
power. The RF voltage was in the 250–400 kV range well
below the maximal value of 700 kV, due to the excitationof synchrobetatron oscillations. Optical losses of thecavity were 1% per roundtrip.
The radiant power meter manufactured by Oriel (model
70260) was placed downstream of the optical cavity tomonitor FEL power. The silicon photodiode was used on
the other side to observe envelope of the giant pulse.
Malfunctioning streak-camera prevented us frommeasuring bunch length evolution.
All the dependencies were plotted versus duty factor dequal to the product of the repetition rate and synchrotron
damping time. The ratio of average power in the giant
pulse mode to the power in the CW mode is shown on
Figure 1. At low values of duty factor, the average power
270 MeV
530 MeV

350 Mev
600 MeV450 MeV

1.0
1.5
Duty factor

2.0

0.45
0.40
Pulse FWHM, msec

Giant pulse mode of operation is an extreme case when
the FEL gain is 100% modulated with relatively low
frequency. However, it has the advantage of being fully
controlled.
Duration of the giant pulse is much less than its
repetition period. The longest duration of giant pulse
during the experiments (at 10% level) was 300
microseconds, while the highest repetition frequency was
60 pulses per second. Therefore, it is possible to assume
that energy spread of the electron beam instantly grows to
the maximal value. The induced energy spread is directly
proportional to the energy of the giant pulse [9, 10]. The
synchrotron damping leads to the decay of the energy
spread until the start of next giant pulse.

0.35
0.30
0.25
0.20
0.15
0.10
0.0

0.5

2.5

Figure 3. The dependence of the giant pulse width on
the duty factor.

FEL Experimental Results

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V. Pinayev et al. / Proceedings of the 2004 FEL Conference, 322-324

was proportional to the repetition rate and no changes inpulse shape were observed. With the increase of therepetition rates, the electron beam did not relax to theequilibrium energy spread and therefore the saturation
was reached. This dependence has good fitting curve
PGP/PCW=0.75*d/(1+(d/1.2)4)¼.
270 MeV
530 MeV

350 Mev
600 MeV450 MeV

1.4

Delay, msec

1.2
1
0.8
0.6
0.4
0.2
0.00

0.50

1.00
1.50
Duty factor

2.00

2.50

Figure 4. Dependence of the delay between giant
pulse start and location of the maximal macropulse
power.
270 MeV
530 MeV

350 Mev
600 MeV450 MeV

Background suppression

CONCLUSION
Giant pulse technique can be used to obtain highly
stable pulses of optical radiation from the SRFEL withaverage power constituting only 90% CW mode power.
For the experiments requiring background reduction, theseparation between giant pulses should be 0.8-1.2 ofsynchrotron damping time.

ACKNOWLEDGEMENT

1.2

This work is supported by DoD MFEL Program as
administered by AFOSR, grant F49620-001-0370.

1.0
0.8

REFERENCES

0.6[1] I.V. Pinayev, et al., Nucl. Instr. and Meth. A475
(2001), 222.
[2] V.N. Litvinenko, Nucl. Instr. and Meth. A507 (2003),
265.
[3] V.N. Litvinenko, Nucl. Instr. and Meth. A507 (203),
527.
[4] M.W. Ahmed, et al., Nucl. Instr. and Meth. A516
(2004), 440.
[5] M. Billardon, Phys. Rev. Lett., vol. 65, Number 6(1990), 713.
[6] M.-E. Couprie, et al., Nucl. Instr. and Meth. A429
(1999), 165.
[7] R. Roux, et al., Phys. Rev. E58 (1998), 6584.
[8] M.E. Couprie, et al., Nucl. Instr. and Meth. A358
(1995), 374.
[9] N.A. Vinokurov, A.N. Skrinsky, Preprint 77-67 (1977),
Budker INP, Novosibirsk, Russia.
[10] A. Renieri, Nuevo Cimento B53 (1979), 160.
[11] V.N. Litvinenko, et al., Nucl. Instr. and Meth. A475
(2001), 65.
[12] I.V. Pinayev et al., Nucl. Instr. and Meth. A528
(2004), 283.

0.4
0.2
0.0
0.0

1.0
1.5
2.0
2.5
Duty factor
Figure 5. Dependence of the suppression of theuncorrelated background on the duty factor. The
values are normalized to the level at low repetion
rates. The absolute figures varies from 120 at 530
MeV to 1450 at 270 MeV.

0.5

The leading edge of the giant pulse shows exponential
growth of the optical power [12]. From the time constant
one can easily calculate the net gain of the FEL andknowing the optical cavity losses find its gain. Figure 2
shows changes in the start-up gain with duty factor. The
FEL operation blows up energy spread to the levelsufficient to suppress microwave instability especially forthe giant pulse operation. This fact is very important

THPOS54

because the major source, causing the increase of theelectron bunch length, is eliminated and synchrotron
damping occurs at faster rate. The evidence for this is thatthe initial gain G stays constant until duty factor reaches
the value 0.8. With further rise of the duty factor the startup gain decreases for the same reason as mentioned
earlier. This dependence can approximated with thefollowing fit G=G0/(1+(d/2.1)3), where G0 is gain at low
duty factor.
The reduction of the FEL gain leads to the lengtheningof the giant pulse (Fig. 3) and to growth of the delay
between trigger and location of the giant pulse maximum
power (Fig. 4). Knowing the levels of the optical power in
CW and giant pulse modes it is possible to estimate thesuppression of the background noise for the HIGS
experiments S=PGP/(PCW*T*Frep), where T is giant pulse
duration and Frep is repetition rate. The normalized
dependence is shown in Fig. 5. As well as the FEL gain
the suppression does not change until duty factor d=0.8.
Higher values of the duty factor can be used to reduce thedata collection time due to growth of the average power.

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G. Andonian et al. / Proceedings of the 2004 FEL Conference, 325-328

VISA IB: ULTRA-HIGH BANDWIDTH, HIGH GAIN SASE FEL
G. Andonian, A. Murokh, R. Agustsson, C. Pellegrini, S. Reiche, J. B. Rosenzweig, and G. Travish
UCLA, Los Angeles, CA 90095, USA
M. Babzien, I. Ben-Zvi, J. Y. Huang, V. Litvinenko, and V. Yakimenko
Brookhaven National Laboratory, Upton, NY 11973, USA
M. Ferrario, L. Palumbo, and C. Vicario
Universita di Roma ”La Sapienza”, 185 Roma, Italy
I. Boscolo, S. Cialdi, and A. Flacco
INFN-Milano, 20133, Milano, Italy
Summary of VISA I Results

Abstract
We report the results of a high energy spread SASE FEL
experiment, the intermediary experiment linking the VISA
I and VISA II projects. A highly chirped beam (1.7 %) wastransported, without corrections of longitudinal aberrationsin the ATF dogleg, and injected into the VISA undulator.
The ouput radiation displayed an uncharacteristicly large
bandwidth (12 %) with extremely stable lasing and measured energy of about 2 µJ. Start-to-end simulations reproduced key features of the experiment and provided an
insight into the michanisms giving rise to such a high bandwidth. These analyses have important implications on the
VISA II experiment.

INTRODUCTION
The advent of high-brightness, ultra-short duration Xray radiation from self-amplified spontaneous emission
free-election lasers (SASE FEL) promises to be an invaluable tool for the scientific community. There are current
proposals [1, 2] to construct single-pass high gain free electron lasers that will generate angstrom wavelength radiation with femtosecond pulse lengths [3].
A possible scheme to obtain yet shorter pulses by creating and manipulating frequency chirped FEL output has
been proposed [4]. In the first stage of the scheme, anenergy chirped electron beam injected into the undulator
would produce a frequency chirped output. This light isthen monochromatized, and thus sliced, and injected into asecond stage undulator, where only a short section of theelectron beam is seeded by the shortened radiation pulse
well above the shot-noise power level. This, and similar schemes, give motivation for VISA (Visible to Infrared
SASE Amplifier) and VISA II, an extension of the VISA
program. The ultimate goal of the VISA II experiment is
to run a SASE FEL with the highest electron beam energytime chirp allowable by the modified beam transport at the
Accelerator Test Facility (ATF) in Brookhaven National
Laboratory (BNL), enabling the production and measurement of strongly chirped SASE FEL radiation [5].

Available online at http://www.JACoW.org

A brief review of some results from the VISA (Visibleto-Infrared SASE Amplification) FEL experiment willplace the recent measurements in context. In 2001,
VISA successfully demonstrated saturation of a SASE FEL
within a 4 meter undulator at 840 nm. [6]. An anomalous
electron bunch compression mechanism created beam conditions allowing high-gain lasing. The large negative second order longitudinal time dispersion, T566 [7], yielded alongitudinal compression and an increase in peak current
from 55 A to 240 A.
The nonlinear properties along the dispersive segmentof the ATF transport line were studied using a start-to-end
suite of simulation codes. The electron beam dynamics inthe gun and linac sections were modeled with PARMELA[8], the electron beam transport matrix calculations wereanalyzed with ELEGANT[9], and the FEL studies werecomputed with GENESIS 1.3[10]. The reproduction ofpulse energy, profile and angular distribution of the FEL
radiation, as well as the measurements of the bunch compression process and other aspects of the beam phase space,were significant achievements of the start-to-end simulations. The benchmarking of the code suite against the experimental results at the ATF of the beam production andtransport allowed reliance on the same modeling process toanalyze microscopic aspects of the most recent measurements.

Motivation for VISA II
Although the original bunch compression mechanism facilitated high-gain lasing, it restricted the management andmanipulation of the electron beam and its properties prior
to injection. The ultimate goal of the VISA II programis to inject a linearly chirped beam into the undulator to
produce frequency chirped output radiation. In the experiment, preservation of the electron beam chirp will beaccomplished by elimination of the nonlinear longitudinal
compression through the use of sextupole mangets at highhorizontal dispersion points in the dogleg transport [11].
The sextupoles, installed along the dispersive line, mitigate
second order effects, in particular diminishing T566 to anegligible value. The initial, nearly linear, electron beam

FEL Experimental Results

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G. Andonian et al. / Proceedings of the 2004 FEL Conference, 325-328

chirp applied at the linac, can then be preserved, and evenenhanced by a modest amount of linear compression duringtransport, before injection into the undulator.

1200

Intensity (AU)1000

EXPERIMENT DESCRIPTION

The VISA experimental schematic used in the present
experiments is discussed in detail in Ref. [6]. The postinjector 20o dogleg transport line that delivers beam to the
VISA undulator contains an adjustable collimator locatednear the begining of the dispersive line, the high energy
slit (HES). The measurements of beam size and transmitted
fraction at the HES are used to determine the beam energy
and energy spread at this point, which are important benchmarks for the simulations. The electron beam (500 pC) at
the HES is observed to have a 2.8 % energy spread due
to a correlation between energy and longitudinal position(chirp) after the linac exit. Approximately 330 pC propagates through the fully open HES, collimating the beam toa 1.7 % energy spread. Electron beam charge is measured
by a Faraday cups located after the gun exit and after theundulator exit. The compression process in the dispersive
section is monitored by a Golay cell, installed in front of
the undulator, which measures the coherent transition radiation (CTR) intensity emitted from an insertable metallic
foil. The CTR energy is peaked when the beam central
momentum is chosen to optimize the compression in thedogleg.
The measured FEL radiation displayed an unusual spectrum. The spectrum contained a characteristic double peakstructure with a full width bandwidth as high as 12 percent(Figure 1). An average SASE radiation energy of approximately 2 µJ was recorded; which is within an order ofmagnitude of the saturation energy of the initial VISA experiment. The dual spiked spectral structure indicates there
are 2 distinct lasing modes. The lasing FEL output radiation was also unusually stable in energy, a result of thecollimation at the HES, ensuring that the same energy portion of the beam was being transported on each shot. The
FEL output was far less sensitive to rf fluctuations and laser
and beam centroid jitter, as compared to earlier VISA runs.

THPOS56

600
400
200
0
820

840

860

880

900

920

940

960

Wavelength (nm)Figure 1: Sample shot of the ultra-wide bandwidth observed during the VISA IB runs (Ocean Optics USB2000
Spectrometer).

Simulations and Analysis
The PARMELA-ELEGANT components of the start-toend simulations reproduced the compression process as observed by the combined slit and Golay cell measurements.
The simulations show that the bunch peak current after
nonlinear compression can reach up to 300 A. This peak isvery short in duration (∼200 fs FWHM), containing only
25-30 pC of charge. Unlike the original VISA conditions,however, in the present experiment the compression was insensitive to injection phase fluctuations arising from either
RF or photocathode laser timing errors. This is due to the

137.0
136.5

p (me c)

Before the needed improvements in the linac to undulator transport were made, a set of measurements, performed without sextupole correction, took place at the existing facilities of the ATF. These measurements exploredthe use of a highly chirped pulse, with nonlinear longitudinal compression, and subsequent FEL amplification, asa stepping stone to VISA II. This transitional experimentdemonstrated a previously unobserved large bandwidth of
the FEL radiation of ∼ 12%, at high gain, accompanied
by an anomalously wide far-field angular radiation pattern.
We present these results below, as well as start-to-end simulations that reproduce some of the more striking aspectsof the radiation measurements.

800

136.0
135.5
135.0
134.5
134.0
0

2.0

4.0

6.0

t (ps)

8.0

10.0

Figure 2: Longitudinal phase space of a linearly chirped
electron beam at linac exit.
large energy spread in the initially chirped beam (Figure

327

G. Andonian et al. / Proceedings of the 2004 FEL Conference, 325-3282 ), which guarantees that a component of the beam will
be compressed, and thus have proper conditions for lasing,
because the laser injection and rf phase errors are muchsmaller than the initial bunch length of 10 ps. The electron beam, prior to injection into the undulator, displays ahighly nonlinear longitudinal phase space as a result of thesecond order dispersion effects of the transport line (Figure3). Because of these effects, the beam distribution at theundulator entrance also has a highly distorted distribution
in x − t configuration space. As seen in Fig.4, the highly
compressed lasing core of the beam lies off axis.

simulations showed that the FEL had reached near saturation, with gain comparable to that achieved in prior VISA
runs. Simulations also reproduced some key facets of theobserved spectrum, namely the large bandwidth and double spiked structure (Figure 5). Simulations also showedthat the slice-emittance degradation, due to the large energy spread, compression, and residual dispersion, was nota crucial concern. The overall beam quality, in particular the high current, was sufficient for stable, sustained,
high-gain lasing, close to saturation. The shorter wave-

40
35

136.5
Power Spectrum (A.U.)30

p (me c)

136.0
135.5
135.0
134.5
134.0

15
10

0
860

0

1.0

2.0

t (ps)

3.0

4.0

200
100

x (µm)

20

5

Figure 3: Longitudinal phase space of electron beam at undulator injection (Elegant Simulation).

0
-100
-200
-300

25

0

1.0

2.0

t (ps)

3.0

4.0

Figure 4: The time-position correlation of the electron
beam prior to undulator injection (Elegant simulation).
The GENESIS module of the start-to-end simulation
suite provided some insight into the basis of the observed
FEL spectrum. In terms of general system performance,

880

900

920

940

960

980

1000

wavelength (nm)Figure 5: Wide FEL bandwidth ( 10%) and ”double hump”
structure are numerically reproduced (GENESIS Simulation).

length spike in the spectrum of Fig. 1 is similar to thatobserved in VISA. The second, long wavelength spike isattributed to the amplification of a parasitic mode that is
excited when the beam is off-axis in the undulator. Measurements indicate that the beam is slightly mismatched incentroid and envelope to the undulator quadrupole focusing
lattice, which was incorporated into the simulations. Thismismatch caused the lasing core of the beam to undergo
betatron oscillations with as high as 300 µm secular amplitude. As seen in Figure 6, there is a strong correlation
between the maxima in this core offset and the maxima of
the observed spectral bandwidth. The relationship between
the off-axis betatron motion and the spectrum has a number of components to it. The additional transverse undulation of the lasing electrons’ trajectories due to the periodic
application of alternating gradient quadrupoles (strong focusing) causes the FEL resonant condition to change when
the beam core is off-axis. One may view this scenario asa bi-periodic undulator, with the long wavelength component of the trajectory due to the off-axis alternating, with nodrift in between, quadrupole forces, which have a squarewave “FD” form, yielding an effective undulator parameter of Kq = eB  ∆xLq /2πme c, where ∆x is the average
offset, B  is the quadrupole gradient, and Lq is the period

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G. Andonian et al. / Proceedings of the 2004 FEL Conference, 325-328

CONCLUSION
0.35

0.40

0.30

0.30

Bandwidth (%)

0.10
0.20
0.00
0.15
-0.10
0.10

-0.20

0.05

-0.30

Beam Centroid (mm)

0.20

0.25

-0.40

0.00
0

1

2

3

4

z (m)

Figure 6: Simulations show a strong correlation between
the beam centroid position and the FEL bandwidth (GENESIS Simulation).

of the quadrupole lattice. For the VISA parameters with∆x = 300µm, we have Kq  0.23. When one adds theeffects of this additional oscillation in the central trajectoryon the FEL resonance condition, the relationλu
λr = 22γ

K 2 + Kq2
+ (γθ)2
1+
2


(1)

is obtained, with the on-axis undulator parameter K =1.26. The maximum redshifting of the resonant wavelength
due to this effect in our experiment is predicted to be about
1.5 %. Another significant redshifting of the radiation isdue to radiation into off-axis angles. As in VISA, the farfield angular spectrum is hollow, and has a maximum at
an even larger angle of 2.1 mrad. For our present energies(γ = 137), the redshifting due to this effect is 4.1 %. Thisobviously important effect is also related to the off-axis
motion, as when the beam moves off-axis, it more readily
couples to higher order transverse modes having off-axis
peaks. The gain in these higher order modes utilizes thebunching attained at by the gain at shorter wavelength in
the near-axis lasing, and is therefore considered parasitic.
These two off-axis related effects produce nearly allof the observed redshifting in the long wavelength peak,which is about 5 % increased at its peak from the on-axis
peak. One may have expected that the redshifting arises
from the energy spread in the system. This is not so because the energy spread within the lasing core is quite
small. In fact, when the energy spread of the beam is set
to a near-zero value in the GENESIS simulations, leaving
all other aspects of the phase space unchanged, the SASE
output spectrum obtained is similar to that shown in Fig. 5.

THPOS56

The effects of bandwidth growth from off-axis radiation
would be deleterious in the VISA II experiment, where thegoal is to have the spread in measured frequencies be predominately due to time-correlated energy spread (chirp). In
the case of VISA II, the total energy spread is expected tobe 2 %, and thus the bandwidth due to this spread does notexceed 4 %. Thus the correction of second order distortions in the beam’s transverse and longitudinal dynamics,
through use of sextupoles, is mandatory, in order to avoid
the effects observed in the present experiments.
It may also be of interest to purposefully use the mechanisms for exciting very large bandwidth radiation in a
SASE FEL, for applications where spectral width is advantageous. This may be introduced at the end of a VISA-style
undulator by simply introducing a mis-steering of the beamover the last few gain lengths. The coupling to large-angle
radiation is limited, however, by the coherence angle of thesystem. In our case the lasing core of the beam was very
narrow in the horizontal dimension, σx  20µm, as seen in
Fig. 4, and the beam may radiate coherenty up to very large
angles, θ  2πσx λr . It is therefore easier to employ thismechanism for obtaining bandwidth increase with longer
wavelength FELs.

REFERENCES[1] M. Cornacchia et al., Linac Coherent Light Source Design
Study Report SLAC-R-521 (1998)[2] TESLA-FEL 2001-05, Deutsches Elektronen Synchrotron,
Hamburg, Germany (2001)[3] C. Pellegrini, J. Stohr, Nucl.
ods Phys. Res. A 500 (2003) 33

Instrum.

Meth-[4] C. Schroeder et al., J. Opt. Soc. Am. B 19 (2003) 1782
[5] J. B. Rosenzweig, presented at these proceedings[6] A. Murokh et al., Phys. Rev. E 67 (2003) 066501[7] K. Brown, A First-and Second-Order Matrix Theory for the
Design of Beam Transport Systems and Charged Particle
Spectrometers SLAC 75, (1972)[8] L. M. Young, J. H. Billen, LA-UR-96-1835 (Rev. 2000)[9] M. Borland, Advanced Photon Source LS-287 (2000)[10] S. Reiche, Nucl. Instrum. Methods Phys. Res. A 429 (1999)
243[11] J. England et al., Sextupoles Correction of the Longitudinal
Transport of Relativistic Beams in Dispersionless Translating Sections, Submitted for publication (2004)

329

T. Shaftan et al. / Proceedings of the 2004 FEL Conference, 329-332

PRELIMINARY MEASUREMENTS OF THE HIGH-GAIN FEL RADIATIONPROPERTIES ALONG THE RADIATOR
T. Shaftan*, H. Loos, B. Sheehy, L.H. Yu, NSLS, BNL, Upton, NY 11973, USA
Abstract
We present preliminary experimental results on
evolution of properties of the DUV FEL [1,2] radiation
along the radiator. Intercepting the electron beam at thedifferent locations inside the undulator we recorded andanalyzed transverse profiles, spectra and intensity of the
FEL output. Shot-to-shot fluctuations of the FEL radiation
may significantly affect the accuracy of measurement. In
the paper we present and discuss a single-shotmeasurement technique, based on a special imaging
system.

INTRODUCTION
Significant progress in understanding of high-gain
FEL physics has been achieved during past decades. Bothanalytic and simulation tools are developed and being
used for design of Self-Amplified Spontaneous Emission(SASE) [3,4] or High Gain Harmonic Generation(HGHG) [5,6] Free Electron Lasers. Start-to-end
simulations [7,8] model the entire beam line from thegeneration of the photoelectrons at the gun to the transportof the FEL radiation light to the user station. Because thebeam dynamics changes significantly along the beam line
a series of “expert” codes are used. There are few of FEL
simulation programs that calculate an FEL output forgiven initial shape and distribution of the electron bunch[9,10].
The code accuracy of prediction the FEL performanceis being verified experimentally. FEL radiation transverse
profile, spectrum, energy per pulse, etc. are important test
points for any FEL code. Usually, all of the radiation
parameters are measured and being compared with an
FEL simulation at the end of the undulator. However, oneof the key FEL parameters, gain length, is being measured
by detecting the radiation intensity at the discrete points
along the undulator.
There are several approaches for the gain length
measurement. One of them [11] relies on the special
optical system, transporting the FEL light from different
cross-sections of the undulator to a single detector.
Another approach [12] utilizes few detectors locatedalong the undulator. In both cases, inserting a mirror
deflects radiation to the detector and allows formeasurements of the radiation intensity at the mirror
location. Third approach is based on deflecting theelectron beam by the trajectory corrector [13]. In this casethe only portion of the undulator before the corrector
contributes to the radiation intensity measured at thedetector downstream of the undulator.
*

These measurements provide with a single parameter,that is, with radiation intensity distribution along theradiator. However, many more radiation parameters canbe obtained using similar experimental set-up. Measuringtransverse radiation distribution and spectrum along theradiator would present important data for comparison witha simulation. It is especially important for characterizationof special FEL regimes like seeding with ultra-short laser
pulse [17] or chirped bunch SASE or HGHG [18].
Spectral measurements of the SASE radiation
evolution have been performed at LEUTL FEL (APS)[14,15]. During this experiment SASE radiation spectra
were recorded at the different locations along the radiator.
The analysis for the first and second harmonics has shown
quantitative agreement with predictions of a simulation
code.
Another application of such a “complete”
characterization of the radiation properties along theradiator is in optimization of the FEL performance.
Measured data may be directly compared with theelectron beam parameters, such as emittance, trajectory or
beam size. Necessary optimization of the electron beam
parameters follows as a feedback.
In this paper we present initial results (a single dataset) of the characterization of HGHG radiation evolution
along the radiator.
The radiation spectrum, especially in SASE case issubject of fluctuation. Random set of SASE spikes fromshot to shot makes comparison with simulation to be adifficult task. If measurement takes significant time, thebeam parameters (for both SASE and HGHG) may drift
resulting in incomprehensive set of data. In the closing we
discuss a single-shot version of the spectral measurements
device.

EXPERIMENTThe experiment has been performed at the DUV FELat BNL [1,2]. The 800 nm laser radiation is used as a seedfor HGHG FEL. The radiator is tuned to the third
harmonic of the seed radiation (266 nm). In theexperiment we measured properties of the output at 266
nm.
The experimental set-up is shown in Fig. 1. The 10
meter long NISUS undulator serves as a radiator in
HGHG FEL magnetic system. The undulator is equippedwith variety of diagnostics and correction, including 16
four-wire correctors equally distributed along the whole
length. The diagnostics system at the experimental area
consists of photodiode, CCD camera and spectrometer.

_________________
Corresponding author: shaftan@bnl.gov

Available online at http://www.JACoW.org

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T. Shaftan et al. / Proceedings of the 2004 FEL Conference, 329-332

Fig. 1: Experimental set-up.

3.5
3Spot RMS size (mm)Using four-wire correctors we deflect the electron
beam at consecutive locations along the undulator axis.
We have chosen the kick strength to be sufficient forsteering the beam onto the vacuum chamber wall at
approximately 50 cm downstream of the corrector. Thus
the only radiation from the portion of NISUS preceded thecorrector has been recorded. In the following figures weplot the dependence of a parameter versus location ofdeflecting section along NISUS. The experimental set-up
was installed 7 meters away from the undulator.
The radiation intensity as a function of the distancealong the undulator (gain curve) is plotted in Fig. 2. The
measured HGHG power at the end of NISUS was
measured as 25 µJ.

2.5

.

2
1.5
1

0

2

4
6
8
Distance along NISUS(m)10

Fig. 4: Dependences of the HGHG spot size.
6

Centroid position (mm)

5
4
3
2
1
0

Fig. 2: HGHG gain curve.
Fig. 3 shows the images of the HGHG radiation
observed at different locations along NISUS.

Fig. 3: Transverse images of HGHG radiation
corresponding to beginning, middle and end of NISUS.
Dependence of the recorded transverse spot size on the
distance along NISUS is plotted in Fig. 3.
The next plot (Fig. 5) presents evolution of the spot
center versus distance along NISUS. This dependence
will be compared with electron beam trajectories in theradiator.

THPOS62

1

.

.
0

2

4
6
8
Distance along NISUS (m)10Fig. 5: Dependences of the center position of the HGHG
spot.
Next we discuss the spectral measurements. The
HGHG spectra are plotted in the next figure (Fig. 6). The
black line corresponds to the central wavelength of the
HGHG spectra. Average single-shot spectrum width isshown as blue error bars in red, averaged multi-shot widthis plotted as blue error bars. From the figure we canobserve that the central wavelength shifts byapproximately 0.15 nm at the end of NISUS. Assumingthese losses due to the radiated power we can estimate thepeak power in the HGHG pulse. It can be shown that thepeak power in MW is given by the following expression:

Pp =

mc 2
∆λ
∆λ
γI p
= 0.256 ⋅ γI p [ A]
λ
λ
2e

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T. Shaftan et al. / Proceedings of the 2004 FEL Conference, 329-332

267

0.15
Wavelength (nm)Substituting experimental parameters in thisexpression (γ=350, λ=266 nm, ∆λ=0.15 nm, Ip=400 A) we
get about 20 MW. Assuming HGHG pulse length of 1 ps
we calculate 20 µJ for the pulse energy, which is close to
the measured value.

0.1

0.05

.

Wavelength (nm)

0

0

2

4
6
Distance along NISUS (m)

8

10

266.5

Fig.7: RMS fluctuation of the HGHG single-shot
spectrum width.

266

SINGLE-SHOT METHOD OF SPECTRALMEASUREMENTS

265.5

.
265

0

2

4
6
8
Distance along NISUS (m)10Fig. 6: Evolution of the HGHG spectrum.
On the next figure (Fig. 7) we present RMS
fluctuation of the HGHG single-shot spectrum widthalong NISUS. As it follows from the plot, the RMS
fluctuation of the spectrum width is generally decreasing
towards the end of the undulator.

As we discussed in the Introduction, shot-to-shot
fluctuation of radiation, as well as, accelerator
performance stand technical problems for the accurate
measurements of the radiation properties. In Fig. 8 we
present a proposal for a single-shot spectral measurement
device.
Special optical system (sketched as a green lens in Fig.
8) focuses the radiation downstream of the radiator. Dueto the depth of image, the radiation from the beginning ofundulator is focused later after the lens, vice versa for theend of the undulator. Using auxiliary optics (not shown in
Fig. 8) and beam splitters one can split portions ofradiations emitted along different regions of the radiator.
Then these portions are recombined on the spectrometer
slit.

Fig. 8: Schematics of a single-shot measurements set-up.

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T. Shaftan et al. / Proceedings of the 2004 FEL Conference, 329-332

Using non-dispersive axis of spectrometer wemisalign different rays in order to see different spectral
patterns recorded at the different locations on the
spectrometer CCD. Thus, spectra of radiation fromseveral locations along the radiator can be observed.
We note that the only diverging part of emitted
radiation can be used in this set-up. The optical system
must block the radiation coming at small angles as it isgenerated along the whole radiator. Another issue is thelarge range of the radiation intensity from different partsof the radiator (~7 orders of magnitude). This problem canbe somewhat relieved by choosing an appropriate
transmission of the beam splitters. However in experiment
only last portion of the radiator might be effectively
measured. Also, another problem is in the optical guiding
effect [16] that will occur at the saturation. This will
modify the angular divergence of the radiation, which has
to be taken into account.
The study and optimization of the optical system for
DUV FEL is in progress. Preliminary design is based on
two-lens system with central and iris apertures.

ACKNOWLEDGEMENTS
We would like to thank S. Krinsky, J.B. Murphy and
J.M. Wang for useful discussions. The work was
performed under DOE contract DE-AC02-98CH10886.

THPOS62

REFERENCES[1] L.H. Yu, A. Douyran, L. Di Mauro, et al., Phys. Rev.
Lett. 91, No. 7, 074801-1, (2003).
[2] L. Di Mauro, A. Doyuran, E. Johnson, et al., Nucl.
Instrum. Methods Phys. Res. A A507, 15 (2003).
[3] SLAC Report No. SLAC-R-593, edited by J,
Galayda, 2002
[4] V. Ayvazyan et al., Phys. Rev. Lett. 88, 104802(2002).
[5] L.H. Yu et al., Phys. Rev. A 44, 8178 (1991)[6] I. Ben-Zvi et al., Nucl. Instrum. Methods Phys. Res.,
Sect. A 304, 181 (1991).
[7] M. Borland et al., Proc, of PAC 2001, p. 2707
[8] S. Reiche et al., Proc, of PAC 2001, p. 2751
[9] S.Biedron et al., Proc. of PAC 1999, p. 2486
[10] S.Reiche, Nucl. Instrum. Methods Phys. Res. A
A429, 243 (1999).
[11] A. Murokh et al., Proc. of PAC 1999, p. 2480
[12] A. Doyuran et al., Proc of EPAC 2002, p. 802[13] S. Reiche, Nucl. Instrum. Methods A445, p. 139(2000)[14] V. Sajaev and Z. Huang, Nucl. Instrum. Methods
A507, p. 154 (2003)[15] V. Sajaev et al., Nucl. Instrum. Methods A506, p.
304 (2003)[16] E. T. Scharlemann, A. M. Sessler and J. S. Wurtele,Phys. Rev. Lett. 54, 1925 (1985)[17] W. S. Graves, et al., Proc. of PAC 2003, p. 959[18] T. Shaftan et al., these proceedings

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P. Emma et al. / Proceedings of the 2004 FEL Conference, 333-338

ATTOSECOND X-RAY PULSES IN THE LCLS USING THE SLOTTED
FOIL METHOD ∗Abstract

P. Emma† , Z. Huang, SLAC, Stanford, CA 94309, USA
M. Borland, ANL, Argonne, IL 60439, USA

A proposal has been made to generate femtosecond andsub-femtosecond x-ray pulses in the Linac Coherent Light
Source (LCLS) SASE FEL [1] by using a slotted spoiler
foil located at the center of the second bunch compressor
chicane [2]. This previous study highlighted a simple case,using the nominal LCLS parameters, to produce a 2-fsec
FWHM, 8-keV x-ray pulse. The study also pointed out thepossibility of attaining sub-femtosecond pulses by somewhat modifying the LCLS compression parameters, but did
not undertake a full study for this more aggressive case. We
take the opportunity here to study this ‘attosecond’ case indetail, including a full tracking simulation, exploring thelimits of the technique.

INTRODUCTION
Within the community of synchrotron radiation users
there is a rapidly growing interest in the availability of
extremely short pulses as experimental probes in several fields of research, including structural studies of single biomolecules, x-ray diffraction from a single protein
molecule, and femtosecond chemistry. The interest in subfemtosecond (i.e., attosecond [as] = 10−18 sec) pulses
lies in the fact that electron transfer reaction dynamics
in atomic and molecular systems, providing information
about the most basic reaction mechanisms in chemistry, biology, and soft/condensed matter physics, are on the femtosecond and sub-femtosecond time scales (see e.g., [3]).
A previous study [2], based on the LCLS X-ray FEL,
described the production of a 2-fs FWHM (full-width at
half-maximum) long x-ray pulse generated by differentially spoiling the electron bunch by passing it through athin slotted foil within the second magnetic bunch compressor chicane (see Fig. 1).
The method relies upon the fact that in a magnetic
bunch-compressor chicane the beam is tilted at a large angle relative to the longitudinal axis t (or z ≈ ct) as shownin Fig. 1. At the point of maximum tilt (center of the chicane) a thin foil is placed in the path of the beam. The
foil has a vertically (y) oriented narrow slot at its center.
The Coulomb scattering of the electrons passing throughthe foil increases the horizontal and vertical emittance ofmost of the beam, but leaves a very thin unspoiled slice
where the beam passes through the slit. Spoiling the emittance of most of the beam by a factor of ∼5 will strongly
suppress the FEL gain for these sections, while the very
short unspoiled time-slice will produce an x-ray FEL pulse∗ This work is supported by the U.S. Department of Energy, contract
DE-AC02-76SF00515.
† Emma@SLAC.Stanford.edu

Available online at http://www.JACoW.org

x

a)
t

e−

y
y

b)
Coulomb
scatterede−unspoiled e −Coulomb
scattered2∆xx ∝ ∆E/E ∝ t

Figure 1: a) Sketch of electron bunch at center of magnetic
bunch-compressor chicane with tilted beam in horizontal,
x, and longitudinal coordinates, t. b) The slotted foil at
chicane center generates a narrow, unspoiled beam center.

much shorter than the full 200-fs FWHM electron bunch
length.
The previous study was based on the nominal LCLS machine parameters in order to highlight the compatibility ofthe technique with the baseline LCLS design. As briefly
described therein, the pulse length can be further reduced
by re-optimizing the operational machine parameters. We
describe here the limiting pulse length of the unspoiledelectrons and the necessary parameter adjustments to reachthe limit, highlighting a detailed study which can produce
a 400-as FWHM x-ray pulse duration using the LCLS design, but with a few changes to the operational configuration, such as an increased bunch compression factor anda reduced bunch charge, in order to avoid micro-bunching
instabilities.

NOMINAL ACCELERATORCONFIGURATIONElectron bunch length compression in the LCLS is accomplished in two stages. Each stage relies on an energychirped electron bunch passing through a magnetic chicane
with energy-dependent path length. The chirp, h, is theslope of the relative energy variation along the bunch length
coordinate, z0 , prior to the chicane, and is approximately

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P. Emma et al. / Proceedings of the 2004 FEL Conference, 333-338

100
pk

0

(A)

1

I

∆E/E0 (%)

334

50

−1
−400−200 0 200 400
z (µm)

0−400−200 0 200 400
z (µm)

Figure 2: Chirped bunch (left) at start (red) and center(blue) of chicane with initial energy-chirp (red slope) of:h ≈ 39 m−1 , and extremely narrow uncorrelated width.
The foil slot is indicated as dashed lines and the current
profiles are at right (100-pC case).

equal to the total rms relative energy spread divided by therms bunch length, as shown in Fig. 2 .
In the LCLS layout, the first bunch compressor chicane, BC1, is located at an energy of 250 MeV and nominally compresses the bunch length from 850 µm to 200µm rms, while the second compressor is located at 4.5
GeV and compresses from 200 µm to 20 µm rms. Theenergy-dependent path length coefficient, or momentum
compaction, of the BC2 is R56 ≈ −25 mm, which describes the path length change for a particle with relative
energy error: δ ≡ ∆E/E0 . The minus sign indicates that ahigh energy particle takes a shorter path, ∆z = R56 δ. The
larger momentum dispersion, smaller uncorrelated energy
spread, and smaller transverse beam size in the BC2 makethis location the best choice for producing the shortest duration unspoiled electron pulse.

UNSPOILED ELECTRON PULSELENGTHThe final unspoiled electron pulse duration is limited
by several effects. The time-sliced rms √horizontal betatron beam size at the foil (i.e., σxβ = β, where  isthe horizontal beam emittance and β is the horizontal betafunction at the foil) limits the width of the slit (see σx in
Fig. 3). The slit half-width, ∆x, should be larger than,or similar to, approximately
3-times the betatron beam size√(i.e., ∆x  3 β), otherwise the peak current will be cut,and the FEL gain of the spike will be reduced. Similarly,
the beam size in the slit has a contribution from the intrinsic (uncorrelated) rms relative energy spread (increased by∼ 2 due to half compression at the slit) times the chicane’s
dispersion at the foil (i.e., ∆x  6|η|σδ0 ), although thiscontribution to beam size is typically not significant. These
contributions determine the minimum slit width that will
not cut the peak current.
The minimum length of the unspoiled section of the electron bunch can be calculated in the following way, assuming ultra-relativistic electrons. The final bunch length coor-

TUBIS01

Figure 3: Energy-chirped (and therefore spatially-chirped)
electron bunch at center of chicane.

dinate (after the chicane), z, is expressed in terms of the initial bunch length coordinate (prior to the chicane), z0 , thechicane’s momentum compaction, R56 , the bunch energychirp prior to the chicane, h, and the initial uncorrelated
relative energy deviation of the particle, δ0 .
z = z0 + R56 (hz0 + δ0 ) = (1 + hR56 )z0 + R56 δ0 (1)Similarly, the transverse extent of the beam at the foil, x,
can be written in terms of the momentum dispersion at thefoil, η, the betatron component of the transverse coordinate,xβ , and the energy-chirp, h.
x = xβ + η(hz0 + δ0 )(2)Solving Eq. (1) for z0 and inserting this into Eq. (2) givesx = (1 + hR56 )xβ + hηz + ηδ0 .

(3)

From Fig. 3 the length of the unspoiled section of electrons
is a minimum when the slit width, ∆x, approaches zero
(temporarily ignoring the loss of peak current as describedabove). This is arranged by simply setting Eq. (3) to zero(with the slit at x = 0) and solving for z.
z=−(1 + hR56 )xβ
δ0
−
h
hη

(4)

Since xβ and δ0 are by definition uncorrelated, the rms
length of the unspoiled bunch, z 2 1/2 = σzu , for a zeroslit width, is then1  2 2η σδ0 + (1 + hR56 )2 σx2β ,
(5)
σzu =
|ηh|
where σδ0 is the initial rms uncorrelated relative√ energy
spread at the start of the chicane and σxβ = β is therms betatron beam size at the foil.
From Fig. 3 the contribution to this length from a finite
slit width is the rms of the nearly uniform x-distribution

335

P. Emma et al. / Proceedings of the 2004 FEL Conference, 333-338√
in the slit, ∆x/ 3, converted to the z-direction by 1/|ηh|,and added in quadrature to the betatron beam size term in
Eq. (5). Therefore, the FWHM duration of the unspoiled
portion of the electron bunch is given by
∆τ ≈

2.35
|ηh|c



2

η 2 σδ20 + (1 + hR56 ) [∆x2 /3 + β], (6)where c is the speed of light and 2.35 ≈ 2 2 ln(2).
Equation (6) shows that an increased energy-chirp value,|h|, provides a shorter unspoiled
pulse. It is also clear that√the betatron beam size, β, and the slit half-width, ∆x,
are both effectively compressed by the inverse of the bunch
compression factor: 1/C ≡ |1 + hR56 |  1. The uncorrelated energy spread term, ησδ0 , however, is not compressed
and typically sets the minimum length limit. This small energy spread is established in the electron gun where it has
been measured at about 3 keV rms [4], which agrees wellwith computer simulations. The 3-keV energy spread is
amplified linearly by the bunch compression factor of theBC1. In the case of the LCLS, it is increased by a factor of 4.5, to 13.5 keV, which at 4.54 GeV, prior to theBC2, is an extremely small rms relative energy spread ofσδ0 ≈ 3 × 10−6 .
This very small local energy spread can allow various
micro-bunching instabilities to develop in the linac [5] byproviding no effective Landau damping in the chicanes. In
fact, the LCLS design includes a beam heater system toincrease the local energy spread to 40 keV (prior to BC1compression) to Landau damp the micro-bunching instabilities. This increased energy spread, however, excludes
the possibility to generate sub-femtosecond pulses using
the slotted-spoiler foil, and leads to the 2-fs FWHM xray pulse discussed in reference [2]. For this reason, we
propose a greatly reduced bunch charge of 100 pC for thissub-femtosecond application (rather than 1 nC in [2]). This
reduced charge, and proportionally reduced peak current in
the linac sections leading to BC2, moderates the instability
and allows the preservation of this very small local energy
spread from the RF photo-injector gun, thus enabling subfemtosecond pulse generation with the foil.

ACCELERATOR PARAMETERS AND
ISSUESFor this low charge (100 pC), we assume a transverse
normalized emittance of γx,y ≈ 0.5 µm is possible (rather
than the nominal level of 1 µm at 1 nC); a level which
seems fairly conservative given the factor of ten charge reduction. In addition, the linac RF phases and voltage levels are necessarily adjusted to compensate for the reduced
longitudinal wakefields in the accelerating structures, but
in this example the initial bunch length is unchanged, theBC1 and BC2 chicane strengths are not altered, and thecompression factor of 4.5 in the BC1 is maintained. Because of the factor of 10 charge (and current) reduction
compared to the standard LCLS design, the microbunching

instability driven by longitudinal space charge and coherent synchrotron radiation without the beam heater (assuming only 3 keV initial uncorrelated rms energy spread) isvery mild. For example, for any initial beam modulation
wavelength λ > 50 µm, we estimate that ± 1% density
modulation at the end of the injector can cause no morethan 0.7 × 10−6 rms energy modulation at the BC2 entrance, which adds insignificantly to the intrinsic beam energy spread σδ0 ≈ 3 × 10−6 . Nevertheless, the temporal profile of the photocathode drive laser should be sufficiently smooth in order to not introduce any excessive beam
density modulation. A Gaussian laser profile instead of aflattop profile might be preferable for this attosecond x-ray
generation since only the emittance of the Gaussian coreneeds to be about 0.5 µm.
Table 1: LCLS BC2 chicane and beam parameters.
Parameter
symbol value
unit
bunch charge
Q
100
pC
chicane energy
E0
4.54
GeV
chicane dispersion
η363
mm
momentum compaction
R56−24.7 mmenergy chirp
h
39.0
1/m
rms initial E-spread
σδ0
3
10−6
beta at foil
β8.0m
normalized emittance
γ
0.5
µm
length of each bend
LB
0.50
m
angle of each bend
|θB |
1.98
deg
Table 1 lists the BC2 chicane and beam parameters used
to generate a sub-femtosecond x-ray pulse. Using these parameter values, Fig. 4 shows Eq. (6) plotted (blue) versus
the slit half-width, ∆x, along with an almost identical (red)curve from particle tracking. The dash-dot curve (green)
includes the local energy spread generated from incoherent
synchrotron radiation in the chicane dipoles (3.6 × 10−6
rms per 0.5-m long, 2-degree bend at 4.54 GeV), which is
not included in Eq. (6). The parameters in Table 1, and a
70-µm slit half-width (= ∆x), chosen to preserve at least
1.3 kA of peak current, will produce a FWHM unspoiledelectron pulse of 1.3 fs. This will be ‘gain-narrowed’ in the
FEL producing a FWHM x-ray pulse as short as 400 as,
while the spoiled beam has transverse emittance levels ofγx,y ≈ 6 µm and does not produce FEL radiation.

TRACKING SIMULATIONS
To test these parameters and better estimate the final xray pulse length, the entire LCLS is simulated with threeconsecutive particle tracking computer codes: Parmela [6],Elegant [7], and Genesis 1.3 [8]. The tracking includes
space-charge forces in the RF photo-cathode gun and lowenergy injector systems (Parmela), 2nd-order optics, wakefields, and coherent synchrotron radiation (CSR) in the
dipole magnets (Elegant), and time-dependent FEL exponential gain and saturation in the undulator (Genesis 1.3).

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P. Emma et al. / Proceedings of the 2004 FEL Conference, 333-338

2.5

6

−

I (kA)

4

1.5

pk

e ∆τ (fs)2

1

σt = 33.7 fs

0.5

2

0
−100

0.1

0.2 0.3∆x (mm)0.4

Figure 4: FWHM unspoiled e− bunch duration as a function of slit half-width, ∆x. The blue (solid) curve is Eq.
(6), the red (dashed) is from particle tracking, and the green(dash-dot) is tracking which includes synchrotron radiationin the dipoles.

Although the possibility of <0.5-µm emittance at 100 pC
was verified [9] with Parmela, for convenience, a 1-nC run
was used and each particle’s action was scaled to produce
a 0.5-µm core emittance.
As seen at the top plot in Fig. 5, the narrow section ofelectrons which pass through the slit produce a sharp spikeon the current profile after the BC2 chicane. This spike isthe result of electrons near the edge of the slit scattering in
the foil. The scattering generates a slightly different path
length for the electrons through the last half of the chicane
and causes a small time-smearing inside the bunch according to(7)∆σt ≈ |η|σθ /c,where σθ is the rms Coulomb scattering angle (22 µrad)
through a 50-µm thick Be foil. Some of the scattered electrons then overlap in time with the unspoiled time-slice,
raising the local peak current, and creating both an unspoiled core (the electrons that pass through the slit) anda spoiled halo (the time-smeared electrons from near theedge of the slit). The FEL process amplifies only the cold
beam core and is unaffected by the halo. This sharp spike,however, can potentially damage the bend-plane emittancethrough CSR effects, which is a further reason to choosea very low bunch charge of 100 pC. Calculations with aline-charge (1D) CSR model (50-nm bin size) indicate very
little emittance growth (<2%) in the unspoiled electrons
through all LCLS bend magnets beyond the foil, partially
due to the large tilted transverse beam size in the bends.
The Coulomb-scattered time smearing also keeps thepeak current of the full bunch below 1.5 kA (not including
the spike), limiting the possible CSR-induced beam brightness degradation from the full beam. Without this timesmearing, the peak current may approach 10 kA and thebeam may break up in the chicanes.
The Coulomb scattering in the foil is simulated in Elegant, which includes a model for very thin foils withTUBIS010t (fs)

50

100

0∆t (fs)12

1.5

Ipk (kA)

0
0

−50

1

∆τ =
1.3 fs

0.5

0
−2

−1

Figure 5: Current profile after BC2 (top) with spike created by e− passing through the slit, and unspoiled e− only(bottom) after BC2 with 1.3-fs FWHM and 1.3 kA.

thickness <10−3 of its radiation length [10]. The 50µm thick Beryllium foil is ∼10−4 of its radiation length(X0 ≈ 35 cm), and the angular distribution produced by
Elegant agrees well with theoretical calculations for verythin foils [11].
Finally, a model for the transition radiation wakefield[12] of the foil, but ignoring the slot, has been included inprevious simulations [2] at 1-nC of charge and was found tohave an insignificant effect on the unspoiled beam. In thiscase, at only 100-pC of total charge, the time-consuming
simulation of the wakefield is not included here.
The bottom plot in Fig. 5 shows only the unspoiled electrons after the chicane with a FWHM duration of 1.3 fs
and 1.3-kA of peak current with 1.8-pC of charge. The
emittance of these unspoiled electrons is γx,y ≈ 0.4 µm(smaller than 0.5 µm because they are taken from the coldcore of the Parmela-generated distributions). Their relativerms energy spread at 14.3 GeV is 6×10−5 , including the effects of CSR. It is also estimated, but not included in tracking, that the longitudinal space-charge forces in the 1100m of linac and transport lines beyond the BC2 chicane will
generate an additional rms energy spread of <10−4 within
this unspoiled electron section, which should increase the
FEL gain length by <5%. Similarly, the resistive-wall longitudinal wakefield in a 100-m long undulator with radius
2.5 mm and copper surface, produces an insignificant rms
energy spread of < 2 × 10−5 . The tracked particles, both
spoiled and unspoiled, are transferred to the FEL code Genesis 1.3 for a time-dependent FEL simulation.

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P. Emma et al. / Proceedings of the 2004 FEL Conference, 333-338

60
N (arb.)s ≈ 90 m

P (GW)

6

Ipk = 1.27 ± 0.07 kA

60
N (arb.)840
20s ≈ 80 m

4

0
1

2

40
20
0
0.8 1 1.2 1.4 1.6 1.8∆τ (fs)1.2
1.4
Ipk (kA)−2−1

0∆t (fs)12

3

N (arb.)60
0−3∆τ = 1.33 ± 0.13 fs〈∆t 〉 = 0 ± 0.104 ps
f

40
20

Figure 6: X-ray power profile at s ≈ 80 m (red-dash) ands ≈ 90 m (blue-solid) along the undulator, with 570-as (80m) and 380-as (90 m) FWHM spike duration at 5-7 GW.

0−0.4 −0.2

00.2〈∆t 〉 (ps)f

FEL SIMULATIONSThe FEL performance is simulated using Genesis 1.3 [8]with parameters as listed in Table 2. Only a time window ofabout 6 fs containing the unspoiled 1.3-fs electrons is usedin the simulation, since the spoiled electrons do not participate in the FEL interaction as shown in ref. [2]. The FEL
interaction with the unspoiled electrons saturates around 80
m, with the radiation pulse further narrowed from the unspoiled electron pulse due to the nonlinear interaction. The
x-ray power profile is shown in Fig. 6 at both 80 and 90
meters along the undulator. The pulse at 90 m has a 380-as
FWHM duration with 7-GW of peak power and ∼2×109
8-keV photons in this one spike.
Table 2: LCLS FEL Parameters.
Parameter
symbol value
electron energy
E0
14.3
radiation wavelength
λr
1.5
undulator parameterK
3.71
undulator period
λu3mean beta function
β
30

unit
GeV
Å
cm
m

STABILITY AND SYNCHRONIZATION
In a real operating machine, the beam energy, timing,and charge will vary from shot to shot, as will RF phases
and amplitudes of the various linac sections. If the beamenergy centroid changes prior to the BC2 chicane, the mean
horizontal beam position in the slot will also change. This
may affect the peak current and pulse width of the unspoiled electron pulse, as well as the final bunch arrival
time in the FEL undulator.
To estimate these levels, 1000 2D-tracking runs were
performed (ignoring transverse variations) to simulate an

Figure 7: Peak current (top-left), FWHM unspoiled e−pulse width (top-right), and bunch arrival time (bottomright) variation over 8-sec of LCLS operation at 120 Hz,
using rms machine jitter levels given in Table 3.

8-second span of LCLS operation at 120 Hz. Each beamor machine parameter in Table 3 is randomly varied in a
Gaussian distribution with rms value as listed (1 deg-S ≈1 ps). The RF phase and amplitude errors are applied independently to each of the 5 main linac sections (see ref.
[1], Ch. 7, pg. 7-28, Table 7.10). The tracking also includes the effects of charge-dependent longitudinal wakefields. The final unspoiled beam energy, arrival time, peakcurrent, and pulse width, are then recorded to estimate thestability of the unspoiled beam.
Table 3: Expected short-term machine jitter levels (rms).
Parameter
symbol value unit
Relative bunch charge∆Q/Q
2%
Drive laser-gun timing
∆tg
0.5
ps
RF phase of each linac
φRF
0.1
deg-S
RF amp. of each linac
∆V /V
0.1
%

The fixed slot position determines the energy of the unspoiled beam, after the chicane, to a very high degree,
but the peak current, arrival time, and pulse width vary as
shown in Fig. 7. Although the relative peak current andpulse width each vary by <10% rms, the final bunch arrival
time varies by 100 fs rms, which is quite large in comparison to the 400-as pulse width. This is one clear limitationof this method, where pump-probe experiments may haveto measure this timing variation in order to meaningfully‘time-bin’ the data collection. Longer term machine variations will be stabilized by beam feedback systems.

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REFERENCES[1] LCLS Conceptual Design Report, SLAC-R-593 (2002),
http://www-ssrl.slac.stanford.edu/lcls/cdr/.
[2] P. Emma et al., Femtosecond and Sub-Femtosecond X-ray
Pulses from a SASE-Based Free-Electron Laser, Phys. Rev.
Lett. 92:074801, (2004).
[3] R. Neutze et al., Nature 406 752-757 (2000); M. Drescher
et al., ibid. 419 803-807 (2002).
[4] M. Hüning and H. Schlarb, Measurement of the Beam Energy Spread in the TTF Photoinjector, Proc. of the 2003
Particle Acc. Conf., Portland, OR (IEEE, Piscataway, NJ,
2003).
[5] Z. Huang et al., Suppression of Microbunching Instability
in the Linac Coherent Light Source, Phys. Rev. ST Accel.
Beams 7:074401 (2004).
[6] J. Billen, PARMELA, Los Alamos National Laboratory Report LA-UR-96-1835 (1996).
[7] M. Borland, APS LS-287, Sep. 2000.
[8] S. Reiche et al., Nucl. Instrum. & Methods, A483 (2002)
70.
[9] C. Limborg, private communication, June 2004.
[10] M. Borland, ANL/APS, OAG-TN-2003-007, 2003.
[11] W.R. Leo, Techniques for Nuclear and Particle Physics Experiments, (Springer-Verlag, Berlin, 1994).
[12] K.L.F. Bane and G. Stupakov, Transition Radiation Wakefields for a Beam Passing through a Metallic Foil, SLACPUB-9726, June 2003.

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LARGE-SCALE TIMING DISTRIBUTION AND RF-SYNCHRONIZATIONFOR FEL FACILITIES
J. Kim*, F. Ö. Ilday, F. X. Kärtner, O. D. Mücke, M. H. Perrott, MIT, Cambridge, MA 02139, USA
W. S. Graves, D. E. Moncton, T. Zwart, MIT-Bates Linear Accelerator Center, Middleton, MA 01949, USA

Abstract
For future advances in accelerator physics in generaland seeding of free electron lasers (FELs) in particular,
precise synchronization between low-level RF-systems,
photo-injector laser, seed radiation as well as potential
probe lasers at the FEL output is required. In this paper,
we propose a modular system that is capable of achieving
synchronization of various RF- and optical sub-systems
with femtosecond precision over distance of several
hundreds meters. Typical synchronization methods basedon direct photo-detection are limited by detector
nonlinearities, which lead to amplitude-to-phaseconversion and introduce excess timing jitter. A new
synchronization scheme for extraction of low jitter RFsignals from optical pulse trains distributed by modelocked lasers is demonstrated. It is robust against photodetector nonlinearities. The scheme is based on a transferof timing information into an intensity imbalance between
the two output beams from a Sagnac-loop interferometer.
As a first experimental demonstration, sub-100 fs timing
jitter between the extracted 2-GHz RF-signal and the 100
MHz optical pulse train from a mode-locked Ti:sapphirelaser is demonstrated. Numerical simulations show thescaling to sub-femtosecond precision is possible. Together
with low-jitter mode-locked lasers and timing stabilized
fiber links, this scheme can be applied for large-scale
femtosecond timing distribution and synchronization of
RF- and optical sub-systems in accelerator and freeelectron laser facilities.

INTRODUCTION AND MOTIVATION
Seeding of free electron lasers operating in the EUV
and soft X-ray regime with radiation generated via highharmonics from noble gases may result in a fully coherent
X-ray laser. For seeding of such large-scale facilities
spanning over several hundreds meters, it is critical tosynchronize lasers and RF-systems with low (preferably
sub-femtosecond range) timing jitter in a long-term stablearrangement. Figure 1 shows the schematic outline oftiming distribution and synchronization for such a facility.
The pulse repetition rate of an optical master oscillator
implemented as a mode-locked laser is stabilized to afrequency standard or a low noise microwave oscillator.
The pulse train is distributed to all critical sub-systems byuse of timing stabilized fiber links, i.e., the pulse trains
leaving different fiber links are highly synchronous. The
RF- or optical sub-systems are then synchronized to thepulse trains at the fiber outputs.
* jungwon@mit.edu

Available online at http://www.JACoW.org

Figure 1: Schematic outline of timing distribution andsynchronization for FEL facility.
It has been shown recently that the extraction of a
microwave signal from an optical pulse train emitted by amode-locked laser using direct photo-detection is limited
in precision by excess phase noise [1]. The origin of thisexcess noise has been identified to be amplitude-to-phaseconversion in the photo-detection process, beam-pointing
variations, and pulse distortions by photo-detector
nonlinearities [1]. In addition to this excess phase noise
and timing jitter by photo-detector nonlinearities, thelong-term synchronization stability is limited by thetemperature dependence of semiconductor photodiodes.
Thus, a new synchronization scheme to avoid these
problems is highly desirable.
In the next section, a module for the synchronization
between RF-signal and optical pulse train from a modelocked laser is experimentally demonstrated and discussed
in detail. The same module can also be used for the
optical-to-optical synchronization between various lasers.
The required technical criteria for timing stabilized fiber
links and optical master oscillators are addressed in thelast sections.

RF-SYNCHRONIZATION
Outline of the Scheme
The general idea for suppression of excess noise due tothe photo-detection process is shown in Figure 2. Whilestill in the optical domain, the timing information istransferred into an intensity imbalance between two
beams by sending the pulse train through a pair ofamplitude modulators. The modulators are driven by theoutput signal from a voltage-controlled oscillator (VCO)with 180o phase difference. The intensity difference is
detected with a balanced detector and this signal controls
the input to the VCO via a loop filter. With this step, we
shift the problem of photo-detector nonlinearities on theelectronics side to the realization of amplitude modulatorswith drift-free bias points on the optical side. The 180o

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out-of-phase amplitude modulators can be realized by a
Mach-Zehnder interferometer with a phase modulator in
one arm. However, this scheme will suffer from the phasedrifts in the interferometer arms due to temperaturefluctuations, air currents, and mirror vibrations. To
remove these problems, the interferometer is implemented
in a Sagnac-loop configuration with a phase modulator
inside the loop.
Repetition
Rate: f R

ensures excellent noise performance. The loop filter
output signal drives the VCO and changes the driving
frequency of the phase modulator until it reaches a phaselocked state by balancing the two output powers from theinterferometer. This closes the phase-locked loop
operation. For a stable and drift-free biasing of theinterferometer, an effective quarter-wave plate is inserted
in one of the beams using a thin-film coating covering
only half of the substrate. A very stable and drift-freephase-locked operation is achieved with this scheme.

Phase Noise Measurement Set-up
Amplitude
Modulators~

Loop
Filter

RF: f = m f R
Recovered fromoptical pulse train

VCO

180o
Shift

Figure 2: General idea of synchronization scheme basedon a transfer of timing information into an intensity
imbalance in the optical domain.

Experiments
Figure 3 shows the synchronization scheme.
PLL Board
Loop
FilterBalanced
Detector~

Output 2

VCO(2 GHz)VCO(2 GHz)Optical Pulse
Train at 100 MHz

1

Rep rate
100 MHzThe phase noise of the RF-output signal from the VCO
is characterized in two ways: (i) by the frequency
discriminator technique using a commercial phase noise
measurement setup PN9000 from Aeroflex; (ii) by mixing
the output signal of the VCO in quadrature with the 2
GHz component of the directly detected pulse train inorder to measure the relative phase noise between the
optical pulse train and the extracted RF-signal. Figure 4
shows the measurement set-up. Using method (i), theinput is delayed and mixed with itself in quadrature to
extract the phase noise of the input [3]. Method (ii) is astandard technique to measure the residual phase noise
between two locked RF-signals [4] where an oscilloscopeis used to monitor that the two RF-signals are inquadrature, and a vector signal analyzer is used tomeasure the noise spectrum.

Interferometerand Phase-locked loop~

Output 1

1

800 nmBP filter

Oscilloscope

Phase Modulator

VectorSignalAnalyzer

2
DirectMeasurement

p /2 Phase
Shift Device

Figure 3: The synchronization scheme for extraction of a
2 GHz signal from a 100 MHz repetition rate Ti:sapphirelaser.
A 100 MHz repetition rate mode-locked Ti:sapphirelaser is used as the pulse source. After passing a bandpass
filter at 800 nm to limit the pulsewidth to about 100 fs, theinput optical pulse train is sent into the Sagnac-loop. A
resonant phase modulator at 2 GHz is positioned in the
Sagnac-loop in such a way that the optical delay between
counter-propagating pulses at the phase modulator is set
to half of the RF-signal period. This assures that the twopulses experience opposite phase modulation. The output
beams are detected by a balanced detector that generates adifference signal between the two photocurrents from thetwo Si pin-photodiodes. The output current from thebalanced detector is transferred to a passive loop filter(type II, order 2 topology [2]) for proper filtering. The
passive loop filter structure is advantageous over an active
counterpart since it allows a simple circuit and also

TUAOS03

Phase Noise
Test System

Phase
Shifter2

Ti:sapphire
ML-laser

(i)
(ii)

2 GHz
BP filter

RF AmpMixer

LP filter

Baseband
Amp

Figure 4: Phase noise measurement set-up: (i) frequency
discriminator technique using a commercial phase noise
instrument (PN9000, Aeroflex) and (ii) mixing the output
signal of VCO in quadrature with the same frequency
component of the directly detected pulse train.

Phase Noise Measurement Results
The measured single-sideband (SSB) phase noise
spectra from 1 Hz to 10 MHz are shown in Figure 5.
Curve (1) shows the phase noise spectrum of the freerunning VCO measured with the Aeroflex phase noise
measurement system. Curve (2) shows the phase noise
measured by the same method when the system is locked.
The locking is clearly visible in the spectrum covering therange of 100 kHz to 10 MHz. At lower frequencies, thephase noise of the free-running Ti:sapphire pulse train
dominates.

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J. Kim et al. / Proceedings of the 2004 FEL Conference, 339-342

detection [5,6] or using purely optical means [7] yet.
However, with improved system design, this method will
be able to reduce the relative jitter to the sub-femtosecond
range over the full Nyquist bandwidth in the near future.
For long-term stability, a fiber implementation of the
Sagnac loop is preferable. This will eliminate a large partof the drift problems in the low frequency range. In
addition, a lower-noise VCO combined with a higher
phase detector gain of phase-locked loop will dramaticallyreduce the phase noise of high frequency range.
Numerical simulations also show that scaling down to
sub-femtosecond timing jitter is possible with the
improved design.

OPTICAL-TO-OPTICALSYNCHRONIZATION
Figure 5: Single-sideband phase noise measurement
result: (1) free-running VCO and (2) locked VCO using
method (i); (3) measured phase noise between extracted
RF-signal and the 20th harmonic of directly detected pulse
train using method (ii); (4) noise floor of vector signal
analyzer; (5) estimated phase noise level of extracted RFsignal from result of curve (2).
In order to verify the assumption that the phase noiseof the laser dominates at low frequencies in the frequency
discriminator measurement results, we measured therelative phase noise between the pulse train and the RFsignal by using the second phase noise characterization
method. The result is shown in curve (3) of Fig. 5. Due tothe noise floor of the vector signal analyzer (curve (4) inFig. 5) and excess noise in the photo-detector thatgenerates the reference signal, the high frequency noise
floor is increased in comparison to method (i). But thismeasurement clearly shows that the noise increase at low
frequencies in curve (2) is the phase noise of the freerunning Ti:sapphire laser. This result suggests that bettershielding of the laser against environmental perturbations,higher pulse repetition rate as well as the use of a VCOwith lower phase noise, will lead to drastic improvementsin the timing jitter of the microwave signal extracted fromthe laser source.
Note that the origin of the enhanced phase fluctuations
below 1 kHz may be due to either mechanical vibrationsin the Sagnac-loop or excess phase noise in the photodetection process resulting from converted laser
amplitude fluctuations. These hypotheses will be further
investigated in the near future by building two RFsynchronization systems and beating the two outputs
against each other. Based on the current system andmeasurements, the relative timing jitter between the RFsignal and the pulse train integrated from 100 Hz to 10
MHz can be estimated by the area underneath curve (5),which lines up with the high frequency noise of the
Aeroflex measurement (curve (2) in Fig. 5) and results inabout 60 fs timing jitter.
The demonstrated timing jitter is not as low as using
pure microwave techniques based on high-speed photo-

Synchronization is necessary not only between opticaland RF-subsystems but also between different opticalsystems, for example, the photo-injector laser and themaster oscillator as shown in Fig. 1. Figure 6 shows how
the optical-to-RF synchronization technique can be used
to synchronize two pulsed lasers with each other. By useof the RF-synchronization module described in theprevious section, we first lock the RF signal to the pulse
train from one laser (ML-laser 1 in Fig. 6). This locked
RF-signal drives the phase modulator of another RFsynchronization module. However, instead of driving
VCO, the error signal from balanced detector drives thepiezoelectric transducer (PZT) to control the repetition
rate of the second laser (ML-laser 2 in Fig. 6). In this way,
an effective synchronization of multiple lasers is also
possible by locking lasers to the same RF signal
synchronized to one laser.

Figure 6: Possible optical-to-optical synchronization
scheme with the proposed RF-synchronization technique.

TIMING DISTRIBUTION
Precise transfer of RF-signals through fiber links has
been demonstrated recently [8,9]. For timing distribution
over a large-scale free electron laser facility, timing
stabilized fiber links will be used. If the fiber length is L,

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we assume that no length fluctuations are faster than(2nL)/c, where n is the refractive index of the fiber and cis the vacuum velocity of light. Relative fiber expansion
by temperature change is typically on the order of 10-7/K,
which can be compensated for by a fiber length control
loop as shown in Figure 7 by referencing the backreflected pulse from the fiber end with a later pulse fromthe mode-locked laser. This approach is applicable up to a
precision fundamentally limited by the high frequency
jitter of the laser from frequency of c/(2nL) up to the
Nyquist frequency, i.e., half of the repetition rate.
Therefore this jitter should be on the order of a few
femtoseconds or below if 10-fs overall jitter needs to beachieved. This puts a serious constraint on the highfrequency timing jitter of the optical master oscillator.

Figure 7: Timing stabilized fiber link.

OPTICAL MASTER OSCILLATOR –LOW-JITTER MODE-LOCKED LASERCurrently the most promising candidates for ultra-low
jitter optical master oscillators are Er/Yb-glass lasers [10],passively mode-locked Er-doped fiber lasers [11] and Ybdoped fiber lasers [12]. Particularly, Er/Yb-glass lasers
with sub-20 fs timing jitter have been demonstrated
recently [10]. The crucial performance indicator for sucha source is the phase noise or timing jitter integrated fromc/(2nL) to the Nyquist frequency. This jitter will set an
inherent limitation to the precision in timing achievablewith a given distribution system. Construction andevaluation of several of these lasers with respect to timing
jitter requirements are currently in progress.

CONCLUSION AND OUTLOOKIn summary, we introduce a scalable timing distribution
and synchronization scheme for future accelerator andseeded free electron laser facilities. We demonstrate amodular RF-synchronization scheme between laser andRF-subsystem which is robust against photodiodenonlinearities. This technique can also be used for opticalto-optical synchronization. Together with timing
stabilized fiber links driven by an ultra-low jitter modelocked laser, we anticipate large-scale timing distribution
and synchronization techniques with femtosecond
precision in the near future.

REFERENCES[1] E. N. Ivanov, S. A. Diddams and L. Hollberg, IEEE J.
Sel. Top. Quant. Elec. 9, 1059 (2003).

TUAOS03[2] M. H. Perrott, “PLL Design using the PLL Design
Assistant Program” (MIT High Speed Circuits andSystems Group, Cambridge, MA, 2002), http://wwwmtl.mit.edu/research/perrottgroup/tools.html.
[3] Aeroflex, “PN9000 Automated Phase Noise
Measurement System”, Application Note #2(Aeroflex, Plainview, NY, 2003).
[4] R. P. Scott, C. Langrock, B. H. Kolner, IEEE J. Sel.
Top. Quant. Elec. 7, 641 (2001).
[5] R. K. Shelton, S. M. Foreman, L.-S. Ma, J. L. Hall, H.
C. Kapteyn, M. M. Murnane, M. Notcutt, J. Ye, Opt.
Lett. 27, 312 (2002).
[6] A. Bartels, S. A. Diddams, T. M. Ramond, L.
Hollberg, Opt. Lett. 28, 663 (2003).
[7] T. R. Schibli, J. Kim, O. Kuzucu, J. T. Gopinath, S. N.
Tandon, G. S. Petrich, L. A. Kolodziejski, J. G.
Fujimoto, E. P. Ippen, F. X. Kaertner, Opt. Lett. 28,
947 (2003).
[8] J. Ye, J.-L. Peng, R. J. Jones, K. W. Holman, J. L.
Hall, D. J. Jones, S. A. Diddams, J. Kitching, S. Bize,
J. C. Bergquist, L. W. Hollberg, L. Robertsson, L.-S.
Ma, J. Opt. Soc. Am. B 20, 1459 (2003).
[9] K. W. Holman, D. J. Jones, D. D. Hudson, J. Ye, Opt.
Lett. 29, 1554 (2004).
[10] J. B. Schlager, B. E. Callicoatt, R. P. Mirin, N. A.
Sanford, D. J. Jones, J. Ye, Opt. Lett. 28, 2411 (2003).
[11] G. Lenz, K. Tamura, H. A. Haus, E. P. Ippen, Opt.
Lett. 20, 1289 (1995).
[12] F. Ö. Ilday, J. R. Buckley, H. Lim, F. W. Wise, W.
G. Clark, Opt. Lett. 28, 1365 (2003).

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HIGH TEMPORAL RESOLUTION, SINGLE-SHOT ELECTRONBUNCH-LENGTH MEASUREMENTS
G. Berden∗ , B. Redlich, A.F.G. van der Meer,
FOM Institute Rijnhuizen / FELIX, Nieuwegein, The Netherlands
S.P. Jamison† , A.M. MacLeod, W.A. Gillespie,
School of Computing and Advanced Technologies, University of Abertay Dundee, Dundee, UK
Abstract
A combination of electro-optic detection of the Coulomb
field of an electron bunch and single-shot cross-correlationof optical pulses, is used to provide single-shot measurements of the shape and length of sub-picosecond electron
bunches. This so-called temporal decoding technique has
been applied to the measurement of electron bunches at
the Free Electron Laser for Infrared eXperiments (FELIX),
where electric field profiles with a FWHM of 650 fs havebeen recorded. The measurement temporal resolution islimited primarily by the electro-optic crystal thickness andthe relatively low energy of the electrons (50 MeV), and thebunch length is estimated to be around 635 fs. The singleshot electron bunch longitudinal profile measurement isreal-time and non-destructive, and can therefore be used
as an online diagnostic tool. The temporal decoding technique has also been used to measure the electric field profiles of single far-infrared laser pulses from the FELIX freeelectron laser.

INTRODUCTION
X-ray free electron lasers (FELs) require dense, relativistic electron bunches with bunch lengths significantly
shorter than a picosecond. For operating and tuning theselasers, advanced electron bunch length monitors with subpicosecond temporal resolution are essential. Ideally, nondestructive and non-intrusive monitoring of a single electron bunch should be available in real-time. A promising candidate for such monitors is the determination of theelectron bunch longitudinal-profile via electro-optic (EO)
detection of the co-propagating Coulomb field, an area subject to on-going research and development at the Free Electron Laser for Infrared eXperiments (FELIX) [1-7] and atother laboratories [8-12].
With the EO detection technique, the Coulomb electricfield of the bunch induces birefringence in an EO crystal
placed adjacent to the beam. The birefringence is determined through ellipsometry using a synchronized ultrafast
Ti:sapphire (Ti:S) laser probe pulse. To enable a singleshot measurement, the Ti:S pulse is chirped to a duration
exceeding the measurement window, and the induced birefringence is determined as a function of time within the∗ berden@rijnh.nl† also at: University of Strathclyde, Glasgow, UK

Available online at http://www.JACoW.org

probe pulse. In previously reported experiments, the timing was inferred from the wavelength-time relationship ofthe chirped probe pulse [2]. However, this spectral decoding method is intrinsically subject to limitations on the time
resolution, and can introduce significant measurement artifacts [3, 13, 14, 15].
A recently demonstrated technique [5, 6, 13], which werefer to as temporal decoding, overcomes these limitations.
The envelope of the probe pulse is measured directly inthe time-domain, using single-shot second harmonic crosscorrelation. In this contribution we report temporal decoding measurements of the longitudinal electric field of single
electron bunches and of far-infrared FEL pulses.

ELECTRON BUNCH MEASUREMENTS
Measurements were performed on relativistic electron
bunches (250 pC, 50 MeV) that are produced in the linear
accelerator at the FELIX facility [16]. The electron bunch
profile is measured inside the accelerator beam pipe at theexit of the undulator of the short wavelength IR FEL.
The setup is depicted schematically in Fig. 1. A
near infrared laser pulse is obtained from a femtosecond
Ti:Sapphire amplifier (wavelength 800 nm, pulse energy
1 mJ, repetition rate 1 kHz, pulse length 30 fs) which isactively synchronized to the accelerator rf clock [17]. Thispulse is split into a probe pulse and a reference pulse. The
probe pulse is stretched to a length that is longer than thelength of the electron bunch. Subsequently, the probe pulse
is passed through an electro-optic crystal (ZnTe) that isplaced between two crossed polarizers. In this way, thebirefringence induced by the Coulomb field of a single
co-propagating electron bunch is translated into an intensity modulation of the probe pulse. The temporal profileof this intensity modulation, and thus the temporal profile of the electric field of the electron bunch, is measured with a sub-50 fs resolution in a single-shot crosscorrelator [13, 7] where the intensity modulated probe
pulse is cross-correlated with the 30 fs reference pulse. The
position dependent emission of the second harmonic lightfrom the BBO crystal is imaged onto an intensified CCD
camera.
Binning of the pixels of single-shot images along the direction perpendicular to the plane containing the probe andreference beams provides single-shot electron bunch mea-

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variabledelay
fs laser

CCD

ZnTe
opticalstretcher

BBO
P

P

electron bunch

Figure 1: Scheme for single-shot measurements of the electric field profile of individual electron bunches. The electricfield profile induces an intensity modulation onto a stretched optical pulse via the electro-optic effect. The electric field
profile of the electron bunch is obtained with the temporal decoding method where the intensity modulated probe pulse ismeasured by a single-shot cross-correlation with an ultra-short optical pulse. For the experiments discussed here, the pairof polarizers P are crossed, with minimum transmission in the absence of the electron bunch.
surements. The position of the pixels in the parallel direction is proportional to time.
Examples of single-shot measurements are shown in theleft hand panel of Fig. 2. As a result of the polarizer geometry used, the electro-optic signal scales quadratically withthe electric field strength as has been experimentally verified (see Ref. [7] for more details). The traces shown in
Fig. 2 correspond to electric field profiles with a FWHM of
650 to 700 fs, and have been recorded at the same settingsof the accelerator. From the figure it is clear that the time
jitter between the probe laser pulse and the electron bunch
is of the order of the width of the electron bunch.
The right hand panel of Fig. 2 shows the temporal jitterof 108 electron bunches; the rms value is 390 fs. At FE-

Arrival [ps]

1
0
-1
-2

0

20

40

60

80

100

Recurrence20

σ=0.39 ps

15
10
5
0

0

1
2
Time [ps]

3

-1.5

-1

-0.5

0
0.5
Time [ps]1

1.5

Figure 2: Left panel: a sequence of single shot electron
bunch measurements. Right panel: a graph (top) and a histogram of the relative arrival time of 108 electron bunches.
See text for further details.

TUAOS04

LIX, the timing jitter originates from the synchronisationof the probe laser pulses and the electron bunches to therf clock. The former is determined by the quality of theactive locking of the probe laser cavity round trip time to
the rf clock. The latter is mainly determined by phase fluctuations of the klystron feeding the accelerator. Previous
optical cross correlation measurements between 9 µm FEL
radiation and the Ti:Sapphire laser at 800 nm in a 100 µm
thick AgGaS2 crystal showed a jitter of 400 fs rms [17],a value similar to that presently obtained with the electron
bunch measurements.
For accelerators with a photo-injector, the laser which
triggers the photo-cathode can be used for electro-optic
detection of the electron bunches as well, which gives
a method to directly monitor the time jitter introducedby bunchers and accelerators. The electro-optic detection
method can also be used to produce accurate timing information (triggers) for user experiments.
The temporal resolution is determined by several factors. The increased duration of the Coulomb field at theprobe position, when compared to the electron bunch duration, leads to a temporal resolution of 2R/(γc) where R is
the radial distance between the electron beam and the optical probe in the electro-optical crystal [1]. For a 50 MeV
beam and a distance of 1.5 mm this temporal resolution is
100 fs. The thickness and the material of the crystal contribute to the temporal resolution as well [3, 4, 18]. For
a 0.5 mm ZnTe crystal, electric field Fourier components
with a frequency lower than 2.8 THz will be detected withminimal distortions. These contributions to the temporal
resolution are present for all current electro-optic detection
schemes. However, alternative EO materials, or deconvolution of material response in data analysis, both have potential for surpassing the material dependent limitations. An
analogous single-shot auto-correlation technique routinely

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G. Berden et al. / Proceedings of the 2004 FEL Conference, 343-346

variabledelay
fs laser

CCD

ZnTe
opticalstretcher

BBO
P

WP P
far-infrared light from FEL

Figure 3: Scheme for single-shot measurements of the electric field profile of individual FEL optical pulses. The electricfield profile induces an intensity modulation onto a stretched optical pulse via the electro-optic effect. The electric field
profile of the FEL pulse is obtained with the temporal decoding method where where the intensity modulated probe pulse
is measured by a single-shot cross-correlation with an ultra-short optical pulse. The polarizer (P) and quarter waveplate(WP) angles were varied according to specific experimental requirements.
characterises sub-50 fs optical pulses [19]. Ultimately, thetime resolution is determined by the length of the reference
optical pulse (30 fs).

drical lens had been positioned in the probe pulse path, justbefore the BBO crystal. In the horizontal direction, the position in the image is proportional to time. The time axis
can easily be calibrated since the duration of one cycle (oneFEL PULSE MEASUREMENTS
4000
3000

300

2000

250

1000
0

200

1000

100

200
300
horizontal pixel no.

400

4

5

x 10

430fs

4
CCD Row intensity

The output from a far-infrared FEL can be characterizedwith the electro-optic technique as well [20]. At a wavelength of 150 µm, a 20 ps long optical pulse consists of 40
optical cycles and is quasi-monochromatic. Since the timing jitter of the electron bunches (∼400 fs, see Fig. 2) is of
the same order of magnitude as the duration of one cycle ofthe far-infrared light, it is evident that one needs a singleshot detection technique to resolve the oscillating electricfield.
Figure 3 shows the scheme for single-shot electro-optic
detection with temporal decoding of the electric field of the
FEL pulse. The laser system, the optical stretcher, and thecross-correlator are identical to those used in the electron
bunch measurements. For the experiments described in thissection, FELIX produces light at a wavelength of 130 µm at
a macropulse repetition rate of 5 Hz. The micropulse repetition rate is 25 MHz, and the micropulse energy is about
1 µJ. The far-infrared laser beam and the 800 nm probe
pulse are overlapped in space with an ITO coated glass
plate acting as a far IR - optical dichroic mirror. Alternatively a gold coated mirror with a small hole for the probe
pulse may be used to combine the two beams. A parabolic
mirror with a focal length of 100 mm, not shown in theschematic diagram of Fig. 3, is used to focus the FEL pulse
and the probe pulse onto the ZnTe electro-optical crystal.
The second harmonic light (400 nm) emerging fromthe BBO crystal is imaged onto an intensified CCD camera. The upper panel of Fig. 4 shows an image obtainedby subtracting an image without the presence of an FEL
pulse (background) from an image where an FEL pulse waspresent. The image shows a horizontal line because a cylin-

3
2
1
0
-1

100

200
300
CCD pixel row

400

Figure 4: Electro-optic temporal decoding measurementof a quasi-monochromatic FEL pulse. The wavelength is
130 µm, and one cycle therefore corresponds to 430 fs. The
image has been obtained by subtracting an image without
the presence of an FEL pulse (background) from an image
where an FEL pulse was present. The graph has been obtained by vertically binning the image.

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G. Berden et al. / Proceedings of the 2004 FEL Conference, 343-346

oscillation of the electric field) is λ/c and the wavelengthis known from the online spectrometer. By binning the image along the vertical direction, the electric field profile isobtained and is shown in the lower panel of Fig. 4.
The independently determined oscillating time structureof the FEL pulse measurements makes it attractive to use
such FEL pulse measurements for the quantitative study ofthe capabilities of EO detection. At FELIX, we have used
this approach to undertake initial experiments into alternative EO materials that may have the potential for improved
time-resolution measurements. Furthermore, FEL measurements have been performed, outside the accelerator
vault and with free access, to pre-align the cross-correlator
and imaging setup before undertaking electron bunch measurements.

CONCLUSIONSElectro-optic sampling of the Coulomb field of the electron bunch is a promising method for real-time monitoringof the electron bunches. The method is non-intercepting
and non-destructive. It is largely non-intrusive, although it
is expected that the modification of the beamline and induced wakefields will slightly influence beam properties.
At FELIX we have measured femtosecond longitudinal
electron bunch profiles using the new temporal decoding
technique. The method has also been used to measure theelectric field profile of the optical far-infrared FEL pulse,which is a convenient way to calibrate and test the experimental capabilities of the technique.

REFERENCES[1] X. Yan, A.M. MacLeod, W.A. Gillespie, G.M.H. Knippels,
D. Oepts, A.F.G. van der Meer, and W. Seidel, Phys. Rev.
Lett. 85, 3404 (2000).
[2] I. Wilke, A.M. MacLeod, W.A. Gillespie, G. Berden,
G.M.H. Knippels, and A.F.G. van der Meer, Phys. Rev. Lett.
88, 124801 (2002).
[3] G. Berden, G.M.H. Knippels, D. Oepts, A.F.G. van derMeer, S.P. Jamison, A.M. MacLeod, W.A. Gillespie, J.L.
Shen, and I. Wilke, Proceedings of the 6th European workshop on beam diagnostics and instrumentation for particle
accelerators (DIPAC2003), Mainz, Germany, 2003, p. 20.
[4] G. Berden, G.M.H. Knippels, D. Oepts, A.F.G. van derMeer, S.P. Jamison, A.M. MacLeod, W.A. Gillespie, J.L.
Shen, and I. Wilke, Proceedings of the 2003 Particle Accelerator Conference (PAC2003), Portland (OR), 2003, p. 519.
[5] G. Berden, B. Redlich, A.F.G. van der Meer, S.P. Jamison,
A.M. MacLeod, and W.A. Gillespie, Proceedings of the 25th
International Free Electron Laser Conference, and the 10th
FEL Users Workshop (FEL2003), Tsukuba, Japan, 2003,
p. II-49.
[6] G. Berden, B. Redlich, A.F.G. van der Meer, S.P. Jamison, A.M. MacLeod, and W.A. Gillespie, Proceedingsof the ninth European Particle Accelerator Conference(EPAC2004), Lucerne, Switzerland, 2004.

TUAOS04[7] G. Berden, S.P. Jamison, A.M. MacLeod, W.A. Gillespie, B.
Redlich, and A.F.G. van der Meer, Phys. Rev. Lett. (2004),
in press.
[8] T. Tsang, V. Castillo, R. Larsen, D.M. Lazarus, D. Nikas,
C. Ozben, Y.K. Semertzidis, and T. Srinivasan-Rao, J. Appl.
Phys. 89, 4921 (2001).
[9] M.J. Fitch, A.C. Melissinos, P.L. Colestock, J.-P. Carneiro,
H.T. Edwards, and W.H. Hartung, Phys. Rev. Lett. 87,
034801 (2001).
[10] T. Srinivasan-Rao, M. Amin, V. Castillo, D.M. Lazarus, D.
Nikas, C. Ozben, Y.K. Semertzidis, A. Stillman, T. Tsang,and L. Kowalski, Phys. Rev. ST Accel. Beams 5, 042801(2002).
[11] L. Bentson, P. Bolton, E. Bong, P. Emma, J. Galayda, J.
Hastings, P. Krejcik, C. Rago, J. Rifkin, and C.M. Spencer,
Nucl. Instrum. Methods Phys. Res., Sect. A 507, 205 (2003).
[12] H. Loos, A. Doyuran, J.B. Murphy, J. Rose, T. Shaftan, B.
Sheehy, Y. Shen, J. Skaritka, X.J. Wang, Z. Wu, and L.H.
Yu, Proceedings of the 2003 Particle Accelerator Conference (PAC2003), Portland (OR), 2003, p. 2455.
[13] S.P. Jamison, J. Shen, A.M. MacLeod, W.A. Gillespie, D.A.
Jaroszynski, Opt. Lett. 28, 1710 (2003).
[14] J.R. Fletcher, Opt. Express, 10, 1425 (2002).
[15] S.P. Jamison, et al. (to be published).
[16] http://www.rijnh.nl/felix[17] G.M.H. Knippels, M.J. van de Pol, H.P.M. Pellemans,
P.C.M. Planken, and A.F.G. van der Meer, Opt. Lett. 23,
1754 (1998).
[18] G. Gallot, J. Zhang, R.W. McGowan, T.I. Jeon, D.
Grischkowsky, Appl. Phys. Lett. 74, 3450 (1999).
[19] F. Salin, P. Georges, G. Roger, and A. Brun, Appl. Opt. 26,4528 (1987).
[20] G.M.H. Knippels, X. Yan, A.M. MacLeod, W.A. Gillespie,
M. Yasumoto, D. Oepts, and A.F.G. van der Meer, Phys.
Rev. Lett. 83, 1578 (1999).

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F. Stephan et al. / Proceedings of the 2004 FEL Conference, 347-350

RECENT RESULTS AND PERSPECTIVES OF THE LOW EMITTANCE
PHOTO INJECTOR AT PITZ
F. Stephan#, K. Abrahamyan&, G. Asova§, J. Bähr, G. Dimitrov§, U. Gensch, H.-J. Grabosch,
J.H. Han, M. Krasilnikov, D. Lipka, V. Miltchev, A. Oppelt, B. Petrossyan, D. Pose, S. Riemann,
L. Staykov, DESY, 15738 Zeuthen, Germany
M.v. Hartrott, E. Jaeschke, D. Krämer, D. Richter, BESSY, 12489 Berlin, Germany
I. Bohnet, J.P. Carneiro, K. Flöttmann, S. Schreiber, DESY, 22603 Hamburg, Germany
J. Roßbach, Hamburg University, 22761 Hamburg, Germany
P. Michelato, L. Monaco, C. Pagani, D. Sertore, INFN Milano, 20090 Segrate, Italy
I. Tsakov, INRNE, 1784 Sofia, Bulgaria
W. Sandner, I. Will, Max-Born-Institute, 12489 Berlin, Germany
W. Ackermann, W.F.O. Müller, S. Schnepp, S. Setzer, T. Weiland, TU Darmstadt,
64289 Darmstadt, Germany
Abstract
The Photo Injector Test Facility at Zeuthen (PITZ) was
built to study the production of minimum transverse
emittance electron beams for Free Electron Lasers andfuture Linear Colliders. Until November 2003, theelectron beam from the rf gun has been fully
characterized at PITZ. For a bunch charge of 1 nC a
minimum normalized projected beam emittance of 1.5 π
mm mrad in the vertical plane and a minimum
geometrical average of both transverse planes of 1.7 π
mm mrad have been achieved. This fulfills therequirements of the VUV-FEL at DESY. In thiscontribution, an overview of the measured electron beamand high duty cycle rf parameters including transverse
emittance, thermal emittance, bunch length, momentum,
and momentum spread will be given. In addition, planned
major upgrades and first results towards fulfilling theeven more challenging requirements for the European
XFEL will be discussed. This includes measurementswith increased average and peak rf power and theimprovement of the transverse laser beam profile.

INTRODUCTION AND LAYOUT
The successful operation of short wavelength SASE
FELs requires electron sources providing high phasespace densities. For the case of the VUV-FEL at TTF2 in
Hamburg, a normalized transverse projected emittance atthe undulator entrance of about 3 π mm mrad at 1.5 kA
peak current is needed for saturation at about 30 nm and 2
π mm mrad at 2.5 kA peak current is needed forsaturation at 6 nm, in both cases assuming a rms energy
spread of 1 MeV [1]. For the XFEL, even moredemanding parameters are requested: for a charge of 1 nC
a projected normalized emittance of 1.4 π mm mrad isneeded at the undulator entrance which corresponds to an
emittance of about 0.9 π mm mrad at the injector exit [2,3]. For the development of such electron sources the PITZ

facility was built. After the decision to build the facility at
Zeuthen was taken in September 1999, the civil
construction happened in 2000 and in 2001 the necessary
hardware components were installed. In January 2002, thefirst photoelectrons were produced and the facility wascontinuously upgraded. In November 2003, the firstcavity installed at PITZ was fully characterized, fulfilling
the VUV-FEL parameter requirements. The experimental
results obtained with this cavity (called prototype #2
because it was the second rf gun cavity produced at
DESY) will be summarized in the first half of this paper.
Since January 2004 this cavity has been installed at the
VUV-FEL at TTF2 in Hamburg and went smoothly into
operation [4].
After moving the prototype #2 to Hamburg, the older
gun cavity prototype #1 was installed at PITZ. Although
we knew several shortcomings of this cavity beforehand(limited surface quality, problems with bulk coppermaterial, for more details see [5]), it is suited to study thehigh average power behavior of the rf gun. Those
measurements together with electron beam dynamics
studies will be summarized in the second half of thispaper. Beyond this, the R&D program necessary to reachthe XFEL requirements will be shortly described.
The experimental set-up used for the measurementswith gun prototypes #2 and #1 has essentially been
identical and is shown in Figure 1. It consists of a 1.5 cell
L-band rf gun with a Cs2Te photo-cathode, a solenoid
system for compensating space charge induced emittance
growth, a photo-cathode laser system capable ofgenerating long pulse trains with variable temporal andspatial micro pulse shape, and an extensive diagnostics
section.

___________________________________________#

frank.stephan@desy.deon leave from YERPHI, 375036 Yerevan, Armenia.
§
on leave from INRNE, 1784 Sofia, Bulgaria.
&

Available online at http://www.JACoW.org

Figure 1: Layout of PITZ.

FEL Technology

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F. Stephan et al. / Proceedings of the 2004 FEL Conference, 347-350

LASER PARAMETERS
The laser system operated at PITZ was developed at the
Max-Born-Institute (MBI) in Berlin. Its schematic layout
is shown in Figure 2. The system produces laser pulse
trains up to 800 µs length with a repetition rate of up to 5
Hz and a single pulse repetition rate of 1 MHz.
diode-pumped
Nd:YLF oscillator

Pulse shaper
diode-pumped
Nd:YLF preamplifier

AOM EOM AOM

fround trip = 27 MHz

Faraday
isolatorpulse
picker
1 MHz

Achieved RF Parameterspump
diodesEmicro = 16 µJ
Pburst = 16 W
pulse
pickerfast
current
control

flat-top pulses
fourthharm. Emicro = 30 µJ
Eburst = 24 mJ
UV (262 nm)

fastcurrent
control

pump
diodes

2-stage diode-pumped
Nd:YLF amplifier

tophotocathodeEmicro = 200 µJ
Pburst = 200 W

2-stage flashlamp-pumped
Nd:YLF booster amplifier

shot-to-shot
optimizer

Figure 2: Layout of the PITZ laser system.
The temporal and transverse properties of the individual
laser pulses on the photo-cathode play a major role inobtaining a good electron beam quality. Therefore, thoseparameters are regularly monitored using a streak camera
for the temporal laser profile and a CCD camera at a
position equivalent to the photo-cathode location (virtual
cathode) for the transverse laser shape. Typical
distributions for the optimized laser settings obtained
during the operation of gun cavity prototype #2 at PITZ
are shown in Figure 3. It is obvious that the transverse
profile is not the desired flat-top distribution but moreclose to a truncated Gaussian with some modulations.
Measured
Flat Top Fit

a.u.

120
100

b)

a)
1

80
60

0.5

40
20

FWHM ≈ 18-23 ps
rise/fall ≈ 5-7 ps

0
-20
0

10

20

30
40
t / ps

0
3

50

1

2

60

x,mm

2

1

Measured

a.u.

1

60
0.5

40
FWHM ≈ 19-24 ps
rise/fall ≈ 7-9 ps

0
-20

0

10

20

30
40
t / ps

50

60

1
2

x,mm 1y,mm

3Figure 4: Typical a) temporal and b) transverse laser
profile used for the operation of gun cavity prototype #1.
The temporal profile was measured at a wavelength of
262 nm. The transverse rms beam size on the cathode wasabout 0.58 mm in x and in y.

THBOC02Ex
Ey
SQRT(Ex*Ey)
sim.

2.8
2.6
2.4
2.2
2.0
1.8
1.6
1.4
1.2

3
2

0

After the entire beam diagnostics had been put intoreliable operation an experimental optimization procedure
was started [6]. During the parameter scans it turned outthat the mirror in the vacuum system, which deflects thelaser beam onto the photo-cathode, was affecting thebeam quality [6, 7]. After the beam was steered
horizontally around the vacuum mirror and a fineadjustment of the laser parameters was done (result isshown in Figure 3), a minimum normalized projected
emittance of 1.5 π mm mrad was obtained in the verticalplane and a minimum geometrical average of bothtransverse planes of 1.7 π mm mrad was achieved, see
Figure 5. Details of the emittance measurement procedure
are described in reference [8]. These results agree withsimulations, fulfill the requirements of the VUV-FEL, andwere confirmed several times in different weeks and bydifferent
shift
crews.
3.0

b)

80

20

Normalized Transverse Emittance

y,mm

a)

Flat Top Fit

100

A smooth conditioning procedure of the gun cavity
prototype #2 yielded an operation with rf pulses of up to
900 µs length, a repetition rate of 10 Hz, and a peak rf
power of about 3 MW. This corresponds to a duty cycle of
0.9 % and about 27 kW average power in the cavity.
Since the field strength on the cathode is 11% higher thanin the full cell for gun prototype #2, an accelerating
gradient of about 42 MV/m was obtained on the cathode.

3

Figure 3: Typical a) temporal and b) transverse laser
profile used for the operation of gun cavity prototype #2.
The temporal profile was measured at a wavelength of
524 nm. The transverse rms beam size on the cathode was
0.51 mm for x and 0.63 mm for y.
120

CHARACTERISATION OF THE RF GUN
FOR THE VUV-FEL AT TTF2

norm. emittance / π mm mrad

pump
diodesTo improve the transverse laser profile on the photocathode the laser beam transport line was re-designed andput into operation in June 2004. The laser parameters forthe beam dynamics measurements with the gun cavity
prototype #1 are shown in Figure 4. Now, the transverse
shape is close to a flat-top profile, but modulations arestill visible.

0

10

20

30

40

50

Ibuck, A

Figure 5: Projected normalized transverse emittance forgun cavity prototype #2 as a function of bucking solenoid
current which is used to compensate the magnetic field on
the photo-cathode. The rf phase is 5 degrees lower thanthe phase with maximum mean energy gain, the main

349

Momentum and Momentum Spread

5.4

160

5.2

140

5.0

120
100

4.8

80

4.6

60

4.4

40

4.2

20

4.0

pRMS / keV/cpmean / MeV/c

Using the dipole and screen 5 the momentum
distribution was measured [10]. The mean momentum andthe momentum spread are shown in Figure 6. The error
bars come from the uncertainties in the dipole field andthe mechanical alignment as well as from the non-zerobeam size and divergence at the dipole entrance. Goodagreement between measurement and simulation is
obtained.

0
10

20

30

40
50
φ / degree

60

70

Figure 6: Mean momentum (blue) and momentum spread(magenta) as a function of rf phase for gun cavity
prototype #2. The points are the measurements and theline represents the corresponding ASTRA simulation. The
emitted charge was tuned to be 1 nC for each of themeasurement points. The laser settings used correspond to
Figure 3.

Bunch Length
The electron bunch length was measured using silica
aerogel as Cherenkov radiator, an optical transmissionline, and a streak camera [10]. A minimum bunch lengthof 21ps FWHM was measured at the same phase where
the momentum spread is minimum. The minimum bunch
length is about 3 ps shorter than the emitting laser pulse
used at that time.

MEASUREMENTS WITH THE NEXT RF
GUN AT ZEUTHEN
Achieved RF Parameters
When the older cavity prototype #1 was installed at
PITZ in the beginning of 2004, the main goal was tocondition it up to the maximum rf power available fromthe 5 MW klystron installed [11]. The maximum peak
power was reached with about 4 MW in the gun cavity. A
maximum average power of 30 kW was obtained on July
8th (1000 µs, 10 Hz, 3 MW), limited by the available
water-cooling system. Its upgrade was already scheduledfor Dec. ‘04 to Feb. ‘05. Nevertheless, the cavity has been
operated stable with rf pulse lengths of up to 1300 µs andfull peak power at 5 Hz repetition rate, see Figure 7.

1.E+01
1.E+00
1.E-01
1.E-020

200 400 600 800 100 120 140 160
0000time (µs)

Figure 7: Forward power and reflected power from thegun cavity prototype #1 operated at 5 Hz.

Normalized Transverse EmittanceWith the increased rf input power and the improved
transverse laser profile the emittance has been remeasured [8]. The current status of optimization is shownin Figure 8. The main error contribution comes from thebackground subtraction. Although the optimization is stillin progress, the minimum emittance in one plane and theminimum geometrical average are about the same orslightly better than the year before. One obvious difference is that the emittances in x and y do not cross over fordifferent bucking coil currents anymore. This can be
explained by the difference in the transverse laser beamprofile (compare Fig. 3 and Fig. 4 and the laser beam
sizes on the cathode). Further optimization will include
measurements at different transverse laser spot sizes.
3.2
norm. emittance / π mm mradsolenoid current is 305 A, and the charge is 1 nC. The fatline shows an ASTRA simulation [9] of the geometrical
average using input parameters as described in theprevious sections.

rf power (MW)F. Stephan et al. / Proceedings of the 2004 FEL Conference, 347-350

Ex
Ey
SQRT(Ex*Ey)

2.8
2.4
2.0
1.6
1.2
0.8
0

3

6

9

12

15

18

21

24

27

30

Ibuck, A

Figure 8: Preliminary measurement of the projected
normalized transverse emittance for gun cavity prototype#1 as a function of bucking solenoid current. The rf phaseis 5 degrees lower than the phase with maximum meanenergy gain, the main solenoid current is 326 A, and thecharge is 1 nC.

Thermal Emittance
Measurements for estimating the thermal emittancefrom Cs2Te cathodes have been done with gun cavity
prototypes #2 and #1. Details are described in reference[8]. Average kinetic energies between 0.7 eV and 0.9 eV
have been obtained with different cathodes and different
measurement procedures. For a rms laser spot size on thecathode of 0.55 mm this corresponds to a thermal
emittance of about 0.6 π mm mrad.

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F. Stephan et al. / Proceedings of the 2004 FEL Conference, 347-350

Figure 10: Simplified schematic layout of the PITZ2 set-up. The beam goes from right to left.

Momentum and Momentum Spread

5.4

160
140
120
100
80
60
40
20
0

pmean / MeV/c

5.2
5
4.8
4.6
4.4
4.2
4
10

20

30

40
50
φ / degrees

60

pRMS / keV/cWith the increased rf power in gun cavity prototype #1,
the momentum distribution was re-measured. The mean
momentum and the momentum spread are shown in
Figure 9. The error sources are the same as mentioned
before. Compared to the operation with lower rf input
power, the minimum momentum spread is now reduced
by about a factor 2 and the phase difference between
minimum momentum spread and maximum mean
momentum is reduced to about 5 degrees.

70

Figure 9: Measured mean momentum (blue) andmomentum spread (magenta) as a function of rf phase forgun cavity prototype #1. The emitted charge was tuned tobe 1 nC for each of the measurement points. The usedlaser settings correspond to Figure 4.

R&D PROGRAM TOWARDS THE XFELREQUIREMENTS
To reach the very demanding requirements for the
XFEL mentioned in the introduction, a second phase of
PITZ was started (called PITZ2), which is a large
extension of the facility and its research program. The
work will go into two directions: a) further improve theemittance from the rf gun and b) study the principle forconserving small emittance up to higher beam energy. To
reach the required emittance from the rf gun theaccelerating gradient at the cathode needs to be increased
to ~ 60 MV/m, the rise and decay time in the temporallaser intensity profile of individual pulses has to be
reduced to ~ 2 ps, and the transverse laser profile must be
further improved. For studying the emittance conservation
principle, a booster cavity will be installed and the beamdiagnostics section will be upgraded (for details see [12]).
A schematic layout of PITZ2 is shown in Figure 10.

THBOC02

SUMMARY
The rf gun for the VUV-FEL at TTF2 was optimized at
PITZ. An overview on the results was presented, yielding
a minimum projected emittance in the vertical plane of
1.5 π mm mrad. Experimental results of the next rf gun
cavity installed at PITZ were summarized as well,demonstrating a reliable operation at increased peak andaverage rf power. Although the optimization procedure
for this cavity is not yet finished, very promising results
are already obtained. The future plans at PITZ werebriefly described.

REFERENCES[1] K. Flöttmann and Ph. Piot, “An Upgraded Injector
for the TTF FEL - User Facility”, EPAC’02, Paris,
June 2002.
[2] For a list of beam parameters of the XFEL linac see
http://xfel.desy.de/content/e159/e160/index_eng.html[3] Ph. Piot et. al., “Conceptual Design of the XFEL
Photoinjector”, TESLA FEL report 2001-03,
February 2001.
[4] S.
Schreiberforthe
VUV-FELgroup,“Commissioning of the VUV-FEL Injector at TTF”,
EPAC’04, Lucerne, July 2004.
[5] J.H. Han et. al., “Conditioning and High Power Testof the RF Guns at PITZ”, EPAC’04, Lucerne, July
2004.
[6] M. Krasilnikov et. al., “Optimizing the PITZ Electron
Source for the VUV-FEL”, EPAC’04, Lucerne, July
2004.
[7] S. Setzer et. al., “Influence of Beam Tube Obstacles
on the Emittance of the PITZ Photoinjector”,
EPAC’04, Lucerne, July 2004.
[8] V. Miltchev et. al., “Transverse Emittance
Measurements at the Photo Injector Test Facility at
DESY Zeuthen”, (TUPOS09, these proceedings).
[9] ASTRA manual, http://www.desy.de/~mpyflo/[10] D. Lipka, PhD thesis, Humboldt University Berlin,
May 2004.
[11] J. Bähr et. al., „High Power Conditioning and
Measurements of the Longitudinal Emittance at
PITZ“, (TUPOS03, these proceedings).
[12] A. Oppelt et. al., „The Photo Injector Test Facility at
DESY Zeuthen: Results of the First Phase“,
Linac’04, Lübeck, August 2004.

K. Togawa et al. / Proceedings of the 2004 FEL Conference, 351-354

351

EMITTANCE MEASUREMENT ON THE CEB6 ELECTRON GUN FOR THE
SPRING-8 COMPACT SASE SOURCE
K. Togawa*, T. Shintake, H. Baba, T. Inagaki, K. Onoe, T. Tanaka, SPring-8 / RIKEN Harima
Institute, Hyogo 679-5148, Japan
H. Matsumoto, High Energy Accelerator Research Organization (KEK), Ibaraki 305-5148, Japan
Abstract
A 500 kV pulsed electron gun has been developed forthe injector system of the X-ray FEL project at SPring-8.
A single-crystal CeB6 cathode is chosen as a thermionic
emitter, because of its excellent emission properties, i.e.,high resistance against contamination, uniform emission
density, and smooth surface. A gun voltage of -500 kV
was chosen as a compromise between the need forsuppressing emittance growth and reducing the risks ofhigh voltage arcing. We have succeeded in producing a
500 keV beam with 1 A peak current and 3 µsec width. A
normalized rms emittance of 1.1π mm.mrad has beenmeasured by means of double-slit method. In this paper,
we report on the result of the emittance measurement anddiscuss improvements for X-ray FEL.

Fig. 1 : A side view of the CeB6 electron gun with anemittance monitor bench.

THE CEB6 GUN

INTRODUCTION
In X-ray FEL theory, it is well known that the finestructure of the beam dominates the FEL gain. To achieve
the SASE-FEL in Angstrom wavelength region, the sliced
emittance of the beam should be very low and the peakcurrent should be of the order of kA. Moreover from theapplication point of view, the FEL machine should bestable for long periods of operation.
In the SASE-FEL, the electron beam generated by thegun is accelerated in the main linac, then it is directly
injected into the long undulator and generates the X-ray
beam there. Therefore, any electron bunch fluctuation intransverse position, timing, size, charge, etc., will directly
affect the X-ray lasing. This is markedly different fromthe storage ring type machine situation. As a result, thestability of the electron gun is essential for producing
stable X-ray FEL light.
We decided to use a pulsed high-voltage gun with asingle-crystal CeB6 thermionic cathode followed by abuncher system [1]. A side view of the CeB6 gun with anemittance monitor bench is shown in Fig. 1, and the beam
design parameters at the gun exit are summarized in Table
1 [2].
Table1 : The beam design parameters at the gun exit.
Beam energy
Peak current
Pulse width (FWHM)
Repetition rate
Normalized emittance (rms)_________________________________________* togawa@spring8.or.jp

Available online at http://www.JACoW.org

500 keV3A
1.6 µsec
60 Hz
0.4π mm.mrad

CeB6 CathodeThe normalized rms thermal emittance of electrons
emitted from a hot cathode is described byr2

ε n ,rms = c

k BT
,
mec 2

where rc is the cathode radius, kB is Boltzman's constant,and T is the cathode temperature. From the above relation,in order to obtain the small emittance less than
1π mm.mrad required for the X-ray FEL, the diameter ofthe cathode must be in the range of a few mm at thetemperature of 1000-1500°C. On the other hand, very
high emission density (~50 A/cm2) is required to produce
a several ampere peak current from the small surface.
Only the rare-earth hexaborides, such as LaB6 or CeB6
can emit such an intense current over long lifetimes. A
single crystal is preferable for obtaining low emittancebecause of its extremely flat surface (roughness ≤1 µm)
with low porosity after surface material evaporation [3].
The emission density is more uniform because the crystal
orientation is the same over the whole surface. In recent
years, single crystal CeB6 cathodes are widely used forelectron microscope and superior stability has been
demonstrated [4]. We decided to use a single-crystal CeB6
cathode with a [100] crystal face. The diameter of our
CeB6 cathode is 3 mm. 3 A peak current will be produced
when heated to ~1400°C. The theoretical thermal
emittance is 0.4π mm mrad.
Fig. 2 shows the CeB6 crystal, the cathode assembly
and the cathode being heated in the test chamber. The
CeB6 crystal is mounted in a graphite sleeve. This
produces a uniform electric field over the entire cathodeFEL Technology

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K. Togawa et al. / Proceedings of the 2004 FEL Conference, 351-354

cathode, all the high-voltage components,
namely, the ceramic insulator, pulse
transformer, dummy load, etc., are
immersed in insulating oil to eliminate
discharge problems.
Fig. 3 shows the waveform of the gun
voltage and beam current. The beam current
was measured by a current transformer(CT) located in the beam line right after thegun. The beam energy is 500 keV, and thepeak current is 1 A. The flat-top portion of
the pulse is about 0.8 µsec, which is
sufficient to generate a nsec bunch.

Fig. 2 : CeB6 cathode assembly.
surface. This is quite important for elimination of any
beam emission halo coming from the cathode edge, which
could cause damage to the undulator magnets.
We use a graphite heater rather than the conventional
metallic filament made of tungsten or the like. Graphite ismechanically and chemically stable even at very hightemperatures and does not evaporate like other metals.
Since its electrical resistance does not change much as afunction of temperature, it is easy to control the heater
power. The heater resistance is 0.18 Ω.
A tantalum cylinder covers the graphite heater to shield
the thermal radiation from its surface. A base plate for thecathode assembly is made of silicon nitride, which ismechanically strong even when thermal stresses areapplied.
The cathode was heated up to ~1400°C in the test
chamber by applying 210 W of heater power (see theupper right side of Fig. 2). A reference temperature wasmeasured from the graphite sleeve surrounding thecathode by means of a radiation monitor. We still needmore study in order to determine the cathode temperature
distribution precisely. Up to now, the cathode has been
operated for 4000 hours without failure.

Fig. 3 : Waveform of the gun voltage andbeam current.
The current-voltage characteristic of the CeB6 gun has
been measured for various cathode temperature (Fig. 4).
The gun is operated in temperature limited region. In thisregion, the beam current is dominated by Schottky effect( I ∝ exp( V ) ) rather than Child’s law ( I ∝ V 3 / 2 ), thatis, the slope of the current-voltage curve becomes gentle.
Therefore, it is expected that the beam intensity jitter
caused by the gun voltage jitter is suppressed.

High-voltage Gun
Basically, the gun high-voltage tank follows the design
conventional for a klystron tank. We use the same model
C-band klystron modulator [5] to feed a -24 kV pulsed
voltage to the gun high-voltage tank. The primary pulse is
stepped-up to a -500 kV by a pulse transformer, with aturn's ratio of 1:21. In order to match the impedance ofthe gun to the modulator PFN output circuit, a 1.9 kΩ
dummy load is connected in parallel with the cathode.
Since we need to apply a -500 kV pulse voltage to the

THBOC03

Fig. 4 : Current-voltage characteristic of the CeB6 gun.

EMITTANCE MEASUREMENT
Double-slits Method
We measured the beam emittance by the so-called
double-slits method (Fig. 5) [6]. The upstream slit cut out
a sheet shaped beamlet from the round beam, which

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K. Togawa et al. / Proceedings of the 2004 FEL Conference, 351-354

spreads after passing through the drift space due totransverse thermal motion and space charge. The
downstream slit measures the beamlet profile. Byscanning the both slits throughout the whole beam area,
the intensity profile in the phase space can be obtained.

reconstructed. Fig. 7 shows an example of the animation
screens of the phase space profile evolution.
Using a pair of vertical and horizontal slits, a timeresolved beam profile can be also measured by the same
method.

Fig. 7 : Time evolution of the phase space profile.

Experimental Result

Fig. 5 : Principle of emittance measurement.

We have measured the current density profile for the
500 keV beam with 1.0 A peak current. Fig. 8 shows the
3-dimensional plot of the current density profile. The
width for both the x- and y-slits was set to 0.5 mm × 0.5
mm and the scan step was 0.5 mm. It shows fairly flat top
shape as we expected from the cathode geometry.

We prepared four slits, two for horizontal (x-direction)scan and two for vertical (y-direction) scan. The upstream
x-slit are located at 50 cm downstream from the cathode,followed by a 60 cm drift space and the downstream slit.
The opening width must be narrow enough to ignore thebeamlet broadening due to space charge. Fig. 6 shows thebeamlet intensity profiles for several upstream slit width(25, 50, 100, 200 µm). The original beam energy andcurrent was 400 keV and 0.9 A, respectively. The
downstream slit width was set to 25 µm. Accuracy of thewidth and position is better than 10 µm. The profile
became Gaussian for the narrow width less than 100 µm,
as expected from the thermal spread. The beamlet
broadening due to space charge is ~15% of the thermal
spread at 50 µm width in the experimental condition.

Fig. 8 : Current density profile of the 500 keV, 1.0 A
beam.
Fig. 9 shows the 2-dimensional plot of the phase space
profile (x-direction) measured for the same beam
parameters. The width for both the upstream anddownstream slits was set to 50 µm and the scan step was
0.25 mm for the upstream slit and 0.1 mm for thedownstream slit. From the phase space profile, we
analysed the normalized rms emittance, defined as

ε n, rms = βγ < x 2 >< x' 2 > − < xx' > 2 ,2Fig. 6 : Beamlet profiles for different upstream slit width.
We found that the combination of a slit and a CT
monitor with a digital scope is a very powerful tool toanalyse the beam dynamics in time domain. The subbeamlet current waveform provides the information about
the time evolution of the phase space intensity at a certain
point. From about 1500 waveforms stored by the slit scan,
the time evolution of the phase space profile can bewhere <x >, <x’2> and <xx’2> denote mean square values
weighted by current. The result was 1.1π mm mrad. The
demonstrated beam parameters at gun exit aresummarized in Table 2
The measurement of the rms emittance was very
sensitive to the background noise. The noise signal of theCT monitor became a source of false emittance increase.
The noise level (3σ) was ~1% of the peak intensity. To
reduce the noise influence, we analysed the emittanceusing the signal, which was larger than that of the noiselevel, then corrected it to the expected value without noise.
In order to overcome this ambiguity, we will improve the

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K. Togawa et al. / Proceedings of the 2004 FEL Conference, 351-354

noise reduction and study the method of emittanceanalysis.

smaller than that of the electrons in the beam edge. As aresult, the phase space profile becomes S-shape after
travelling in the drift space. The concept of themechanism is shown in Fig. 10.

Fig. 9 : Phase space profile of the 500 keV, 1.0 A beam.
Table 2: Demonstrated beam parameters at gun exit.
Beam energy
Peak current
Pulse width (FWHM)
Repetition rate
Normalized emittance (rms)

500 keV
1A
3 µsec10 Hz
1.1π mm.mrad

IMPROVEMENTS FOR X-RAY FELBased on the experimental results, the following
improvements will be done for the real injector system:
1) Beam current: we need to increase the beam current
by a factor of 3 for operation. The current cathodeemission may not be activated well as possible. The
increase in cathode temperature to obtain a 3 A peakcurrent is estimated to be ~120°C.
2) Pulse width: the high-voltage pulse width turned out
to be two times longer than the design value. The fairly
big stray capacitance of the dummy load resistors no
doubt causes the pulse to be stretched out to this long
duration. As a result, the heat load that must be removed
from the high-voltage tank was higher than the design
expectation. The large size of the high-voltage tank is also
determined by the resistors. In order to shorten the pulse
width and to make the tank more compact, we are now
developing an electron tube dummy load, which will
replace the load resistors.
3) Emittance: we successfully achieved a very small
emittance, but even so, it was somewhat larger than thetheoretical predicted value. A small tail at the profile edge
is a source of the emittance increase. It may be generated
in the following mechanism. The electrons around thebeam edge diffuse to the outside of the beam by thetransverse thermal motion. In this region, radial electricfield generated by the space charge is not linear, that is, it
decreases in inverse proportion to radius. Therefore, thediverging angles of the diffusing electrons become

THBOC03

Fig. 10 : Mechanism of the emittance increase by thermal
diffusion and space charge force.
The emittance without this tail can be roughly
estimated by making the product of the rms diverging
angle at the beam centre (σx') and the rms beam radius(~r/2). The 0.6π mm.mrad value obtained is near thetheoretical thermal emittance. Since the nonlinear tailcomes from the edge region of the round beam, it could
be removed by using a beam collimator. We expect thatdoing that we should realize the required small emittanceof less than 1π mm.mrad.

REFERENCES[1] T. Shintake et al., "SPring-8 Compact SASE Source,
SPIE2001, San Diego, USA, June 2001
[2] K. Togawa et al., "CeB6 Electron Gun for the Soft Xray FEL Project at SPring-8", FEL2003, Tsukuba,
Japan, Sept. 2003, Nucl. Instr. Meth. A 528 (2004)
312[3] H. Kobayashi et al., Emittance Measurement for
High-Brightness Electron Guns, 1992 Linear
Accelerator Conference, Ottawa, Canada, August
1992[4] http://www.feibeamtech.com/[5] H. Matsumoto et al., "A Closed Compact Modulator
for 50 MW C-band (5712 MHz) Klystron" 25th
International Power Modulator Symposium and 2002
High Voltage Workshop, Hollywood, USA, 2002,
ISBN 0-7803-7540-8[6] K. Togawa et al., "Emittance Measurement on the
CeB6 Electron Gun for the SPring-8 Compact SASE
Source FEL Project", APAC2004, Gyeongju, Korea,
March 2004

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I. Ben-Zvi et al. / Proceedings of the 2004 FEL Conference, 355-358

AMPERE AVERAGE CURRENT PHOTOINJECTOR AND ENERGYRECOVERY LINAC*
I. Ben-Zvi#, A. Burrill, R. Calaga, P. Cameron, X. Chang, D. Gassner, H. Hahn, A. Hershcovitch,
H.C. Hseuh, P. Johnson, D. Kayran, J. Kewisch, R. Lambiase, V. Litvinenko, G. McIntyre, A.
Nicoletti, J. Rank, T. Roser, J. Scaduto, K. Smith, T. Srinivasan-Rao, K.-C. Wu, A. Zaltsman, Y.
Zhao, BNL, Upton, NY, USA
H. Bluem, A. Burger, M. Cole, A. Favale, D. Holmes, J. Rathke, T. Schultheiss, A. Todd, Advanced
Energy Systems, Medford, NY USA,
J. Delayen, W. Funk, L. Phillips, J. Preble, Thomas Jefferson National Accelerator Facility, Newport
News, VA USA
Abstract
High-power Free-Electron Lasers were made possibleby advances in superconducting linacs operated inenergy-recovery mode. In order to get to very high power
levels, say a fraction of a megawatt average power, manytechnological barriers are yet to be broken. We describe
work on CW, high-current and high-brightness electron
beams. This will include descriptions of asuperconductinglaser-photocathode RF gun employing a
new secondary-emission multiplying cathode and asuperconducting accelerator cavity, both capable ofproducing of the order of one ampere average current, as
well asand plans for an ERL based on these units.

INTRODUCTION
A frontier of very high power Free-Electron Lasers(FEL) is opening up. The Energy Recovery Linac (ERL)
based FEL at Jefferson Laboratory [1,2] demonstrated thepotential of ERL- based FELs to obtain kilowatts ofaverage power, with a record of 10 kW recently achievedin the JLAB ERL upgrade, operating with an average
current of the order of 10 mA and energy of the order of
100 MeV, or a beam power of the order of one megawatt.
However, much higher FEL powers are possible with theright technology; hundreds of kilowatts should bepossible. An ERL current of the order of one ampere isdesirable with reasonably good emittance, of the order ofa few microns normalized RMS. This level of highbrightness, high-power beam performance does not yet
exist. The purpose of this paper is to describe work
carried out at Brookhaven National Laboratory incollaboration with industry (Advanced Energy Systems,Inc.) and Jefferson Laboratory to push the frontier ofhigh-brightness ERLs. There are three main elements inthis effort:
1. Development of an electron source providing CW,
ampere-class electron beams with low emittance.
2. Development of an ampere-class linac structure
3. Demonstration of an ampere-class ERL.
We define ampere-class current refers to currents of
between a few hundred mA to one ampere____________________________________________*Work supported by the US Department of Energy and Office of Naval
Research.
#
ilan@bnl.gov

Available online at http://www.JACoW.org

micron-class emittance refers to normalized RMS
emittances of one to a few microns.
While beam optics and dynamics also play an importantrole in the systems under discussion, this paper will notcover these subjects for reasons of compactness.

AMPERE-CLASS CURRENT, MICRONCLASS EMITTANCE ELECTRON GUN
There are two aspects that must be considered in orderto obtain ampere-class currents and micron-classemittance in CW gun operation. First is the attainable RF
field needed for accelerating high-charge low–emittanceelectron bunches. Second is a cathode capable ofgenerating high charge electron bunches at the right
repetition rate. As we will se later, these aspects areclosely related.

The RF gun
A simple argument can be made to narrow down therange of technological possibilities for ampere-class,micron-class electron sources. Since the accelerator isnecessarily an RF linac at the frequency range of the orderof one giga-Hertz, (say from 0.7 GHz to 1.5 GHz), andthe electron bunches must occupy no more than a few
degrees of RF phase, the bunch-length in the linac must
be of the order of 10 picoseconds. A much longer bunch
would lead to distortions of the longitudinal phase-spacethat would be difficult to correct even with cavity
harmonics. The transverse emittance is also increased due
to time dependent RF forces. A much shorter bunch
would lead to increased wake fields and High-Order
Mode (HOM) power, as well as other potential problems
such as coherent synchrotron radiation (CSR). It is wellknown from the experience of developing and operating
electron guns with space-charge related emittance growth,that high electric fields are essential for obtaining a goodemittance at a reasonable bunch charge. High bunchcharge of the order of one or more nano-Coulomb withshort bunches of the order of a few pico-seconds to a few
tens of pico-second have been demonstrated only withphotocathode RF guns. At low duty factors it is possible
to achieve accelerating fields of a few tens to slightly over
100 megavolts per meter. Using these accelerating
gradients laser-photocathode RF guns achieved

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spectacular successes with sub-micron emittance at abunch charge of about half a nano-Coulomb [3], and a
few microns for bunch charges of one to a few nanoCoulomb. The problem is to combine high fields with
CW operation. The best performance to-date of nearly
CW RF gun (to be precise, 25% duty factor) has been
demonstrated with the Boeing photoinjector [4]. Los
Alamos and AES are developing a CW photoinjector [5].
It is clear that even with a large fraction of a megawatt
spent on maintaining the field in a copper cavity, the fieldis limited to under 10 MV/m.
Since it is clear that the ERL will be based on
Superconducting Radio Frequency (SRF) technology
based on considerations of efficiency and sheer size, it isnatural also to seek an SRF photoinjector. A SRF
photoinjector will convert all the input RF power (whichis to be on the order of one or two mega-Watts) into beam
power and permit an accelerating field significantly larger
than 10 MV/m. Why has this obvious solution beenplaying catch-up to other gun technologies? To understandthis we have to look into the cathode issue.
The Collider-Accelerator Department at Brookhaven
National Laboratory, in collaboration with Advanced
Energy Systems and Jefferson Laboratory, is developing a
superconducting gun that will accept a high-quantum
efficiency photocathode. As a first step we are testing a
1.3 GHz superconducting photoinjector that is used forphotocathode development. The initial development has
been done by using the niobium as the photocathode.
Following that we plan to install a high quantumefficiency cathode package and test it in the gun.
Following that, we are working on the development of a703.75 MHz half-cell gun with a demountable cathodeand couplers for megawatt power. The megawatt CW RF
power system, shielding and cryogenics are being
installed at BNL.
The performance requirements of this gun are:
1. A frequency of 703.75 MHz to match a RHIC
revolution harmonic and the ERL cryomodule frequency(see below)
2. Achieve coupling of 1 MW into the half-cell (withpossible upgrade to twice this power) using two opposed
input couplers
3. Deliver a current of 0.5 ampere (example: 1.42 nC at
351.87 MHz), requiring a high quantum efficiency
cathode insertion
4. Provide a high average accelerating field of about 20
MV/m.
Figure 1 shows the electric field lines of a half-cell gun
cavity with a cathode insertion using a double choke-joint.
This design allows the cathode itself to be at liquid
nitrogen temperature while the gun cavity is at liquid
helium temperature. The cathode stalk is slightly recessedto provide RF focusing for the emerging electrons. The
beam port is large to allow High-Order Modes (HOM) to
escape the cavity to be dumped by a ferrite beam-pipe
HOM absorber. Not shown are the input coupling ports,
which are a non-trivial part of the gun package, since the

THBOC04

amount of CW power required to accelerate the beam isextremely high.

Figure 1. Superfish simulation of a half-cell gun cavity
showing part of a choke-joint for the photocathode. The
cathode surface is slightly recessed to provide focusing of
the electrons.

The photocathode and laser
The photocathode is an enabling technology for thehigh-current accelerator system. The list of photocathodesthat can produce ampere-class average current is short tobegin with, and has much to do with laser technology.
Without going into details, one must understand thatmode-locked lasers operating in CW mode are limited to a
few tens of watts in the near IR or visible range of thespectrum, and take a huge penalty (in terms of the numberof photons per pulse) when converted to UV. Even a 30
watt average power visible laser is a complicated andexpensive device, costing over $0.5M. The higher
quantum efficiency photocathodes such as multi-alkaline
and cesiated gallium arsenide are short lived unlessprovided with an ultra-high vacuum, and have volatilematerials that are not compatible with superconducting
RF technology, since even minute quantities of a material
like cesium would lead to field emission andmultipactoring in a superconducting cavity by lowering
the work function of the niobium. An additional problem
with gallium arsenide is non-prompt emission of thephotoelectrons. There is a critical requirement for a
photocathode that will have the following properties:
1. It should be compatible with a superconducting gun,the only gun that can provide the high accelerating fields
to preserve emittance.
2. It should have high quantum efficiency to make thedrive laser reasonably feasible.
3. It should have long life, to provide a usable MTBF
(mean time between failures).
4. It should have prompt emission, to avoid blowup of
longitudinal and transverse phase-space.
5. It would be advantageous to have a sealed cathodecapsule that can be exposed to air yet not lose its otherproperties, to simplify servicing the photoinjector.
6. It would be also advantageous in some cases to havea low thermal emittance.
The last requirement, low thermal emittance, is
important only for very low bunch charge, much lower
than a nano-Coulomb, since at higher charge the357

I. Ben-Zvi et al. / Proceedings of the 2004 FEL Conference, 355-358

emittance is dominated by collective effects and nonlinearities.
Single stage photocathodes simply do not possess theseproperties. A solution to this problem was recently
proposed [6] and R&D on the system is in progress. The
basic concept is shown in Figure 2. The idea is to use
secondary emission to amplify by a large factor (between
one and two orders of magnitude) the emission from a
photocathode. A thin (of the order of 20 micrometers)
diamond window is positioned between a photocathode(taken to be cesium potassium antimonite in the figure)and the gun (not shown, above the capsule). The primaryelectrons are generated in the photocathode by the laser(shown coming in on the left), accelerated in the gap
between the photocathode and the diamond and strike thediamond with 5 to 10 KeV. The accelerating field isprovided by the gun cavity field that penetrates thediamond window. The primary electrons produce a large
shower of secondary electrons (up to 100 secondaries per
primary, depending on the primary energy). The
secondary electrons drift through the diamond,
thermalizing to a small fraction of an electron volt in theprocess and exit the diamond to the gun. A criticalelement here is endowing the diamond side facing the gun
with a negative electron affinity, by bonding hydrogen to
the diamond’s dangling bonds.

achieve ampere-class currents it is clear that a dedicateddesign must be done.
Higher order modes are one of the dominating factors
influencing the design of high current cavities. These
modes give rise to two limits on the performance andoperation of a cavity:• Multi-pass, multi-bunch instabilities driven by highimpedance dipole modes resulting in beam-breakup.
• Power loss into the HOMs which must be removed
safely from the cavity and the cryogenic system.
We designed a 5-cell linac cavity optimized for mostefficient removal of HOM power. The cavity has been
described in detail in various conferences [7,8]. The shapeof the cavity is shown in Figure 3.

Figure 3. The 5-cell ERL cavity copper model in its
tuner. Note the large iris and beam pipe diameters,
designed for removal of HOM power to ferrite absorbers.
The main performance measures of the cavity are given
in Table 1.
Table 1: Electric properties of the ERL 5-cell cavity

Figure 2. A schematic diagram of an encapsulated
diamond amplified photocathode. The diamond is coatedwith a very thin gold layer on the primary injection side,
the one facing the CsK2Sb photocathode.
Starting with the quantum efficiency of cesium
potassium antimonite, which is typically 5 to 10 percent
for visible photons, the effective quantum efficiency of
the amplified cathode is a few hundred percent. The
diamond window protects the superconductor from thecathode materials and the cathode from poisoning by
back-streaming contaminants. The emission is prompt andhas very low thermal energy. The diamond properties are
such that the heat generated by the various processes(mainly the primary energy deposition, RF heating of thegold and the heat generated by the transport of thesecondaries through the diamond) is conducted efficiently
to the walls with an insignificant temperature gradient. In
addition, the mechanical strength of the diamondpromises that the capsule may hold atmospheric pressure
for transporting the evacuated photocathode.

AMPERE-CLASS ERLSUPERCONDUCTING CAVITY
ERLs need a specially designed cavity for best
performance. Until now, cavities used in ERLs have beendeveloped as a non-energy-recovering linac structures. To

Property

Units

Value

Frequency

MHz703.75

Ep/Ea

-

2.0

Hp/Ea

mT/(MV/m)

5.8

R/Q

Ω

807

Geometrical factorΩ

225

Cell-to-cell coupling%

3

Expected unloaded Q-

2x1010

Dynamic power loss

Watt

22

External Q

-

2x107

Max. amplifier powerkW

50

1 Mechanical resonanceHz

96

Lorentz detuning

Hz/(MV/m)2

1.5

Loss factor

V/pC

1.2

st

Ep/a is the peak surface electric field to accelerating
field ratio; Hp/Ea is the peak surface magnetic field toaccelerating field ratio; R/Q is the shunt impedance
normalized to the Q. The number given for the expected

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Q is assuming a total surface resistance of 10 nΩ. The
dynamic power loss assumes this surface resistance and afield of 20 MV/m (or 20 MV acceleration, given that thelength is 1 meter). Non-linear Q droop at this field may
make this figure worse, however the Tesla experience
shows that at this field the droop may be negligible.
The assembled cryomodule is shown in Figure 4.
The cavity has been extensively simulated using the
MAFIA FEA code and the results were reported
elsewhere [7,8]. The simulations show that the HOMs arevery effectively damped, leading to loaded Q of the
HOMs that range from 102 to a few times 103 in the worst
case. No trapped modes were found. Using the calculated
values of the Q and R/Q of the HOMs, we used the
TDBBU code to estimate the beam breakup (BBU)
threshold current for a 4 cavity ERL and found a BBU
threshold of about 1.5 (+/-0.2) amperes based on a
Gaussian distribution of 3 (+/- 2) MHz of the HOMs.
Using the ABCI code we find that the longitudinal loss
factor of the cavity is 1.2 volts per pico-Coulomb (just thebare cavity, not including other beam line elements suchas ferrites, valves etc.). This is an excellent value, about afactor of 6 or more lower than the TESLA cavity. We canconclude that we have designed a cavity that has a very
high BBU threshold current and which generated
significantly less HOM power than previous linac
cavities, making it ideal for ampere-class ERL service.

Figure 4. The cryomodule assembly configuration.

AMPERE-CLASS ERL
The only way to prove the performance of thephotoinjector and linac cavity as a platform to produce
high-brightness, ampere-class CW current is to use themin an energy recovery linac. For this purpose we aremoving forward with the construction of such anaccelerator. The superconducting gun described in section
2 will be combined with the accelerating structure
described in section 3 to form an energy recovery linac. A
schematic layout of this ERL is shown in Figure 5.
The return loop of the prototype ERL includes allnecessary controls for studying the electron beam
dynamics in ERLs: the arcs are achromatic with tunablelongitudinal dispersion (R56) and the lattice provides forfull control of the phase advances and the optics in both x
and y directions.

THBOC04

Figure 5. Schematic layout of the ERL-prototype based on
5-cell SRF linac. Details of the gun and dump beam optics
and high-energy beam separation are left out.
The circumference of the entire ERL loop will be about
20 meters and will be determined after the final latticedesign is frozen. It is important that the time of flight ofelectron from the exit of the SRF cavity till its entrance
must be equal to an exact integer number and a half of RF
cycles – this insures that after passing through the recirculating loop the accelerated beam returns in the
decelerating field with exactly same amplitude (but with
opposite sign).
Each arc has an achromatic lattice, which comprises ofthree bending magnets and up to six quadrupoles (thenumber of quadrupoles is to be finalized later). This
structure provides adjustable longitudinal dispersion (socalled R56, where R is the transport matrix of the system)
while remaining achromatic. A preliminary simulationshows that β and D functions can be kept under 5 and 0.6m, respectively.
The straight section will have from six to twelve
quadrupoles, which will provide for complete control ofthe elements of the one turn matrix, including theelements R12 and R34, which will determine threshold of
the transverse beam break-up instability.

REFERENCES[1] G. R. Neil et al., Phys. Rev. Lett., 84 (4), 662 (2000)[2] G. R. Neil, Proceeding of this conference.
[3] V. Yakimenko, et al., Nucl. Instr. and Meth. A483,
277 (2002)[4] D. H. Dowell et al., Appl. Phys. Lett. 63 (15), 2035
(1993)[5] H. P Bluem, et al., MOPLT156, Proc. EPAC’04, 5-9
July 2004, Lucerne, Switzerland.
[6] I. Ben-Zvi et al., Accelerator Physics Note CA/AP/149, BNL April 2004.
[7] R. Calaga et al., Proc. 11th Workshop on RF
Superconductivity, 8-12 September 2003 Lubek,
Germany.
[8] R. Calaga et al., Proc. EPAC’04, 5-9 July 2004,
Lucerne, Switzerland.

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D. Janssen et al. / Proceedings of the 2004 FEL Conference, 359-362

STATUS OF THE 3 ½ CELL ROSSENDORF SUPERCONDUCTING RF GUN
D. Janssen#, H. Büttig, P. Evtushenko, U. Lehnert, P. Michel, Ch. Schneider, J. Stephan, J. Teichert,
Forschungszentrum Rossendorf, Dresden, Germany
V. Volkov, S. Kruchkov, O. Myskin, BINP SB RAS, Novosibirsk, Russia
Abstract

The status of the Rossendorf superconducting RF gun
is discussed. This gun allows continuous wave operation
with an energy of 9.5 MeV and an average current of
1mA. The 3½ cell niobium cavity contains a normal
conducting photocathode. A special choke flange filter at
the cathode side prevent the RF leakage of the cavity. The
design of the cavity, the tuner, the RF coupler the LHevessel together with the cryostat is finished and now inmanufacturing. In the paper three features are discussed,
which follows from the special demands of the 3½ cellsuperconducting RF gun. The first feature is the tuning
system. For the cavity two different tuners are necessary,
one for the half cell (gun cell) and one for the accelerating
cells. The second feature is the tuning of the cathode. The
beam properties depend very sensitive on the cathodeposition. Therefore a special cathode tuner has beendeveloped, which allows to move and to adjust thecathode position inside the cavity. The third no
conventional feature is the excitation of a second RF
mode inside the cavity. This is a magnetic mode (TEmode) which replaces the static magnetic field in normal
conducting RF guns and decreases the transverse
emittance of the beam by more than a factor of two.

INTRODUCTION
The success of many evolving future accelerator
applications is contingent upon the development of an
appropriate source to generate the electrons.
Today photo cathode RF guns are the most advanced
type of electron injectors. They are able to produce highpeak currents and low emittances, which is necessary for
FEL application. However their low duty factor can limit
the performance of superconducting accelerators. Efforts
are under way to increase the duty factor of RF guns forthe price of cooling problems, high demands on klystronpower and low power conversion efficiency. The moreelegant way is to combine the high brightness of RF gunswith the low RF losses of superconducting technology.
Superconducting RF (SRF) photo injectors offer great
promise for cw mode operation with high average
current. At present four groups are working on SRF photo
injector projects. There are the Peking University [1],Advanced Energy Systems (AES) [2], Brookhaven
National Laboratory (BNL) [3] and Forschungszentrum
Rossendorf (FZR) [4]. In 2002, the successful operationof a SRF injector with a half cell cavity was demonstrated
at FZR for the first time [4].
The design and treatment of superconducting cavities
with there specific geometry, the much more complex
tuning system and the RF choke flange filter causes
additional difficulties and requires new technical solution.
#janssen@fz-rossendorf.de

Available online at http://www.JACoW.org

These new technical solutions enter in the design of a
new injector in Rossendorf, working with a 3 ½ cellsuperconducting cavity. The first overview about thedesign of this injector has been represented in [5]. In thesec. 2 and 3 we will discuss some new developments.
A disadvantage of the superconducting technology is its
sensitivity to external magnetic fields. It is not possible toapply a static magnetic field of the required strength foremittance compensation as described in the case of
normal conducting RF guns. In [6] it has been shown, thatthe focussing by the static field can be replaced by RF
focussing, which is applicable also in the case of
superconducting RF guns. The RF focusing is achievedby pulling the cathode backward, somewhat behind theback plane of the cavity. After extensive beam dynamic
calculations for different bunch charges this concept is
integrated into the gun design of the new 3 ½ cell
Rossendorf injector.
A new idea to compensate the emittance growth in the
RF gun is to apply a magnetic RF field, which is aneigenmode of the cavity. This mode can be excited
together with the accelerating RF field in the
superconducting cavity. First results concerning magnetic
modes in superconducting cavities are published in [7].
The excitation of magnetic modes in the Rossendorf 3 ½
cell gun cavity and the influence of these modes on the
beam dynamics is described in sec. 3 together with firstexperimental results.

DESIGN, FIELD AND BEAM
PARAMETERS OF THE NEW
ROSSENDORF GUN
The superconducting cavity inside the He vessel isshown in Fig. 1. A choke filter, which prevent the leakageof RF power is connected with the gun cell by a small
superconducting tube. This tube contains the cathode,which is isolated by a vacuum gap of 1mm from thesurrounding cavity. The cathode is cooled down to LN2
temperature and exchangeable. The length of the gun cellis small in comparison to the following TESLA like cells.
This has the advantage, that the optimal phase angle forthe start of the electron bunch is near 90° where theelectric RF field has its maximum. In contrast to the
TESLA cavities the two HOM coupler the main coupler
and the pic-up probe are arranged in a single planeoutside the He vessel. Possible “cross over talking” of thisarrangement has been discussed in [8]. A second pic-up
allocated on the cathode side of the cavity allows themeasurement of the field amplitude in the gun cell.
Fig.2 shows some details of the cryostat. It contains amagnetic and only one LN2 shield to protect the cavity
from the magnetic earth field and from heat transfer. The
LHe and the LN2 supply have a common port and thecavity support system contains special damping elements

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D. Janssen et al. / Proceedings of the 2004 FEL Conference, 359-362

against microphonics. The drivers for the tuning system
are arranged outside of the cryostat.

In Fig.3 and Fig.4 the principle of the tuning system isshown, which is adapted from the cryostat of theRossendorf ELBE project [10].

Cathode transfer rod

TESLA-cell tuner
LN2 reservoir
cathode cooler
cathodeHOM filter

choke filter
gun cellHe-vessel

gun-cell tuner
RF power coupler

Figure 1: 3 ½ cellsuperconducting RF gun

cavityFigure 3: Tuner system of the cavity
oftheRossendorf

cathode exchangesystemvacuum vessel
He & N2 ports

cathode storage &transportation chambercavity alignment
Beam line
connection

tuner motors

Figure 2: Cryostat of the Rossendorf superconducting RF
gun
In the following we will discuss two features of thedesign, which are not standard. The first feature resultsfrom the circumstance, that the cavity of the RF gun
contains two different type of cells, the gun cell and the
TESLA cells with two different stiffness. Therefore it is
not possible, to get the same frequency and approximately
the same field amplitude in all cells of the cavity, using
one tuner only. To avoid this difficult, our design of the
gun contains two tuner and two pic-up probes for fieldmeasuring, one for the gun cell and one for the TESLA
cells respectively. The tuners are able to change thethickness of the gun cell by ± 0.25 mm and that of the
TESLA cells together by ± 0.3 mm, which corresponds toa frequency shift of ± 137 kHz for the gun cell ± 286 kHz
for the TESLA cells. Furthermore we are able to adjust
the choke flange cell at LHe temperature inside thecryostat.

THBOC05TESLA-cellchoke-cell
gun-cellFigure 4: Sectional view of the tuning system
Now we will discuss the second feature, which is notstandard.
For this gun the results of beam dynamic calculation are
published in [5]. Accelerating a bunch with a charge of
1nC to an energy of 9.5 MeV, a transverse emittance of
2.5 mm mrad has been obtained. The axis RF field, usedin this calculation is given in Fig.5. Immediately after thecathode the radial component of the electric field isnegative and has a minimum. This behaviour results fromthe position of the cathode, which is located 2 mm behindthe back wall of the gun cell. The negative value of theradial field focus the beam after the cathode, where theenergy is small. This effect of “RF focusing” has been

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D. Janssen et al. / Proceedings of the 2004 FEL Conference, 359-362

described in [6]. The RF focusing replaces in the
superconducting cavity the static magnetic field, which isused inside the cavity of normal conducting RF guns forbeam focusing and emittance reduction.

EMITTANCE COMPENSATION WITH A
MAGNETIC MODE
In the proceeding section we discussed the compesationof transverse emittance of the superconducting gun by the
RF focusing of the beam. Another possibility to preventthe growth of transverse emittance is to excite together
with the accelerating TM mode a magnetic RF mode (TEmode) inside the superconducting cavity. This possibility
has been extensively discussed in [7]. In the case of theRossendorf gun cavity we use the TE021 mode. The
corresponding RF field, which has been calculated by thecode SUPERLANS is shown in Fig. 7. The field of the
TE mode is concentrated in the last TESLA cell and caneasy excited by a coupling loop in the beam pipe. At thecathode surface the magnetic field is equal to zero.

Figure 5: RF field near the axis of the gun cell
The focusing by the RF field and also the axial alignmentof this field are very sensitive with respect to the cathodeposition. So the second special feature of our design work
is a cathode tuner. This tuner allows to adjust the cathodewith respect to the cavity axis and to move it ±1mm inaxial direction. The scheme of this tuner is given in Fig.
6.
titanium bridge

cathodez[mm]Figure 7: Field pattern and axis fields of the electric andmagnetic mode inside the Rossendorf gun cavity
In superconducting cavities the quench limit for thesurface magnetic field is 0.18 T [9]. Fig.8 shows thesurface magnetic fields of the Rossendorf gun cavity.

B[T]cavity flange
LN2 cooling

Figure 6: Cathode tuner
superconducting RF gun

back wall of the gun cell

of

the

Rossendorf

Three movable titanium bridges connect the flange of thecavity with the LN2 cooling system. This cooling system
has a ridged connection with the cathode and the steeringof the bridges follows outside of the cryostat.

z[m]Figure 8: Surface magnetic field of the TE mode, the TM
mode and the vector sum of both fields for the Rossendorf
gun cavity

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D. Janssen et al. / Proceedings of the 2004 FEL Conference, 359-362

The peaks of the magnetic TE mode are disposed between
the peaks of the accelerating TM mode. The resulting
field, which is the vector sum of both modes has an
maximum amplitude comparable with that of the separate
modes.
Table 1: Parameter and results of the tracking calculation
Beam parameter

Field parameter

Laser parameter

εx[mm
mrad]

0.78 –
0.98

BTMsurf[mT]

115

Puls length
[ps]

σx
[mm]

3.06

BTEsurf[mT]

136 Raise time [ps]εz[keVmm]

72.4|BTM+ BTE |surf[mT]

144 Spot size [mm] 2.6

∆z
[mm]

2.79

ETM,axis[MV/m]

50

Eav
[MeV]

8.82

φTM[grad]

75

∆Erms
[keV]

53.9

φTE[grad]0 - 180Bunchcharge[nC]emittance depends only weak on the phase of themagnetic mode.
•
The sum of the surface magnetic fields of the TM
mode and the TE mode is clearly below the quench
limit.
The last statement is confirmed by Fig.10. Here the firstmeasurement of the peak magnetic surface field for a TE
and a TM mode in a single cell cavity is represented

20

1

1

(surface)

Figure 10: Quench limit and Q values for the TM and the
TE mode in a single cell cavity.

After the calculation of the RF fields we did tracking
calculation using the ASTRA code. The parameters andresults of this calculation are given in Table 1. Anelectron bunch of 1 nC starts with a length of 20 ps at thecathode. At a distance of 4.44 m it has a length of 9.3 ps
and its transverse emittance changes between 0.78 and0.98 mm mrad in dependence on the phase of the TE
mode. This dependence is explicitly shown in Fig.9.

ε[mm
mrad]

•
•

The cathode and the cavity tuner are newelements in the design of superconducting RF
guns.
The magnetic RF mode replaces the static
magnetic field and decreases the emittance by afactor of more than two.
The new Rossendorf superconducting RF gun isin manufacturing, first components are finished.

REFERENCES

φTE[grad]180

Figure 9: Dependence of the transverse emittance fromthe start phase with respect to the magnetic mode.
The results of this calculation are the following:•
By exciting an magnetic mode in the last cell of the
gun cavity the transverse emittance decreases bymore than a factor of two.
•
The frequency of the magnetic mode is notnecessary a harmonic of 1.3GHz. The transverse

THBOC05

SUMMARY•[1] K. Zhao, et al., NIM A475 (2001) 564.
[2] H.Bluem, et al, EPAC’04, Lucern, Swiss, July 5-9,
2004
[3] T. Srinivasan-Rao, et al., PAC’03, Portland, USA,May 12-16, 2003.
[4] D. Janssen, et al., NIM A507 (2002) 314[5] D. Janssen, et al., FEL’03, Tsukuba, Japan, Sept. 812, 2003, NIM A(2004) in print.
[6] D. Janssen, V. Volkov, NIM A452 (2000) 34-43.
[7] D. Janssen, V. Volkov, EPAC’04, Luzern, Swiss,
July 5-9,2004
K. Flöttman, D. Janssen, V. Volkov, Phys. Rev. ST
accepted[8] Yongxiang Zhao, Michael Cole, PAC’03, Portland,
USA, May12-16, 2003
[9] K. Saito, Proc. of the PAC’03, p.462, Portland,
Oregon, USA, May12-16, 2003
[10]F. Gabriel, et al., NIM B 161-163 (2000) 1143.
[11]G.Ciovati, P.Kneisel, privat communication

C.H.G. Hernandez-Garcia et al. / Proceedings of the 2004 FEL Conference, 363-366

363

LONGITUDINAL SPACE CHARGE EFFECTS IN THE JLAB IR FEL SRF
LINAC
C. Hernandez-Garcia*, K. Beard, C. Behre, S. Benson, G. Biallas, J. Boyce, D. Douglas, H. F.
Dylla, R. Evans, A. Grippo, J. Gubeli, D. Hardy, K. Jordan, L. Merminga, G. Neil, J. Preble, M.
Shinn, T. Siggins, R. Walker, G. P. Williams, B. Yunn, S. Zhang, TJNAF, Newport News, VA
23606, USA
Abstract
Observations of energy spread asymmetry when
operating the Linac on either side of crest and longitudinalemittance growth have been confirmed by extending
PARMELA simulations from the injector to the end of thefirst SRF Linac module. The asymmetry can be explainedby the interaction of the accelerating electric field withthat from longitudinal space charge effects within theelectron bunch. This can be a major limitation to
performance in FEL accelerators.

INTRODUCTION
During the commissioning of the Jefferson Lab 10 kW
Upgrade IR FEL several intriguing questions regarding
the performance of the injector and the longitudinal phasespace management were encountered. The full-energy
momentum spread of the beam showed an asymmetry as afunction of linac gang phase. Furthermore, thecompressed bunch length at the wiggler and therefore thelongitudinal emittance showed a clear dependence ontransverse match into and through the linac and was asmuch as a factor of 4 larger than the emittance predicted
at the end of the injector. Operational and performanceissues in the linac such as cavities being out of phase
and/or wake fields were ruled out as the source of the
problem after careful investigation. Then, PARMELA
modeling was extended from injection to the end of thefirst cryo-module to study the longitudinal beam
dynamics as a function of linac gang phase [1].
The machine design for the Jefferson Lab 10 kW
Upgrade IR FEL has been described in detail elsewhere[2]. It consists of a 10 MeV injector, a linac comprised ofthree Jefferson Lab cryo-modules, and a recirculation
lattice. The machine layout is shown in Figure 1.

Recirculation
Arc

SLM1

Injector
CM3

CM2

CM1

Optical
Klystron

Energyrecoverytransport

The injector consists of a high-voltage-DC GaAs
photocathode gun driven by a frequency-doubled Nd:YLF
laser, a 10 MeV quarter cryo-unit with two 5-cell CEBAF
cavities, a transverse match section and a bunch
compressor [3]. The photocathode gun delivers 135 pC,
23 ps rms-long electron bunches operating at 350 kV inpulse (demonstrated up to 8 mA) and CW (demonstrated
up to 9.1 mA) modes [4]. The photocathode gun
performance has been studied earlier [5]. After initialacceleration at 10 MeV, the electron beam is transversely
matched to the linac by means of a quadrupole telescope,longitudinal match is provided by an achromatic
compressor chicane [6].
The linac further accelerates the electron beam atenergies between 80 and 200 MeV. The first (CM1, see
Figure 1) and third (CM3) cryo-modules are conventional
5-cell CEBAF cavities, while the middle module (CM2) isbased on a new 7-cell JLab design [7]. The beam isaccelerated off-crest to impose a phase correlation on thelongitudinal phase space.
The first part of the recirculator transports the beam
after acceleration to the FEL. A six quad telescopetransversely matches the high-energy beam to a 180°recirculator arc, which is based on a Bates geometry [8].
At the middle of the arc, a synchrotron light monitor(SLM1, see Figure 1) is employed to measure the energy
spread after acceleration. The beta function is always verysmall at this location so the spot size is dominated by theenergy spread. After interaction with the FEL, the beam is
re-circulated for energy recovery by a second Bates-stylearc.

MEASUREMENTS AND MODELINGWith only the first and third cryo-modules installed in
the machine at the time (CM1 and CM3), an asymmetry
in the beam momentum spread as a function of linac gangphase was observed during the FEL commissioning
activities. The injector had been setup accordingly to
PARMELA to produce an upright longitudinal phasespace distribution at the entrance of the linac [4], asshown in Figure 2.

Figure 1: Jefferson Lab 10 kW Upgrade IR FEL. CM1,
CM2, and CM3 are CEBAF-type cryo-modules. SLM1 isa synchrotron light monitor.
__________________________________________* Corresponding author: Tel: 1-757-269-6862;
fax:1-757-269-5519; E-mail address: chgarcia@jlab.org

Available online at http://www.JACoW.org

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C.H.G. Hernandez-Garcia et al. / Proceedings of the 2004 FEL Conference, 363-366(in ps) can be established by back-propagating the
average of energy spreads at either side of crest via thefollowing∆EW (1 + E I E L ),(2)
EWω tan φEW is the full energy spread at the wiggler,∆t =where ∆EW

E I is the injector energy, E L is the energy gain in the

If the distribution is upright at injection, then the beam
momentum spread after acceleration (measured at SLM1
in Figure 1) should be symmetric around crest. This was
not the case. With the injector se up to produce the phasespace in figure 2, the beam full momentum spread when
accelerating 15° ahead of crest (nominal operating
conditions for a longitudinal match to the wiggler) was
1%, and 1.5% when accelerating 15° behind crest, was
1.5%. The full-energy momentum spread is establishedfrom a spot size measurement at a point of high dispersion
by∆EW ∆x
=
,
ηx
EW

(1)

where ∆EW is the beam full-energy spread, EW is thebeam energy at the high dispersion point (SLM1 at the
middle of the first recirculator arc, see Figure 1), ∆x is
the spot size and η x is the dispersion function of the arc
dipole (70 cm). The calibration was performed bymeasuring the displacement of the centroid of the spot in
the SLM1 video screen when the beam energy waschanged by 1%. Figure 3a shows a snapshot of thesynchrotron light at SLM1. The spot size is measured bymeans of a frame grabber software that gives the spot size
profile in pixels for both x and y-axis [9]. Figure 3b
shows the frame grabber output generated from the spotshown in Figure 3a.
ablinac, ω is the accelerator frequency, and φ is off-crest
phase. With the downstream cavity in the injector
operating at 20° off crest and the linac at 15° off crest, themeasured average of the energy spread is 0.0125. For
EW = 80 MeV, and Einj =9.2 MeV, equation 2 yields∆t = 5.6 ps. This result agrees quite well withPARMELA (see Figure 2).
The performance of the injector regarding longitudinal
phase space management was questioned after eliminating
operational and performance issues in the linac as asource of the problem (i.e. one or more cavities being outof phase, wake fields, etc.). PARMELA modeling wasthen extended from the injector to the end of the firstcryo-module. The electron beam energy at injection is 9.2
MeV, therefore no transverse space charge effects are
expected from PARMELA through the cryo-module.
However, PARMELA indicates that longitudinal spacecharge will induce what appears to be a phase-dependent
asymmetry in the beam momentum spread during andafter acceleration. When accelerating 15° ahead of crest
the model predicts an increase in the rms energy spreadfrom 45.3 keV at the entrance of the first cryo-module to520 keV at the exit. For acceleration behind crest thepredicted full energy spread is 659 keV at the exit of thecryo-module. These results are shown in figure 4.
700
Energy spread (keV)

Figure 2: PARMELA longitudinal distribution at theentrance of the first cryo-module. The predicted fullenergy spread is 44.3 keV, the full bunch length is 6 ps
(or 11.1°), and the longitudinal emittance is 16.8 ps-keV-15 deg off-crest SC ON

600+15 deg off-crest SC ON

500-15 deg off-crest SC OFF

400

Analytical (equation 3)+15 deg off-crest SC OFF

300
200
100
0
0

1

2

3

4

5

6

7

8

9

Exit at each cavity along the cryo-module

Figure 3: (a) Snapshot of the synchrotron light monitor in
the middle of the first recirculation arc. (b) Output
generated by the frame grabber to measure the spot size ofthe synchrotron light shown in (a).
Assuming that the asymmetry in the energy spread is alinear effect (this assumption was later confirmed by
PARMELA simulations), the injected bunch full length

TUBOS02

Figure 4: PARMELA calculations at either side of crest
show the growth in the imposed correlated energy spread(Space Charge ON). The correlated energy spread (SCOFF) grows as well and is in close agreement withequation 3 (which has been multiplied by 4).
The predicted asymmetry is on the order of 27% after
the first cryo-module alone (which is as far as the365

C.H.G. Hernandez-Garcia et al. / Proceedings of the 2004 FEL Conference, 363-366

22
σ E = σ Einj
+ (Vlinac sin (φ )σ t ) ,(3)

where σ Einj is the injected rms energy spread, Vlinac is
the total accelerating voltage in the linac to that point, φis the off-crest phase, and σ t is the injected rms bunch
length in radians. PARMELA is in good agreement with
the Equation 3 when the simulation is carried out with thespace charge option turned off, as shown in Figure 4.

ANALYSIS
The longitudinal space charge force within the electron
bunch accelerates the head and decelerates the tail,creating a tilt in the longitudinal phase space: the headgoes to higher energy, and the tail to lower as the beam
travels down the linac. This is the correlated energy
spread of the beam due to space charge. When
accelerating ahead of crest (nominal operating conditions
for longitudinal phase space management), the head of thebunch is driven to lower, and the tail to higher energy by
the RF field. This imposed phase/energy correlation adds
to the correlated energy spread, and the observed
momentum spread is reduced. On the other hand,acceleration behind crest drives the head of the bunch tohigher energy, and the tail to lower. The imposed
phase/energy then adds to the correlated energy spreadand the final energy spread is increased. Figure 5
illustrates this mechanism.

Figure 5: In acceleration ahead of crest, the final
momentum spread is reduced. In acceleration behindcrest, the final momentum spread is increased.
PARMELA also shows that the longitudinal emittance
grows by 57% at the end of the first cryo-module alone.
Since the length of the cryo-module is 1/6 of the distanceto the wiggler, the longitudinal emittance at the wiggler isaround 3 times larger that the longitudinal emittance at
injection.
If the injected bunch length is increased, thelongitudinal space charge forces are reduced, the energy
spread asymmetry alleviated and the longitudinalemittance growth less severe. For a fixed bunch charge,
the imposed correlated energy spread depends on the

inverse square of the bunch length [10], while theimposed energy spread from the RF system depends
linearly on the bunch length (see Equation 3). The
optimum bunch length to minimize the correlated energy
spread while maintaining the imposed energy spread
acceptable for the FEL is about 1.5 times the bunch lengthwith the original injector configuration (1.5 ps rms) [10].
PARMELA predicts that the injected rms bunch length
increases from 1.5 ps to 2.37 ps if the downstream cavity
in the injector is operated closer to crest (10°, instead ofthe design value at 20° ahead of crest). The predicted fullenergy spread at injection decreases from 44.3 keV to40.5 keV, but the longitudinal emittance increases from
16.8 ps-keV to 19.6 ps-keV. Also, the longitudinal phasespace distribution is no longer upright at the entrance tothe linac.
The phase/energy slew imposed to the longitudinal
distribution by the RF system and space charge effects
can be cancelled out with proper longitudinal phase space
management elements in the transport system, but thecompressed bunch length at the wiggler is limited by the
intrinsic longitudinal emittance of the beam due tothermal effects during its creation. The intrinsic
longitudinal emittance growth along the cryo-module canbe calculated by removing from the bunch particle
distribution the quadratic term and the phase/energy slew
imposed by the RF. The bunch particle distribution is
written by PARMELA at specified intervals along thecryo-module to a separate log file. In another program,each bunch is read back in from the log file, has its
longitudinal momentum vs. position fit to a in 2nd orderpolynomial, then that dependence removed from the
distribution and the energy spread recalculated based on
the corrected distribution.
Figure 5 shows that the intrinsic energy spread throughthe cryo-module grows by 76% with for a 1.5 ps rms
injected bunch, while for a 2.5 ps rms bunch the intrinsic
energy spread increases by 64% at the exit of the cryomodule.
Intrinisc energy spread (keV)

simulation has progressed so far). This result is quiteconsistent with observed momentum spread asymmetry(50%) at the end of the two cryo-modules (exit of CM3,
see Figure 1).
The imposed energy spread (by the RF system during
acceleration, without space charge) should be symmetricaround crest after acceleration, as expressed by

21.00
19.00
17.00
15.00
13.00
11.00
9.00
7.00
5.00
1100

1.5 ps rms
2.4 ps rms

1300

1500

1700

1900

z (cm)

Figure 5: PARMELA-based calculations of the intrinsic
energy spread growth along the first cryo-module
operating at 15° ahead of crest for two different injectedbunch lengths.

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C.H.G. Hernandez-Garcia et al. / Proceedings of the 2004 FEL Conference, 363-366

The calculations confirm that with a longer injectedbunch the longitudinal space charge forces are less severe
and the intrinsic energy spread is not only smaller, but it
grows slower. Figure 5 also shows that the longitudinalemittance is slightly larger for the longer injected bunch,but grows slower.
When this was implemented, it was quickly confirmedthat the asymmetry in the energy spread after acceleration
was reduced from 50% to less than 20%. PARMELA
shows a reduction in the energy spread asymmetry from
30% to 17%. In fact, with the longitudinal space charge
effects less severe with longer bunch at injection, thecompressed bunch length at the wiggler was reduced fromabout 0.8 ps FWHM (injector at 20°, linac at 15° off crest)
to less than 0.5 ps FWHM. Laser gain with thisconfiguration was about as strong as the previous
configuration but peak efficiency in the detuning curve
was much higher (1.25%) efficiency.
The FEL lased better with a non-design buncher
gradient, about 10% higher than the one that produces thesmallest energy spread at injection. PARMELA showsthat the injected bunch is around 20% longer (which isgood for alleviating longitudinal space charge forces), but
the energy spread is about 30% larger. The optimal
injector configuration for the FEL seems to be acompromise between the bunch length and energy spreadat injection.

CONCLUSIONS
Extending the injector PARMELA model through thefirst cryo-module confirmed observations of anasymmetry in the final energy spread of the electron beam
after acceleration and a significant growth in thelongitudinal emittance. The asymmetry can be explainedby the interaction between the electric field within theelectron bunch created by space charge forces, and theelectric field from the RF system during acceleration.
Injecting a long bunch alleviates the longitudinal spacecharge force. PARMELA modeling provided guidance
towards achieving a longer bunch at injection, simply
operate the downstream cavity of the injector closer tocrest. Once this was implemented in the machine, theasymmetry in the final beam energy spread was reduced,
the longitudinal match throughout the accelerator becamevery close to lattice design, and the growth in thelongitudinal emittance was decreased.
The interaction of the longitudinal space force with the
RF system will be an important factor to consider in thedesign of high charge accelerators for FELs. Since the
FEL gain depends on peak charge, it is desirable to have ashort bunch with high charge at the wiggler. The present
study reveals that bunch length at the wiggler is limitedby the intrinsic longitudinal emittance of the beam
generated during its creation, since the imposed
phase/energy correlation in the energy spread by the RF
system is removed by proper longitudinal phase space
management, and the correlated (space charge) energy
spread can be reduced by means of a long injected bunch.

TUBOS02

ACKNOWLEDGMENTS
This work supported by The Office of Naval Research,
the Joint Technology Office, NAVSEA PMS-405, the Air
Force Research Laboratory, U.S. Army Night Vision Lab,
the Commonwealth of Virginia, and by DOE Contract
DE- AC05-84ER40150.

REFERENCES
1 Parmela_fel0.2: FEL Injector Simulation, JLAB-TN-03028, K. B. Beard, B. Yunn, C. Hernandez-Garcia
2 D. Douglas et al., “Driver accelerator design for the 10
kW Upgrade for the Jefferson Lab IR FEL”,
LINAC2001, pp. 867-9, Monterey, CA 2001.
3 D. Engwall, et al., PAC’97, pp. 2693-5, Vancouver,May 1997.
4 C. Hernandez-Garcia, these proceedings.
5 T. Siggins et al., “Performance of a GaAs DC
photocathode gun for the Jefferson Lab FEL”, Nucl.
Inst. Meth. A 475 (2001) 549-553.
6 B. C. Yunn, “Physics of the JLab FEL injector”,
PAC’99, pp. 2453-5, New York, April 1999.
7 J. R. Delayen et al., PAC’99, pp. 934-6, New York, 29
March-2 August 1999.
8 J. Flanz et al., Nucl. Inst. Meth. A421:325 –33 (1985).
9 WesCam, developed by W. Moore, JLab FEL.
10 D. Douglas, private communication.

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LCLS UNDULATOR DESIGN DEVELOPMENT
Isaac Vasserman, Roger Dejus, Patric Den Hartog, Elizabeth Moog, Shigemi Sasaki,
Emil Trakhtenberg, Marion White, ANL/APS, Argonne, Illinois 60439, USA
Abstract
The undulator segments of the 130.4-m-long undulator
line for the Linac Coherent Light Source project (LCLS)[1] must have a deflection parameter Keff that matches thenominal value for that segment to within ∆Keff/Keff< 1.5 × 10-4. Mechanical shims were used to set theundulator gap to control K in the prototype, but this is too
tedious a procedure to be used for all 33 undulator
segments. Although the prototype undulator [2-4] met allof the LCLS specifications, development continued inorder to simplify the system. Various other alternatives
for adjusting the field were considered. A canted-polegeometry was chosen, allowing the K value to be changed
by lateral translation of the entire undulator segment. This
scheme also facilitates tapering the undulator line toaccommodate electron beam energy loss. The prototype
undulator was subsequently modified to test the cantedpole concept. Magnetic measurements demonstrated thatthe undulator with canted poles meets all LCLS
specifications, and is more cost effective to implement.

INTRODUCTION
The LCLS prototype undulator cross section is shownin Fig. 1. Wedged spacers are located between thetitanium core and the aluminum bases. Translation of acanted undulator segment in the transverse horizontal
direction (X) allows the desired Keff to be achieved withthe required accuracy during initial tuning.

Figure 1: LCLS prototype cross section for the modified
design with canted pole-gap.
Remote control of the device’s X position can serve tokeep the field stable despite temperature changes. It canalso be used to tune the phase between devices whenparticle energy loss has disrupted the phasing. The rangeof X motion could be as large as ±5 mm to compensate forthe beam energy loss at saturation. It is important to keep

Available online at http://www.JACoW.org

the performance (phase errors, trajectory straightness,etc.) of the undulator segments within the required
tolerances [1] in this wide transverse position range. To
confirm that this can be done, the LCLS prototype
undulator was modified to introduce a 3-mrad cant.
Measurements of the rms phase errors, Keff and the Xdependence of the field integrals are described below.
Alignment of the magnetic elements is critical for thisproject. The option of using magnetic needles to locate
the magnetic center of the undulator segment is discussed.
Additional design changes that were implemented
recently are described elsewhere [5].

MAGNETIC MEASUREMENT OF THE
PROTOTYPE UNDULATOR
Phase Errors
The LCLS undulator will use the first harmonic of theradiation so its output is not very sensitive to phase errors
between the particle beam and radiation [6-8]. The
allowable upper limit of rms phase errors is 6.5º. The X
dependence of the rms phase error was measured in therange of ±3 mm and was found to be negligible.

Effective Field
Figure 2 shows the X dependence of the effective field(Beff) and the effective deflection parameter (Keff). Thisdependence is linear in X, and close to the 1.9 G/µm
previously measured for the gap dependence. The
difference can be attributed to the initial wedging in thepole gap created by pole sorting to allow for easy gap
measurement [3].

Figure 2: Beff and Keff dependence on X. ∆X = 0.3 mm
corresponds to the alignment accuracy needed for thetolerance ∆Beff/Beff = 1.5 × 10-4 ~ 2 Gauss.
The 3-mrad cant is small so that the alignment accuracy
required in the X direction, 0.3 mm, is not difficult toachieve. With this cant angle, the change in field strength

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I.B. Vasserman et al. / Proceedings of the 2004 FEL Conference, 367-370

due to a temperature change of 1°C can be compensatedby a lateral shift of the undulator segment by 1.2 mm,
which can be done remotely.

Horizontal and Vertical Trajectories
The horizontal trajectories for different X positions in
the range of ±3 mm are shown in Fig. 3.

Figure 3: Horizontal trajectories at different X positions
for a beam energy of 14.1 GeV.
The trajectories are well behaved and well within thetolerance requirement of 2 µm maximum walk-off from astraight line for a particle energy of E=14.1 GeV. Thechange in the vertical field integrals can be calculated
from Maxwell’s equation ∂By/∂x=∂Bx/∂y, using thehorizontal trajectory measurements. Final tuning of theundulator segments may require tuning of the verticaltrajectories as well.

Magnetic Field Fine Tuning
The method for adjusting Keff is: a) Select amongspacers with thickness step ~ 15 µm to set the effective
field within ±30 G (1 µm in gap corresponds to ~ 2 Gaussin field); b) Set the horizontal position of the spacers toadjust the effective field to ~ ±6 Gauss (for a 3-mrad cant,
6 G corresponds to a 1-mm shift in horizontal position);c) Set the horizontal position of the undulator segment as
a whole so that the effective field is in the range of ±2 G(∆Beff/Beff ~ ±1.5 × 10-4). The last step saves shimmingtime and provides better accuracy.

PHASE TUNING
The phase slippage along the undulator can becalculated using [9]:ϕ ( z) =

z
z

k 
2
(
)
z
I
z
'
dz
'
I 12y (z ' ) dz ' , where
+
+
1x
2 
∫
∫
2γ 
0
0


k is the fundamental harmonic wave-vector of theradiation, γ is the relativistic factor, and I1x and I1y are thenormalized particle angles in the vertical and horizontal
directions, respectively. In free space, with zero field andzero angle we have:ϕ ( z) =

k
2γ 2

z,

L free = nλu (1 + K eff 2 / 2) , where

Lfree is the required distance in free space for n periods ofphase slippage. An initial magnetic tuning will be

TUBOS04

required for each undulator segment to match its phasing
to the standard mechanical break length. Full-width
magnet shims (phase shims) will be applied to correct thefield, if needed. Such shims were successfully used in the
APS FEL project. The result of the phase shim test is
shown in Fig. 4. The physical break length will be chosen
to match what is typical for an undulator with six phaseshims. This will allow adjustment in either direction.
Other ways of tuning break length, such as Keff tuning andtrajectory shims, will be used if necessary.

Figure 4: Break length and phase change from 0.2-mmthick phase shims applied at one end of the undulator. The
first two shims were applied to magnet #7, one each on
the top and bottom jaws, the next two to magnet #6, etc.
Particle energy loss results in a change of phase in andbetween the undulator segments that must be corrected.
The estimated energy loss in the first 100 m of undulator
is 0.26%; 0.4% is estimated for the last 30 m withsaturation [1]. The resulting phase slippage in theundulator segment can be corrected by remotely changing
the Keff of the undulator segment. The phase change in thedrift space must also be corrected. The previous prototype
undulator design had active end-gap corrections to correct
the phasing, but modifying Keff instead is simpler. Tests
were conducted to demonstrate the feasibility.
Polar plots based on the complex radiation amplitude
are powerful tools in understanding phasing issues. The
complex radiation amplitude A is defined as [9]:zA (z) = ∫ I1y (z ' ) e−iϕ (z ')dz ' .
0

The magnitude of A is plotted as the radius, and thecomplex phase angle of A is plotted as the angle. These
values, calculated for a sequence of points along theundulator, are plotted. A properly phased undulator will
be represented as a straight line, radially outward from thecenter of the graph. Phasing errors appear as curved lines
or kinks. The absolute value of the complex radiation
amplitude at the undulator segment end A(L) isrepresented in the polar plot as the distance between theinitial and final points of the vector. The radiation
intensity is proportional to |A|2.
Consider the case with a long line of ideal undulatorsand ideal particle beam energy, followed by two
undulators separated by a long break section with three
periods of phase slippage in the drift space. Also, assume
that the particle beam energy is 0.4% too low throughthose two undulators, due to a beam energy loss. Figure 5
is a polar plot through those two undulators and the drift

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I.B. Vasserman et al. / Proceedings of the 2004 FEL Conference, 367-370

space between them. The line curvature is so extreme thatthe radiation intensity from the two undulators is sharply
reduced. The performance of the undulator is seen to bevery sensitive to the particle energy.
The curvature in Fig. 5 can be understood because
spontaneous radiation from the undulators and the
reduced particle beam energy would not be at the nominal
wavelength. Figure 6 shows what happens when themagnetic field strength of the two undulators is adjusted
so the spontaneous radiation is at the nominal wavelength,
despite the reduced beam energy. The traces through thetwo undulators are straight, as they should be, but now
there is a kink between the two undulators, showing thatthe drift space is not the right length for the reduced beamenergy. This type of plot can clearly show and help
diagnose the origin of an effect that only impacts the final
radiation amplitude by 2% of the ideal value.

slippage in the undulator segments, but the net effect isthat the radiation amplitude is 99.1% of ideal.
It may at some time be desirable to remove an
undulator segment from the undulator line. An issue thatmust be considered before doing so, however, is what
becomes of the phasing between the undulator segments
immediately upstream and downstream of the removed
one. If the new undulator-long drift space is the samelength as an integer number of free-space slippage
lengths, then the phasing between the adjacent undulator
segments will be good. (Some steering correction may beneeded, however, to compensate for the environmental
magnetic field.) If, as is more likely, the drift length isn’tright, resulting in a phase error, then an adjustment of the
Keff of the undulators may be able to compensate.
90
8

90

6

1.5

4
2

1

180

0

0.5

0

270

E
9.0

Figure 5: After passing through a line of undulator
segments where the undulators are perfect and the beamenergy is ideal, the beam loses 0.4% of its energy prior topassage through two undulators that are separated by adrift space with three periods of phase slippage. The
magnitude and complex phase angle of A are plotted inpolar coordinates at points along the two undulators. The
radiation amplitude from those two undulators,
represented by the length of a vector from the beginningto the end of the trace, is very small.
8

Figure 7: Same as Fig. 6, but with Keff of the two
undulators adjusted to maximize the overall |A|. The Keffthrough the undulators is not perfect, as can be seen by
the slight curvature, but the overall |A| is 99.1% of ideal.
An example of such an adjustment is shown in Fig. 8.
When Keff = 3.62, the drift-space length is nearly an
integer number of slippage lengths so the required Keffadjustment is small. Another example is shown in Fig. 9
for nominal Keff = 3.44. (The electron beam energy is alsochanged, to keep the wavelength of the radiation at
1.5 Å.) At this new nominal Keff , the drift space length isnearly perfectly wrong, so even tuning Keff is not enough.
The phasing correction would be easier in this case if two
undulators were removed.
90

6
8

4
6

2
4

80

0
2

80

0

.1

0

270

Figure 6: Same type of plot as in Fig. 5. The Keff of thetwo undulators has been adjusted so that the spontaneousradiation is at the nominal wavelength, despite the beamenergy loss. The lines through the undulators are straight,
and the kink between them indicates a phasing error in thedrift space. The radiation amplitude from these undulators
is now 98.2% of ideal.
An additional improvement can be obtained if, insteadof adjusting Keff to match the spontaneous radiation to thenominal wavelength, Keff is adjusted to maximize theoverall |A|. The polar plot resulting from such a change isshown in Fig. 7. As can be seen by the curvature in the
traces through the undulators, there is a small phase

270

4

4

4

4

4

Figure 8: Polar plot (left) and trajectory (right) with one
device removed. Keff was changed by 0.03% (0.6-mm shiftin X) to compensate for the phase distortion in the drift
space. Nominal Keff =3.62. |A| is 99.3% of ideal for two
undulators.

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I.B. Vasserman et al. / Proceedings of the 2004 FEL Conference, 367-370

90

6

4

2

80

0

Figure 9: Same as Fig. 8 but with nominal Keff = 3.44. The
drift space length is 17.54 slippage lengths, making thesecond undulator almost exactly out of phase. |A| was
optimized by a 0.16% change in Keff (3.2-mm shift in X),
but still only 81.6% of ideal was reached.

MAGNETIC NEEDLES
With a canted gap undulator, accurate alignment in boththe horizontal and vertical directions is critical, and amethod to accomplish this has been studied. The magnetic
center of the undulator can be determined using a Hall
probe. The position of the Hall probe’s sensitive area isdifficult to determine, therefore the probe will be used torelate the undulator magnet centerline to positions ofmagnetic needles attached to the undulator.
A Sentron Hall probe was used to scan past a magnetic
needle and the results are shown in Figs. 10 and 11.

with finer resolution will be used in the final system.
Alignment in the Y direction is shown in Fig. 11. The
needle points horizontally in this case, and the Hall probe
scan direction is vertical. The magnetic center of theundulator is at y = 0. By = 0 is the center of the needle.
The distance between them can be determined from theplot to within 5 µm.

SUMMARY
Wedged spacers were inserted between the aluminumbase plates and the titanium strongback of the existing
LCLS prototype undulator, to give a 3-mrad cant to thepole gap. (A 4.5-mrad cant has since been determined to
be preferred for the final LCLS undulator.) The measured
variation of the magnetic field with horizontal position
was as expected, making it possible to move the undulator
laterally to adjust the on-axis field strength. The rms
phase error did not change significantly with X, so theundulator can be used at different lateral positions. Coarse
adjustment of the field strength can be done by the choiceof spacer thickness, and by sliding the chosen spacer
horizontally. The fine adjustment will be accomplishedby lateral translation of the undulator. Horizontaltranslation of the undulator can also be used to correct thetemperature dependence of the field strength. Magnetic
needles were found to be effective alignment tools.

ACKNOWLEDGMENTS
The authors would like to thank Dr. J. Pflueger for his
suggestion to cant the undulators. This work is supportedby the U.S. Department of Energy, Office of Basic
Energy Sciences, under Contract No. W-31-109-ENG-38.

REFERENCES
Figure 10: Horizontal scan past the tip of a verticalpointing magnetic needle.

Figure 11: Vertical scan past the tip of a horizontalpointing magnetic needle. The magnetic center of theundulator is at y = 0. By = 0 is the center of the needle.
The distance between them can be determined from theplot to within 5 µm.
The vertical field distribution along the X-axis is shownin Figure 10. The spacing between data points wasdetermined by the 50-µm encoder resolution. An encoder

TUBOS04[1] Coherent Light Source Project, SLAC-R-593, April
2002, http://www-ssrl.slac.stanford.edu/lcls/cdr/.
[2] E.R. Moog et al, “Design and Manufacture of a
Prototype Undulator for the LCLS Project,” Proc. of
PAC 2001, Chicago, June, 2001.
[3] I.B. Vasserman et al., “Magnetic measurements andtuning of the LCLS prototype undulator,” Nucl.
Instrum. Methods A, 507 (2003) 191-195.
[4] LCLS Prototype Undulator Report, R.J. Dejus, editor,
ANL/APS/TB-48 (2004).
[5] E. Trakhtenberg et al., “Undulators for the LCLS
Project – from the prototype to full-scale
manufacturing,” XV Int’l. Synchrotron Radiation
Conf., July 19-23, Novosibirsk, Russia (2004).
[6] B.M. Kincaid, J. Opt. Soc. Am. B, 2 (1985) 1294.
[7] B. Diviacco, R.P. Walker, Nucl. Instrum. Methods A,
368 (1996) 522.
[8] L.H. Yu et al., Phys. Rev. A, 45 (1992) 1163.
[9] E. Gluskin et al., Nucl. Instrum. Methods A, 475(2001) 323.

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COMMISSIONING OF THE TTF LINAC INJECTOR AT THE DESY
VUV-FELK. Honkavaara∗ , DESY, 22603 Hamburg, Germany
for the VUV-FEL Injector group
Abstract
The upgrade of the TESLA Test Facility (TTF) at DESY
is almost completed. With electron beam energies up to
1 GeV, it serves the new SASE FEL user facility (VUVFEL) in the wavelength range from VUV to soft X-rays.
The first installation phase of the redesigned photoinjector
is finished. We report on its commissioning during spring
2004, including the first measurements of electron beam
parameters. Since this injector is also a prototype for the
XFEL injector, the results obtained are important for future
SASE XFEL drive linacs.

INTRODUCTION
The TESLA Test Facility Linac, phase 1 (TTF1) [1]has been operated at DESY until November 2002. Besides performing various tests and experiments related to
the TESLA linear collider project [2], the TTF linac wasused to drive a SASE free electron laser at wavelengths in
the range of 120 nm to 80 nm [3, 4]. Presently the TTF
linac is upgraded to drive a new SASE FEL user facility(VUV-FEL) [5]. The VUV-FEL is also a piloting project
for the XFEL project [6, 7].
In present stage of the upgrade, five accelerating modules with eight 9-cell superconducting TESLA cavities ineach are installed providing electron beam energies up to
800 MeV. Later, one or two more modules can be added toincrease the beam energy to 1 GeV, or even beyond. Beginning of the year 2004 the installations in the accelerator tunnel have been almost completed, and from March
to June 2004 the redesigned photoinjector has been successfully commissioned, which has already been briefly reported in [8].

THE VUV-FEL
With the electron beam energies available at TTF1 it
was possible to produce SASE radiation down to the wavelength of 80 nm. To reach shorter wavelengths, the energyof the linac has to be increased. Also several other upgrades
are needed to meet the more demanding beam parameterrequirements in terms of transverse emittance, peak current, and energy spread. Taking these requirements and ourexperience at TTF1 into account, both the linac and the injector have now been redesigned to extend the wavelength
range down to 6 nm. For a detailed discussion on the linac
and the parameter choices refer to [5].
∗ katja.honkavaara@desy.de

Available online at http://www.JACoW.org

For the start-up and commissioning phase this year, emphasis is put on achieving lasing and saturation at a wavelength of 30 nm, which requires an electron beam energyof 450 MeV. For the longer wavelength the requirementson the beam parameters are relaxed, which eases the commissioning. Later, lasing at longer and shorter wavelengths
will follow.

THE INJECTOR CONCEPTThe upgrade of the VUV-FEL photoinjector [9] implements the main ideas of the XFEL injector proposal [10].
The optimization of the XFEL injector concept is going on,
and the experience and results achieved by the VUV-FEL
injector are important for its final layout.
Figure 1 shows a schematic overview of the VUV-FEL
injector. Electron bunch trains with a nominal bunchcharge of 1 nC are generated by a laser-driven RF gun.
The design normalized emittance is 2 mm mrad. In orderto reduce space charge effects, the design shape of the laser
pulse is flat, both transversally and longitudinally, having alength of 20 ps (FWHM). The design rms bunch length at
the gun exit is 2.2 mm.
A complete TESLA module with 8 accelerating cavities is used to boost the beam energy to 130 - 150 MeV.
To avoid strong focusing, the first four cavities are operated with a moderate gradient (12 MV/m). In the last four
cavities full acceleration (> 20 MV/m) is used. The firstmagnetic chicane bunch compressor is placed downstreamof the first accelerating module. A second compression
stage follows after two additional accelerating modules at ahigher energy. With the two compression stages the bunch
can be compressed down to 50 µm (design).
Off-crest acceleration is required for magnetic bunch
compression. The sinusoidal accelerating field induces acurvature in the longitudinal phase space. The compression of the off-crest accelerated bunch leads to a longitudinal bunch structure with a high peak current spike and along tail. This irregular bunch structure complicates the useof the second bunch compressor. The energy-phase planecurvature can be removed by using a superconducting third
harmonic cavity (3.9 GHz) [11] before the bunch compressor. This cavity is under construction, and thus not yet
available. Therefore the start-up lasing strategy is similar
than at TTF1: The leading spike after the first compression
stage is used to produce the required peak current [12].
During the injector commissioning reported here, thefirst accelerating module has been operated with a constantgradient of 12 MV/m in all the cavities yielding to beam en-

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K. Honkavaara / Proceedings of the 2004 FEL Conference, 371-374

12 MV/m

RF Gun> 20 MV/m

Accelerating module
Laser

Diagnostics section

3rd harmonic
cavity4−5 MeVBunchcompressor
130−150 MeV

Figure 1: Schematic overview of the TTF VUV-FEL injector (not to scale). Beam direction is from left to right, and thetotal length is about 37 m. During the commissioning the beam was dumped into a small temporary beam dump before
the second accelerator module. The 3rd harmonic cavity is not installed yet.
ergy around 100 MeV. The beam was dumped into a temporary beam dump before the second accelerator module.

THE RF GUN
The new RF gun has been successfully commissioned
and characterized at PITZ (DESY Zeuthen) [13]. It is a 1.5
cell L-band cavity (1.3 GHz) powered by a 5 MW klystron.
The design of the photocathode system is the same as
at TTF1. The Cs2 Te photocathode is inserted via a loadlock system to the back of the half cell of the RF gun. The
new cathodes have higher quantum efficiency than the ones
used at TTF1 [14].
The maximum accelerating field on the cathode is determined by the available klystron power, and it is currently
limited to 42 MV/m. In order to reduce space charge induced emittance growth, the electron beam is focused by asolenoid magnet. A bucking solenoid is used to compensate the magnetic field on the cathode surface to zero. The
RF power and the RF phase in the gun are regulated by a
low level RF system based on digital signal processors.
The RF gun was transported from Zeuthen (PITZ) to
Hamburg and installed at the TTF tunnel in January 2004.
At PITZ, the gun has been operated at 10 Hz with an RF
peak power of 3 MW and an RF pulse length of up to 0.9 ms[15]. After a short commissioning period a similar performance was achieved also at TTF. However, for convenience, during most of the commissioning time 5 Hz repetition rate, and shorter RF pulse length was used.

THE LASER SYSTEMThe TTF1 laser system [16] has been upgraded. A similar system is tested and operated at PITZ. The laser system
is based on a mode-locked pulse train oscillator synchronized to the 1.3 GHz RF of the accelerator. In contrast to
the old system, two of the four laser amplifiers use laser
diodes instead of flashlamps for pumping. The remaining
flashlamp pumped amplifiers will be replaced later. One
advantage of using diode pumping is the increased laser
pulse energy stability: before the upgrade the measured
fluctuation in the electron bunch charge from shot to shot
was 3 to 6 % rms, now it is only about 1 % rms.

TUBOS05

After the conversion of the initial wavelength of 1047
nm to UV (262 nm), the laser beam is transported to the RF
gun cathode by an optical beam line consisting of lenses
and mirrors. The laser spot position on the cathode is controlled by a set of remote movable mirrors. A remotely
controlled iris allows controlling the laser beam size on thecathode. The nominal laser spot size at the cathode is 3 mmdiameter.
The laser system is designed to produce pulse trains withup to 800 µs length with pulse spacing of 1 µs (1 MHz). A
9 MHz operation mode is in preparation. The laser pulse
length and shape has been measured in the UV wavelengthwith a streak camera. The shape is near gaussian and has
a length of σ = 4.4±0.1 ps, which is shorter than before
the laser upgrade. However, in order to obtain a smalltransverse emittance, a flat laser pulse profile, both in transverse and longitudinal, is preferred. At PITZ, a laser pulse
shaper producing longitudinal flat-hat profile laser pulsesof ∼ 20 ps has been tested. The measured transverse emittance has been reduced by a factor of two compared to agaussian laser pulse [17]. However, since for the start-upof the VUV-FEL the gaussian laser profile is sufficient, thispulse shaper will be installed at TTF only later, when thedevelopment at PITZ is completed.

MEASUREMENTS OF BEAM
PARAMETERS
The first electron beam was produced by the new RF gun
at TTF in the middle of March 2004. The first month ofbeam operation was dedicated to the commissioning of the
hardware and software components of different measurement and control devices as well as to study the basic beam
parameters in the RF gun section.
In the gun section the charge can be measured by two
devices: a toroid and a Faraday cup located close to eachother at the gun exit. During the commissioning we operated with a charge of 1 nC per bunch. The number ofbunches in a bunch train was 1 to 10.
The energy of the beam produced by the RF gun has
been measured by means of a spectrometer dipole installed
before the first accelerating module. The beam energy corresponding to the nominal 3 MW RF input power is 4.6

K. Honkavaara / Proceedings of the 2004 FEL Conference, 371-374

MeV. The measured data agree well with the expectationfrom the simulation [8].
Typically, in order to have the smallest transverse emittance, the RF phase of the gun with respect to the laser
phase is tuned to a phase between 30 to 40 ◦ from zerocrossing. The rms phase stability of the laser is estimatedto better than 0.2 ◦ (0.5 ps) from shot to shot and within thepulses of the pulse train.
The commissioning of the injector including the firstaccelerating module, the first bunch compressor, and the
diagnostics section started in April 2004. The accelerating module has been operated with a gradient of 12 MV/myielding a beam energy around 100 MeV. An energy stability of 8.5·10 −4 rms has been achieved by using a feedback
system regulating the phase and amplitude of the accelerating structures.
The uncorrelated energy spread has been estimated fromthe beam image on the dispersive section of the bunch compressor. The energy spread has a leading peak with an rms
width of about 30 keV and a tail of about 200 keV.
One of the eight accelerating cavities in the first accelerating module has been prepared by using a surface
treatment technique based on electropolishing. The performance of this cavity was tested with the electron beam.
An accelerating gradient of 35 MV/m was achieved.[18]The transverse beam shape and size after the acceleration is measured using optical transition radiation (OTR).
The OTR system is designed and constructed by INFNLNF and INFN-Roma2 in collaboration with DESY. The
measured resolution (rms) of the system is 11 µm (magnification 1:1). More details of the system are in [19, 20].
For the measurements of the transverse emittance andTwiss parameters, 4 OTR monitors combined with wire
scanners are embedded in a FODO lattice of 6 quadrupoles
with a periodic beta function. During the commissioning only the OTR monitors were available. The emittanceand Twiss parameters are obtained by fitting the measured
beam sizes to the expectation from the lattice. The projected rms beam sizes are estimated from the beam images
with different methods. In the first method, the sigma of a
gaussian fit on the projected profiles is used to estimate therms beam size. In the second, the true rms is calculated
from the data within 90 % of the intensity of the beam.
In the latter case, two different image analysis codes areused to determine the rms size. Especially when the beam
shape is irregular and far from a gaussian shape, the different methods and codes yield different results.
Figure 2 shows the normalized horizontal and verticalemittance as a function of the solenoid current. The RF
gun and the module have been operated with nominal parameters. The bunch compressor was by-passed to avoid
dispersive effects. The data are partly taken at differentdays and with different optics to match into the FODO lattice. The emittance values using different analysis methods
on the same data set are indicated. The expected emittancefrom simulation is shown as well.
For accurate emittance measurements it is important to373

Figure 2: Normalized emittance measured at 100 MeV fora bunch charge of 1 nC as a function of the solenoid current.
Horizontal and vertical projected emittances are shown fordifferent beam conditions and matching optics. In addition,
three different ways to obtain the rms beam size are shown:
the rms size from a 90 % intensity cut with 2 different image analysis methods and an estimate from a gauss fit. Error in beam size is assumed to be 10 %. The two lower
plots are zooms of the upper ones. The data are still object
to further analysis and have to be treated preliminary.
have the FODO lattice well matched such that the beam
image on each of the four monitors is regular and has similar dimensions. During this first commissioning phase, thiswas only sometimes the case. Therefore further measurements with better measurement conditions are needed toconfirm the results. The study of measurement errors andsystematic effects of different analysis methods is not yet
finalized, and the data is still subject to a further analysis. Therefore, the emittance results shown here have to betreated preliminary.

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Nevertheless, the emittance results obtained are already
now useful to determine a tentative working point in termsof a preferred solenoid current. We can also see that in
the horizontal case, the data scatter largely. Typically thebeam quality in the horizontal plane is worse than vertical.
The reason is not yet understood, but possible candidates
are non-optimized injection into the first module, a nonuniform laser beam, and a beam passing too close to thelaser mirror, which is inside the beam pipe. The latter has
been observed at PITZ as well.
The rms bunch length has been measured using synchrotron radiation (SR) from the last dipole of the bunch
compressor. This radiation is guided out of the accelerator
tunnel and used in bunch length measurements by an interferometer and a streak camera [21]. The analysis of theinterferometer data is on going.
The uncompressed bunch length measured by the streak
camera is σ = 1.7±0.2 mm as expected. In the compressed
case, we expect to have a bunch structure consisting ofa 100 µm leading peak (FWHM), and a tail (rms size of
0.5 mm). We observed that the bunch shortens as expected
when the phase of the accelerating module is changed.
However, accurate measurements of the shape and size ofshort bunches have not yet been possible due to too low
number of SR photons on the streak camera, which prevents us from using a wavelength filter. The filter is essential to avoid smearing the data due to dispersion effects inthe streak camera optics [22]. Since the number of SR photons increases with the electron beam energy, the situation
should be improved when the full acceleration in the last
four cavities of the first accelerating module is used.

SUMMARY AND OUTLOOKThe new photoinjector of the TTF linac driving the
VUV-FEL has been successfully commissioned. Beam parameters are mostly understood, although fine tuning andmore accurate measurements are still needed. Improvements in the reliability and beam stability are also necessary. After the short shutdown from June to August 2004,
the beam operation of the whole linac will start in the beginning of September. The goal is to obtain first lasing at
30 nm by the end of this year.

ACKNOWLEDGMENT
I would like to thank all colleagues participating in therealization of the new injector, as well as the PITZ and TTF
staff and operators for its successful commissioning. Special thanks are due to S. Schreiber for help on preparationof this paper.

REFERENCES[1] “TESLA Test Facility Linac: Design Report”, ed. D. A. Edwards, DESY-TESLA-95-01[2] “TESLA: The superconducting electron positron linear collider with an integrated X-ray laser laboratory. Technical de-

TUBOS05

sign report. Part 2: The accelerator”, ed. R. Brinkmann etal., DESY-01-011[3] V. Ayvazian et al., Phys. Rev. Lett. 88 (2002) 104802.
[4] V. Ayvazian et al., Eur. Phys. J. D 20 (2002) 149.
[5] “SASE FEL at the TESLA Facility, Phase 2,” DESYTESLA-FEL-2002-01[6] “TESLA XFEL: First stage of the X-ray laser laboratory.
Technical design report, supplement”, ed. R. Brinkmann etal., DESY-02-167[7] H. Weise, “The TESLA X-FEL Project”, EPAC 2004,
Luzern, Switzerland, July 5-9, 2004
[8] S. Schreiber, “Commissioning of the VUV-FEL injector at
TTF”, EPAC 2004, Luzern, Switzerland, July 5-9, 2004
[9] K. Flöttmann and P. Piot, “An upgraded injector for the TTF
FEL-user facility”, EPAC 2002, Paris, France, June 3-7,
2002[10] K. Flöttmann et al., “The TESLA X-FEL injector,” PAC
2001, Chicago, Illinois, June 18-22, 2001[11] J. Sekutowicz et al., “A design of a 3rd harmonic cavity for
the TTF2 photoinjector,” DESY-TESLA-FEL-2002-05[12] S. Schreiber et al., “Performance of the TTF Photoinjector
for FEL Operation”, Workshop ”The physics and applications of high brightness electron beams”, Chia Laguna, Sardinia, July 1-6, 2002, ed. J. Rosenzweig, G. Travish, L. Serafini, World Scientific, Singapore, ISBN 981-238-726-9[13] M. Krasilnikov et al., “Optimizing the PITZ electron source
for the VUV-FEL”, EPAC 2004, Luzern, Switzerland, July
5-9, 2004[14] S. Schreiber et al., “Properties of cathodes used in the photoinjector RF gun at the DESY VUV-FEL”, EPAC 2004,
Luzern, Switzerland, July 5-9, 2004[15] J.P. Carneiro et al., “Behavior of the TTF2 RF gun with longpulses and high repetition rates”, DESY-TESLA-2003-33[16] S. Schreiber et al., Nucl. Instrum. Meth. A 445 (2000) 427.
[17] V. Miltchev et al., “Transverse Emittance Measurements at
the Photo Injector Test Facility at DESY Zeuthen”, theseproceedings[18] L. Lilje, “Achievement of 35 MV/m in the TESLA Superconducting Cavities Using Electropolishing as a Surface
Treatment”, EPAC 2004, Luzern, Switzerland, July 5-9,
2004[19] K. Honkavaara et al., “Design of OTR Beam Profile Monitors for the TESLA Test Facility, Phase 2 (TTF2)”, PAC
2003, Portland, Oregon, May 12-16, 2003[20] A. Cianchi et al., “Commissioning of the OTR Beam Profile
Monitor System at TTF/VUV-FEL Injector”, EPAC 2004,
Luzern, Switzerland, July 5-9, 2004[21] O. Grimm et al., “Synchrotron Light Beam Line for TTF2”,
EPAC 2004, Luzern, Switzerland, July 5-9, 2004[22] Ch. Gerth et al., Nucl. Instrum. Meth. A 507 (2003) 335

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A NOVEL DIAGNOSTICS OF ULTRASHORT ELECTRON BUNCHESBASED ON DETECTION OF COHERENT RADIATION FROM BUNCHED
ELECTRON BEAM IN AN UNDULATOR
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany

Abstract
We propose a new method for measurements of the longitudinal profile of 100 femtosecond electron bunches for
X-ray Free Electron Lasers (XFELs). The method is basedon detection of coherent undulator radiation produced bymodulated electron beam. Seed optical quantum laser isused to produce exact optical replica of ultrashort electron
bunches. The replica is generated in apparatus which consists of an input undulator (energy modulator), and output
undulator (radiator) separated by a dispersion section. The
radiation in the output undulator is excited by the electron bunch modulated at the optical wavelength and rapidly
reaches a hundred-MW-level power. We then use the nowstandard method of ultrashort laser pulse-shape measurement, a tandem combination of autocorrelator and spectrum (FROG – frequency resolved optical gating) providing
real-time single-shot measurements of the electron bunch
structure. The big advantage of proposed technique is thatit can be used to determine the slice energy spread andemittance in multishot measurements. We illustrate withnumerical examples the potential of the proposed method
for electron beam diagnostics at the European X-ray FEL.

INTRODUCTION
The past decade has been tremendous progress in the development of electron accelerators that produce ultrashortbunches approaching sub-100 femtosecond durations [1].
The use of ultrashort electron bunches for both fundamental studies and applications is increasing rapidly, too [2].
As electron bunches shrink in length and grow in utility, theability to measure them becomes increasingly important.
There are several reasons for this. First, precise knowledgeof the bunch properties is necessary for verifying theoretical models of bunch creation [3]. Second, in order to makeeven shorter bunches, it is necessary to understand the distortions that limit the length of currently available pulses.
Third, in experiments using these bunches, it is always important to know at least the pulse length in order to determine the temporal resolution of a given experiment. Moreover, in many experiments – studies of X-ray SASE FELs,
for example - additional details of the bunch structure play
an important role in determination of the outcome of the experiment. Of particular importance is the variation of peakcurrent, emittance and energy spread along the bunch. Finally, numerous applications have emerged for emittance-

Available online at http://www.JACoW.org

shaped ultrashort electron bunches and, of course, it is necessary to be able to measure the emittance, or energy spread
shape of the electron bunch used in these experiments [4].
The new principle of diagnostic techniques described
bellow offers a way for full characterization of ultrashortelectron bunches [5]. It is based on a construction of an
exact optical replica of an electron bunch.

OPTICAL REPLICA SYNTHESIS
A basic scheme of the optical replica synthesizer and optical replica of a complex test electron bunch is shown in
Fig. 1 [5]. A relatively long laser pulse is used to modulate
the energy of electrons within the electron pulse at the seedlaser frequency. The electron pulse will be timed to overlap with the central area of the laser pulse. The duration of
the laser pulse is much larger than the electron pulse time
jitter of a fraction of ps, so it can be easily synchronizedwith the electron pulse. The laser pulse serves as a seed formodulator which consists of a short undulator and dispersion section. Parameters of the seed laser are: wavelength
1047 nm, energy in the laser pulse 1 mJ, and FWHW pulse
duration 10 ps. The laser beam is focused onto electron
beam in a short (number of periods is equal to Nw = 5)
modulator undulator resonant at the optical wavelength of
1047 nm. Optimal conditions of focusing correspond to
the positioning of the laser beam waist in the center of themodulator undulator. The size of the laser beam waist is
10 times larger than the electron beam size. The seed laser
pulse interacts with the electron beam in the modulator undulator and produces an amplitude of the energy modulation in the electron bunch of about 250 keV. Then the electron bunch passes through the dispersion section (momentum compaction factor is about of R56  50µm) where
the energy modulation is converted to the density modulation at the laser wavelength. The density modulation
reaches an amplitude of about 10%. Following the modulator the beam enters the short (number of periods is equal
to Nw = 5) radiator undulator which is resonant at laser (ordouble) frequency. Because the beam has a large component of bunching, coherent emission is copiously producesby the electron bunch. The bandwidth-limited output radiation pulse (see Fig. 2) has 10 µJ-level pulse energy and isdelivered in a diffraction-limited beam.
The optical replica synthesizer is expected to satisfy certain requirements which can be achieved by suitable design

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Electric field [a.u.]

Figure 1: Schematic diagram of the optical replica synthesis through optical modulation of electron bunch and coherent
radiation in the output undulator. Signal beam filter based on polarizer: y-polarized light is transmitted, while x-polarized
light is reflected

0

50

100

150

input undulator operates at a seed frequency, and an output
undulator operating at a multiple of this frequency.
When propagating in vacuum, the radiation field is fasterthan the electron beam, and it moves forward (slips) by one
wavelength, λ, per one undulator period, λw . It is clear thatthe resolution of the electron pulse shape is determined by
the slippage of the radiation with respect to electrons in the
output undulator. If the slippage time is much less than theelectron pulse duration, Nw λ/c  τe , then one can neglect
the slippage effect.

t [fs]

Figure 2: Optical replica (rapidly oscillating curve) of atest electron bunch. Radiator operates at the wavelength of
1047 nmand choice of the components. A complete optimizationof the proposed diagnostic device can be performed onlywith three-dimensional time-dependent numerical simulation code. Numerical results presented in this paper are
obtained with version of code FAST [6] modified for simulation of optical replica synthesis. This code allows one toperform simulations of coherent undulator radiation taking
into account all physical effects influencing the synthesizer
operation.
One important point in the construction of replica synthesizer is separation of the optical replica from the seedlaser pulse. Numerous designs are possible – for example,
the combination of two planar undulators placed in crossed
positions, as it is illustrated schematically in Fig. 1. In another scheme a frequency doubler can used to distinguishthe optical replica from the intense seed laser pulse. when

THPOS65

MEASUREMENT OF ELECTRONCURRENT PROFILE
The study and detailed understanding of the cause andnature of collective effects is important for successful design of replica synthesizer. Proposed design is conductedto eliminate collective effects as much as possible throughinstallation of short input and output undulators. The signal
produced by replica synthesizer is thus a pulse of electricfield amplitude:
E(t) = F (I(t), n (t), ∆E(t)) = I(t)f (n (t), ∆E(t)) ,where n (t) is the normalized slice emittance and ∆E(t) is
the slice energy spread in the electron bunch. If longitudinal beam dynamics in the synthesizer is governed by purely
single-particle effects then this field directly proportional tothe peak current I(t).
Within the scope of the electrodynamic theory the output characteristics of the replica synthesizer are controlled
by three dimensional parameters: λ, Lw , σ, where λ is
the radiation wavelength, Lw = Nw λw is the radiator undulator length, and σ is the electron beam transverse size.

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E.L. Saldin et al. / Proceedings of the 2004 FEL Conference, 375-378

At an appropriate normalization of electrodynamic equations, the coherent undulator radiation is described by only
one dimensionless parameter [5]:N = 2πσ 2 /(λLw ) .
The parameter N can be referred to as the electron beamFresnel number, or as diffraction parameter. In general casethe electric field of the wave radiated in the undulator depends on the transverse size of the electron beam. For aproposed diagnostic technique it is of great interest to minimize the influence of the transverse emittance on the radiation field amplitude. In the case of a wide electron beam
λLw  2πσ 2 ,

or

N 1,

(1)

the most of the radiation overlaps with electron beam andfield of the wave is inversely proportional to the square ofelectron beam [5]:E(t) ∝ I(t)/σ 2 (t) .
Reducing the particle beam cross-section by diminishing the betatron function reduces also the size of the radiation beam and increases the total power of output radiation. This process of reducing the beam cross-section is,
however, effective only up to some point. Further reduction of the particle beam size would practically no effecton the radiation beam size and total radiation power because of diffraction effects (see Section 4). In the limitof a thin electron beam the transverse radiation beam size
tends to the constant value and the dependence of the output radiation on the transverse size of the electron beam israther weak. The boundary between these two asymptotes
is about σ 2  λLw .
From the preceding discussion we may want to optimize
the beam geometry as follows. The transverse size of theelectron beam has to be much smaller then the diffraction
limited radiation beam size
σ 2  λLw /(2π) ,

or

N 1,

(2)

The radiation wavelength and the undulator length dictate
the choice of the optimum transverse size of the electron
beam. Let us present a specific numerical example. Suppose γ = 103 , n = 2πµm, λw = 6.5 cm, Nw = 5,
λ = 1µm. If the focusing beta function is equal to 1 m thediffraction parameter is N = 2πσ 2 /(λLw )  0.04. We
come to the conclusion that we can treat this situation asa coherent undulator radiation generated by a thin electron
beam. This condition may be easily satisfied in practice.
Proposed design is conducted to eliminate emittance effects as much as possible through installation of a special
electron beam focusing system. In the radiator undulator
the betatron function should reach small values (of about
1 m) forming a narrow beam waist. The signal generated
by a replics synthesizer is thus a pulse of electric field withamplitude:

E(t) = F (I(t), n (t), ∆E(t)) = I(t)f (∆E(t)) .
Optimum parameters of the dispersion section can be estimated in the following way. The expression for the fundamental component of the bunched beam current is i1 (t) =2I(t)J1 (X), where X = 2πR56 δE/(λE0 ) is dimensionless quantity known as the bunching parameter, δE is theamplitude of energy modulation induced in the modulator
undulator. The function J1 (X) approaches X/2 for small
X; thus the microbunching approaches i1 (t)  XI(t).
We see that microbunching depends on the choice of thedispersion section strength. One might think that all wehave to do is to get microbunching amplitude to maximum– we can always increase R56 of the dispersion section andwe can always increase output power. It is not impossible to build dispersion section that has large R56 function.
In fact, one of the main problems in the modulator operation is preventing the spread of microbunching due to local
energy spread in the electron beam. For effective operation of replica synthesizer the value of suppression factor
should be close to unity. To get a rough idea of the spreadof electron density modulation, the position of the particles within the electron beam at the dispersion section exit
has a spread which is equal to ∆z   R56 ∆E/E0 , where∆E is the local energy spread in the electron bunch. We
know that uncertainty in the phase of the particles is about∆ψ  2π∆z  /λ. Therefore, a rough estimate for the microbunching spread to be small is
2πR56 ∆E/E0  1 .

(3)

The result of more careful analysis (see Section 3) showsthat in our case the optimal condition can be written as
X  0.1, δE  max(∆E)/3  250 keV. The amplitudeof energy modulation dictates the choice of the seed laserparameters. In our case the optimal peak power of the seedlaser is about of 100 MW.
In general, radiation field depends on the peak current,
I(t), local energy spread, ∆E(t), and local emittance,
n (t). However, under conditions of a thin electron beam
(2) and of a microbunching spread to be small (3), the electric field of the wave radiated in the replica synthesizer
is directly proportional to the peak current of the electron
beam:
E(t) = F (I(t), n (t), ∆E(t)) = const. × I(t) .
Thus, conditions (2) and (3) should be treated as optimal
tuning of undulator length, strength of the dispersion section and focusing beta function for measurement of theelectron bunch profile.

MEASUREMENT OF SLICE EMITTANCEAND ENERGY SPREAD
We found that longitudinal profile of the electron bunch
I(t) can be reconstructed on the basis of a single-shot measurements. The next problem is determination of slice

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εn [mm-mrad]

I [kA]

4
3
2

1.0

2.0

0.8

1.5
1.0
0.5

1
0

2.5

σE [MeV]

5

0

100

200

300

0.0

400

0.6
0.4
0.2

0

100

200

t [fs]

300t [fs]

400

0.0

0

100

200

300

400

t [fs]

Figure 3: Target (solid curve) and retrieved (circles) electron beam peak current, slice emittance and slice energy spread.
The nominal energy of electrons is equal to E0 = 500 MeV. Number of undulator periods is equal to Nw = 5. The optical
replica is generated at the radiation wavelength 1047 nm. Calculations were performed with code FAST.
energy spread (∆E(t)) and slice emittance (n (t)). Thiscan be done on the basis of multishot measurements. If
the electron pulse shape, I(t), is known, the local energy
spread ∆E(t) can be determined from the dispersion section strength scan. In this way, the problem of slice energy
spread measurement is transformed into a relatively simple
task of measuring the radiation field amplitude maximum(max E(t) ∝ max i1 (t)). An attempt to increase of theamplitude of the fundamental harmonic, by increasing thestrength of dispersion section, is countered by decrease theenergy spread suppression factor. In Section 3 we demonstrate that the microbunching i1 (t) has clearly a maximum
max i1 (t) = const. × δE[I(t)/∆E(t)] ,and the optimum strength of the dispersion section is
R56 =

λE0
.
2π∆E(t)Thus, measuring the max E(t) is strictly equivalent to measuring the local energy spread variations along the electron
bunch: I(t)/[max E(t)] = const. × ∆E(t). Since the optimal strength of the dispersion section is known, that of theunknown absolute value of slice energy spread, ∆E(t), iseasily found too.
Slice emittance can be measured in the following way.
Let us consider for illustration of the method a simple
model of the electron bunch, assuming that slice emittances are different, but Twiss parameters are the same inall slices (more general model is discussed in section 5).
The solution in our case is to realize that in a wide electron beam asymptote (1) the most of the radiation overlaps with the electron beam and the field of the wave isinversely proportional to the square of the electron bunch,
E(t) ∝ I(t)/σ 2 (t). If the electron pulse shape, I(t), is
known, the problem of the slice emittance measurement istransformed into a simple task of measuring the radiation
field amplitude in the case of a wide electron beam
I(t)/E(t) = const.×σ 2 (t)asmin(σ 2 )  λLw /(2π) .

Since the value of beta function and projected emittanceare known (from a standard method using a screen and

THPOS65

quadrupole scan), then the unknown absolute value of slice
emittance n (t) is easily determined, too.
In Fig. 3 we illustrate retrieval of the slice bunch properties from the optical replica of the electron bunch. Numerical calculations were performed using code FAST. The
nominal energy of electrons is equal to E0 = 500 MeV.
Number of undulator periods in the modulator and radiator
undulator is equal to Nw = 5. Period length is 6.5 cm.
The optical replica is generated at the radiation wavelength
1047 nm. The seed laser power is 100 MW, FWHM pulse
duration is 10 ps. Upper plots in Fig. 3 show comparison of target and reconstructed values for the beam current. When taking these data, parameters for the numericalexperiment were set according to conditions (2) and (3):focusing beta function in the radiator is 1 meter, and net
compaction factor of the dispersion section is 50 µm. Calculations show that pulse energy in the optical replica exceeds 30 µJ. Slice energy spread was determined by meansof the scan of dispersion section strength at the value ofbeta-function of 1 meter (lower plots in Fig. 3). The values of slice emittance were extracted with the help of additional set of calculations with large value of beat functionof 50 m which corresponds to the limit of a wide electron
beam. We see that slice bunch properties can be retrieved
with high accuracy if optical replica can be characterizedwith high accuracy.

REFERENCES[1] V. Ayvazyan et al., Phys. Rev. Lett. 88(2002)104802.
[2] P. Audebert et al., “TESLA XFEL: First stage of the X-ray
laser laboratory – Technical design report (R. Brinkmann etal., Eds.)”, Preprint DESY 02-167, DESY, Humburg, 2002.
[3] M. Dohlus et al., Preprint DESY 03-197, DESY, Humburg,
2003.
[4] P. Emma et al., Phys. Rev. Lett. 92(2004)074801.
[5] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Preprint
DESY 04-126, DESY, Humburg, 2004.
[6] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A429(1999)233.

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INDUSTRIAL PRODUCTION OF
SUPERCONDUCTING 1.3 GHZ ACCELERATOR MODULES
AND COMPONENTS FOR FEL APPLICATION
Michael Pekeler, Hanspeter Vogel, Peter vom Stein,
ACCEL Instruments GmbH, Bergisch Gladbach, Germany
Abstract
Daresbury Laboratory contracted ACCEL in April forthe delivery of two superconducting 1.3 GHz modules for
the R&D phase of their 4GLS [1] project. The modules
are delivered with guaranteed performance on cavity
voltage and cryogenic losses. The modules contain 2
TESLA [2] type cavities each and are of the design
developed at Forschungszentrum Rossendorf [3]. To
investigate the capabilities of our cavity treatment andpreparation techniques, our infrastructure was further
upgraded to allow chemical treatment and high pressurerinsing of TESLA cavities. First test results on TESLA
cavities produced for BESSY are very encouraging. 23
MV/m accelerating gradient were achieved in the cold
vertical test. In addition 12 power couplers of the TTF III
type were produced for DESY and BESSY. The
conditioning of those couplers was performed at DESY ina very short time of approximately 50 hours
demonstrating our high quality surface treatment
capabilities.
Figure 1: SRF bi-cavity module (courtesy FZ-Rossendorf)

SRF BI-CAVITY MODULES
The superconducting bi-cavity modules (s. fig.1) are
optimized for operation in cw mode with moderate beam
currents. The module design has been developed at
Forschungszentrum Rossendorf and is used under alicense agreement. ACCEL performs beside the module
integration the whole cavity manufacturing andpreparation including guaranteed performance values (s.
tab.1). Each module is equipped with two TESLA typecavities, which run at 2 K in superfluid helium. Bothcavities are mechanical coupled to a rigid string, which
improves the stiffness against microphonic oscillations.
The diameter of the two phase helium line connection to
the helium tank is increased compared to the TESLA
design to improve the performance with high dynamic rf
losses.
RF frequency
1300 MHz
Operating temperature
2K
Accelerating gradient
15 MV/m guaranteed
20 MV/m goal
Q0 @ 15 MV/m
5x109
Rf power per coupler
8 kW cw
Stand by losses<15 W
Length (flange to flange)
3.26 mTable 1: Basic parameters srf bi-cavity module

Available online at http://www.JACoW.org

The power capability of the rf input coupler is approx. 10
kW cw per cavity. The thermal shield of the module iscooled by liquid nitrogen at atmospheric pressure. The
magnetic shielding is provided by a mu-metal shieldhoused at the inner side of the vacuum tank.

TESLA TYPE CAVITIES AND COUPLERS
Two 1.3 GHz TESLA cavities have been prepared at
ACCEL for vertical test so far. The preparation including
tuning to field flatness was done this spring. Figure 2
shows one of the cavities during the high pressure rinsing
procedure.
Figure 3 and 4 show the results of cavities BE1 andBE2. The RF test was performed at DESY. The twocavities were produced for BESSY for FEL studies.
During preparation of the first cavity (BE2) a leakoccurred and the cavity needed to be vented and sealed
again. In addition, this cavity was shipped under N2
atmosphere whereas the second cavity (BE1) was shipped
under vacuum. Shipping under vacuum has the advantagethat one only needs to open the all metal valve located at
the cavity after pumpout of the insert pump line. Thus
there is no risk of contaminating the cavity by dust
accumulated in the pumping line.

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Cavity BE1 is now at ACCEL for the helium vessel
welding. After that they will be prepared at ACCEL forhorizontal test. The needed input power couplers of the
TTF III style were produced also at ACCEL and havebeen conditioned on a test stand at DESY already. Afterapprox. 50 h of conditioning the power couplers reached
the design values [4]. The horizontal test of the cavities
will be done at BESSY.

Figure 2: High pressure rinsing of a nine cell 1300 MHz
TESLA cavity at ACCEL.

Figure 3: Test result of first prepared TESLA cavity BE1.
Field emission was observed above 10 MV/m.

Figure 5: TTF III style power coupler

REFERENCES[1] M.W.Poole et al.,”4GLS: A New Prototype of Fourth
Generation Light Source Facility”, PAC 2003,
Portland, May 2003, p.189[2] F. Richard ed.,”TESLA TDR”, ECFA 2001-209,
March 2001
[3] A. Büchner et al.,”The ELBE-Project at DresdenRossendorf”, EPAC 2000, Vienna, June 2003, p. 732[4] W. D. Möller, private communication

Figure 4: Test result of second prepared TESLA cavity
BE2. No field emission was observed. The Q drop at
highest fields is without indication of x-rays. The cavity
was limited at 23 MV/m by a quench.

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T. Kamps / Proceedings of the 2004 FEL Conference, 381-384

COLLIMATION SYSTEM FOR THE BESSY FEL∗
T. Kamps
Berliner Elektronenspeicherring-Gesellschaft für Synchrotronstrahlung
BESSY, D-12489 Berlin, Germany
Abstract
Beam collimation is an essential element for the successful running of a linear accelerator based free electron laser.
The task of the collimation system is to protect the undulator modules against mis-steered beam and dark-current.
This is achieved by a set of apertures limiting the succeeding transverse phase space volume and magnetic dogleg
structure for the longitudinal phase space. In the following the design of the BESSY FEL collimation system is
described together with detailed simulation studies.

MOTIVATION
Experiences from linac driven FEL operation (for example at TTF1 [1]) indicate that beam collimation is essential
in order to provide protection of the undulator modules ensuring safe FEL operation.
The collimator section serves as transverse and longitudinal phase space filter which lets particles within a certain energy bandwidth and transverse phase space volume
pass. Particles outside this region are blocked and cannot
be lost in the undulator modules. In the transverse plane
this is achieved by a set of apertures limiting the succeedingtransverse phase space volume. In addition the collimator
is designed to remove halo and dark-current created andtransported through the linac upstream. The various halosources include the bunch compressor, wakefield generated
tails in the linac, mis-matched and mis-steered beam, andparticles produced by Coulomb Scattering. In the longitudinal plane off-energy particles are dark current electronsand energy tails produced in the bunch compressors. Dark
current is mainly created in the gun and through field emission in the super-conducting cavities [2]. Another important role for the collimator is set during the commissioningof the machine as linac and collimator tune-up dumps arepart of the system.

magnet undulators. Each undulator is composed of modules with length ranging from 1.6 m to 3.9 m, the total
length of the high energy FEL line is 70 m. A FODO lattice is superimposed onto the undulator structure with thequadrupole magnets located at the intersections between
the undulator modules. For the present analysis in total 14
undulator modules are taken into account for the simulation
studies. The gap between the undulator poles is 10 mm, thebeampipe radius is 4 mm. The undulator magnets are madeof NdFeB in order to obtain large undulator K parameters.
This material is very sensitive to irradiation, especially tothe reduced dose deposited by high-energy electrons (>20 MeV). From studies with NdFeB under electron irradiation [4] the limit for acceptable beam loss in the undulator chamber has been derived. It can be shown that for 1%
demagnetization the acceptable beam loss in the vacuum
chamber is 300 nC [3]. It is evident that a collimator system together with a fast-acting machine protection system
must be included in the FEL design.

Machine Protection System
The three FEL lines will initially operate at a bunch repetition frequency of 1 kHz each. With a bunch charge of
2.5 nC and a beam energy of ≤ 2.3 GeV the beam poweris 3 × 6 kW. At no location in the accelerator the structures
can withstand the power load for 6 successive incidents, thevacuum chamber wall will be destroyed within 2 ms. The
goal of the machine protection system will be to limit therelative beam loss to 10−5 of the maximum beam current.
This can be achieved by comparing the signals of a series offast current monitors that allow one to measure the bunchcharge at a precision of better than 0.2 pC. Together with
two other systems based on NaI beam loss monitors andoptical fibers this safety chain of triple redundancy will beable to enable machine operation in case of sudden beamlosses.

Undulator Protection
The BESSY FEL facility [3] will provide light fromthree different lines running at different energies. EachFEL line will have its own collimator section directly infront of the undulator modules. The collimator is designedwith the high energy beamline running at 2.3 GeV electron beam energy in mind but is without any modifications
adaptable for all other FEL lines. The modulators and radiators of the FEL are realized as planar pure permanent∗ Funded by the Bundesministerium für Bildung und Forschung, thestate of Berlin and the Zukunftsfonds Berlin

Available online at http://www.JACoW.org

SYSTEM OVERVIEWIn Fig. 1 the general layout of the collimator section
is depicted. After the last accelerating module the beam
enters first the transverse collimation section containing
a matching quadrupole triplet and the two transverse collimator apertures. From there the beam passes anothermatching section before going through a dogleg structure
made up with two dipole magnets separated by a drift region with a quadrupole triplet. The two energy collimators
are located before the first and after the third quadrupole.

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T. Kamps / Proceedings of the 2004 FEL Conference, 381-384

TUNE−UPDUMP COLL

ENERGYCOLLIMATION
TRANSVERSECOLLIMATION

LINAC MODULE

FELMATCHING
TUNE−UPDUMP LINAC

APERTURE
BLOCK

SEXT
BEND

QUAD

Figure 1: Collimator beamline including the last accelerating module and the beginning of the FEL undulator section.

Transverse Collimation

BETAFUNCTION

For transverse collimation many configurations withaperture slots or holes are possible [5]. The most common
solution is to place a thin (∼ 1/2 radiation length) spoiler
with a small aperture in front of a long (∼ 20 radiation
length) absorber block with a slightly larger aperture. The
spoiler produces a large transverse momentum spread in
the intercepted particles. The increased transverse momentum spread is converted into a large radial spread whichis completely attenuated by the following absorber block.
Two or more pairs are located in an optics channel with adequate twiss functions, which could be a FODO lattice with
π/2 phase advance between two pairs.

βx

PHASE ADVANCEβyCT2CENTERs

Figure 2: Transverse collimation scheme with two apertures CT1 and CT2.
In order to keep the BESSY FEL collimator system ascompact as possible and the total length under 50 m thescheme with two spoiler-absorber pairs was dropped in favor of a setup with two single absorbers. Recent studies for
the TTF2 collimator [6] show that with this scheme a highcollimation efficiency can be achieved with just two apertures working in parallel for both transverse dimensions.
The transverse collimation section contains two absorber

TUPOS02

0.4
0.3

UNDULATORCHAMBER

CT1

0.2
CT2

0.1

σ

0

10σ

−0.1
−0.2
−0.3
−0.4
−4

−3

−2

−1

0
x [mm]

1

2

3

4

Figure 3: Phase space portrait at the center between CT1
and CT2. Also shown is the inner boundary of the backtransformed undulator vacuum chamber.

π /2

CT1

blocks separated by π/2 phase advance. Each block is fitted with a small round aperture limiting the passage forthe horizontal and vertical direction at the same position.
This scheme requires that the twiss parameters for both dimensions are the same as well as the phase advance. Thisis achieved by producing a waist with the beam comingfrom the linac by means of a quadrupole triplet as shown in
Fig. 2. The beam enters the transverse collimator from left
coming out of the last accelerating section. The quadrupole
triplet focuses the beam in both dimension to waist, which
is located at the center between the two apertures CT1 andCT2. The horizontal phase space portrait at the center between CT1 and CT2 is illustrated in Fig. 3. The innerx’ [mrad]An additional set of sextupoles is placed close to thesequadrupoles. In order to minimize the flux of photons
escaping the transverse collimation section the dogleg isplaced between undulator and transverse collimation section. The collimator beamline ends with the last matching
section preparing the twiss parameters according the specification of the undulator lattice. The section contains twotune-up dump beam exits. One directly after the linac, theother just before the entrance of the undulator. The whole
section is less than 43 m long.

boundary of the undulator vacuum chamber is completely
shaded by the two apertures. The area inside the parallelogram is the upper limit for the collimator acceptance andis given by the beam stay clear distance ∆xclear and the
maximum beta function in the undulator βmax accordingto2(rpipe − ∆xclear )(1)acoll ≤
2βmax
and for the given case the collimator acceptance is acoll =0.3575 µm. From√ this the aperture radius can be calculatedwith gcoll = acoll · Lcoll where the transverse collimator
length Lcoll is the distance between the two apertures CT1
and CT2 which is equal to the value for the betafunction
at these location. The collimator aperture radius is then
2.6 mm. In the following copper is assumed for the absorber material. More studies are underway to compare the383

T. Kamps / Proceedings of the 2004 FEL Conference, 381-384

ACC

CT2

CE1
CE2

tures.
CT1

performance for copper and titanium. The length of theabsorber is around 10 radiation length and thus 140 mm.
In order to minimize wakefield effects and to keep the total block length within limits a step-in plus taper combination was chosen for the transition between gap radius tobeampipe radius. At the step-in the aperture changes from20 mm beam pipe radius to 5 mm at the taper start. The taper length is 200 mm bringing the radius down to the valueof 2.6 mm as required at the aperture. The exit face of thecollimator block is of the same design. Taper radius andlength have been chosen to minimize the transverse wakefield kick on the beam. The same type of absorber blocks
are also used in the energy collimation section.

FEL

Energy Collimation
Energy collimation is achieved with apertures in a closed
dispersion bump created by a magnetic dogleg structure.
The scheme is depicted in Fig. 4. The optics consists of
BETA

βy

βx

s

DISP

Dx

s
Dpx

CE2
CE1

Figure 4: Energy collimation scheme with dogleg bend andtwo apertures CE1 and CE2.
two bending magnets with 2.5o bending angle separatedby 2π phase advance. The phase advance is realized overthe short length of the dogleg of roughly 9 m by a three
quadrupoles. Sextupoles are added at locations of highdispersion to reduce orbit deviations at the undulator entrance for off-energy particles. The apertures are also located at points where the electrons are mainly sorted according to their energy deviation close to the outer two
quadrupoles. The first aperture CE1 has a slightly larger radius of 3.75 mm providing an energy cut at ±10% for darkcurrent rejection. The second aperture is of the same kindas the apertures in the transverse collimation part. With alocal dispersion function of around 0.1 m the acceptancebandwidth is around 5% energy spread. The total length ofthe dogleg is 8.8 m producing an orbit offset of 0.36 m.

SIMULATION STUDIESThe twiss parameters in the collimator beamline are plotted in Fig. 5 together with the locations of the various aper-

Figure 5: Twiss parameters in the collimator and undulator
sections.
Particle losses and and the energy bandwidth of the collimator system have been simulated using the elegant simulation package [7]. In Fig. 6 results for a seed with 5 ∗ 105
particles filling the whole beam pipe with an emittance of5250 mm mrad with an energy spread of dp/p = 0.10. The
plots in Fig. 6 show the loss distribution along the beamline and phase space portraits at the end of the undulator
beamline. The energy bandwidth of the system is ±4.7%.
From these simulations it can be concluded that no primaryparticle can hit the inner vacuum chamber of the undulator
beampipe. The sextupole magnets inside the dogleg keep
the orbit deviation for off-energy particles down. Switchingthese magnets off results in orbit deviation of up to 1 mm
for electrons with 5% energy deviation.
Back-reaction on the electron beam in terms of wakefields and coherent synchrotron radiation (CSR) effects
have been estimated. The emittance growth due CSR effects in the bending magnets leads to an emittance growthof 0.1% for the vertical and 2% for the horizontal emittancefor an input emittance of 1.5 mm mrad and energy spreadof 0.01%. The taper angle was chosen such that the resistive and geometric wakefield kicks are equal [8]. This
results with a bunch length of σt = 1 ps and gap radius of
2.6 mm to a taper angle of roughly 75 mrad. After the local
radius has reached 5 mm a step-in realizes the transition to
the nominal beam pipe radius.

Diagnostics
The collimator section is a key component in the linac
beamline as it is positioned directly in front of the FEL undulator. All phase space parameters like emittance, bunch
length and energy spread can be measured here. For orbit steering some quadrupoles in the beamline will beequipped with stripline BPMs. For tuning of the transverse collimator an OTR station is planned for the location of the beam waist between CT1 and CT2. The energy
spread can be measured with another OTR station in thedispersive arm. To study the efficiency of the dark cur-

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T. Kamps / Proceedings of the 2004 FEL Conference, 381-384

Lost Particles

Energy Bandwidth

4
3

CE1
CE2

CT2

2
1
0
0

dp = 422, dE = +/− 4.7%

MOMENTUM [me c]

4700

CT1

PARTICLES [10 5 ]

5

4600
4500
4400
4300

20

40

60
s [m]

80

1

100

Surviving Horizontal

2

3t [ps]

4

5

1

2

Surviving Vertical

0.2
0.2
y’ [mrad]x’ [mrad]

0.1
0

0

−0.1
−0.2
−0.2
−2

0
x [mm]

2

−2

−1

0
y [mm]

Figure 6: Performance studies for particle losses. Top left: Particle losses along the beamline. Top right: Final energy
bandwidth of the particle distribution. Bottom left and right: Horizontal and vertical phase space at the undulator exit.
rent suppression current transformers are located in frontof and after the dogleg. Besides that more current transformers will be put at the beginning and the end of the collimator section to monitor overall transmission through thesystem. The dipole chambers will all have exit windows
to enable detection of the synchrotron radiation for beamprofile measurements. For commissioning the collimator
section is equipped with two tune-up dumps, one straightafter the linac enabling commissioning of the linac without the need to bring the beam through the collimator. The
other tune-up dump is located just in front of the first FEL
undulator module.

CONCLUSION AND OUTLOOKA collimator system for the BESSY FEL has been discussed. The system is compact and protects the undulator
against impact by off-momentum and mis-steered particles.
With the next steps damage limits for the collimator material have to be derived. Furthermore the performance forsecondary particles will be studied.

ACKNOWLEDGMENTS
The author would like to thank M. Abo-Bakr, N. Golubeva and M. Körfer for their interest and many useful discussions.

TUPOS02

REFERENCES[1] H. Schlarb, “Design and performance of the TESLA Test Facility collimation system,” AIP Conf. Proc. 693 (2004) 209,
EPAC’02, Paris, June 2002.
[2] H. Schlarb, “Simulation of dark current transport through the
TESLA Test Facility linac,” DESY-M-02-01ZG, EPAC’02,
Paris, June 2002.
[3] The BESSY Soft X-ray Free Electron Laser, TDR BESSY
March 2004, eds.: D. Krämer, E. Jaeschke, W. Eberhardt,
ISBN 3-9809534-0-8, BESSY, Berlin (2004).
[4] T. Bizen, T. Tanaka, Y. Asano, D. E. Kim, J. S. Bak, H. S. Lee
and H. Kitamura, “Demagnetization of undulator magnets irradiated high energy electrons,” Nucl. Instrum. Meth. A 467(2001) 185.
[5] D. R. Walz, A. McFarlane, E. Lewandowski and J. Zabdyr,“Momentum slits, collimators and masks in the SLC,” PAC
1989, Chicago, Ill., March 1989.
[6] V. Balandin, K. Flottmann, N. Golubeva and M. Korfer,“Studies of the collimator system for the TTF phase 2,”
DESY-TESLA-2003-17.
[7] M. Borland, “elegant: a flexible SDDS-compliant code foraccelerator simulations,” Advanced Photon Source LS-287.
[8] NLC Zeroth Order Design Report, 1996.

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J. Baehr et al. / Proceedings of the 2004 FEL Conference, 385-388

HIGH POWER RF CONDITIONING AND MEASUREMENT OFLONGITUDINAL EMITTANCE AT PITZ
J. Bähr*, K. Abrahamyan&, G. Asova§, G. Dimitrov§, H. Grabosch, J. H. Han, M. Krasilnikov, D.
Lipka, V. Miltchev, A. Oppelt, D. Pose, B. Petrosyan, S. Riemann, L. Staykov, F. Stephan, DESY,
D-15738 Zeuthen, Germany
M. v. Hartrott, D. Richter, BESSY, D-12489 Berlin, Germany
I. Bohnet, J. P. Carneiro, K. Flöttmann, S. Schreiber, DESY, D-22603 Hamburg, Germany
P. Michelato, L. Monaco, D. Sertore, INFN Milano, 20090 Segrate, Italy,
Abstract
In 2003 the PITZ rf gun at Zeuthen has been
completely characterized. After the rf conditioning, 3.0
MW peak input power at 10 Hz and a rf pulse length of
0.9 ms have been reached. This corresponds to a gradientof 42 MV/m at the cathode. The goal is to increase theaccelerating gradient of the gun and the duty cycle
significantly. The motivation is based on the expectationof a remarkably increase in beam quality at higher
gradients. A high duty cycle is of advantage for FEL
users. The conditioning procedure of a new gun cavity
was started in spring 2004. The paper will report aboutprocedure and results of the conditioning. The preparationof an experimental setup for the measurement of thecomplete longitudinal phase space at about 5 MeV using a
streak camera will be finished in summer 2004.
Cherenkov light created by Silica aerogel radiators in thedispersive arm of PITZ is transmitted to a streak camera
by an optical transmission line. The light distribution of
the momentum spectrum is projected onto the entrance
slit of the streak camera. The setup will be presented.

INTRODUCTION
The photo injector PITZ at Zeuthen [1] is a dedicatedfacility for the investigation of rf guns for FELs, i.e. the
VUV-FEL and the European XFEL and future linear
colliders. The experimental setup consists of a 1.5 cell Lband rf gun with a Cesium-Telluride photo-cathode. A
solenoid system is used for space charge compensation.
The photocathode laser is capable to generate pulse trains
up to 0.8 ms length with a pulse to pulse separation of 1
µs. An extended diagnostics section is used for theexperimental investigation of the produced electron beam.
The first stage of the PITZ project (PITZ1) was
successfully finished in fall 2003 with the completecharacterization of the rf gun [2] which was thentransferred to the VUV-FEL project of DESY in
Hamburg. A schematic of the PITZ1 setup is shown in
Fig.1.

In spring 2004 another rf gun was installed at PITZ anda dedicated program of rf conditioning was started. The
goals of this high power conditioning are essentially thefollowing:• maximize the gradient at the cathode• increase the duty cycle
The maximization of the gradient is aimed to
optimize the beam quality, especially for minimization of
the transverse emittance. The increase of the duty cycle isuseful for the user community of the future FELs. The
results of the conditioning program are outlined in thenext chapter.
The preparation of the longitudinal emittancemeasurement is described in the third chapter. The aim is
the measurement of momentum spread and bunch length
as well as the correlation between them. The principle ofthe measurement will be outlined with emphasis on
optical problems of light collection and imaging.

HIGH POWER RF CONDITIONING
OF THE PITZ GUN
Status reached in 2003
The results of the rf conditioning of the rf gun in 2003
are shown in Table 1.

Figure 1: Scheme of the PITZ setup* juergen.baehr@desy.de&§on leave from YERPHI, 375036 Yerevan, Armenia
on leave from INRNE, 1784 Sofia, Bulgaria

Available online at http://www.JACoW.org

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Table 1: Results of rf conditioning of the gun achievedin 2003

Program for gun conditioning
A longer term program for the conditioning of rf guns
at PITZ was set up, which considers also the availabilityof a high power klystron and further hardware conditions.
This program consists of four steps:
1) Conditioning up to the status reached for the gun
operated in 2003
2) Conditioning to the maximum reachable peak
power, rf pulse length, mean power and duty cycle
using the currently available 5 MW klystron3) Replace the 5 MW klystron by a 10 MW klystron,
perform conditioning to the maximum reachable
parameters of peak power, mean power and duty
cycle4) After performing R&D on the rf system increase
the repetition rate (and such the duty cycle andmean power) in a first step to 50 Hz repetition rate
for a future RF gun

Status of conditioning using a 5 MW klystronConcerning most of the essential parameters of last year
[3] the status of conditioning was again reached in spring
2004. After that, a dedicated conditioning with threeparameter sets was performed. The goals were themaximization of the rf peak power using the 5 MW
klystron, the maximization of the rf pulse length, themaximization of the mean rf power and of the duty cycle
for the given hardware conditions. The three parameters
sets are characterized by a repetition rate of 10 Hz and alength of the rf pulse of 0.5 ms for the first set, by 5 Hz
repetition rate and 1.3 ms pulse length for the second set
and 10 Hz and 1.0 ms for the third set. The results areshown in Table 2. The high energy edge of the darkcurrent spectrum for a 0.5 ms rf pulse is shown in Fig.2.

Figure 2: High energy part of dark current spectrum forthe parameter set with 0.5 ms rf pulse
The maximum rf peak power, the mean power, theduty cycle and the beam momentum could already be
increased compared to 2003. At present, the current watercooling system is a limitation for reaching higher mean
power. At the end of 2004 the cooling system will be
upgraded to higher cooling power. The program will be
continued afterwards.

Dark current
The measured dark currents are about a factor 10 higher
for this gun than for the former one. It is assumed that thereason for the higher dark currents is based on a limited
copper surface quality of the present gun [4]. The darkcurrent depending on the solenoid current is shown in Fig.
3 for an input power of 4 MW.

Outlook
The conditioning program will be continued. The next
essential milestone will be the replacing of the 5-MWklystron by a 10-MW-klystron in 2005. This will allow anessential increase of the peak power and mean power.

Table 2: Results of rf conditioning in 2004
Repetition rate

10 Hz

5Hz

10 Hz

rf pulse length

0.5 ms

1.3 ms

1.0 mspeak power at gun

4 MW

4 MW

3 MW

mean power

20 kW

26 kW

30 kW

duty cycle

0.5%

0.65 %

1%

maximum momentum

5.17 MeV/c

5.17 MeV/c–

TUPOS03

Figure 3: Dark current vs. current of main solenoid for 4
MW input power for the current PITZ gun (prototype #1)

J. Baehr et al. / Proceedings of the 2004 FEL Conference, 385-388

MEASUREMENT OF THE
LONGITUDINAL EMITTANCE AT PITZ
The goal is the quasi-simultaneous measurement of
momentum, momentum spread and bunch length as wellas the correlation between the last two items.
The measurement of momentum and momentum spread
will be performed in the usual way [5] in the magnetic
spectrometer of PITZ. The measurement of the bunch
length will be realized using a streak camera. The lengthof the electron bunches is measured by transforming theelectron bunch in light pulses of same length. This ismainly done using Cherenkov effect, but Optical
Transition Radiation (OTR) is also used for cross-check.
At a beam energy of less than 5 MeV OTR is less suitablebecause of the low light output and the spatial emission
characteristics which make it difficult to collect the light.
The streak camera to be used for the measurement is asynchroscan camera type C5680 from Hamamatsu [6]with a time resolution of about 2 ps.
The light created by the radiators (Cherenkov, OTR) [5]is transmitted by an Optical Transmission Line (OTL) to
the streak camera. For PITZ the length of the OTL is 27 m
which is a challenge for the design of the optical system.

Optical transmission line
A simplified schematic of the OTL is shown in Fig. 4:

Figure 4: Schematic of an optical transmission line
The light is emitted by the radiator. It is collected by the
first lens of the optical chain mainly consisting of several
telescopes. The object light distribution is imaged onto theentrance slit of the streak camera. The light distribution in
the slit plane is projected onto the photocathode of thestreak camera by an internal optical system.
Most of the time during data taking, the streak camera
at PITZ is also used for the measurement of the length ofthe photocathode laser pulse and the corresponding
optimization of the temporal profile. The laser emits lightin the UV region, therefore the internal optics should havetransmission for 262 nm. System 1 in Table 3 is suitable
for these conditions but has a small aperture. For
measurements of light from radiators a high aperture of
the internal lens is needed in some cases. This is realizedwith system 2 which has the largest aperture, but is notsuitable for the measurement of the laser pulse length in
the UV region. Furthermore the internal lens should notcontribute to the time dispersion. System 3 in Table 3387

fulfills these demands but has a rather small aperture.
Therefore three different internal optical systems areavailable at PITZ to match the different demands of theexperiment properly.
Table 3: Properties of the internal optical systems of thestreak camera

There are several demands to the optical transmission
line:• project the image of the light distribution of theradiators onto the entrance slit of the streak camera• assure, that the readout for the streak camera
measurement is possible for screen 5 in thedispersive arm and for screen 4 in the straightsection behind the dipole• match the optical system of the OTL to different
input optical systems
Two principle solutions of the optical input system
directly behind the radiators are foreseen. The reason isthe condition, that one cannot simultaneously image an
extended object, for example the object light distributionof the beam momentum spectrum with a width of about
40mm, with a high aperture by a chain of lenses.
Therefore we have foreseen two input optical systems,
one for high aperture and small object extension using thefull Cherenkov cone (“full cone”), the second for imaging
the full momentum spectrum with small aperture, i.e. witha small angular section of the Cherenkov cone. Basing onthese design considerations and further design principles[7] the OTL was designed. The schematic of the full OTL
is shown in Fig. 5.
It includes two branches for the dispersive arm(measurement of the longitudinal emittance) and two
branches for measurements at screen 4.

Figure 5: Schematic of the optical transmission line, theabbreviations are presented in Table 4

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Table 4: Explanation of abbreviations in Figure 5

Special subsystems
Two special subsystems are included in the OTL:
• the Image Rotating System (IRS)• the Image Turning Box (ITB)The Image Rotating System is used to rotate the image
such that the azimutal direction of the image light
distribution of the momentum spectrum matches to thehorizontal orientation of the entrance slit of the streak
camera. This is needed because the axis of the dispersivearm has an inclination of 60 degrees and consequently theorientation of the light distribution of the momentum
spectrum too. The Image Turning Box is used to check
whether the Image Rotating System introduces unwanted
contributions to fractions of the image distribution in thelight propagation direction. The Image Turning Box turns
the image by 180 degrees. Measurements with andwithout the Image Turning Box allow to correct on such
unwanted contributions. Besides these two systems,
several diagnostics tools are foreseen, for example several
illuminated objects which can be moved in a plane
corresponding to the object plane. These objects can beused to adjust the OTL and find the low level light image
distribution in front of the streak camera slit. The use of
an illuminated slit object helps to prove the azimutalorientation of the image of the momentum spectrum light
distribution. The elements are mounted in a box
containing switchable optical components near to theoptical port.

Time dispersion
The optical transmission line mainly consisting of large
achromats causes a non-negligible time dispersion [8].
The main sources of the time dispersion are chromaticaberrations of the diffractive systems as could bedemonstrated by the use of optical bandpass filters [5],see Fig. 6. For a small bandwidth the time dispersion is
negligible. The use of the internal optical system of thestreak camera consisting of reflective optics results in adecrease of the measured bunch length by 3 ps. A R&D
project which aims in replacing refractive optics byreflective optics is ongoing.

Status of the project
The optical transmission line will be mounted andadjusted in September 2004. The first measurements withelectron beam will start end of September 2004.

TUPOS03

Fig. 6: Optical pulse length vs. filter bandwidth

OUTLOOK
Besides the conditioning program, the preparation of
the longitudinal emittance measurement, and a complex
measurement program for the characterization of the rf
gun currently in use [9], an essential upgrade of PITZ, thePITZ2 project [10], is in preparation. The main goal is
studying the principle of conserving small emittance tohigher beam energy and further improving the emittancegenerated in the gun. A minimal version of PITZ2 will becommissioned in the beginning of 2005. The
measurement of the longitudinal emittance is foreseen at
PITZ2 in the low energy and high energy section atseveral ports basing on the principles explained in thispaper.

REFERENCES[1] F. Stephan et al., Photo injector test facility underconstruction at DESY Zeuthen, FEL’00, Durham,
September 2000.
[2] M.Krasilnikov et al., Optimizing the electron source
for the VUV-FEL, EPAC’04, Lucerne, July 2004.
[3] J. Bähr et al., Behavior of the TTF2 RF gun with longpulses and high repetition rates, TESLA 203-33[4] J. H. Han et al., Conditioning and high power tests of
the RF guns at PITZ, EPAC’04, Lucerne,July 2004.
[5] D. Lipka, Untersuchungen zum longitudinalen
Phasenraum an einem Photodetektor für minimale
Strahlemittanz, PhD thesis, Humboldt University
Berlin, May 2004
[6]Hamamatsu Photonics K.K., Systems Division, 812
Joko-cho, Hamamatsu city, 431-9196 Japan[7] J. Bähr et al., Optical transmission system for streak
camera measurements, DIPAC’03, Mainz, May2003.
[8] J. Bähr et al., Measurement of the longitudinal phasespace at the Photo Injector Test Facility at DESY
Zeuthen, FEL’03, Tsukuba, September 2003.
[9] F. Stephan et al., Recent results and perspectives of thelow emittance photo injector at PITZ, FEL’04, Trieste,
September 2004.
[10] A. Oppelt et al., Future plans at the Photo Injector
Test Facility at DESY Zeuthen, FEL’03, Tsukuba,
September 2003.

389

R.W. Dekorsy et al. / Proceedings of the 2004 FEL Conference, 389-391

AN ELECTROMAGNETIC UNDULATORFOR THE FAR INFRARED AT ELBE
Th. Dekorsy, K. Fahmy, E. Grosse, P. Michel, W. Seidel, A.Wolf, R. Wünsch
FZ-Rossendorf, Dresden, Germany
Abstract
The first lasing in the mid infrared (IR) at the ELBE
FEL [1, 2] allows us to specify the parameters of an additional undulator for longer wavelengths to complement
the U27 undulator which is useful up to about 25 microns
at most. In the longer wavelength range FELs constitutea unique radiation source with appealing properties. Radiation quanta in this range are appropriate for the lowenergy spectroscopy of various interesting modes in solidstate quantum-structures as well as in complex biologicalsystems (e. g. DNA molecules).
We envisage an electromagnetic undulator with a periodof roughly 12 cm. Using the electron beam of ELBE, IR
light from 15 to 150 microns and beyond can be produced.
To keep the transverse beam extension small, the IR beam
is to be guided by a partial waveguide. An appropriate bifocal resonator mirror minimizes the mode coupling losses
at the exit of the waveguide. Detailed calculations andcomputer simulations predict an outcoupled laser power ofroughly 15 W at 150 microns which will be transported toexperimental stations. The maximum power is expected to
be 35 W at wavelengths between 40 and 90 µm.

we propose an undulator period of λu = 12 cm which should
preferably be made of electromagnets with an undulator
gap of 18 mm. To get a sufficiently high single-pass gain
30-40 undulator periods are necessary resulting in a total
undulator length of 4-5 m. The design of the electron beamline requires an asymmetric installation of this long undulator. Its middle is located roughly 1 m downstream fromthe resonator center. The maximum undulator parameterof Krms ≈ 2.5 corresponds to a field amplitude of 0.3 T on
the undulator axis.
Fig. 1 shows the wavelength range covered by such an
FEL. It slightly overlaps the range of the U27 undulator [2]and allows to produce light up to 200 µm. Above 150 µm
the diffraction losses in the presently designed IR beam line
diminishes the power available in the user laboratories considerably.

WHY ANOTHER UNDULATOR?
At present the U27 undulator at the radiation source
ELBE is producing IR light between 16 and 22 µm at electron energies around 16 MeV. Soon a second cryostat with
18 more accelerator cells will be installed. The higher
electron energy (up to 40 MeV) extends the range down to3 µm. To extend the range to the far infrared (λ ≤ 150 µm)
another undulator with a larger period is envisaged.
In the far infrared a FEL constitutes a unique radiation
source. Radiation quanta with this energy (10 - 100 meV,2 - 20 THz) are appropriate for the spectroscopy of lowenergy elementary and collective excitations. Such excitations are observed in solid-state quantum-structures and incomplex biomolecules as well. Their study establishes thebasis for understanding complex phenomena in solids andliquids and for elucidating processes in biological material.
Technological and medical innovations are the long-term
output of such investigation.

ITS PARAMETERS
To produce radiation in the THz region by means of the
ELBE beam an undulator with a period λu of several centimeters is needed. To avoid the use of electron energies below 20 MeV, where the energy spread is larger than 0.3%,

Available online at http://www.JACoW.org

Figure 1: Wavelength ranges of the existing U27 and theplanned U120 undulator of ELBE as a function of the kinetic electron energy Eekin . The colored areas indicate thewavelength λ1 of the first (fundamental) harmonic.
Above roughly 50 µm the diffraction of the IR beam has
seriously to be taken into account. It increases the beam
radius in the resonator and the beam line and reduces thecoupling with the electron beam in the undulator (filling
factor). Big resonator mirrors, large diffraction losses and asmall laser gain are the result. The long resonator (11.53 m)
and the long undulator (4-5 m) make it even more difficult.
That is why we propose a vertical beam compression bymeans of a rectangular waveguide spanning from the undulator entrance to the downstream resonator mirror (seeFig. 2). It should be 10 mm high. To avoid ohmic losses inthe side walls the waveguide has to be broad enough to al-

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R.W. Dekorsy et al. / Proceedings of the 2004 FEL Conference, 389-391

low a free beam propagation in the horizontal direction [4].
The free propagation on the upstream side of the resonatorsimplifies the passage through the dipole and quadrupole
magnets and provides an approximately round beam profile at the outcoupling mirror (M1). The downstream mirror(M2) has to be cylindrical. The proposed setup is similar
to that used at the FELIX facility [5]. Alternatively a complete waveguide without mode-coupling losses but with arather asymmetric outcoupled beam profile can be used.
To minimize the optical beam cross section in the undulator we propose an asymmetric resonator with the horizontal beam waist located in the undulator center and aRayleigh length of half the undulator length (≈ 2.5 m). The
proposed height of the waveguide and the resulting pole
gap are large enough for the electron beam and allows asufficiently large magnetic field on the axis (0.3 T) at a reasonable current in the undulator coils.
r
irro
lm
rica 2
d
in M
cyl
r
lato
du
un
ror
mir
cal
bifo M1

e
uid
veg
wa

Figure 2: Optical mode compression by means of a resonator with partial waveguide.
While the horizontal radii of curvature are solely determined by the Rayleigh length and the waist position thevertical curvature of M1 can be used to minimize the mode
conversion losses at the waveguide entrance. In general the
optimum curvature depends on the wavelength (black line
in Fig. 3).
Calculations using the code GLAD [6] have shown thata radius of curvature which is equal to the distance between
resonator mirror and waveguide entrance (407 cm, far-field
limit, red curve in Fig. 3) minimizes the mode conversion
losses at λ > 30 µm. Here, the losses per resonator pass
do not exceed 7%. At shorter wavelengths the losses growup to 12% per pass at 20 µm. For short electron pulses thegain exceeds this value. Using a larger radius of curvature(500 cm, blue curve) the losses can be reduced to 7%. But
this mirror has an advantage only between 15 and 25 µm.
The parameters of electron beam, undulator and resonator are summarized in Table 1. The beam parameters
are close to the actual beam parameters of ELBE. Putting
into operation the superconducting RF-gun [3] the energy
range can be extended to roughly 50 MeV.

EXPECTED GAIN AND POWER
Using the parameters of Table 1 we have calculated thesingle-pass gain (Fig. 4) and the outcoupled average laser

TUPOS04

Figure 3: Resonator round-trip losses as a function of the
wavelength λ calculated for various vertical radii of curvature Rv . The black line indicates the minimum losses while
the red and blue lines stand for definite radii of curvature.
Additionally to the mode conversion the absorption (2 x0.7%) on the mirror surfaces has been taken into account.
Electron beam(10) 20-45 (50) MeV
Kinetic energy
70 pC
Pulse charge
60 keV
Energy spread
15 mm mrad
Norm. transv. emittance
Undulator
12 cm
Undulator period
40
Number of periods
Magnetic field amplitude on axis ≤ 0.3 T≤ 2.5
Undulator parameter (Krms )18 mm
Pole gap
Resonator
1153 cm
Length2.5 m
Horizontal Rayleigh length
M1: 768.9 cm,
Horizontal radii of curvature
M2: 607.7 cm
M1: 407 cm
Vertical radii of curvature
M2: ∞
10 mm
Waveguide height (internal)
746 cmWaveguide length

Table 1: Parameters of electron beam, undulator and resonator

power [7] (Fig. 5). Changing the rms pulse length from
1 to 4 ps the λ of maximum gain is shifted from 40 µm(45%) to 150 µm (30%). Notice that Fig. 4 displays thegain maximum with respect to resonator desynchronization. Maximum power is obtained at a smaller desynchronization where the gain is considerably smaller. That is
why the maximum gain should clearly exceed the losses in
the resonator. The maximum average outcoupled power ispredicted to be approximately 35 W independently of the391

R.W. Dekorsy et al. / Proceedings of the 2004 FEL Conference, 389-391

1 ps

electron pulse length. The wavelength with the highest
power varies from 12 µm at 1 ps to 70 µm at 4 ps. The pronounced drop of average power around 20 µm is caused by
the large mode-coupling losses in this region (see Fig. 3).
1 ps

2 ps

2 ps

4 ps

4 ps

Figure 5: Maximum outcoupled average laser power predicted for 1, 2 and 4 ps (rms) electron pulses of ELBE as afunction of undulator parameter Krms and kinetic electronenergy Eekin . Calculation for the parameters of Table 1.

Figure 4: Laser gain predicted for 1, 2 and 4 ps (rms) electron pulses of ELBE as a function of undulator parameter
Krms and kinetic electron energy Eekin . Calculation for theparameters of Table 1 and optimum cavity desynchronization.

[2] P. Michel et al., these proceedings;
http://www.fz-rossendorf.de/FELBE.
[3] D. Janssen et al., Nucl. Instr. Meth. A507 (2003) 314.
[4] L.R. Elias and J. Gallardo, Appl. Phys. B31 (1983) 229.
[5] http://www.rijnh.nl.
[6] GLAD, Applied Optics Research, Woodland, WA 98674,
USA.

REFERENCES[7] S.V. Benson, CEBAF TN#94-065.

[1] F. Gabriel et al., Nucl. Instr. Meth. B161-163 (2000) 1143;
http://www.fz-rossendorf.de/ELBE.

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B. Steffen et al. / Proceedings of the 2004 FEL Conference, 392-394

BUNCH LENGTH MEASUREMENTS AT THE SLS LINAC USINGELECTRO OPTICAL SAMPLING
Bernd Steffen, Sara Casalbuoni, Peter Schmüser, Stefan Simrock (DESY, Hamburg)
Manfred Tonutti, Axel Winter (RWTH Aachen)
Timo Korhonen, Thomas Schilcher, Volker Schlott, Hans Sigg, Daniel Suetterlin (PSI, Villigen)
TR-Screen
Abstract
Electron BeamAn electro optical sampling experiment has been carriedout at the 100 MeV electron linac of the Swiss Light Source(SLS). Coherent transition radiation produced by the relativistic electron bunches was focused by parabolic mirrors
onto an optically active ZnTe crystal. The induced birefringence was sampled with ultrashort titanium sapphirelaser pulses. The laser repetition frequency of 81 MHz wasphase-locked to the 500 MHz radio frequency of the linac
with a relative timing jitter of less than 40 fs. The minimum measured bunch length amounts to 3.0 ps (FWHM)
with an estimated resolution of 300 fs (rms).

INTRODUCTION
Bunch length measurements in the 100 femtosecond
regime are of high interest for VUV and X ray free electron
lasers and for the planned femto-slicing experiments at the
Swiss Light Source and BESSY. The technique of electrooptical sampling (EOS) provides the possibility to measure
the longitudinal charge distribution with very high resolution, determined by the width of the optical laser pulse, therelative time jitter between electron bunch and laser pulse
and the dispersion of the electric field pulse in the nonlinear optical crystal. A 15 fs titanium-sapphire (Ti:Sa) laser
is used to sample the birefringence which is induced in anonlinear optical crystal by the co-moving electric field of a
relativistic electron bunch or, alternatively, by the coherent
transition radiation (CTR) generated by the bunch. The initial linear polarization of the laser pulse is converted into aslightly elliptical polarization which is then converted into
an intensity modulation. By shifting the timing of the laser
pulse relative to the bunch in sub-picosecond steps the time
profile is obtained by sampling over many bunches. Previous accelerator-related EOS experiments have been carriedout at the infrared free electron laser FELIX [1], Fermilab,
the TESLA Test Facility TTF [2] and SLAC. Here we report on the successful continuation of our TTF experiments
at the 100 MeV injection linac of the SLS.

EXPERIMENTAL SETUP
A schematic drawing of the experimental setup inside
the tunnel of the SLS linac is shown in figure 1. Transition
radiation is produced at a screen made from a 380 µm thicksilicon wafer with a 1 µm thick aluminum coating. Bothoptical and coherent transition radiation are coupled out of
the beam pipe through a 60 mm diameter quartz window.
The coherent transition radiation (CTR) is focused onto the

TUPOS06

Polariser for CTR

OTR-Radiation
CTR-Radiation
Laser Beam

Polariser
mo

ri
r se
moto

d

tori

Pellical BS

Screen

sed

BS
Lens

ZnTeCrystal
ris e
moto

d

Golay
Cell

Quarter-wave plate
Wollaston-Prism

Linear Stage with
CCD, PMT and 35ps GaAs Diodemotorised

Fibre couplers

Figure 1: Scheme of the setup inside the linac area.

ZnTe crystal by two parabolic copper mirrors with focal
lengths of 200 mm. The optical transition radiation (OTR),
having only a small divergence of ≈ ± γ1 = ±10 mrad,
passes a 12 mm hole in the first mirror and is focused ontoa photomultiplier which registers also the laser pulses andallows to adjust the temporal overlap of the Ti:Sa pulses
and the electron bunches with sub-nanosecond precision.
The Ti:Sa laser has a pulse width of 15 fs, a central wavelength of 800 nm and a bandwidth of 65 nm. It is mounted
on a vibration-damped optical table in the technical galleryof the SLS. The laser beam is guided into the linac bunker
by a 15 m long optical transfer line equipped with five mirrors and two lenses (f = 4 m) which image the Ti:Sa laser
onto the ZnTe crystal. The dispersion in the lenses stretches
the laser pulses to about 120 fs FWHM. Since the expected
length of the linac bunches is far longer, no attempt wasmade to compensate for the pulse lengthening. The beamtransfer line has proven very stable, neither short-term nor
long-term motions of the laser spot position inside the linac
tunnel were observed.
A simplified view of the signal detection scheme isshown in figure 2. ZnTe is optically isotropic at vanishing field but acquires a birefringence in the presence of astrong electric field. The crystal is cut in the (110) planewith the the crystallographic (-1,1,0) axis oriented horizontally. Both the CTR and the Ti:Sa pulse are polarized horizontally. The induced birefringence can be described by arefractive index ellipse whose large axis is rotated by 45 ◦with respect to the horizontal axis. The laser polarisation

Available online at http://www.JACoW.org

B. Steffen et al. / Proceedings of the 2004 FEL Conference, 392-394

Electron
Beam

393

Beam
Splitter
Diode
Detector

Polariser
ZnTe
CTR Screen

λ/4

WollastonPrism

TiSa-Pulse

Figure 2: Simplified view of the signal detection using aquarter-wave plate, Wollaston prism and a balanced diodedetector. The laser and CTR radiation are polarized horizontally, parallel to the (-1,1,0) axis of the ZnTe crystal.
components along the two main axes of the index ellipse
acquire a phase shift difference when passing the crystal ofΓ ∝ r41 ECT R where r41 is the electro optical coefficientof ZnTe and E CT R the electric field of the CTR pulse. Behind the ZnTe crystal the laser pulse will then be elliptically polarized. The most sensitive method to measure thisellipticity is to pass the beam through a quarter wave plate,transforming the slight elliptic polarisation into a slightly
perturbed circular polarisation, and then through a Wollaston prism, which serves for a spatial separation of the two
orthogonal polarisation components. These are then coupled into optical multimode fibers and guided to a balanced
diode detector located outside the linac tunnel. In the caseof coincidence between CTR pulse and laser pulse the balanced detector signal is proportional to sin Γ and thereby
roughly proportional to the electric field of the CTR pulse
while without CTR the balanced detector signal will vanish.
The EOS technique as a tool for ultra precise longitudinal bunch diagnostics depends critically on the synchronisation between the femtosecond laser pulses and the radio
frequency (RF) of the linac. This proved to be a considerable challenge since the linac RF of 500 MHz has no
subharmonics close to the 81 MHz repetition frequency of
the Ti:Sa laser. The synchronisation scheme is describedin [3, 4].
An rms time jitter of σt = 35 fs was reached in the synchronisation. However, this does not include the relative
jitter between the electron bunches and the linac RF.

DATA ANALYSIS AND RESULTS
Transfer function for coherent transition radiation
The CTR produced by the SLS linac bunches ranges up
to 500 GHz. Diffraction has strongly limiting effects on
the transfer of this radiation to the ZnTe crystal. The optics code ZEMAX was used to compute the frequencydependent transmission of the radiation from the CTR
screen to the ZnTe crystal. The finite radius of the CTR
screen (r = 23 mm) and the aperture limitations provided

Figure 3: CTR electric field distribution at the crystal for
100 GHz. The center of the crystal, and so the laser spot,has been shifted to the position where a movable Golay cellhas registered the maximum signal.
by the vacuum window (r = 30 mm) and the parabolic
mirrors (r ≈ 130 mm) were taken into account. The finite
laser spot size (σ = 2 mm) is responsible for the strong
suppression of frequencies below 50 GHz. The spatial intensity distribution of the laser pulse and the CTR electricfield (f = 100 GHz) on the ZnTe crystal is shown in figure
3. The center of the ZnTe has been moved to a position
where a movable Golay cell has registered the maximum
signal.

Data acquisition
The linac was operated with 3.125 Hz bunch repetition
frequency. After having established the coarse time overlap
between the bunch arrival at the CTR screen and the Ti:Sa
laser by means of the photomultiplier, a time interval of±500 ps was scanned in ps steps to find a coincidence signal in the balanced detector. This turned out to be straightforward. Once this signal was found, a narrow interval wasscanned in 200 fs steps. At each time step the photomultiplier signal as well as the balanced detector signal for 10
consecutive bunches were recorded by a 7 GHz digital oscilloscope and stored in the internal memory of the scope.
The first EO-signal seen is shown in figure 4. The signal of
the balanced detector is plotted in figure 5 (top) as a function of the time delay. One observes a peak of several ps
width with undershoots at the front and rear end due to the
suppression of the low frequency components of the CTR
signal.

Determination of the longitudinal bunch profile
Starting from an assumed shape of the bunch a Fouriertransformation was made and the CTR transfer function applied. The resulting frequency spectrum was Fourier backtransformed and compared to the measured signal. A sin-

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B. Steffen et al. / Proceedings of the 2004 FEL Conference, 392-394

Figure 4: Oscilloscope screenshot with electro-optic signal. Top trace: Signal of the timing photomultiplier withlaser pulses; Center trace: Signal of the balanced diode detector; Bottom trace: Linac trigger
Figure 6: Two measurements taken directly after one another with positive and negative phase steps respectively.
30

ampl i t ude [ mV]

20

10

5

10

15

20

25

30

t ps ec- 10

ter of σt = 300 fs over a time span of 5 minutes. Hereall sources of time jitter are included. The reproducibility
was tested by two consecutive measurements with positive
and negative time steps but otherwise identical parameters(figure 6). No significant difference between the measurements was seen, suggesting a high reproducibility over thetime of 9 minutes needed to take the two measurements.

CONCLUSION AND OUTLOOK

Figure 5: Top: The measured time profile of the CTR pulse(green with error bars) and the fit obtained with bunch profile composed of three Gaussians (see below). Bottom: Assumed bunch profile composed of three Gaussians whoseparameters are optimized to obtain the best fit of the measured profile (red curve in the upper plot).

gle Gaussian for the bunch shape turned out to be inadequate. The best fit was found for an assumed bunch profile
composed of three Gaussians of different amplitude, position and width, see figure 5 (bottom). At optimum bunch
compression the FWHM of the electron bunch is 3.0 ps.
The overall time resolution of this experiment can be estimated by measuring the amplitude fluctuation of the balanced detector signal when the laser pulse is put on therising edge of the CTR pulse. The amplitude jitter is thendominated by the arrival time jitter of the electron bunches.
Assuming a linear dependence between time and amplitude
on the flank of the signal, we derive an overall timing jit-

TUPOS06

The electro-optic technique has been successfully applied for bunch length measurements at the SLS linac. The
synchronisation accuracy of the 81 MHz laser repetition
frequency to the 500 MHz linac RF was better than 40 fs.
Further improvements appear possible by employing a digital control scheme. This is planned for the electro optical sampling experiment at the DESY VUV FEL. Here the
ZnTe crystal will be mounted inside the beam pipe of thelinac to permit a direct measurement of the bunch field.
This has the further advantage that the EOS measurements
no longer need a transition radiation screen intercepting theelectron beam. Hence longitudinal bunch diagnostics will
be possible in parallel to FEL operation.

REFERENCES[1] D. Oepts et. al. Picosecond electronbunch length measurement using an electro-optic sensor. In Proceedings of the 21stInternational FEL Conference, Hamburg, 1999.
[2] M. Brunken et. al. Electro-Optic Sampling at the TESLA Test
Accelerator: Experimental Setup and First Results. DESY,
2003. TESLA Report 2003-11.
[3] A. Winter et al. Bunch length measurements at the SLS
linac using electro optical techniques. In Proceedings of the
EPAC’04, Lucerne, 2004.
[4] A. Winter. Bunch length measurements using electro-opticalsampling at the SLS linac. Master’s thesis, DESY, 2004.
DESY-THESIS-2004-027.

395

O.G. Grimm et al. / Proceedings of the 2004 FEL Conference, 395-398

LONGITUDINAL BUNCH SHAPE DIAGNOSTICS WITH COHERENTRADIATION AND A TRANSVERSE DEFLECTING CAVITY AT TTF2
L. Fröhlich, O. Grimm∗ , K. Klose, M. Nagl, O. Peters, J. Rossbach, H. Schlarb
DESY, Hamburg, Germany
M. Ross, T.J. Smith, D. McCormick, P.J. Emma
SLAC, Menlo Park, USA
Abstract
At the DESY TTF2 linear accelerator three special techniques to characterize the longitudinal charge distributionof the electron bunches that drive the free-electron laser
are currently under study: electro-optical sampling, farinfrared spectral analysis of coherent radiation and the useof a transverse deflecting cavity to streak the bunch. The
principles and implementations of the latter two are described in this paper. Details on electro-optical sampling
can be found in [1].

INTRODUCTION
The VUV-FEL at DESY, Hamburg, will require novel
techniques to characterize the longitudinal charge distribution of the electron bunches that drive the free-electron
laser. Conventional methods, e.g. streak cameras, are inadequate due to both the short bunch lengths of the linac
and the high sensitivity of the lasing process to spikes in
the charge distribution which therefore need to be knownwith high resolution. Three techniques are currently investigated at TTF2:• Analysis of the far-infrared spectrum of synchrotron,transition, diffraction and undulator radiation. At
wavelengths comparable to or longer than the bunch
length or a particular longitudinal feature of the bunch,
the spectrum will be modified by coherent effects.
• Streaking the bunch with a transverse deflecting RF
structure. The longitudinal profile is converted intotransverse space and thus becomes observable with acamera on, e.g., an optical transition radiation screen.
• Measuring the electric field strength through electrooptical sampling. The interaction of a laser pulse
much shorter than the electron bunch with the bunchelectric field in a nonlinear crystal gives rise to a detectable effect on the laser polarization (see [1] for details).
The first technique, working in the frequency domain, has
no requirements on timing or triggering precision, but thebunch shape is accessible only through an ambiguous inversion process, whereas the latter two techniques are directly sensitive to the longitudinal charge distribution andneed precise timing.
∗ Corresponding author. E-Mail: oliver.grimm@desy.de

Available online at http://www.JACoW.org

A new method, consisting essentially of the generationof an optical replica of the longitudinal bunch shape andthen a two-dimensional measurement of this replica in frequency and time domain simultaneously, has recently been
proposed in [2].

FAR-INFRARED ANALYSIS OF
COHERENT RADIATION
Analysis principle
The bunch shape is imprinted on the radiation spectrum
dU/dλ through the form factor F (λ),



dU 
dU
2
N + N (N − 1) |F (λ)| ,
(1)
=
dλ
dλ 0
where (dU/dλ)0 is the emission spectrum of one single
electron, N is the total number of electrons and the form
factor is the Fourier transformof the normalized longitudi∞
nal charge distribution S(z) ( −∞ S(z) dz = 1),


 ∞
−2πi
z dz.
(2)
F (λ) =
S(z) exp
λ−∞The basic assumption in the derivation of these equations
is that each electron generates a time-dependent electricfield at a given position that is the same for all electrons
except a time delay (corresponding to a spacial distance), 0 (t + ∆ti ).1
 i (t) = E
i.e. E
Measurement of the total spectrum and knowledge ofthe number of electrons and the single-electron spectrum
then gives access to the modulus of the form factor. The
final step of inverse Fourier transforming this to arrive atthe bunch shape requires knowledge of the phase of theFourier transform. The phase is not completely arbitrary
but also not unambiguously determined by the modulus[3], therefore a full bunch shape reconstruction is impossible. The technique of Kramers-Kronig analysis, however, allows to retrieve some of the missing phase information. If one writes for the complex form factor F (ω) =|F (ω)| exp(iψ(ω)), with ω the angular frequency, then2ω ∞ ln(|F (x)|/|F (ω)|)dx(3)
ψ(ω) = −π 0x2 − ω 2
1 This limits the allowable transverse size: particles offset from thecentre will contribute with a time delay just as particles further behind,thus washing out spacial structures. Additionally, the emission spectrum
generally changes with angle, also limiting the tolerable transverse size.

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O.G. Grimm et al. / Proceedings of the 2004 FEL Conference, 395-398

is the minimum phase value consistent with the measured
modulus [4]. Application of the Kramers-Kronig analysis requires knowledge of the form factor modulus fromzero to infinite frequency, thus an extrapolation of measured data. Some extrapolation has been suggested in [4],but experiences from the first run of TTF show that the results are quite sensitive to these extrapolations and detailed
studies of their effects are necessary [5].
Currently, the opposite way is pursued: simulations are
performed to calculate the spectrum for some expectedbunch shapes and then compared to the measurements. An
example, referring to the synchrotron radiation beamline
described in the next section, where the actual magnetic
field of the fourth BC2 magnet, the vacuum chamber cutoff (see [6]) and the form factor for three bunch shapes
have been taken into account is shown in Fig. 1. The spectrum is averaged over the clear aperture of the window. A
parametrization for the two sharply peaked shapes is given
in [7]. Not yet included is the transmission characteristic of
the beamline and the frequency response of the pyroelectricdetectors. Interference with radiation from the third magnet will modify the spectrum, but also requires further understanding of the beamline optics and has been neglected
here.
−17

8

Average spectrum: Magnet D4BC2 onlyx 10

Geloni et al. (5 keV local energy spread)
Geloni et al. (10 keV local energy spread)
Gaussian (σ=300 µm)

7

6

4000

3000
Charge density (a.u.)

Energy (J/Hz)

5

4

2000

1000

3
0
–600

–400

–200

0

200

400

600

800

1000

z (um)

2

1

0

0

0.5

1

1.5
Frequency (Hz)

2

2.5

3
12

x 10

Figure 1: Simulated spectrum after (1). Included are theform factor for the bunch shapes shown in the inset, thechamber cut-off and the window transmission.
Precise knowledge of all spectral modifications by thevacuum chamber, beamline mirrors and apertures, interferometer and detectors is required to extract the form factor. One experimental approach to determine these factors is to use a blackbody source (having a known emission spectrum) at the beginning of the beamline and then tomeasure the spectrum with the interferometer as used forbunch length determination. This way, all effects are taken
into account correctly except the coupling between sourceand beamline. The intensity in the far-infrared of such asource is very low, but might be sufficient if a sensitive

TUPOS07liquid Helium cooled bolometer is used. The other, calculational approach is to use optical simulation software toassess the transmission characteristics of the beamline andthe interferometer and to calculate vacuum chamber cutoff and detector response from detailed considerations of
their geometries and configurations. A combination of alltechniques appears to be necessary to get to a sufficiently
precise answer.
An interesting alternative would be a synchrotron radiation source that is guaranteed to emit only incoherent radiation at the frequencies of interest. This requirement would
be fulfilled by long, smooth bunches, but it is currently notclear how this could be assured at TTF2. Even small bunch
structures would easily dominate due to coherent emission.

Synchrotron radiation beamline at TTF2
A beamline to guide both far-infrared (50–3000 µm) andvisible synchrotron radiation from the first bunch compressor (BC2) of the TTF2 linear accelerator to a diagnostic
station outside of the controlled area at some 10 m distancehas recently been constructed [8]. It will allow a directcomparison between streak camera and far-infrared measurements for features on length scales above some 100 µm(the streak camera resolution). Later, infrared techniques
extending to shorter wavelengths, i.e. to shorter bunch
lengths, will also be used further downstream the accelerator, employing synchrotron, transition and undulator radiation.
The principle design of the beamline relies on simple optics: a paraboloid mirror close to the synchrotron radiation
viewport transforms radiation originating from an arc of
about 7 cm length in the source region at some 81 cm distance into a nearly parallel beam which is then transported
by large flat mirrors through Aluminium pipes to the experimental station. The beamline including the interferometeris flushed with dry Nitrogen to reduce the strong absorption of water vapour in the far-infrared. It is already partly
prepared for later evacuation to fore-vacuum in case the absorption needs to be reduced further. A crystalline Quartz
window (z-cut, clear aperture 60 mm, 4.8 mm thick) isused as viewport.
Outcoupling port The synchrotron port at the fourthBC2 magnet (D4BC2) is at 18° relative to the beam axis,
seeing approximately the first 2.5° of the beam trajectoryarc. With a nominal bending radius of about 1.6 m at
130 MeV, this corresponds to an arc length of 7 cm. A
photo of the port is shown in Fig. 2, a sketch of the geometry in Fig. 3.
The radiation is emitted along the arc into a cone of typical half-opening angle of 2.4° (42 mrad) at 250 µm andof 0.2° (3.5 mrad) at 500 nm. In the vertical the radiation
beam is restricted by the vacuum chamber height of 16 mm,
in the horizontal by the 60 mm diameter window. To transport this beam over some 10 m distance requires focusingof the infrared radiation soon after the chamber window

O.G. Grimm et al. / Proceedings of the 2004 FEL Conference, 395-398

397

the tunnel is of no security concern.
Interferometer A polarizing Martin-Puplett interferometer2 is used to analyze the spectrum of the far-infrared
radiation. The wire grids are wound from 10 µm goldplated Tungsten wire with 30 µm spacing, so that the interferometer works at wavelengths longer than about 60 µm.
The clear aperture of the device is about 10 cm diameter.
Currently, DTGS pyroelectric detectors are used, a liquid
Helium cooled bolometer will also be available for the next
TTF2 run. Details of the device can be found in [9, Chapter
7].
Compared to a Michelson interferometer, this type has
the advantage of an almost perfect beam splitter characteristic for wavelengths longer than about twice the wire
spacing and full transmission of the incoming radiation to
the detectors (whereas on average half is reflected back tothe source with a Michelson device).

Figure 2: Outcoupling port of the beamline.
Synch.
Rad.

D1BC2

D4BC2
D3BC2

Electrons

First results

on
cti !
fle rdRe pwau

Magnetic field region
500 mm18°

Quartz window
60 mm

D2BC2

Chamber height: 16 mm

2,50°

100 m
m

Mirrorfocus

Figure 3: BC2 layout and D4BC2 vacuum chamber.
to limit the necessary mirror sizes. To this end, a 90° offaxis paraboloid mirror is installed after the window, reflecting the parallelized beam upwards to the tunnel roof. The
paraboloid is machined from Aluminium, has a projected
diameter of 100 mm and 810 mm focal length.
Depending on the bunch compressor settings, the electron beam can enter the dipole chamber at any position
allowed by its 100 mm width. The mirror can be rotatedaround its vertical axis, such that the focal point follows
the emission region of the synchrotron radiation. The rotation plane is aligned with the nominal electron beam plane.
The focusing is not very sensitive to the exact longitudinal
position, so that no translation of the mirror in this axis isnecessary.
Transport line The approximately parallel beam fromthe paraboloid is reflected by a flat mirror under the tunnel roof straight out to further flat mirrors in the diagnostic
container that feed the radiation into the interferometer orthe streak camera. For the latter, narrow wavelength filters
are used to avoid resolution loss due to dispersion in thewindow. The beam travels within large Aluminium pipesof 250 mm diameter (200 mm over a short section throughthe radiation protection wall) to avoid additional diffraction
losses. Nitrogen is flushed from the diagnostic station into
the tunnel at flow rates below 1 l/s, so that effluence into

During the first run of TTF2 in May/June 2004, the infrared beamline was commissioned and first interferograms
were taken. Fig. 4 shows one example. Clearly visible
is one advantage of the Martin-Puplett interferometer: itallows suppression of radiation intensity fluctuations bynormalizing the detector signals to the total intensity, i.e.
their sum. Such fluctuations were strong during this startup
phase.
The interferogram shows a small secondary signal at
about 67 ps delay, coming from reflections within the
4.8 mm thick Quartz window, also reflected in the spectrumby the interference structure. The spectral shape shows
agreement on a broad scale with the first simulations (seeFig. 1), but more detailed understanding of transmission
and detector effects is necessary to extract quantitative information.

TRANSVERSE DEFLECTING CAVITY
LOLA3 is a disk-loaded waveguide structure with constant impedance, using the TM 11 hybrid mode. It was
originally build as a separator for secondary particles withthe same momentum but different mass, and is used now asa transverse deflector to streak electron bunches.
The main parameters of the structure are: length 3.66 m,
iris aperture 44.88 mm, peak deflecting voltage 26 MV (at20 MW), frequency 2856 MHz, filling time 645 ns (quality factor 12100). The latter characteristic allows to streak
only a few bunches from the TTF2 bunch train, working inquasi parasitic-mode. Because of the constant impedance,
the transverse deflecting electric field is decreasing along
the structure. The phase shift per cell (35 mm length) is
120°. A photograph of the structure installed in the TTF2
tunnel is shown in Fig. 5.
2 Build by RWTH Aachen.
3 The name comes from its designers: Greg LOew, Rudy Larsen andOtto Altenmueller. It was built at SLAC 1968.

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O.G. Grimm et al. / Proceedings of the 2004 FEL Conference, 395-398

Raw detector signal amplitudes

2004−06−06T075843.asc−0.05

detector signal [V]

−0.1

−0.15

−0.2

−0.25
35

40

45
50
55
roof mirror position [mm]6065Difference Interferogram
0.4

Here, βc and βp are the beta function values at the cavity
and at the screen, respectively, ∆ψ y the beta function phaseadvance between them, V 0 the peak deflecting voltage andλ the wavelength of the structure, E 0 the electron energy
and ϕ the phase angle between RF zero crossing and thebunch origin [10]. The observed spot size on the screen σ yis related to the bunch length σ z through (see Fig. 6)

2

2πeV0
2 + σ2 β βσy = σy,0
sin
∆ψ
cos
ϕ
, (5)
c
p
y
z
λE0

0.3
2004−06−06T075843.asc

intensity [arb. units]

0.2
0.1
0
−0.1
−0.2
−0.3

where σy,0 is the bunch transverse size along the streak
direction on the screen.

−0.4
−0.5

−1

−0.5

0.5

1
−10

x 10

Reconstructed spectrum with cutoff

−3

3.5

0
time shift τ [s]x 10

2004−06−06T075843.asc

intensity [arb. units]

3
2.5
2
1.5
1
0.5
0

1

2

3

4

5
frequency [Hz]

6

7

8

9
11

x 10

Figure 4: Measured raw (top) and normalized difference (middle) interferogram and the reconstructed spectrum (bottom) from the first run of TTF2 in May/June 2004.

Figure 6: LOLA operation principle.
From (5) it is obvious that σ y is not very sensitive to ϕfor small ϕ, but (4) shows that the centroid offset is thenproportional to ϕ. For high resolution, the bunch should
be streaked over a large fraction of the screen. The phasestability is then required to be significantly better than thephase length of the bunch: ≈0.1° for a bunch length of
25 µm and the 105 mm wavelength of the structure. Otherwise, the spot on the screen will jitter by more than thescreen size.
Energy change due to beam loading from the LOLA
structure within a bunch train is confined to approximately
the first 80 bunches and amounts to no more than 0.03%[11].

REFERENCES[1] B. Steffen, this conference (Paper ID TUPOS06)[2] E.L. Saldin et al., DESY 04-126 (July 2004), also this conference (Paper ID THPOS65)[3] J.S. Toll, Phys. Rev. 104,1760 (1956)[4] R. Lai, A.J. Sievers, Nucl. Instr. Meth. A397(1997) 221[5] J. Menzel, private communication

Figure 5: Photograph showing LOLA in the TTF2 tunnel.

[6] M. Dohlus, T. Limberg, Nucl. Instr. Meth. A407(1998) 278[7] G. Geloni et al., DESY 03-031 (March 2003)[8] S. Casalbuoni et al., EPAC ’04, 5–9 July 2004, Lucerne,
Switzerland (Paper ID THPLT046)

Analysis
A particle within a bunch with position z relative to someorigin will, after traversing the deflecting structure, have an
offset ∆y(z) on a screen given by∆y(z) =TUPOS07eV0 βc βp sin ∆ψy
E0




2πz
cos ϕ + sin ϕ .
λ(4)[9] M.A. Geitz, DESY-THESIS-1999-033 (November 1999)[10] M. Nagel, FEL Report 2004 (to be published)[11] K.L.F. Bane et al., SLAC-PUB-10160/TESLA Report 200324 (September 2003)

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V.V. Miltchev et al. / Proceedings of the 2004 FEL Conference, 399-402

TRANSVERSE EMITTANCE MEASUREMENTS AT THE PHOTO
INJECTOR TEST FACILITY
AT DESY ZEUTHEN
V. Miltchev∗ , K. Abrahamyan† , G. Asova‡ , J. Bähr, G. Dimitrov§ , H.-J. Grabosch, J.H. Han,
M. Krasilnikov, D. Lipka, A. Oppelt, B. Petrosyan, D. Pose, S. Riemann, L. Staykov, F. Stephan
DESY, Zeuthen, Germany
M.v. Hartrott, D. Richter, BESSY GmbH, Berlin, Germany
J.P. Carneiro, K. Flöttmann, S. Schreiber, DESY, Hamburg, Germany
P. Michelato, L. Monaco, D. Sertore, INFN Milano-LASA, Segrate (MI), Italy
I. Tsakov, INRNE Sofia, Sofia, Bulgaria
I. Will, Max-Born-Institute, Berlin, Germany
W. Ackermann, S. Schnepp, S. Setzer, TU Darmstadt, Darmstadt, Germany
Abstract
This contribution summarizes the transverse emittancestudies done at the Photo Injector Test Facility at Zeuthen(PITZ) for producing an electron beam that meets the requirements of the VUV-FEL. Systematic measurements ofthe beam emittance in a wide range of parameters (e.g.
bunch charge, rf phase, solenoid fields) will be presented
and compared with simulations.

This phase φm will be used as a reference phase throughout this paper. The electric field gradient on the cathodesurface was about 41 MV/m. A single slit scanning tech-

INTRODUCTION
The main goal of PITZ is the development of electron
sources for Free Electron Lasers. Since the first productionof photoelectrons in January 2002 several upgrades havebeen realized. An important step was the transition from
temporal gaussian laser profile to flat top distribution in thespring of 2003. This change was motivated by the resulting significant emittance reduction, which will be demonstrated in the first part of this paper. In the second part ofthe paper the optimization of the rf gun toward the VUVFEL requirements is summarized. In the third part the measurements of thermal emittance are discussed and finallysome of the latest emittance measurements are presented.

MEASUREMENTS WITH VARIOUS
TEMPORAL PROFILES OF THE UVLASER PULSE
The emittance was measured as a function of the mainsolenoid current using gaussian temporal profile of the laser
pulse of 6.0±1.0 ps FWHM. The bunch charge was set to0.49 ±0.02 nC. The radial laser beam profile was about
flat top, but with a modulation depth of ∼20 % , σ x =0.53 ±0.02 mm, σ y = 0.65 ±0.02 mm. The rf phase φwas set to the phase with maximum mean energy gain φ m .
∗ velizar.miltchev@desy.de† on leave from YERPHI, Yerevan, Armenia‡ on leave from INRNE Sofia, Sofia, Bulgaria§ on leave from INRNE Sofia, Sofia, Bulgaria

Available online at http://www.JACoW.org

Figure 1: Projected normalized emittance as a function of
the main solenoid current I main : (a) for a bunch charge of
0.5 nC and a gaussian laser pulse with a length of 6.3 ps
FWHM, and (b) for a bunch charge of 1.0 nC and a flat top
laser pulse with a length of 23 ps FWHM. I focus denotes
the solenoid current to focus the beam on the position of
the slit mask.
nique was used for the emittance measurements [1, 3].
Results of the measurements compared with ASTRA [4]simulation are presented in Fig. 1(a). The minimal emittance is about 4 mm mrad. Since the emittance scaleswith the charge, we expect the emittance for the gaussian

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V.V. Miltchev et al. / Proceedings of the 2004 FEL Conference, 399-402

case at 1 nC to be even larger. The same set of measurements has been repeated with a flat top longitudinal laser
pulse profile of 23.0±1.0 ps FWHM. The bunch charge was
set to 1.00±0.02 nC. The laser beam transverse sizes are:σx =0.52±0.02 mm, σ y =0.63±0.02 mm. The rf phase was
set to φm ; the electric field gradient on the cathode wasabout 42 MV/m. The parameters have not yet been optimized for minimum emittance, these measurements are tocompare flat hat with gaussian laser pulses. The measurements compared with an ASTRA simulation are presented
in Fig. 1(b). The minimal emittance is about 2.3 mm mrad.
Since the measurement conditions for both solenoid scans
are about the same, a flat hat laser profile yields a more than
two times smaller emittance than the gaussian profile.

−5◦ , 0◦ , +5◦ at a maximum accelerating gradient on thecathode of 42 MV/m. During this first optimization step themagnetic field at the photo-cathode was not compensatedby the bucking solenoid. Later on, for the settings {I main ,φ} with the smallest emittance, the bucking solenoid current has been fine tuned. During the measurements, thelaser temporal and transverse properties were frequently
monitored and adjusted. The laser pulse temporal profile
was a flat top of 18 to 23 ps FWHM with a rise and falltime of 5 to 7 ps. The transverse shape was slightly asymmetric: σx = 0.50 to 0.52 mm, σ y = 0.61 to 0.63 mm.

EMITTANCE OPTIMIZATION TOWARD
VUV-FEL REQUIREMENTS
After the upgrade of the laser system an extended measurement program was carried out at PITZ in order to characterize and optimize the VUV-FEL rf gun (cavity prototype #2) for TTF [2, 5].

Figure 3: Projected normalized emittance for different
bucking solenoid currents. The bunch charge is 1.0 nC, themain solenoid was set to 305 A. The the gun phase is: (a)φ − φm = 0◦ , and (b) φ − φm = −5◦ . The horizontal andvertical emittance as well as their geometrical average areshown. The solid line in the lower graph represents a corresponding ASTRA simulation at the geometrical average.

Results of the solenoid and phase scans
Figure 2: Projected normalized horizontal (a) and vertical(b) emittance for different main solenoid currents and gun
phases φ − φm = −10◦ , −5◦ , 0◦ , +5◦ . The bunch charge
is 1.0 nC.

Optimization strategy
As a first optimization step, the emittance for a bunchcharge of 1 nC is measured as a function of the mainsolenoid current I main for the rf phases φ − φ m =−10◦ ,TUPOS09

According to the strategy described above, the emittance
was measured as a function of the main solenoid current
for various rf phases. Results of these scans are presented
in Fig. 2. The smallest emittance is about 2 to 2.5 mm mradmeasured in both transverse planes for a main solenoid current of 305 A and for rf phases φ − φ m = 0◦ , −5◦ .

Further optimization by scanning the bucking
solenoid
As pointed out, for the measurements plotted in Figure
2 the residual magnetic field on the photo cathode has not

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V.V. Miltchev et al. / Proceedings of the 2004 FEL Conference, 399-402

been compensated. Therefore, additional scans with thecompensating bucking solenoid were performed for the settings with the smallest emittance: {305 A, φ − φ m = 0◦ }and {305 A, φ − φm = −5◦ }. The results are shown in Fig.
3. Error contributions of the background noise [3], finite
optical resolution and statistical fluctuations are all taken
into account and propagated to the final measurement errors represented with the error bars. As shown in [5] andin Fig. 3(b) the experimental data agree well with simulations. The smallest vertical emittance is 1.5 mm mrad,√a minimum geometrical average x y of 1.7 mm mrad is
obtained.

to the rf field should be negligible (≤ 2 %) compared tothe expected thermal emittance  th . The final goal of themeasurements is to estimate the average kinetic energy E kof the electrons emitted from the Cs 2 Te photo-cathode. An
emission model introduced in [7] is assumed, such that:2Ek
th = σ(1)
3m0 c2

Impact of vacuum components

Emittance scaling with the laser spot sizeHence,
Ek = 1.5m0 c2

 d 2th(2)

dσwhere σ denotes the r.m.s. laser spot size.

The PITZ experience shows that the impact of the vacuum components on the beam emittance should be studied
and must be in the list with optimization items. For the firstof the two sets of measurements shown in Fig. 4, the electron beam has been horizontally shifted with respect to its
design orbit. The beam is steered 6 mm closer to the laser
vacuum mirror then the nominal distance of 12 mm. This
metallized glass mirror is being charged up by the beamand dark current and the resulting electrostatic field affects

Figure 5: Transverse emittance vs. laser spot r.m.s. size
measured with the slit scanning technique at 3 pC.

Figure 4: Impact of the laser vacuum mirror (VM) on theemittance. The bunch charge is 1.0 nC, the gun phase φ −φm = −5◦ .
the beam quality. As it is demonstrated in the second measurements set in Fig. 4 an emittance reduction of 0.5 to
1.0 mm mrad is achieved by steering the beam away fromthe vacuum mirror. A detailed simulation study of this phenomena [6] agrees well with the presented measurements.

THERMAL EMITTANCEMEASUREMENTS
The thermal emittance is limiting the emittance reachin photo-cathode rf guns. Therefore, its measurement isof high importance to understand the ultimate performance
limit of rf gun based electron sources. The thermal emittance measurements use a laser pulse with a gaussian temporal profile of 6 to 8 ps FWHM. Simulations with ASTRA
show that for these short pulses the emittance growth due

Figure 5 shows the normalized emittance for different
r.m.s. laser spot sizes measured with the single slit scanning method at a charge of about 3 pC and an accelerating
gradient at the cathode of 32 MV/m. For these conditions(tiny charge, low gradient) simulations predicts an emittance growth of less than 5 % due to space charge effects.
d=1.0 to 1.1 mrad.
From a straight line fit one obtains dσ
Inserting the fit values into Eq. 2 yields:
Ek = 1.5m0 c2

 d 2dσ= 0.8 ± 0.1 eV(3)For comparison a second set of measurements similar tothe set presented in Fig. 5 has been done using the solenoid
scan method to determine the emittance. The analysis of
the solenoid scan data takes into account the evolutionof beam energy along the magnetic axis as well as spacecharge effects and yields about the same kinetic energy as
the slit technique.

Dependence of the emittance on the accelerating
gradient
The emittance was measured at a charge of 2 to 3 pC as
a function of the accelerating field E at the cathode. The
single slit scanning technique was used for these measurements. The electric field amplitude E 0 was varied in the

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V.V. Miltchev et al. / Proceedings of the 2004 FEL Conference, 399-402

ongoing. Figure 7 shows emittance measurements done fora bunch charge of 1 nC at the current stage of optimization.

SUMMARY

Figure 6: Emittance as a function of the accelerating fieldon the cathode surface E for a charge of 2 to 3 pC.
range from 24 to 37 MV/m. The laser spot size of σ x =0.46 mm, σy = 0.51 mm was kept fixed. The solenoid current was adjusted such that the beam was focused on theposition of the slit mask. The rf phase φ was set to φ m foreach measurement. In addition, before each measurement
the charge was measured as a function of the rf phase. From
the rising edge of the phase scan the zero crossing phase φ 0
was determined. Finally the applied field at the cathode iscalculated as E = E0 sin(φm − φ0 ). The results presented
in Fig. 6 show an increasing emittance with the accelerating
field. The simulation predicts a constant emittance. It includes the beam dynamics in the rf gun, but does not scale
the kinetic energy of the emitted electrons with the appliedfield at the cathode. The increasing thermal emittance corresponds to a rising kinetic energy of the emitted electrons.
This phenomena can be explained by assuming a modified
Schottky effect [8].

RECENT MEASUREMENTS WITH
CAVITY PROTOTYPE #1

The impact of the temporal laser pulse profile on theemittance has been demonstrated. A longitudinal flat top
laser pulse yields a significantly better emittance than agaussian shape. The characterization of the rf gun cavity
for the VUV-FEL was presented. The smallest normalized
projected emittance is measured with 1.5 mm mrad in thevertical plane. The smallest geometrical average emittanceof both transverse planes is 1.7 mm mrad. Measurements
to estimate the thermal emittance have been done using avery small bunch charge and moderate accelerating gradients. The average kinetic energy of the emitted photo electrons is estimated to be 0.8±0.1 eV. An increasing of thethermal emittance with the accelerating field on the cathode has been observed. The characterization of the next
cavity at PITZ is ongoing and shows promising results.

REFERENCES[1] M. Krasilnikov et al., “Characterization of the Electron
Source at the Photo Injector Test Facility at DESY Zeuthen”,
FEL 2003, Tsukuba, Sept. 2003.
[2] F. Stephan et al., “Recent results and perspectives of the low
emittance photo injector at PITZ”, these proceedings.
[3] V. Miltchev et al., “Transverse Emittance Measurements at
the Photo Injector Test Facility at DESY Zeuthen (PITZ)”,
DIPAC2003, Mainz, May 2003.
[4] ASTRA manual, http://www.desy.de/∼mpyflo/[5] M. Krasilnikov et al., “Optimizing the PITZ electron source
for the VUV-FEL”,EPAC 2004, Luzern, July 5-9, 2004.
[6] S. Setzer et al., “Influence of Beam Tube Obstacles on the
Emittance of the PITZ Photoinjector”, EPAC 2004, Luzern,
July 5-9, 2004.
[7] K. Flöttmann, ”Note on the Thermal Emittance of Electrons
Emitted by Cesium Telluride Photo Cathodes ”,TESLA-FEL
97-01 (1997).
[8] G. Suberlucq, “Development and Production of Photo Cathodes for the CLIC Test Facility”, FEL 1996, Rome, August
1996.
[9] J. Bähr et al., “High power rf conditioning and measurementof longitudinal emittance at PITZ”, these proceedings.

Figure 7: Measurements with cavity prototype #1.
After cavity prototype #2 was fully characterized at
PITZ and installed at TTF, cavity prototype #1 was put into
operation at PITZ in the beginning of 2004 [2] followed by
the rf conditioning [9]. The beam dynamics optimization is

TUPOS09

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P. Craievich et al. / Proceedings of the 2004 FEL Conference, 403-406

THE SHORT-RANGE WAKEFIELDS IN THE BTW ACCELERATINGSTRUCTURE OF THE ELETTRA LINAC
P. Craievich∗ , G. D’Auria, Sincrotrone Trieste, Trieste, Italy
T. Weiland, I. Zagorodnov† , Technische Universitaet Darmstadt, Darmstadt, Germany
Abstract
Future FEL operations in the ELETTRA LINAC requirea high quality beam with an ultra short bunch. The knowledge of the short-range wakefields in the backward traveling wave (BTW) accelerating structure is needed to predict
the beam quality in term of the single bunch energy spreadand emittance. To calculate the effect of the longitudinal
and transverse wakefields we have used the time domain
numerical approach with a new implicit scheme for calculation of wake potential of short bunches in long structure[1, 2]. First the wake potentials of the BTW structure are
numerically calculated for very short bunches, than an analytical approximations for wake functions in short range
are obtained by fitting procedures based on analytical estimations. Finally the single bunch energy spread inducedby short-range longitudinal wakefields is analyzed for the
first phase of the project FEL-I (up to 40 nm).

INTRODUCTION
The FERMI@ELETTRA project aims to construct asingle-pass FEL user-facility in the spectral range 100-10
nm using the exiting normal conducting 1.0 GeV linac.
Figure 1 shows the proposed machine layout for the twophase of the project: FEL-I (100-40 nm) and FEL-II (4010 nm) [3].

PRE-INJECTORPHOTOINJECTORVERTICALRAMP

1st BUNCHCOMPRESSORHIGH
HARMONICCAVITYS1 – S5 LINACACCELERATINGSECTIONS

FEL-I

S6 — S7
for FEL-II
2nd BUNCHCOMPRESSOR

Figure 1: Schematic layout of the configuration for the
FEL-I and FEL-II stages.
The new scheme foresees the installation of an RF photocathode gun [4], providing a high quality electron beam,with parameters directly related to those required at the entrance of the undulator lines [3]. At the photoinjector exit
the beam is further accelerated with a 100 MeV preinjector,
composed by two 3 m accelerating sections with focusing
solenoids, that get the beam out of the space-charge energy domain and creates an energy-position correlation for∗ paolo.craievich@elettra.trieste.it† This work was supported in part by the Deutsche Forschungsgemeinschaft under contract WE1239/22

Available online at http://www.JACoW.org

bunch compression. After the first magnetic chicane, fiveaccelerating structures of the exiting linac, each equippedwith an RF pulse compression system (SLED), allow thebeam to reach the energy required by FEL-I, 700 MeV. In
total the present linac includes seven 6 m accelerating sections, the remaining two accelerating sections will be located after the second bunch compression and will be used
for the FEL-II to rise the beam energy up to 1 GeV. Eachaccelerating section is a backward traveling wave (BTW)
structure composed by 162 nose cone cavities magneticallycoupled and operated in the 3/4π mode. In this scenario,
to avoid undesirable beam degradations, in term of energy
spread and emittance, the wakefileds effects have to becarefully considered. We have studied the longitudinal andtransverse cases using the time domain code ECHO witha new implicit scheme for the calculation of the wake potentials of short bunches in long structures [1, 2]. We haveconsidered the wakefields evolution for bunches of different lengths passing through a single cell, a multi-cell and acomplete accelerating structure [5]. This paper reports thelongitudinal and transverse wakefields calculations for acomplete BTW accelerating structure and the single bunchenergy spread induced by short-range longitudinal wakefields for the FEL-I. A preliminary optimization of the energy spread has been carried out by varying the energy gain
and RF phase of the accelerating structure.

LONGITUDINAL WAKE FUNCTION OF
THE BTW STRUCTURE
The wake potentials of Gaussian bunches with length
ranging from 1000µm to 50µm are calculated for a whole
BTW accelerating structure. In figure 2 the calculated longitudinal wake potentials (solid lines) are reported. To findan analytical approximation of the wake function we havechosen a combination of periodic [7] and one cell [6] dependence since the BTW structure can be treated as a periodic structure of finite length. From the fit of the numericalwake potentials we have obtained an analytical expression
approximating the wake function (in V /pC):
w10 (s) = A01 e−

√

s/s0

A02
+ √
s

(1)

where A01 = 7300, s0 = 3.2 · 10−4 and A02 = 3.4.
Figure 2 shows the longitudinal wake function (1) (black
dotted line), which tends for small s to be an envelope
function to the wakes and fits the numerical results up to
1.5mm. To find an analytical approximation up to 5mm,
we have added to expression (1) an additional term with

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P. Craievich et al. / Proceedings of the 2004 FEL Conference, 403-406

0

0

0

−w1||(s)−500
σ=1000µm−1000−w20(s)

−1500
−2000
−2000
W0 [V/pC]

W0|| [V/pC]

σ=1000µm

−1000

||

−2500

||

−3000

−3000
−4000
−3500
σ=50µm−4000
σ=50µm

−5000
−4500
−6000
−0.5

0

0.5

1

1.5

2
2.5
σ [mm]

3

3.5

4

4.5

−5000
−3

5

Figure 2: Longitudinal wake potentials (solid lines) andlongitudinal wake functions (1)(black dotted line) and (2)(black dashed line) of the BTW structure.

−2

−1

0

1
s/σ

2

3

4

5

Figure 3: Longitudinal numerical (blue solid lines)and analytical (red dashed lines) wake potentials of the BTW structure.

√

4

0

s dependence. Taking into accoutn the last correction
term the fit gives the following analytical expression for
the wake function:

−6

(2)

where A01 = 7450, s0 = 3.1 · 10−4 , A02 = 3 and A03 =3000.
The previous relation approximates the longitudinal wake
function on a wider range compared to expression (1).
Figure 2 shows the longitudinal wake function (2) (black
dashed line) that tends to be an envelope function to thewakes up to 5mm. Figure 3 presents the calculated longitudinal wake potentials (blue solid lines) together withanalytical approximation (2) (red dashed lines). A moredetailed analysis of figures 2 and 3 shows that the analytical expression 2 approximates very well the longitudinal
wake function up to 5mm.

TRANSVERSE WAKE FUNCTION OF
THE BTW STRUCTURE
Figure 4 shows the calculated transverse wake potentials(solid lines) for different bunch length σ. As in the previous
case, the BTW structure is treated as a periodic structure offinite length and to find an analytical approximation for thetransverse wake function, a combination of periodic [7] andone cell [6] dependence was chosen. The expression for thewake function is obtained with a fit of the numerical wakepotentials (in V /pC/m):



  √
√
s
1
(s) = A11 1 − 1 +e− s/s1 + A12 s (3)w⊥s1where A11 = 1.7·105 , s1 = 1.2·10−4 and A12 = 8.5·104 .
Figure 4 shows the transverse wake function (3) (black
dashed line), which tends to be envelope function for the

TUPOS10

−4

⊥

√
A02
s/s0
+ √ + A03 ss

σ=50µm−2

W1 [V/pC/m]

w20 (s) = A01 e−

√

x 10

−8
−10
−12
σ=1000µm
−14
−16
−18
−0.5

w1⊥(s)
0

0.5

1

1.5

2

2.5

3

3.5

s [mm]

Figure 4: Transverse wake potentials (solid lines) andtransverse wake functions (black dashed line) of the BTW
structure.
wakes up to distance s = 2mm after the bunch center. Figure 5 plots the calculated transverse wake potentials (bluesolid lines) together with their analytical approximations(3) (red dashed lines). For transverse case no additionalterm is introduced and the wake function fits the results up
to 2mm.

SINGLE BUNCH ENERGY SPREAD IN
BTW STRUCTURE
The first phase of FERMI foresees a bunch acceleration
up to 700 MeV with bunch length σ = 120µm and total charge Q=1nC. At the exit of each accelerating module, the single bunch energy spread is determined by the
RF accelerating fields produced by the external generator
and the wakefields excited by the beam in the accelerating
structure. As already shown in [8], for Gaussian bunch the405

P. Craievich et al. / Proceedings of the 2004 FEL Conference, 403-406

4

0

x 10

−2

Table 1: Numerical and analytical integral parameters of
the wake potentials of Gaussian bunches in the BTW structure.
√
σ
K||
Icos
Isin
∆W 2
[µm] [V /pC]
[V /pC][V /pC][V /pC]
Numerical integral parameters (a)50-2861.7 -0.001477 -4.368020 1459.8
120 -2298.3 -0.009598 -7.860948 1118.4
150 -2145.5 -0.015227 -8.964911 1029.0
Analytical integral parameters (b)50-2861.2 -0.001546 -4.307913 1441.2
120 -2295.4 -0.009476 -7.831107 1112.5
150 -2145.8 -0.014982 -8.961020 1026.3

σ=50µm−4

W1⊥ [V/pC/m]

−6
−8
−10
−12
−14

σ=1000µm

−16
−18
−3

−2

−1

0

1
s/σ

2

3

4

5

−3

10

Figure 5: Transverse numerical (blue solid lines)and analytical (red dashed lines) wake potentials of the BTW structure.

x 10

9

RMS energy spread can be evaluated by knowing four integral parameters of the wakefields: the loss factor K|| , the√average wake energy spread ∆W 2 , the cosine-Fourierpart Icos and the sine-Fourier part Isin . The last two parameters are needed to take into account the correlation
between the wake potentials and the accelerating voltage[8]. Table 1 summarizes the four integral parameters forbunches of different length obtained with numerical time
domain simulation (a), and analytical calculations (b) using (1): an excellent agreement between the two sets ofdata is shown. Figures 6 and 7 show the relative energy
spread ∆U/U  and relative average energy gain U /U0
as a function of the RF phase φ, for different energy gain
per section U0 . The calculations have been made under theassumption that the energy spread is negligible with respect
to the total energy gain for acceleration section and considering a maximum energy gain for section up to 170 MeV.
We can see that the average energy gain at optimum phase
φopt is approximately 27% lower than the corresponding
value on crest, φ = 0o , for each value of the peak of theacceleration voltage (figure 7). Table 2 contains the relative energy spread when the beam is accelerated on crest,
RF phase φ = 0o , and the minimum relative energy spreadat the optimum phase φopt . These parameters are given
for different peak of the accelerating voltage. The relative
energy spread decrease with the increase of the accelerating voltage. With an maximum energy gain of 170 MeV
the minimum relative energy spread is about 2 times lower
than the corresponding at φ = 0o .
To obtain the required 700 MeV of FEL-I, the BTW
strucutres have to be operated with a gradient of 21 MV/m[9]. Figure 8 shows different behaviors of the relative
energy spread as a function of the electric filed gradient(changing the RF phase from −50o to 10o ) for different peak accelerating voltage U0 , for a bunch with length
σ = 120µm with a charge Q = 1nC. Considering the∆U / 〈U〉8

U0=130MeV
U =140MeV
0
U =150MeV
0
U =160MeV
0
U =170MeV
0

7

6

5

4

3
−50

−40

−30

−20

−10

0

10

φ [degree]

Figure 6: Relative energy spread as a function of the RFphase in the BTW structure (bunch length σ = 120µm and
Q = 1nC).
21M V /m required, we can see that the relative energy
spread is near its minimum value only for U0 = 170M eV .
With lower values of U0 the relative energy spread don’t
get its minimum value through the tuning of RF phase.

CONCLUSION
Calculations of the wakefields for short bunches passing through a complete BTW accelerating structure havebeen presented. The short-range longitudinal and transverse wake potentials are been calculated in time domain
with the code ECHO. From the numerical results analytical
approximations of the point-charge wake functions were
found. For the analytical model we have chosen as a combination of periodic and one-cell dependences. In the longitudinal case the term that describes the finite structure(one cell behavior) is very small compared to the periodic
structure term. Hence in range of σ we have considered,
the longitudinal wakes shows mainly a periodic structure
behavior. In addition, for better fitting of the data up to 5

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P. Craievich et al. / Proceedings of the 2004 FEL Conference, 403-406

−3

0.9

U =130MeV
0
U =140MeV
0
U =150MeV
0
U =160MeV
0
U =170MeV
0〈U〉 / U0

U0=130MeV
U =140MeV
0
U0=150MeV
U =160MeV
0
U =170MeV
0

8

7

6

5

4

3
12

14

16

18
20
22
24
Gradient of the electric field [MV/m]

26

28[5] P. Craievich, T. Weiland, I. Zagorodnov, Report ST/M-04/02,
Sincrotrone Trieste, 2004.

0.8

0.75

[6] K. Bane, M. Sands, “Wakefields of very short bunches in an
accelerating cavity”, SLAC-PUB-4441, 1987.

0.7[7] K. Bane, “Shortrange dipole wakefields in accelerating structures for the NLC”, SLAC-PUB-9663, LCC-0116, 2003.

0.65

−40

−30

−20
φ [degree]

−10

0

10

Figure 7: Relative energy gain as a function of RF phasein the BTW structure (bunch length σ = 120µm and Q =1nC).
mm, we have used an additional term in the model. Furthermore, the single bunch energy spread induced by longitudinal wakefields has been analyzed for the first phaseof the project FEL-I. We have seen that the wakefield effects can be compensated by shifting the bunch injection
phase to optimum values, decreasing the energy gain of
about 27%. For the 700 MeV energy design of FEL-I and apeak gradient of 27.8 MV/m (170 Mev energy gain for section) this means to operate at φ = −41.8o and a gradientof 21 Mv/m.

REFERENCES[1] A. Novokhatski, M. Timm, T. Weiland, “Transition Dynamics of the Wake Fields of Ultra Short Bunches”, Proceedingof the ICAP 1998, California, USA.
[2] I. Zagorodnov, T. Weiland, “Calculation of Transverse Wake
Potential for Short Bunches”, ICAP 2002.
[3] “FERMI@ELETTRA machine project update”, Sincrotrone
Trieste, 2003.

TUPOS109[4] V.A. Verzilov et al., “Photo-injector study for the ELETTRA
linac FEL”, FEL-2003, Tsukuba, Japan.

0.85

0.6
−50

x 10

Figure 8: Relative energy spread as a function of the gradient of the electric field in the BTW structure (bunch length
σ = 120µm and Q = 1nC).

1

0.95

10

∆U / 〈U〉

Table 2: Energy gain and energy spread in the BTW structure (bunch length σ = 120µm and Q = 1nC).
U0
RF phaseU ∆U/U [M eV ]
[M eV ]%
130.0
φ = 0.0o
127.700.87
φopt = −41.6o
94.96
0.59
140.0
φ = 0.0o
137.700.81
φopt = −42.6o 100.69
0.51
150.0
φ = 0.0o
147.700.76
φopt = −43.0o 107.48
0.45
160.0
φ = 0.0o
157.700.71
φopt = −42.6o 115.44
0.40
170.0
φ = 0.0o
167.700.67
φopt = −41.8o 124.47
0.36[8] A. Novokhatski, M. Timm and T. Weiland, “Single Bunch
Energy Spread in the TESLA Cryomodule”, TESLA Report99-16, 1999.
[9] S. Di Mitri et al., “Start-to-end simulation for the FERMI
project at ELETTRA”, this conference.

407

D. A. Alesini et al. / Proceedings of the 2004 FEL Conference, 407-410

THE SPARX PROJECT:
R&D ACTIVITY TOWARDS X-RAYS FEL SOURCES
D.Alesini, S.Bertolucci, M. Bellaveglia, M.E.Biagini, R.Boni, M.Boscolo, M.Castellano, A.Clozza,
G.Di Pirro, A.Drago, A.Esposito, M.Ferrario, D. Filippetto, V.Fusco, A.Gallo, A.Ghigo, S.Guiducci,
M.Incurvati, C.Ligi, F.Marcellini, M.Migliorati, A.Mostacci, L.Palumbo, L.Pellegrino, M.Preger, P.
Raimondi, R.Ricci, C.Sanelli, M.Serio, F.Sgamma, B.Spataro, A.Stecchi, A.Stella, F.Tazzioli,
C.Vaccarezza, M.Vescovi, C.Vicario, INFN-Frascati
F.Alessandria, A.Bacci, I.Boscolo, F.Broggi, S.Cialdi, C.De Martinis, D.Giove, C.Maroli, M.
Mauri, V.Petrillo, M.Romè, L.Serafini, INFN-Milano
M.Mattioli, P. Musumeci, INFN-Roma1
L.Catani, E.Chiadroni, A. Cianchi, C. Schaerf, INFN-Roma2
F.Ciocci, G.Dattoli, A. Di Pace, A.Doria, F.Flora, G.P.Gallerano, L.Giannessi, E.Giovenale,
G.Messina, L.Mezi, P.L.Ottaviani, S. Pagnutti G. Parisi, L.Picardi, M.Quattromini, A.Renieri,
C.Ronsivalle, A. Torre, A. Zucchini, ENEA-Frascati
S. De Silvestri, M. Nisoli, S. Stagira, Politecnico/Milano
J.B. Rosenzweig, S. Reiche, UCLA - Dept. of Physics and Astronomy
P.Emma, SLAC
Abstract
SPARX is an evolutionary project proposed by acollaboration among ENEA-INFN-CNR-Universita` diRoma Tor Vergata aiming at the construction of a FELSASE X-ray source in the Tor Vergata Campus. The firstphase of the SPARX project, funded by Government
Agencies, will be focused on R&D activity on criticalcomponents and techniques for future X-ray facilities as
described in this paper.

techniques and other beam physics issues, like emittancedegradation in magnetic compressors due to CSR, (b)explore production of soft and hard X-rays in a SASEFEL with harmonic generation, in the so called
SPARXINO test facility, upgrading in energy andbrightness the existing Frascati 800 MeV Linac at present
working as injector for the DAΦNE φ-factory (Fig. 1).

INTRODUCTIONSPARX is an evolutionary project proposed by acollaboration among ENEA-INFN-CNR-Universita` diRoma Tor Vergata aiming at the construction of a FELSASE X-ray source in the Tor Vergata Campus. The firstphase of the SPARX project, funded by Government
Agencies with 10 Million Euro plus a preliminary
contribution of 2.35 Million Euro by INFN, will befocused on R&D activity on critical components andtechniques for future X-ray facilities. A R&D program
towards a high brightness photoinjector (SPARC project[1]) is already under way at LNF-INFN. Its aim is thegeneration of electron beams with ultra-high peakbrightness to drive a SASE-FEL experiment at 500 nm,
performed with a 14 m long undulator [2]. The R&D
plans for the X-ray FEL source will be developed along
two lines: (a) use of the SPARC high brightness photoinjector to develop experimental test on RF compression

Available online at http://www.JACoW.org

Figure 1: View of the Frascati linac
A parallel program will be aimed at the development ofother critical component for X-rays FEL sources like highrepetition rate S-band gun, high Quantum Efficiency
cathodes, high gradient X-band RF accelerating structures

FEL Technology

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D. A. Alesini et al. / Proceedings of the 2004 FEL Conference, 407-410

and harmonic generation in gas. In the next sections we
describe preliminary start to end simulations for the
SPARXINO test facility, the required R&D efforts and apossible solution for the DAΦNE linac upgrade.

THE SPARXINO TEST FACILITY
The spectral range from 10 nm to 1 nm, has been
considered for the radiation source. In order to generate
the SASE-FEL in this wavelength range, it is necessary to
produce a high brightness beam to inject inside theundulators. A preliminary analysis of the beam
parameters required for such a source leads to the values
reported in Tab. 1.

The preliminary design of the injector for the SPARXINO
test facility is a copy of the SPARC high brightness
photoinjector [1]. It considers a 1 nC bunch 10 ps long(flat top) with 1 mm radius, generated inside a 1.6-cell Sband RF gun of the same type of the BNL-SLAC-UCLA
one [5] operating at 120 MV/m peak field equipped with
an emittance compensating solenoid. Three standard
SLAC 3-m TW structures each one embedded in asolenoid boost the beam up to 150 MeV.

Table 1: Electron beam parameter
Beam Energy
Peak current
Emittance (average)
Emittance (slice)
Energy spread (correlated)

1
2
2
1
0.1

GeV
kA
mm-mradmm-mrad%The basic scheme is shown in Fig. 2 and consits of anadvanced high brightness photoinjector followed by a firstlinac driving the beam up to 350 MeV with the correlated
energy spread required to compress it in a following
magnetic chicane. The second linac drives the beam up to
1 GeV while damping the correlated energy spread taking
profit of the effective contribution of the longitudinal
wake fields provided by the S-band accelerating
structures.

Figure 3: rms current (left), rms norm. emittance and rms
beam envelope (right) along the injector, up to 150 MeV.
With a proper setting of the accelerating section phaseand solenoids strength it is possible to increase the peakcurrent preserving the beam transverse emittance. In thepresent case we have got with PARMELA simulation abunch average current of 300 A with a normalized rms
emittance below 1 mm-mrad.

1 GeV

Figure 2: Scheme of the SPARXINO test facility.
A peculiarity of this linac design is the choice to integratea rectilinear RF compressor in a high brightness
photoinjector, as proposed in [3], thus producing a 300500 A beam in the early stage of the acceleration. The
SPARXINO linac will be the first SASE FEL experiment
operating with RF and magnetic compressors in the samelinac. The potentially dangerous choice to compress thebeam at low energy (<150 MeV) when it is still in thespace charge dominated regime, results from simulations
not too difficult provided a proper emittancecompensation technique is adopted [4], a possibility thatis not viable in a magnetic chicane. In addition the
propagation of a shorter bunch in the first linac reduces
the potential emittance degradation caused by transverse
wake fields and longitudinal wake fields result to beunder control by a proper phasing of the linac. A
comparison between the two compression techniques isscheduled during the SPARC phase II operation.

TUPOS11

Figure 4: Energy spread, peak current and transverse
emittances along the bunch, at the linac exit.
The low compression ratio (a factor 3) has been choosen
to keep the longitudinal and transverse emittances as low
as possible in order to simplify the second compression
stage. We used the first two TW sections as compressor
stages in order to achieve a gradual and controlled
bunching, the current has to grow at about the same rateof the energy, and we increased the focusing magnetic
field during the compression process. Fig. 3 (left) shows
the current growth during bunch compression until 150
MeV, envelope and emittance evolution are also reported

D. A. Alesini et al. / Proceedings of the 2004 FEL Conference, 407-410(right), showing the emittance compensation process
driven by the solenoids around the accelerating sectionthat keep the bunch envelope close to an equilibrium size
during compression.
The 10k macro-particles beam generated by PARMELA[6] has been propagated through Linac1, Magnetic
Compressor and Linac2 with the code ELEGANT [7].
The correlated energy spread induced by Linac1 is 0.7%
in order to compress the beam by a factor 6 in the 10 mlong magnetic chicane with R56 = 34 mm. At the exit of
Linac2 the required parameters for FEL operation havebeen achieved over more than 30% of the bunch length,
as shown in Fig. 4. A further improvement is expected byfully optimizing the compression scheme and by using a
4th harmonic cavity [8] for the linearization of thelongitudinal phase space distribution

THE SASE FEL SOURCE
Time dependent FEL simulations, performed with thecode GENESIS [9] using the particle distributions
produced by the Linac simulations presented in theprevious section are in progress showing saturation for
30% of bunch slices after 16 m of active undulator length.
We assume to use the same undulator of the SPARC
project [2] with two additional 2.13 m long modules
required to saturate at 10 nm, see Fig. 5. These firstpreliminary results are encouraging and will be thestarting point for further optimizations

available at the linac output for the installation of theundulator.
The Linac energy upgrade to 1 GeV can be achieved, as
shown in figure 6, by pushing the accelerating field of theexisting units up to 26 MV/m, which is today easily
attainable and by adding 2 new SLAC-type sections toreach 1.1 GeV. The Linac waveguide network must also
be modified in order to supply two accelerating units per
RF station. This system configuration requires two new
45 MW klystrons.
High beam brightness can be achieved by installing a
copy of the 12 m long SPARC photoinjector upstream the
DAFNE linac with a minor modification of the existingbuilding and a magnetic compressor at 350 MeV in thearea of the Positron Converter, thus keeping thepossibility to operate the linac as DAΦNE injector. A
detailed analysis of the SPARXINO test facility
compatibility with the proposed DAΦNE energy upgrade
operation is under way [10].

Figure 6:Scheme of the Frascati linac upgrade for
SPARXINO and DAΦNE operation. Existing elements(white). Additional SPARXINO elements (red).
Additional elements for positron acceleration (yellow).

1010

108
106

CONCLUSIONS

104

102

409

0

5

10

15

20

Z (m)

Figure 5: Power vs. z for the 10 nm SPARXINO SASEFEL source, GENESIS simulation (slice energy spread
8*10-4, slice norm. emittance 1 mm mrad, slice peakcurrent 2 kA , undulator parameter K=2.2)

DAΦNE LINAC UPGRADEThe DAΦNE injection system is a 60 m long. LINAC
equipped with 15 S-band (2.865 GHz) SLAC-type 3 mlong accelerating structures driven by four 45 MW
klystrons each followed by a SLED peak power doubling
system. At present it delivers 0.8 µ s RF pulses at arepetition rate of 50 Hz as required for DAΦ N E
operation. A quadrupole FODO focusing system is
distributed along the entire linac. It accelerates the
positron bunches emerging by the Positron Converter, up
to the maximum energy of 550 MeV and the electron
bunches up to 800 MeV. A drift space of about 15 m is

The SPARX R&D project has been approved by the
Italian Government and funded in June 2004 with aschedule of three years. The critical components for an Xray FEL source will be tested during phase II of the
SPARC project and assembled in a high energy and highbrightness linac, the SPARXINO test facility, by
upgrading the existing Frascati linac.

REFERENCES[1] SPARC Project Team, Sparc Injector TDR
www.lnf.infn.it/acceleratori/sparc/[2] A. Renieri et al., “Status Report on SPARC Project”,
this conference.
[3] L. Serafini and M. Ferrario, Velocity Bunching in
PhotoInjectors , AIP CP 581, 2001, pag.87[4] M. Boscolo et al., Beam Dynamics Study of RF
Bunch Compressors for High Brightness Beam
Injectors, Proc. of EPAC 2002, Paris.
[5] D.T. Palmer, The next generation photoinjector , PhD.
Thesis, Stanford University[6] J. Billen, “PARMELA”, LA-|UR-96-1835, 1996.

FEL Technology

410

D. A. Alesini et al. / Proceedings of the 2004 FEL Conference, 407-410[7] M. Borland, “elegant: A Flexible SDDS-Compliant
Code for Accelerator Simulation” LS-287, ANL,
Argonne, IL 60439, USA.
[8] A. Bacci, M. Migliorati, L. Palumbo, B. Spataro, “An
X-Band structure for a longitudinal emittancecorrection at Sparc”, LNF - 03/008 (R), and D.
Alesini, A. Bacci, M. Migliorati, A. Mostacci, L.
Palumbo, B. Spataro: "Studies on a Bi-Periodic XBand Structure for SPARC", LNF-03-013(R).
[9] S. Reiche, Nucl. Instrum. & Meth. A429,243 (1999).
[10] R. Boni, “Feasibility of the DAFNE-Linac energy
doubling”, Proc. of the Workshop on e+e- in the 1-2
GeV range, Alghero, Italy, September 2003

TUPOS11

411

M.Q. Quattromini et al. / Proceedings of the 2004 FEL Conference, 411-414

SPECTRAL ANALYSIS OF CHARGE EMISSION SPATIALINHOMOGENEITIES AND EMITTANCE DILUTION IN RF GUNS
M. Quattromini, L. Giannessi, C. Ronsivalle,
ENEA, C.R. Frascati, Via E. Fermi, 45
I - 00044 Frascati (Rome), Italy.
Abstract
The effects of fluctuations in cathode’s quantum efficiency and other sources of dis-homogeneities in the performances of a typical RF photo-injector have been investigated with PARMELA and TREDI numerical codes. The
RF gun layout includes a focusing solenoid in a configuration aimed at minimizing the emittance growth due to spacecharge effects.

INTRODUCTION
Many applications from X-ray Free electron lasers tohigh energy colliders require high brightness beams produced by photo-injectors. The final performances of thesedevices are strictly linked to the beam quality produced by
the electron source. In the case of FELs the role played byemittance becomes crucial at sub-nm wavelengths where
the emittance is related to the transverse coherence of theoutput radiation. Most of the emittance budget that characterizes the beam at the undulator is produced at the injector
in the first stages of the beam acceleration. The emittance
optimization procedure rely on the linear theory[1] which
has been verified both experimentally and numerically.
In this paper we extend the analysis presented in Ref.[2]where the role played by a non uniform electron emissivity was examined. This study has been performed by using
two different codes based on different algorithms: the Los
Alamos version of PARMELA (PARMELA-LANL)[3] andTREDI[4]. TREDI has been used in "static" mode, i.e. ignoring effects associated to the finite velocity propagationof signals within the bunch.

PROBLEM DESCRIPTION
The aim of this work is to study the effect of charge
in-homogeneities at the cathode surface, by decoupling
in a transverse Fourier space, the in-homogeneities occurring at a specific wave-number , on a scale of the beam
spot radius R, and higher. We have considered a standard S-Band (2856 MHz). 1.6 cells, BNL type photoinjector configuration[5], in a set-up optimized at minimizing the emittance in terms of accelerating gradient, extraction phase, beam spot size, focusing solenoid strength.
Space charge effects compensation is achieved assuming
both transverse and longitudinal flat charge distribution at
extraction. The gun starts at z=0 and the drifts ends at z=2
m. The peak electric field in the gun and the solenoid peakmagnetic field have been set respectively to 120 MV/m and2.73 kG. The longitudinal shape of the pulse is square with

Available online at http://www.JACoW.org

a length of 10 ps and the charge is 1 nC. The phase of thecentre of the bunch is 35◦ . No thermal emittance is included. The beam spot radius R is 1 mm. In Ref.[2] thecharge distribution extracted from the cathode was modelled as a perturbation with respect to the ideal case withthe following cosine function showing a maximum on thecentre of the spot:ρp (x, y) = ρ0 [1 + δ · cos (kn x)] [1 + δ · cos (kn y)] (1)forx2 + y 2 ≤ R2

and

kn = n2π
R

In this contribution we analyze the effect of a sin-like (odd)perturbation of the typeρp (x, y) = ρ0 [1 + δ · sin (kn x)] [1 + δ · sin (kn y)] (2)Assuming that the values of δ and kn are small, we may
write in first approximation
an,j δ j(3)
 (kn , δ) = 0 +nwhere 0 is the value of the unperturbed emittance and thecoefficients an,j show the sensitivity of the emittance inthis injector configuration to the charge in-homogeneities
at the frequency .
The study has been performed by varying the two parameters δ and n and estimating the effect on the normalized
rms emittance at the location of the first minimum (fig.1).
The parameter δ has been varied between 0 and 40% and n
has been given the values n = 1/2, 1, 2, 4.
A previous comparison between codes in the ideal configuration, i.e. at δ = 0, has shown a good agreement[6].

RESULTSThe behaviour of the transverse emittance as a functionof the longitudinal coordinate at δ = 20%, for different values of kn is shown in figs. 1 and 2 for perturbed charge densities as of eqs. (1) and (2), respectively, as computed by
TREDI. The emittance undergoes a typical series of oscillations due to the changes in correlation between longitudinalslices along the bunch which are subject to different focusing as a function of the extraction phase. These oscillations
exhibit the well known structure with a double minimum
located at the places where the correlation is maximized.
In this analysis the second minimum does not appear since
it falls behind the final longitudinal coordinate.

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M.Q. Quattromini et al. / Proceedings of the 2004 FEL Conference, 411-414

4

2.5

2
1

0.5

1

1.5

2

2.5

Figure 1: RMS transverse normalized emittance vs z forδ = 20% and n = 1/2, 1, 2, 4 and perturbed density ρ as ineq. (1).

4

1
0

1

2

3

4

n
Figure 3: Emittance growth vs n in the position of the firstminimum of the emittance as computed by TREDI for ρ asin eq. (2).

∆0.0
∆0.2 n0.5∆0.2 n1.0∆0.2 n2.0∆0.2 n4.0

5

2

1.5

zm

ΕΡ mm mrad

δ=0.1
δ=0.2
δ=0.4

3

ε(n)/ε(0)ΕΡ mm mrad

related to the reduced transverse coupling of the beam with
the RF photo-injector at the early stage of extraction[7].

∆0.0∆0.2 n0.5∆0.2 n1.0∆0.2 n2.0∆0.2 n4.0

5

3

δ=20%

PARMELA
TREDI

2

1.3

0.5

1

1.5

2

2.5

zm

ε(n)/ε(0)

1

1.1

0.9

Figure 2: RMS transverse normalized emittance vs z forδ = 20% and n = 1/2, 1, 2, 4 and perturbed density ρ as ineq. (2).

0.7

0.5

1

2

3

4

n
As an indication of the emittance of the beam we haveconsidered the first minimum, whose position may dependon the in-homogeneity parameter δ especially at the lower
perturbation frequencies kn . The effect of the asymmetry
in perturbed density (2) induces clearly a much larger emittance dilution at lower values of the transverse “frequency”
kn . As expected, at higher frequencies, for the same valueof δ, the effect of different parity in charge distribution is
negligible. In figure 3 the value computed by TREDI of thehorizontal normalized rms emittance divided by the value
obtained with a completely uniform distribution is plotted
as a function of n. The data at n = 4 may be affected bysome aliasing. The transverse mesh size used to describe
the space-charge fields is 20×20 and could not be sufficient
to resolve the fluctuations at n = 4. This may explain theslight emittance diminution observed in fig. 3. A more visible effect is predicted by TREDI for n = 0.5 and δ = 10%(see fig. 4) for the charge distribution described by eq. (1).
While this result is not evidenced by PARMELA, and require a further investigation, for n ≥ 1 the two codes arein fairly good agreement and both give the maximum emittance increase for n = 1. A possible explanation could be

TUPOS12Figure 4: Emittance growth vs n in the first emittance minimum for δ = 20% as computed by PARMELA and TREDIfor ρ as in eq. (1).
This behaviour may be understood by looking at the xy space shown in fig.5 in three longitudinal positions: atthe cathode (z = 0), near the minimum of emittance (z ≈1.30m) and the local maximum of emittance (z ≈ 1.5m).
The non-linear space charge forces induced by the non uniform transverse distribution at the cathode give a deformation of the beam shape. The distortion is stronger when
the non-uniformities are more localized respect to the cases
in which they are more diffused and tend to a partial recompensation along the drift.
In fig 5 the action of the solenoid focusing is also visible
as a rotation of the distribution around the axis.
The emittance degradation increases with the modulation depth δ, as expected. An analysis of the data similar tothat performed in [2] yielded the same scaling law at highvalues of kn . In fig 6 the result of a fit of  (δ) /0 for
n = 2 is shown. Clearly the function a0 + a3 δ 3 fits the413

M.Q. Quattromini et al. / Proceedings of the 2004 FEL Conference, 411-414

Figure 5: X-Y plots derived from TREDI computations for δ = 20% in different longitudinal positions for ρ as in eq. (2).
2a0+a2δ
3
a0+a3δ

n=1

2.2

ε(δ)/ε(0)data better than a0 + a2 δ 2 . By converse for n = 1 (see fig7) the quadratic law fits the data better than the cubic. This
result is probably related to the asymmetry induced by the
charge distribution (2) and is in agreement with the analysis developed in Ref. [8] where a quadratic scaling law
was shown to reproduce well the emittance behaviour due
to beam misalignments.

1.8

1.4
a0+a2δ2
a0+a3δ3

2.2

n=2

1

ε(δ)/ε(0)

0

1.8

0.1

0.2 δ

0.3

0.4

Figure 7: Emittance growth vs δ for n = 1 in the position of
the first minimum of the emittance as computed by TREDIfor ρ as in eq. (2).

1.4

CONCLUSIONS

1
0

0.1

0.2 δ

0.3

0.4

Figure 6: Emittance growth vs δ for n = 2 in the position of
the first minimum of the emittance as computed by TREDIfor ρ as in eq. (2).

In this contribution we have extended the analysis of theemittance dilution as a function of the frequencies associated to a non axi-symmetric perturbation of the ideal transverse density extracted from the photocathode. A scaling
law of this effect in function of the perturbation amplitude
has been derived and some indications of the dependenceof the effect with the transverse frequency have been ob-

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M.Q. Quattromini et al. / Proceedings of the 2004 FEL Conference, 411-414

tained. In the future we plan to further refine this analysis
and check the scaling laws derived here against the predictions from other numerical codes. At high kn the results
observed for a sine-like (odd) perturbation of the type (2)are similar to the predictions for a cos-like (even) perturbation like (1). At low n the results are substantially different since the parity of the initial charge distribution plays asignificant role. We plan to continue this study to the beamslice emittance, which is not affected by correlations between slices and is probably a better indicator of the influence of cathode inhomogeneities on the beam quality. This
work will require a significant computational effort since
the number of macroparticles and the transverse mesh fineness for the evaluation of the fields grow non-linearly withthe frequency associated to the transverse mode.

REFERENCES[1] L. Serafini, J.B. Rosenzweig, "Envelope analysis of intense
relativistic quasilaminar beams in RF photoinjectors: a theoryof emittance compensation" Phys. Rev. E55 (1997) p.7565.
[2] L. Giannessi, M. Quattromini and C. Ronsivalle, “Emittance
dilution due to 3D perturbations in RF-photoinjectors”, Proceedings of 9th European Particle Accelerator Conference, 5
to 9 July, 2004, Lucerne, to be published.
[3] L. Young, J. Billen "PARMELA" LA-UR-96-1835.
[4] L. Giannessi, M. Quattromini, “TREDI simulations for highbrilliance photoinjectors and magnetic chicanes”, PRST-AB
6 120101 (2003), Web site: http://www.tredi.enea.it.
[5] AA.VV., LCLS Design Report, SLAC-R-593, April 2002.
[6] C. Limborg et al. "Code comparison for simulations of photoinjectors ", Proceedings PAC2003.
[7] M. Ferrario, private communication.
[8] F. Ciocci et al., Nucl. Instr. and Meth. A393, (1997), 434.

TUPOS12

p. Nicolosi et al. / Proceedings of the 2004 FEL Conference, 415-418

415

ON-LINE SPECTRAL MONITORING OF THE VUV FEL BEAM AT DESY
P. Nicolosi, L. Poletto#, M.G. Pelizzo, INFM & Dep. of Information Engineering, Padova (Italy)
J. Feldhaus, U. Jastrow, U. Hahn, E. Ploenjes, K. Tiedtke, HASYLAB-DESY, Hamburg (Germany)
Abstract
A stigmatic spectrometer for the 2.5-40 nm EUV region
has been realized. The design consists of a grazingincidence spherical variable-line-spaced grating with flatfield properties and of a spherical mirror mounted in the
Kirkpatrick-Baez configuration that compensates for theastigmatism. The spectrum is acquired on a fluorescentscreen optically coupled to an intensified CCD detector,
that can be moved along the spectral focal curve to selectthe spectral region to be acquired. The spectral and spatial
resolution of the system have been characterized by using
the emission from an hollow-cathode lamp or a laserproduced plasma. At present, the instrument is installed at
the VUV-FEL at DESY for the spectral monitoring of the
FEL beam in the 20-45 nm region.

INTRODUCTION
The FEL at the TESLA Test Facility (TTF) at DESY
achieved first self amplified spontaneous emission(SASE) in the vacuum-ultraviolet in early 2000 [1] and it
reached gain up to saturation between 80–120 nm in 2001[2]. During an on-going upgrade which will be completed
at the end of 2004, the VUV-FEL at DESY is beingtransformed into the worldwide first FEL user facility for
vacuum-ultraviolet (VUV) and soft X-ray radiation from100 to 6 nm wavelength.

Fig. 1. Layout of the VUV-FEL at DESY
Fig. 1 shows the layout of the linear accelerator. The
complete accelerator is currently newly constructed to
finally reach energies of up to 1 GeV [3]. A new
photoinjector/bunch compression concept is used, and thegun has reached a minimum normalised emittance of 1.5
and 1.7 π mm mrad in the vertical and horizontal plane
respectively. In addition, a special collimator system has
been designed to protect the undulators, the electron beamfocusing along the undulator has been changed, andimproved diagnostics have been developed both for theelectron and the photon beam. A short accelerator section
with third-harmonic cavities to linearize the energy chirp
along the electron bunch, which is required for optimum
bunch compression, as well as the 6th accelerator module
will not be installed into the injector until 2006.
___________________
Contact person: poletto@dei.unipd.it#

Available online at http://www.JACoW.org

Consequently, the wavelength range of the FEL will
initially be limited to approximately 20 - 60 nm.
FELs based on self-amplified spontaneous emission
produce highly intense, transversely coherent radiation
within a single pass of a relativistic electron bunch
through a long undulator. The exponential amplification
process of a SASE FEL starts from spontaneous emissionof the electron beam. Hence, individual radiation pulses
differ in intensity, temporal structure, and spectral
distribution. Extensive characterization of the FEL beam
[4] as well as a first set of experiments on the interactionof such VUV radiation with cluster beams [5] andsurfaces [6] was carried out during TTF Phase 1. For
commissioning of the VUV-FEL various photon
diagnostic units used for beam intensity and profile
measurements during the proof-of-principle experimentson TTF1 have been modified and will be installed at theend of the accelerator tunnel, above the electron beam
dump. Initial start-up of the FEL is planned in the 30-40
nm spectral region.
A grazing incidence grating
spectrometer will replace the normal incidence
spectrometer used for TTF1 in this area to measure thespectral structure of the FEL pulses on a single shot basis.
An important feature of the SASE FEL pulses is theirshort duration of 40-200 femtoseconds. An estimate of thepulse duration can be derived from the spectra of thespectrometer already during the commissioning phase,since the spectral width of each peak shown in a single
shot-spectrum is related to the radiation pulse length [1].
Tab. 1. Expected parameters of the FEL beam.
Wavelength
100 – 6 nm
Pulse energy
0.1 – 1mJ
Pulse duration (FWHM)
30 – 400 fs
Peak power
0.3 - 2.8 GW
Spectral width (FWHM)~0.5 %
Spot size at undulator
1.4 – 0.14 mmexit (FWHM)
Angulardivergence
170 – 24 µrad
(FWHM)
Peak brillance
1·1028–3·1030
ph/s/mrad2/mm2/0.1 %bw
The expected parameters of the VUV-FEL aresummarized in Tab. 1 [7]. It is developed into a full user
facility with five experimental stations using the FEL
beam alternately [3]. Three experimental stations use thedirect SASE FEL beam and are equipped with focusing
mirrors providing spot sizes of approximately 100 or 10µm. Two experimental stations for experiments requiringa spectral bandwidth narrower than the natural FEL
bandwidth are served by a high resolution plane grating

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p. Nicolosi et al. / Proceedings of the 2004 FEL Conference, 415-418

monochromator, that has a resolution of 80000-10000
while providing a wide tuning range from 10 eV to 1 keV.
Alternatively to the monochromator beamlines, thespectral distribution of individual FEL pulses will be
determined online by a variable-line-spacing (VLS)
grating spectrometer serving the three “SASE beamlines”[8]. One of the plane mirrors in the FEL beam distribution
system will be replaced by the VLS grating which reflects
most of the radiation in zeroth order to the experimentand disperses only a small fraction in first order forspectral analysis.
The grazing-incidence stigmatic spectrometer that will
be used to measure the single-shot spectral structure of
the FEL pulses in the 20-46 nm spectral region ispresented here. The instrument was designed and realized
by the INFM-LUXOR laboratory (Padova, Italy) for
absorption spectroscopy on laser-produced plasmas in the
5-45 nm spectral region [9]. The main system
requirements are high spatial and spectral resolution and aplane focal curve with the detector used at almost normal
incidence, such as in the case of using grazing-incidence
spherical variable-line-spaced (SVLS) gratings [10]. The
design consists of a SVLS grating with flat-field
properties and of a spherical mirror mounted in the
Kirkpatrick-Baez configuration that compensates for theastigmatism. The spectrum is acquired on a fluorescentscreen coupled to an intensified CCD detector, that canbe moved along the spectral focal curve to select the
spectral region to be acquired. The spectral and spatial
resolution of the system have been characterized by using
the emission from an hollow-cathode lamp.

SPECTROMETER DESIGNAND REALIZATION
The design principle of the SVLS grating for flat-field
spectrographs is already well established [10] and will behere briefly resumed. The groove density along thegrating surface is expressed as
æ

b

0ç
è

R

σ( y ) = σ ç1 + 2

2

y+3

b
R

3
2

y2 + 4

b
R

4
3

ö

y3 ÷
÷
ø

(1)

where σ0 is the central groove density, R is the gratingradius and b2, b3, b4 are the ruling parameters for spacevariation.
The main aberration to be corrected is the spectral
defocusing, which increases linearly with the width of theilluminated area. The spectral focal curve, that is thecurve where the spectral defocusing zeroes, is given byb
cos 2α cos 2β cos α + cos β+ 2(sin α + sin β ) 2 = 0 (2)
+
−
R
r
r'
R
where r, r’ are respectively the grating entrance and exit
arms, and α and β are the incidence and diffraction
angles, which are related to the grating equation
sinα − sinβ = mλσ0 .
(3)To minimize the defocusing on the detector, it isnecessary to make the focal curve given by Eq. (2) as
close as possible to the detector surface in the spectral
range of interest, by acting on the parameters R and b2.

TUPOS13

Similarly it can be shown that the parameters b3 and b4
can be chosen to minimize coma and spherical aberration.
The main difference between the grazing-incidence
SVLS design and the classical grazing-incidence
Rowland configuration with uniform-line-spaced gratings
is that the focal surface as given by Eq. (2) is almost flatwith the detector operated at near normal incidence.
The astigmatism in the plane perpendicular to the planeof spectral dispersion is corrected by a spherical mirror
mounted with its tangential plane coincident with theequatorial plane of the grating, i.e. a Kirkpatrick-Baez
configuration in which one of the two elements is a
grating [11]. The mirror does not provide any focusing in
the plane of spectral dispersion, leaving unchanged thegrating focal properties given by Eq. (2) that determine
the spectral resolution. On the other side, the grating does
not provide any spatial focusing, that is in a plane
perpendicular to the plane of dispersion, so the spatial
performances are determined only by the characteristicsof the mirror. The radius of the mirror Rm is determined
as
æ 1
1 ö÷
ç
Rm =
+
q ÷
cos θ ç p
m ø
m è m

2

−1

(4)

where pm and qm are respectively the mirror entrance andexit arms and θm is the incidence angle.
It can be shown [9] that such a configuration has also
spectral and spatial resolution capability for extended
sources (e.g. a laser-produced plasma), due to the
Kirkpatrick-Baez configuration that maintains separated
the spectral and spatial focal properties on two different
optical components. The spectral resolution is constantalso for off-axis points, while the spatial resolution
decreases with the off-axis distance. In case of a 2 mm
source size, the spatial resolution with 5 mrad acceptanceangle and a mirror operated at 87° is 25 µm on-axis and130 µm at the extremes of the field-of-view (i.e. ±1 mm
off-axis distance). In other stigmatic designs withspherical or plane VLS gratings, the astigmatism iscorrected by an additional mirror mounted on the sameplane as the grating [12, 13]: in this case, the spectral andspatial focusing properties are coupled on the mirror andboth spectral and spatial resolutions decrease for extended
sources far from the optical axis.
The layout of the configuration is shown in Fig. 2. The
central groove density of the SVLS grating is 1200
lines/mm; the parameters for groove space variation havebeen optimized to have an almost flat focal surface in the
10-40 nm spectral region. The calculated focal curve isshown in Fig. 3: it is almost perpendicular to the tangent
to the grating on its vertex. Given the low acceptedangular aperture of the grazing-incidence system (5 mradin the spectral plane) and the detector pixel size (20-25µm), the depth of focus for this system is considered
about 5 mm.

417

p. Nicolosi et al. / Proceedings of the 2004 FEL Conference, 415-418

Meridional plane(spectral plane)
Slit

α

β
F
F

Sagittal plane(spatial plane)

SVLS grating
Spherical mirror

Fig. 2. Layout of the grazing-incidence spectrometer.

250

x (mm)

40 nm

200

30 nm

20 nm
150

10 nm
100
690

695

700

705

the best the focal curve in the region of interest. In orderto do this, the detector is mounted on a linear drive andconnected to the spectrometer with a system with threelaminar bellows. An acquired spectrum is shown in Fig.
4. Additional details of the optical design are presented
elsewhere [9].
The parameters of the spectrometer are resumed in Tab. 2.
Tab. 2. Parameters of the spectrometer.
Accepted aperture
5 mrad (spectral plane)
10 mrad (spatial plane)
Spherical mirror
Entrance/exit arms
400 mm / 1000 mm
Incidence angle
87.5°
CoatingGold
SVLS gratings
Central groove density
1200 gr/mm
Spectral range
5-50 nm
Entrance/exit arms
650 mm / 750 mm
Incidence angle
87°
Coating
Platinum
Detector
Phosphor screen diameter 25 mm
Objectives
50 mm f/1.0
105 mm f/1.8
Intensified CCD camera
MCP and cooled CCD
Detector format
1280 pixel × 1024 pixel

710

y (mm)

Fig. 3. Spectral focal curve of the SVLS grating. The x
and y axes are defined respectively parallel to the grating
normal and parallel to the tangent to the grating on its
vertex. The origin of the reference system is the grating
vertex.

Fig. 4. He spectrum. The wavelength is increasing fromleft to right. The two most intense lines are HeII
25.6 nm (pixel 130) and 24.3 nm (pixel 275).
The spectrum is acquired on a fluorescent screen
optically coupled to an intensified CCD detector. Since
the length of the spectrum is larger than the detector size,
the latter must be translated along a straight line fitting at

INSTRUMENT PERFORMANCEThe spectrometer was aligned and calibrated in the 2446 nm spectral region using as source an hollow-cathodelamp. The measured performance are very close to thetheoretical predictions: the spectral lines have FWHM of
about two pixels. Being the optics aligned at the best, thedetector was positioned on the straight line fitting at thebest the spectral focal curve. The spectral region ofoperation is selected by moving the detector along thisstraight line. An absolute encoder gives the relativetranslation of the detector with respect to a reference
point.
The system calibration is divided in two steps: 1) the
measurement of the detector scale factor and 2) the
wavelength calibration.
The scale factor (µm/pixel) expresses the size of thephosphor screen imaged in one CCD pixel: it has beenmeasured as 8.0 µm/pixel.
The wavelength calibration is performed by measuring
the position of the focal plane with respect to the grating
vertex. The parameters that allow to identify the detector
plane (i.e. the straight line where the detector is moved)
are calculated by acquiring some known spectra from thehollow-cathode source together with the encoder
measurements on the detector position, and then applying
a fitting procedure. The residual calibration errors are lessthan 0.03 nm and are mainly due to the intrinsicalprecision of the encoder.

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p. Nicolosi et al. / Proceedings of the 2004 FEL Conference, 415-418

The actual spectral dispersion is shown in Fig. 5
assuming 32 µm pixel size (i.e. a binning factor of 4 on
the CCD). The resolution, calculated as the ratio λ/∆λ2px
with ∆λ2px evaluated within two pixels, is 1500@30 nm
and 1900@45nm, definitely higher than the expected
FWHM of the FEL emission.
Some calibrated spectra are finally shown in Fig. 6.
At present, the instrument is installed at the VUV-FEL
at DESY for the spectral monitoring of the FEL beam in
the 20-45 nm region.

REFERENCES

a)[1] J. Andruszkow et al, Phys. Rev. Lett. 85 (2000), 3825
[2] V. Ayvazyan et al, Phys. Rev. Lett. 88 (2002), 104802[3] http://www-hasylab.desy.de[4] R. Ischebeck et al, Nucl. Instr. and Meth. A 507(2003), 175[5] H. Wabnitz et al, Nature 420 (2002), 482[6] A. Andrejczuk et al, HASYLAB An. Rep. 1 (2001),
117[7] K. Tiedtke et al, to be published in AIP Conf. Proc.
2004 (SRI 2003, San Francisco, CA, U.S.A.)[8] R. Reininger et al, to be published in AIP Conf. Proc.
2004 (SRI 2003, San Francisco, CA, U.S.A.)[9] L. Poletto et al, Appl. Opt. 41 (2002), 172[10] T. Harada and T. Kita, Appl. Opt. 19 (1980), 3987
[11] L. Poletto and G. Tondello, Appl. Opt. 39 (2000),
4000[12] P. Fan et al, Appl. Opt. 31 (1992), 6720
[13] M. Hettrick and S. Bowyer, Appl. Opt. 22 (1983),
3921

dispersion (pm/pixel)

12

11

10

9

8
20

25

30

35

40

45

wavelength (nm)Fig. 5. Actual spectral dispersion. The pixel size isassumed 32 µm.

TUPOS13

wavelength [nm]b)Fig. 6. Spectra acquired with the hollow-cathode lamp. The
plots are horizontal cross-sections across the CCD
image. a) He spectrum (HeII 30.4 nm line); b) Ne
spectrum (NeII 44.62, 44.66, 46.07 and 46.24 nm lines).

419

Z.F. Seidov et al. / Proceedings of the 2004 FEL Conference, 419-422

ABCD MATRIX METHOD: A CASE STUDY
Z. Seidov∗ , Y. Pinhasi, A. Yahalom,
The College of Judea and Samaria, P.O. Box 3, Ariel 44837, IL

Abstract

Md (I) =In the Israeli Electrostatic Accelerator FEL (EAFEL),
the distance between the accelerator end and the wiggler
entrance is about 2.1 m. A 1.4 MeV, 2 Amp electron
beam is transported through this space using four similar quadrupoles. The transfer matrix method (ABCD matrix method) was used for simulating the beam transport.
We found a reasonable agreement between experimental
results and simulations. The inverse problem of finding
the electron beam emittance at S1 screen position (before
quads) by using the spot dimensions at S2 screen (after
quads) as function of quad currents is considered. Spotand beam are described as ellipses by using STB (Spot-toBeam) procedure [1], and the trace-ellipse transformation
is used to find the emittance.

EXPERIMENTAL LAYOUT
The scheme of quadrupoles Q1-Q4 and diagnostic
screens S1 and S2 between the end of accelerator and thewiggler entrance at the Israeli EAFEL [2] is shown in
Fig. 1. We use the following numerical values of paramd1 dq

Acc

S1

d

Q1

d2

Q2

Q3

Q4

S2

TRANSFER MATRICES
We need transfer matrices of two kinds: for drift spaceand for quads (see, e.g., [3], [4]).
Drift space matrices are
1
0

d
1




, Di =1 di
0 1


, i = 1, 2.

Converging and diverging quadrupole matrices are


c
s/t
c = cos (t dq ) ,Mc (I) =,−s t cs = sin (t dq ) ,∗ seidov@bgumail.bgu.ac.il

Available online at http://www.JACoW.org

α I,

α=



ch = cosh (t dq ) ,sh = sinh (t dq ) ,(3)eη= 24.78 A−1 m−2 ,
γ mv

(4)

,

where I is quad’s current, e, m, v, γ are electron’s charge,
mass, velocity, and relativistic parameter, η is quad’s magnetic field gradient, η = 0.1522 T/m for quads used in
EAFEL, and value of α is given for E=1.4 MeV beam energy.
It is of interest to mention, comparing (2) and (3), that
Md (I) = Mc (−I).
The combined transfer matrix from S1 to S2 for Xcoordinate is a scalar product of all relevant matrices
Mx= D2 · Md (I4 ) · D · Mc (I3 )·D · Md (I2 ) · D · Mc (I1 ) · D1 .

(5)

Without loss of generality we consider in (5) the case when
the first quadrupole is converging in X (and diverging inY , but we consider here only X-coordinate of the beam).
To simplify notations, we write down the matrix Mx as


Ax Bx
Mx =
,
(6)
Cx Dx

Ax Dx − Bx Cx = 1.

eters: E = 1.4 MeV, electron beam energy; d = 0.205 m,
drift space between quadrupoles; dq = 0.140 m, effective
length of quadrupoles; d1 = 0.207 m, drift space between
S1 screen and first quadrupole; d2 = 0.308 m, drift space
between last quadrupole and S2 screen; however all formulas are quite general and valid for any value of the parameters involved.



√

sh/t
ch

with det (Mx ) = 1, that is:

Wig

Figure 1: Experimental layout (not in scale).

D=

t≡

ch
sh t

(1)

(2)

(7)

Relation between initial, at screen S1, beam parameters(x1 , x1 ), and final, at screen S2, beam parameters (x2 , x2 )
is




x1
x2
·
=
M
.
(8)
x
x2
x1

BEAM WAIST AT S1
Of particular interest is the case where initially, at screen
S1, there is a waist of circular beam with emittance εx =εy = ε · π and radius Rx = Ry = r1 ; then the equation of
the trace-ellipse is (without loss of generality, hereafter weconsider only X-coordinate) 2   2
x1
x1
+
= 1.
(9)
r1
ε/r1
We note that ”area” of the ellipse (9) is S = π ε, that is thearea of trace-ellipse is a measure of beam emittance. The
maximal values of x1 and x1 are r1 and ε/r1 , respectively.
Expressing (x1 , x1 ) in terms of (x2 , x2 ) from Eq. (8),




−1
x1
x2
= Mx ·
,
(10)
x1
x2

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Z.F. Seidov et al. / Proceedings of the 2004 FEL Conference, 419-422

and inserting (x1 , x1 ) from Eq. (10) into Eq. (9), we obtain
the equation for the final trace-ellipse at screen S2
2ax x22 + 2 bx x2 x2 + cx x2 = 1,
2 
2
Dx
Cx
ax =
+
,
r1
ε/r1
Bx Dx
Ax Cx
bx = −−,
r12(ε/r1 )2

2 
2
Bx
Ax
cx =
+
.
r1
ε/r1

By Dy ε2 = −Ay Cy r14 .

(11)



(12)

Here coefficients ax , bx , and cx are functions of all
twelve input parameters: d1 , d, d2 , dq , η, r1 , ε, I1 , I2 ,I3 , I4 , E. Note that due to the paraxial approximation,
determinants of all used transfer matrices are equal to 1,
hence the area of final trace-ellipse (11) is equal to the areaof initial trace-ellipse (9), that is emittance of the beam ispreserved (in both X- and Y -coordinates).
We notice that(13)
ax cx − b2x = 1/ε2 ,analog of Courant-Snyder invariant. Thus coefficientsax , bx , cx are analogs of the transport parameters or Twiss
parameters.

Beam envelope at S2
From Eq. (11) we may find parameters of the beam at S2
screen position. The envelope of beam in X is√cx
= ε cx .
(14)
r2 = x2,max =ax cx − b2x(19)Equations (18, 19) are two equations for four free parameters, quad currents, so we have in principle a 2D set of possible solutions (not all of them having physical meaning).
Equation (17) allows a fully analytical study of beam radius r2 at S2 as function of any variable parameter (mainly
quad currents) assuming that beam at S1 is at its waist
and has emittance ε, while we can measure radius r1 fromspot at S1. As an example, for beam waist at S1 with
r1 = 14 mm and ε = 6 mm mrad, expansion of transfer
matrix elements up to terms linear in quad currents gives
Ax = 1 − 4.90 I1 + 3.71 I2 − 2.51 I3 + 1.31 I4 ,Bx = 1.69 − 1.35 I1 + 2.30 I2 − 2.42 I3 + 1.72 I4 ,Cx = 3.47 (−I1 + I2 − I3 + I4 ),Dx = 1 − 0.961 I1 + 2.16 I2 − 3.35 I3 + 4.55 I4 ,r2 = 14.02 − 68.6 I1 + 51.8 I2 − 35.1 I3 + 18.4 I4 .
(20)
In another case with I1 = I2 = I3 = I4 = I, expansion
can be easily made up to I 4 :Ax = 1 − 2.39 I − 3.57 I 2 + 1.26 I 3 + 1.32 I 4 ,Bx = 1.69 + 0.242 I − 1.68 I 2 − 0.128 I 3 + 0.336 I 4 ,Cx = −7.18 I 2 + 3.77 I 4 ,Dx = 1 + 2.39 I − 2.84 I 2 − 1.26 I 3 + 0.944 I 4 ,r2 = 14.02 − 33.46 I − 49.77 I 2 + 18.21 I 3 + 20.21 I 4 .
(21)
Note that in practice approximations (20) can be usedfor values of currents lower less than ≈ .1 A, while (21)are good up to I ≈ .25 A, see Fig. 2.
r, mm

The slope of the beam envelope is
ε bx
r2 = (x2,max ) = − √ .
cx

If we require that beam has a waist also in Y-direction thenwe have similar equation

30

(15)

20
10

The area of the final trace-ellipse is equal to area of theinitial trace-ellipse that is the emittance is preserved. Maximal value of x2 is(x2 )max =√ax /ε.

(16)

Notice the difference between (x2,max ) and (x2 )max : thefirst is x2 at point x2 = x2,max , while the second is x2
at the point where x2 is maximal. From (14) and (12) theradius of beam in X-coordinate is

2
ε Bx
+ A2x .
(17)
r2 = r1
r12
Also from (15) and (12) the condition r2 = 0 for the beam
waist at S2 isBx Dx ε2 = −Ax Cx r14 .

TUPOS14(18)

0.25 0.5 0.75

11.25 1.5

I, A

-10

Figure 2: Radius r2 of beam at S2 vs. current I =I1 = . . . = I4 ; beam has waist at S1, with emittanceε = 6 mm mrad, and radius r1 = 14 mm. Blue dashedline is approximation for r2 in Eq. (21). Note that, at minima, the radius of beam is very small, yet non-zero.

Beam emittance at S1
We can reverse Eq. (17) to find emittance from experimentally measurable radii of beam, r1 and r2 , at S1 and S2(and known quad currents)
r1
r22 − (r1 Ax )2 .
(22)
ε1 =
Bx

Z.F. Seidov et al. / Proceedings of the 2004 FEL Conference, 419-422

Though in paraxial approximation the beam emittance ispreserved, that is ε1 = ε2 , still we keep index 1 at ε1
taking into account that real experimental errors (and nonlinearities in electron-optic elements) will give a set of values of emittance (for various quad currents) and all theserefer to beam emittance at S1 (and should be properly averaged). Also we note that the procedure of emittance finding by Eq. (22) is applicable for any electron-optic element (e.g. solenoid) which can be described in terms oftransfer matrix. The only (but very essential) assumption
is that beam has a waist at S1. The other (not so essential for the real parameters used in EAFEL) assumption
is neglecting space-charge effects, which is admissible inour first approximation. Also of interest is to mention thatfor switched off quads (all quad currents are zero) we have
Ax = 1, and Bx = 1.69 m (full distance from S1 to S2),and we recover from (22) the well-known envelope equation for free-space expansion of beam with non-zero expansion. In this relation we note that distance Bx = 1.69 m
is too small to deduce the emittance by usually used formula ε ≈ r2 r1 /Bx , which gives a much smaller value ofemittance. The exact formula is
ε=

r1
Bx



r22 − r12 .

(23)

EXPERIMENT AND SIMULATIONS
Experimental data
In Fig. 3 some pictures are presented of spot at S2for various currents of Q3 and Q4, while I1 =1.26 A andI2 =1.14 A are kept constant. The quality of pictures does
not allow to measure accurately the dimensions of spot(and beam), though general feature (strong dependence on
I3 and very weak dependence on I4 ) is evident. Spot at
S1 (not depending on quad currents) was treated by STB
procedure [1] and found to have radii rx = 15 mm andry = 9 mm.

Figure 3: Spot at S2 for various currents I3 and I4 , forI1 =1.26 A and I2 =1.14 A.

421

Simulations
In Table 1 the radii in X- and Y-coordinates areshown according to Eq. (17), for two emittances, 6 and
18 mm mrad.
Table 1: Radii of beam at S2, in mm, for various I3 and I4 ,for fixed currents I1 =1.26 A and I2 =1.14 A
I4=.67
I4=.77
I4=.87
I3 / ε
rx
ry
rx
ry
rx
ry
1.26 / 6 11.8 2.4 14.3 1.2 16.7 0.23
1.26 / 18 11.8 2.6 14.3 1.5 16.7 0.69
1.36 / 6
1.8 4.1
3.7 2.8
5.7
2.8
4.3 6.8
3.0 4.6
5.7
1.7
1.36 / 18
1.46 / 6
8.1 5.9
6.7 4.4 20.1
5.0
8.2 6.1
6.7 4.5 20.1
5.1
1.46 / 18

The values of radii of beam at S1 rx = 15 mm andry = 9 mm are used. The general tendency is in agreement with experimental data. The very small dependenceof spot dimensions on beam emittance is good from one
point of view (the simulation results are safe), and not sogood from the other point of view (defining the beam emittance is very difficult, practically impossible for given quadcurrents). We note, that though not so critical in defining
the beam dimensions at S2, the value of the emittance iscritical for the beam quality and for getting lasing in the
wiggler.

DISCUSSION
We reported here briefly on the procedure used for simulation of electron beam transport between accelerator section and the wiggler of the Israeli EA FEL. The formulas for envelope Eq. (17) and for emittance Eq. (22) of
the beam at S2 are valid under the assumption that at S1
there is the beam’s waist (in the relevant coordinate). Another assumption is neglecting the (small) space-charge effects. We note also that Eq. (17) and Eq. (22) are valid forany current distribution (without ”holes”) across the beamcross-section. The case of converging/diverging beam at
S1 screen can be treated by introducing a virtual focusing/defocusing coil at the S1 position. It changes the resultant transfer matrix while Eq. (17) and Eq. (22) are
not changed. Also included in the program (mainly in
MATEMATICA) are cases of arbitrary trace-ellipse andnon-circular non-centered beam at S1, and due to space reasons we only mention them here.
The problem with finding beam emittance at S1 from spot
at S2 (spot’s variation with quad currents) is that, for mostquad currents practically used in the EAFEL, the spot at S2
depends on emittance very weakly. We attempted to findthe situation when the influence of emittance on spot is essential. Note that transfer matrix elements Ax and Bx in
Eq. (17) and Eq. (22) do not depend on beam emittance orradius at S1 but only on quad parameters (and beam en-

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ergy). For example, the situation Ax = 0 is the most favorite for defining emittance. In this case the beam radiusat S2 is proportional to the beam emittance at S1 and inversely proportional to the beam radius at S1. However, in
all considered cases when Ax = 0 the resulting spot/beamradius at S2 screen is very small (due to small value of Bx )and the exact measurements are impossible (also due to arather poor quality of pictures obtained by the frame grabber hardware and software available to us at present). Still
we believe that the ”quad scanning method” (which is notclaimed to be quite novel, see, e.g., [5]) can be successfully
applied in the future experiments in EAFEL. What we reported here are only the preliminary results.

ACKNOWLEDGEMENTS
The idea of the virtual coil should be credited to
A. Gover. The work was supported by Israeli Ministries
of Immigrant Absorption, Science, and Environment.

REFERENCES[1] Z. Seidov, Y. Pinhasi, A. Yahalom, Spot-to-beam procedure,
these Proceedings, TUPOS15.
[2] A. Gover et al, Nucl. Instr. and Meth. A 528 (2004) 23;
arXiv.org/physics/0408054.
[3] M. Reiser, Theory and Design of Charged Particle Beams,(John Wiley & Sons, Inc., New York, 1994).
[4] S. Humphries, Jr., Charged Particle Beams, (Wiley, New
York, 1990).
[5] R. Chaput et al, Nucl. Instr. and Meth. A 393 (1997) 474.

TUPOS14

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SPOT-TO-BEAM PROCEDURE
Z. Seidov∗ , Y. Pinhasi, A. Yahalom,
The College of Judea and Samaria, P.O. Box 3, Ariel 44837, IL
Abstract
We describe the interactive spot-to-beam MATHEMATICA procedure for a) approximating the spot image at thescreen (and beam at screen position) as an ellipse, b) getting five parameters of the elliptic beam (two diameters,
center coordinates, and orientation angle). The basic idea
is to ”map” the reference holes at the diagnostic screen onto
the XY plane normal to the beam propagation direction (Zaxis). All distortions of the image, e.g., due to camerascreen disposition can be, in principle, taken into account.
With the non-linear LSM fitting, the ”curved” coordinate
system of the holes at image is transferred to the Cartesian ”Laboratory” coordinate system (C.S.) at XY plane.
Then the fitting ellipse is found in the C.S., by solving thesystem of N linear equations for 5 unknown parameters ofbeam ellipse, where N>5 is a number of the sample points
on edge (boundary) of the spot image. Examples of the realmeasurements in the Israeli Electrostatic Accelerator FEL(EAFEL) are demonstrated. The accuracy of the beam diameter values is ≈.5 mm depending on picture quality andthe operator’s experience (and patience!). The procedure is
to be used in routine measurements of EAFEL to improvethe electron beam transport.

We use the following numerical values of parameters:
E = 45 keV, electron beam energy; Z-coordinates ofscreens and coils (assuming that electron gun is at Z=0):
zsp = 859 mm, position of pepperpot screen SP (TiAl2 O3 ), zs0 = 1713 mm, position of S0 screen (ceramic);
z1 = 241 mm, z2 = 475 mm, z3 = 1235 mm, andz4 = 1532 mm, positions of focusing coils C1, C2, C3
and C4, respectively.
Note that SP screen is rotated by 45 deg around vertical(Y) axis, while S0 screen is rotated by 45 deg around horizontal (X) axis, both X and Y axes being normal to Z axis,
direction of beam propagation. For the spot measurement
purposes, there are made reference holes at all diagnostic
screens of EAFEL. Due to the various optical distortions(mainly caused by too close and not proper camera-screen
disposition), the problems with the frame grabber hardware
and software etc., there is no direct way to measure thespot (and beam) parameters from the raw images. That is
why the special interactive Spot-to-Beam (STB) procedure(written in MATHEMATICA [2] ) was developed in the
EAFEL group.

STB PROCEDURE
INTRODUCTION
In the EAFEL [1], the distance between the electron gun
cathode and the accelerator’s entrance is about 1.9 m and45 keV, 2 Amp electron beam is transported through thisspace by using (among other electron-optics elements) four
focusing coils C1-C4 and two diagnostic screens SP and
S0. Unfortunately the hardware and software used by us
at present do not provide a brightness distribution in a spot
image and even the spot boundary is not always well defined. Hence we had to try to measure the spot (and beam)geometric parameters to the best of our ability.

EXPERIMENTAL LAYOUT
The scheme of the focusing coils C1-C4 and the diagnostic screens SP and S0 is shown in Fig. 1.

Gun C1 C2 SP
Acc
C3
C4 S0
Z=0 241 475 859 1235 1532 1713 1954 mm

Figure 1: Experimental layout (not in scale).
∗ seidov@bgumail.bgu.ac.il

Available online at http://www.JACoW.org

Basic assumptions of STB
The basic assumptions of the STB procedure are:a) the reference hole positions at the diagnostic screen
are well known and their centers are perfectly aligned along
straight lines (that is we ignore manufacture errors if any)b) the screen position is known (the screen center is on
Z-axis which is not necessarily position of the spot andbeam centers), the screen rotation angle is 45 deg, and onlyaround one of axes, X or Yc) we neglect the difference in the ray paths to the√nearest and farthest sides of screen (this difference is D/ 2 ≈0.71 D ≈ 3.6 cm for the screen diameter D = 5 cm); we
do such not because we think that this difference is negligible but rather because right now we do not know how
properly to take it into account in the STB procedured) the other essential assumption is that the beam (necessarily) and the spot (optionally) can be described as theelliptical figurese) it is assumed that the beam propagates (at least near
the screens) along the Z-axis; otherwise the procedure
gives the parameters of the cross-section of the elliptic
beam normal to Z-axis (that is the real dimension of theelliptic beam is smaller than that given by the procedure).

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The ”flow-chart” of STB
The STB procedure of the spot/beam treatment is highlyinteractive: it requires the experimentalist/operator’s active
involvement. If the specialized hard/sofware is available
the whole procedure can be fully automated.
At present, the STB procedure comprise of the following
stages.
Reference picture of the screen First we need the reference picture of the diagnostic screen with the best seenreference holes. By using any graphical software we savethe reference file in any suitable format.
Spot image at diagnostic screen We need the pictureof spot image at diagnostic screen with all necessary data,
focusing/steering coil currents, quad currents etc. If (which
is most preferable) the image of spot with clearly seen reference holes is available, the ”reference picture” is not necessary. Also we note that the reference picture and the spot
picture should be got for the same camera-screen disposition etc. Again we save the spot image file in any suitableformat.
Import the image file STB procedure itself starts withusing MATHEMATICA’s ”Import” command to input thereference and spot image files (in any format) into MATHEMATICA notebook.
Getting coordinates of reference holes Then by using ”Get Graphic Coordinates” command we obtain coordinates of the reference holes (in the coordinate system of
the imported image), and save them as the ”holes” variablewith 2 x Nx x Ny elements (each of them being 2-vector,{xi , yi } of i-th hole), where N x is the number of holes
in each x-row, and N y is the number of holes in each ycolumn (for rectangular array of reference holes, otherwise
the procedure is slightly more complex). For example, at
SP screen, Nx = Ny = 5, while at S0 screen, Nx = 3 and
Ny = 5.
Getting coordinates of spot boundary Similarly, thecoordinates of the N (N should preferably be 5) ”sample”
points at the spot image boundary are got and saved in the”spot” variable with 2xN elements (each of them being 2vector, {xi , yi } of i-th spot boundary point).
This finishes the ”data extracting” procedure and the further treatment operations are simply done by ”clicking” therelevant cells in MATHEMATICA notebook with right sequence. Still some knowledge of ”what is going on” is useful.
Mapping reference holes to the Laboratory C.S.
The ”holes” variable is used to ”map” the holes (their coordinates, (xi , yi )), to the ”Laboratory” Coordinate System (C.S.), (X,Y),: e.g. x[central hole]→X = 0, y[centralhole]→Y = 0; x[next-to-central right hole]→ X (= 10 mm

TUPOS15√
for S0 screen, and = 5/ 2 mm for SP screen), y[next-tocentral√ upper hole]→ Y ( = 5 mm for SP screen, and =10/ 2 mm for S0 screen).
√
Very important is the scaling by 1/ 2 for x-coordinates
at SP screen and y-coordinates at all other screens of
EAFEL. At this stage it is assumed that the diagnostic
screen is perfectly aligned with its central hole’s center at
Z-axis and the angle of the√screen rotation is exactly 45 deg.
Otherwise instead of 1/ 2 we should use 1/ cos ϕ where
ϕ is an inclination angle. We mention√that ϕ = 45 ± 1 deg
gives 2% relative deviation from 1/ 2. In contrary, if rotation (around second axis) is (erroneously) non-zero, theeffect is much less: for ϕ < 12 deg the deviation from 1 isless than 2%.
Transition from image c.s. to Lab. C.S. Now using
the fact that reference holes ”are connected” to the laboratory coordinate system, we find the transition rule fromthe whole {x,y} c.s. of the given image to the laboratory{X,Y} C.S. To this end we solve by LSM (actually we use”Fit” command of MATHEMATICA), N y · Nx non-linear
equations, separately for X(x,y) and Y(x,y). In the simplest
case we use only the linear and cross-terms in (x,y), that ise.g X(x, y) = c0 + c1 x + c2 y + c3 x y and the similar”rule” (with other coefficients of course ) is for Y(x,y).
Transformation of reference holes and spot to Lab.
C.S. Using the transition rules X(x,y) and Y(x,y) we
transform the reference holes positions at image to points inLab. C.S., and also do the same for sample points of spot
boundary. We present, in Fig. 2, left panel , the example
for the case of I4 = .8 A. In getting beam in Fig. 2, we used
20

20

10
-30-20-10
-10

10
10 20

-30-20-10
-10

-20

-20

-30

-30

-40

-40

10 20

Figure 2: (Color) Left panel: the ”true beam” and referenceholes as obtained by STB for the case of I4 = .8 A. Rightpanel: additionally fitting ellipse found by STB is shown.
32 reference points. We may note that reference points are
nicely aligning in the ellipse-like order. By checking sucha figure one may notice the outlying points (which are mostprobably due to non-accurate clicking when getting coordinates of spot boundary). Then you may simply remove
them from the ”spot” variable, or try to obtain more accurate sample points.
This finishes the important part of the STB procedure:
we obtained the ”true beam”; and now we deal with anotherparticular problem: how to draw ellipse through the given
set of points and find the parameters of the ellipse.

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Z.F. Seidov et al. / Proceedings of the 2004 FEL Conference, 423-426

FITTING ELLIPSEEXPERIMENT AND SIMULATIONSThis section describes another essential part of STB. We
note that the problem of fitting the given set of point by any
given curve is quite general and solved in many fields ofscience and technics. We only briefly outline the procedureused in STB.
Let us have N (in our particular case N=32) points withcoordinates {xi , yi }, i = 1, . . . , N . To fit elliptic curvethrough this set of points, we first write the general equation of the ellipse in the form

We consider the case when the first focusing coil current
is of the negative sign (according to agreement in EAFEL
group), that is C1 coil rotates the image counter-clockwise.
Other coil current signs are positive or negative with respect to C1 current. In the case considered here (and usually used in EAFEL), the current signature is -/+/+/+ that is
only I1 is negative.

2

2

a x + 2 b x y + c y + 2 d x + 2 e y + 1 = 0.

(1)

If i-th point lies exactly on the ellipse (1) then we may put
x → xi and y → yi and Eq. (1) will be exactly valid. In
general this equation will be valid only approximately, andwe may ask which ellipse (that is which set of coefficientsa, b, c, d, e) fits the given set of N points best. To findthese coefficients we write the system of N equations
a x2i + 2 b xi yi + c yi2 + 2 d xi + 2 e yi + 1 = 0,

Experimental data
In Fig. 3, four spots at S0 screen are shown for values of
C4 coil I4 = .8, 2.5, 3, and 4 Amp with three other focusing coil currents fixed as I1 = −7.25 A, I2 = 3.75 A, andI3 = 3.6 A. Also shown are the elliptical approximationsof spots found by STB procedure.

(2)

and the solve the system (2) by one of LSM methods. In
MATHEMATICA the relevant command is{a, b, c, d, e} = PseudoInverse [mat] .B,(3)

where mat is the 5xN matrix of coefficients in system (2),and B is N-vector with all elements equal to -1.

Parameters of fitting ellipse
Now when we have coefficients of the ellipse equation,
we can define parameters of ellipse.
First we write three so-called invariants of the ellipse


a b d
 = det  b c e  , δ = a c − b2 , S = a + c. (4)d e 1Now, ellipse’s center coordinates are
xc = (b e − c d)/δ, yc = (b d − a e)/δ;(5)

diameters of the ellipse are
1/2

D1,2 = 2 [−/(δ u1,2 )],Figure 3: (Color) Spots at S0 vs. current of C4. Note thatat the screen surface, the distance between neighbor holes
are 10 mm in both x- and y-directions. Screen S0 is rotatedaround horizontal (X) axis by 45 deg, so that at images,
the vertical√ distances between holes are (or rather shouldbe) 1/ 2 ≈ 7.1 mm. Note also a rather strong distortionof images apparent from the holes misalignment. First, ingeneral, the camera is too close to the screen, then it seems
that the camera is closer to the upper side of the screen
than to the lower side of the screen, and again it seems
that the orientation angle is not exactly 45 deg. Also shown
are the elliptical spot approximations (and reference holes!)as defined by using STB. The beam ellipses are shown in
Fig. 4.

(6)

where u1,2 are solutions of the quadratic u 2 − S u + δ = 0.
Finally, the angular coefficient of the X-diameter of theellipse is
k = c − a + (c − a)2 + 4 b2 /(2 b).
(7)
Example of resulting fitting ellipse is shown at the rightpanel of Fig. 2, see also Fig. 4.
With this we finish the description of the STB procedureand pass to describe EAFEL experiments, STB treatment,
EGUN simulation and comparison of the results.

STB treatment results
The most important is of course to present the beam near
the given diagnostic screen as ellipse, and this is exactly
what was done by STB procedure. Results of the STB procedure treatment are presented in Fig. 4, where four beams
at S0 screen are shown for the values of C4 coil current
I4 = .8, 2.5, 3, and 4 Amp with three other coil currents
fixed as I1 = −7.25 A, I2 = 3.75 A, and I3 = 3.6 A.
With an increasing current, the elliptical beam at S0 rotatescounter-clockwise, its center moving almost vertically upward, and both diameters decreasing.

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Z.F. Seidov et al. / Proceedings of the 2004 FEL Conference, 423-426

Also we mention that all beams are (curiously enough)touching each other in one point.
The analysis of such a behavior of the beam with changing coil currents will be the subject of another paper.
Here we present only numerical results. For C4
coil currents I4 = .8, 2.5, 3, and 4 Amp, the coordinates of beam centers, in mm, are {X c , Yc } ={−0.4, −11.1}, {5.1, 0.3}, {4.6, 4.9}, and {2.6, 13.2},
respectively.
Apparently the beam, at least near the S0 screen position,is off-axis, non-circular and moves at some angles (in XZand YZ-planes) in respect to Z-axis.
20

10

-30

-20

-10

10

20

1
0.8
52 mm
0.6 .8 A
0.4
0.2
5 10 15 20 25

1
0.8
42 mm
0.6 2.5 A
0.4
0.2
5 10 15 20

1
0.8
0.6 3 A
0.4
0.2
5

1
0.8
0.6 4 A
0.4
0.2
5

35 mm

10

15

28 mm

10

14

Figure 5: Current density distribution (in arbitrary units)
in the cross-section of the axially-symmetric circular beam
at S0 screen position, as calculated by using EGUN, forvarious values of C4 coil current. Value of C4 current, in
Amp, and assumed beam diameter, in mm, are shown ateach panel. Note a spurious increase of current density atthe edge of beam. This ”hump” in the beam edge current
distribution is (unwilling) characteristic of EGUN code.

30

-10

-20

-30

-40

Figure 4: (Color) Beams at S0 screen position (as foundby using STB procedure) for four values of current of C4
coil: .8 A (the light-red largest ellipse), 2.5 A (the dark-bluesecond-largest ellipse), 3 A (the dark-red second-smallest
ellipse), and 4 A (the light-green smallest ellipse). With
increasing current, the elliptical beam at S0 rotates counterclockwise, its center moving almost vertically upward, andboth diameters decreasing.

beams (with a due account of space-charge effects), while
in reality, beam at SP and S0 positions are off-axis, noncircular and even not-parallel to Z-axis. This precludes
the rigorous comparison of simulations and experiments.
Still we mention a very good agreement between the ”simulated” circular-beam diameters and the lower/upper diameters of the ”experimental” beam ellipses. The relative variance in the beam diameter is about 10% for I4 = .8 Amp andis much less for the larger currents of C4 coil.
D, mm
60
50
40
30
1.5

EGUN simulations
We used the EGUN code [3] to calculate the beam projectiles from the electron gun (of Pierce type) up to S0
screen. We present here only the current density distribution across the (circular) beam cross-section, which allow
to estimate the beam dimension.
In Fig. 5, four beams at S0 screen position (found byusing EGUN code) are shown for values of C4 coil I1 =.8, 2.5, 3, and 4 Amp with three other coil currents fixed
as I1 = −7.25 A, I2 = 3.75 A, and I3 = 3.6 A.

Experiment/simulation comparison
In Fig. 6, the red lines show the upper and lower diameters (obtained by using STB) of beams at S0 screen position, for values of C4 coil I1 = .8, 2.5, 3, and 4 Amp,
with three other coil currents fixed as I1 = −7.25 A,
I2 = 3.75 A, and I3 = 3.6 A. The ”simulated” (by
EGUN) values (blue dash line) are close to the lower diameters of ”experimental” beam ellipses (obtained by STB)
for smaller I4 and to the upper ”experimental” diameters
for larger I4. Note that EGUN code (at least in its standard
operational mode) can treat only axially symmetric circular

TUPOS15

2

2.5

3

3.5

4

I4, Amp

Figure 6: (Color) Beam dimensions at S0 position vs C4
coil current. Red curves: ”experimental” (as obtained byusing STB) minor and major diameters of elliptic beam.
Blue dash line: diameter of the circular beam simulated by
EGUN. Ordinates: diameters in mm; abscissas: current of
C4 coil in Amp.

ACKNOWLEDGEMENTS
The idea of ”mapping” the reference holes to the ”laboratory” coordinate system should be credited to Y. Lurie.
The work was supported by Israeli Ministries of Absorption, Science and Environment.

REFERENCES[1] A. Gover et al, Nucl. Instr. and Meth. A 528 (2004) 23;
arXiv.org/physics/0408054[2] http://www.wolfram.com[3] W.B. Herrmannsfeldt, SLAC-Report-331, (Stanford Univ.,
1988)

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GUIDING OPTICS SYSTEM FOR LEBRA FEL USER FACILITY
T. Tanaka*, K. Hayakawa, Y. Hayakawa and I. Sato, LEBRA, Institute of Quantum Science,
Nihon University, 7-24-1 Narashinodai, Funabashi, 274-8501 Japan
Abstract
The FEL guiding optics system for the LEBRA user’s
experimental facility was completed in 2003. The opticalbeam extracted from the Infrared FEL resonator has been
guided through a long vacuum system to the user’s
experimental rooms, where a maximum of 17 aluminiumcoated mirrors have been used in the guiding optics. The
maximum length of the optical line is approximately 50 m.
The divergent FEL beam extracted from the resonatorthrough a coupling hole has been converted into a parallel
beam. An approximately identical diffraction pattern of aguide laser was observed at the output ports of theexperimental facility. The guiding optics has two FEL
monitoring ports, each containing a CaF2 beam sampler
and a total reflection mirror, which has advantages for
simultaneous measurement of the power and the spectrumof the FEL during user’s experiments. The transport
efficiency of the guiding system depends on the FEL
wavelength and the radius of the coupling hole in theresonator mirror.

INTRODUCTION
Use of the infrared free-electron laser (FEL) for
experiments in medical science and material science wasstarted in 2003 at the Laboratory for Electron BeamResearch and Application (LEBRA) of Nihon University.
The FEL guiding optics completed prior to the beginningof user’s experiments was designed to transport the FEL
and its higher harmonic undulator radiations. The lights inthe wavelength region of 0.2 to 6 µm are extracted fromthe FEL resonator through a coupling hole in one of theresonator mirrors. After converted to a parallel beam, thelights are transported to user’s experimental rooms usingaluminium-coated plane mirrors. The top view of the
LEBRA accelerator facility and the user’s experimental
facility is shown in Fig. 1.
This paper reports on the present status of the LEBRAFEL system and the optical guiding system for the FEL
user facility.

Fig. 1. Top view of the LEBRA accelerator facility and the user’s experimental facility.
____________________________________________*

E-mail address: tanaka@lebra.nihon-u.ac.jp

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THE FEL SYSTEM OF LEBRA
Table 1 shows the specifications of the infrared FEL
system installed in LEBRA. A schematic layout of thesystem is shown in Fig. 2. The FEL guiding optics systemin the accelerator room is also shown in Fig. 2. The planar
FEL undulator consists of Halbach-type NdFeB
permanent magnets [1]. The electron beam wiggles in a
vertical direction in the undulator so that the focusing
field of the undulator binds the electron beam orbit in ahorizontal direction.
The highest electron energy is currently restricted to
100 MeV due to the maximum klystron output rf power.
The minimum undulator gap width was reduced by 5 mmcompared with the earlier design specification byreplacing with a thinner undulator vacuum duct, which
increased the maximum undulator K-value from 1.5 to 2.
The wavelength of the FEL is variable in the range from
0.9 to 6.5 µm, which is accomplished by adjusting theelectron beam energy and the undulator gap width i.e. theundulator K-value [2].
The electron beam from the linac has a longitudinalbunch structure with a period of 105 mm corresponding to
the accelerating rf of 2856 MHz. The separation D
between the two resonator mirrors is 6.718 m, i.e. 64
times the free space wavelength of the microwave. The
curvature radius R of the resonator mirrors was decided to
be 4.0 m. Then the Rayleigh length LR of the FEL in theresonator, given by the relation [3]LR = D(2 R − D) / 2 ,(1)Table 1. Specifications of the LEBRA infrared FEL
system.
Maximum electron beam energy
Maximum undulator K-value
Micropulse beam current
Period of undulator field
Number of periods
FEL wavelength range

125
2
> 20
48
50
0.6 - 6

MeV
A
mm
µm

is 1.47 m, which is slightly longer than the half of theundulator length. For the resonator mirrors, silver-coatedcopper mirrors with a diameter of 25 mm were
manufactured at Rocky Mountain Instrument Co. (RMI).
The nominal reflectance of the mirrors is greater than
99.3 % for the wavelength range from 1 to 20 µm. The
FEL power is extracted from the resonator through asmall coupling hole on the center of the upstream mirror.
The radius a of the coupling hole at the mirror incurrent use is 0.15 mm. Provided that the FEL in theresonator is a Gaussian beam, the FEL beam radius w on
the surface of the resonator mirror is given by

w=

λL LR
{1 + ( D / 2 LR ) 2 } ,πwhere λL is the FEL wavelength. Then the coupling
coefficient κ of the hole, defined as a ratio of the opticalpower contained in the cross section of the hole to thetotal power incident on the mirror, is given asκ = 1 − exp( −2a 2 / w 2 ) .

(3)For the FEL wavelength of 0.9 µm, obtained with theelectron beam of 100 MeV and the K-value of 0.93, thecoupling coefficient deduced from Eq. (3) is 0.017.
Therefore the sum of the mirror loss and the external
coupling loss for each round-trip of lights in the resonatoris approximately 3.1 % of the total power.
Lasing by this system has been experimentallyconfirmed over the K-value range from 1 to 2, whichsuggests a broad variability of FEL wavelength at fixed
electron energy. Lasing at 0.6 µm is feasible with thepresent system by increasing the electron energy up to
125 MeV, though the estimated total loss in each roundtrip increases to about 5 % due to a decrease of the mirror
reflectance and an increase of the coupling loss.

THE BEAM EXPANDER SYSTEMThe FEL extracted from the resonator through the small
coupling hole has a divergence angle due to a diffraction
effect referred to as the Fraunhofer diffraction. For the
first dark ring or the central core of the diffraction patternthat contains 84 % of the extracted optical power, thedivergence angle θ of the radius is approximated as [4]θ=Fig. 2. Schematic layout of the LEBRA FEL systemand the FEL guiding optics system in the accelerator
room.

TUPOS17(2)

3.833λL
.
2π a

(4)

For the 5 µm fundamental FEL, the coupling-hole radiusof 0.15 mm causes the divergence of the core radius with
θ = 20 mrad. The maximum distance between the FEL
output mirror and the user’s port is approximately 50 m.
Therefore, a conversion optics system is necessary for
efficient guiding of the light beam to user’s experimentalrooms. In the optical guiding system of LEBRA, thedivergent beam has been converted to a parallel beam bymeans of a beam expander system consisting of anellipsoidal mirror and a parabolic mirror. The expander
mirror system was manufactured and aligned by CANONInc..

T. Tanaka et al. / Proceedings of the 2004 FEL Conference, 427-430

Fig. 3. Geometrical configuration and ray trace of thebeam expander system. The rear surface of the upstream
mirror lies at the position equivalent to one of the focal
points of the ellipsoidal mirror.
The geometrical configuration of the mirrors in the
expander system is shown in Fig.3. The basic idea of the
optics system is the same as which was installed in FELSUT MIR FEL beam line [5]. The FEL extracted throughthe coupling hole in the upstream mirror is reflected withthe primary and the secondary plane mirrors, and thendirected toward the ellipsoidal mirror. The optical path
length between the coupling hole and the ellipsoidal
mirror decided to be approximately 2.5 m so that the rearsurface of the upstream mirror or the exit of the couplinghole is placed at the position equivalent to one of the focal
points of the ellipsoidal mirror. Therefore the divergent
light beam which comes out of the coupling hole isfocused at another focal point of the ellipsoid.
As seen in Fig. 3, the ellipsoidal mirror and theparabolic mirror have been aligned to form a confocal
configuration so that the light beam, once focused at thecommon focal point, is converted to a parallel beam by
the parabolic mirror, where the focal length is 420 mm forboth mirrors. These mirrors have a common central axis
parallel to the FEL resonator axis. Then, the collimatedbeam obtained at the exit of the beam expander has
approximately the same profile as that on the surface ofthe ellipsoidal mirror.

PARALLEL BEAM TRANSPORT AND FELMONITOR SYSTEMAs seen in Fig. 2 the output parallel beam from the
expander chamber is sent to the next room through a
rectangular chicane section. This section was installed tosuppress the leakage of gamma rays and neutrons to the429

next room through the vacuum duct in the shielding wall.
Concrete, lead and plastic blocks surrounding the fourth
mirror chamber in the chicane section effectively shield
the direct radiations from the electron beam dump.
The parallel beam is guided to nine separate
experimental rooms by switching the beam line withretractable plane mirrors. The guiding system in the user’s
facility was installed in the pit under the floor. Everyswitching section is equipped with a total reflection
mirror (aluminium coated) and a partial reflection mirror(CaF2 plate), which allows for parallel experiments in the
different rooms.
For the purpose of monitoring and control of the FEL
lasing during user’s experiments, two monitor chambers
have been inserted in the midstream of the guiding system.
Each chamber contains a CaF2 beam sampler and a totalreflection mirror for alternate monitoring of high intensity
fundamental FEL and higher harmonics during user’s
experiments, or low intensity spontaneous emission
during electron beam adjustments.
The FEL monitor chambers and associated optics
placed in the large experimental hall are shown in Fig. 4.
The output from the upstream side chamber has been used
for the measurement of the FEL macropulse waveform bymeans of an InSb detector. The output from anotherchamber has been used for the measurement of the FEL
macropulse energy and the spectra of higher harmonics.
Use of separate beams in simultaneous measurement ofdifferent FEL properties requires no wide-band half
mirror. Also, it allows easy alignment of the devices on
the optical base.
The wavelength of the fundamental FEL has not beenmeasured directly in the wavelength range longer than 1.6µm due to the restricted range of the array detector andthe spectrometer in LEBRA. Instead, the spectra of thehigher harmonics in the visible region have been used to
extrapolate the wavelength of the fundamental FEL.

Fig. 4. The picture of the FEL monitor chambers andassociated optics on the optical base. Each chamber
contains a CaF2 beam sampler and a total reflection
mirror for an alternative use.

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CONSIDERATIONS ON THE POWER
LOSS IN THE GUIDING SYSTEM
The radius of the plane mirrors used in the guiding
system downstream from the beam expander is 50 mm,
which results in an effective radius of 35 mm due to thereflection angle set at 45 °. The minimum inner radius of
the vacuum duct is about 25 mm. Therefore, the apertureof the vacuum duct is the main restriction for the transport
efficiency of the FEL power except for the mirror
reflectance.
The profile of the parallel light beam transported to theuser’s facility is primarily determined by the wavelengthof the light, the radius of the coupling hole in the
upstream mirror, and the distance between the couplinghole and the ellipsoidal mirror. From Eq. (4) the coreradius aA of the diffraction pattern at the ellipsoidal mirror
is given byaA =3.833λL d
,
2π a

(5)

where d (= 2.5 m) is the distance between the couplinghole and the ellipsoidal mirror. The radius is assumed tobe conserved in the travel to the experimental rooms.
The guiding system was originally designed to use aresonator mirror with a coupling hole of 0.5 mm radius
for the lasing in the wavelength range of 5 µm or longer,
where the core radius is greater than 15 mm but still lessthan the inner radius of the vacuum duct. On the other
hand, the mirror with the coupling hole of 0.15 mm radiusin current use was intended for use in lasing at the
wavelengths shorter than 2 µm by taking into account the
coupling coefficient. For this mirror, the core radii of the
FELs with the wavelength of 2, 3, 4 and 5 µm areapproximately 20, 30, 40 and 50 mm, respectively.
Thus, the use of the current mirror for lasing in the
wavelength range longer than 3 µm results in a large

TUPOS17

power loss due to the eclipse caused by the aperture of thevacuum duct.
The current FEL system takes at least 1 day to replace
the mirror. However, a more efficient optical beamtransport and a relatively high coupling coefficient by an
optimised mirror will allow for the use of considerably
higher FEL power at the user’s experimental rooms forlonger wavelength FELs.

SUMMARY
The FEL in the wavelength range from 0.9 to 6.5 µm
has been lased with the LEBRA infrared FEL system. The
divergent beam extracted through a small coupling hole in
the FEL resonator mirror has been converted into aparallel beam with the beam expander system consistingof an ellipsoidal mirror and a parabolic mirror. The
transport efficiency for long-wavelength FELs is low dueto the large radius of the parallel beam. However, theefficiency in the long wavelength region can be improvedby replacing the current mirror with a resonator mirror
which has a larger coupling hole.

REFERENCES[1] K.Halbach, Nucl. Instr. and Meth. 187 (1981) 109.
[2] T.Tanaka et al., “Tunability and PowerCharacteristics of the LEBRA Infrared FEL”,
FEL2004, Trieste, Italy, Aug. 2004.
[3] H.Kogelnik and T.Li, Applied Optics 5, No.10(1966) 1550.
[4] M.Born and E.Wolf, Principles of Optics, Cambridge
University Press (1999).
[5] K.Nomaru et al., Nucl. Instr. and Meth. A445 (2000)
379.

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T.T. Taniuchi et al. / Proceedings of the 2004 FEL Conference, 431-434

UPGRADE OF A PHOTOCATHODE RF GUN AT SPRING-8
T. Taniuchi#, T. Asaka, H. Dewa, H. Hanaki, T. Kobayashi, A. Mizuno, S. Suzuki, H. Tomizawa,
K. Yanagida, JASRI/SPring-8, Hyogo 679-5198, Japan
M. Uesaka, NERL, University of Tokyo, Tokai, Ibaraki 319-1188, Japan
Abstract
A new test bench for a photocathode RF gun has been
built to verify the beam characteristics in higher energy
regions up to 30 MeV and develop a sophisticatedinjector system for practical use. The accelerator roomhas been expanded, and two beam lines including a 3-mlong accelerating structure, have been installed. A clean
room for the driving laser system was also expanded inwhich the air temperature control was improved andhigher humidity could be maintained to reduce thecharge-up on the optical elements. RF conditioning has
been completed and the electric field gradient on thecathode of the RF gun reached up to 183 MV/m. The
first beam has been successfully commissioned and a
new emittance monitor using the quadrupole scan has
been tested. We have investigated a new gun cavity
system to improve the emittance in higher charge regions
exceeding 1 nC/bunch. Presently we are investigating a
multi-cavity system, in which the current single-cellcavity is used as the first cavity.
According to asimulation result, the normalized emittance of 2.4
πmm•mrad can be achieved in a two-cavity system at acharge of 1.4 nC/bunch. The second RF cavity and ahigh power distributor system have been also designed.

parameter and phenomena in a high-gradient fieldsituation such as RF breakdown, dark current and so on.
In these experiments, the lowest emittance of
2π mm•mrad at a beam charge of 0.1 nC/bunch [1] and amaximum field gradient of 175 MV/m at the cathodesurface has been achieved [2] and we understood how tocontrol parameters to minimize the beam emittance.
The next step of this R&D project is to verify the beam
performance, especially the emittance, in the higher
beam energy region because the single-cell cavity can
only accelerate beams up to 4.1 MeV and the emittancecan easily grow in this energy region. There were someproblems in the laser system. A fluctuation of the airtemperature in the clean room made the laser unstable
and a charge up on optical elements collected dust andcause damages. To improve these problems, a new test
bench has been constructed that includes an expandedradiation shield and an air temperature- and humiditycontrolled clean room for the driving laser system. The
construction began in March 2003 and was completed in
December of that year. In parallel with the experiments
using this facility, a new gun system is underinvestigation to achieve a lower emittance in highercharge regions.

INTRODUCTION

NEW TEST BENCH

A photocathode RF gun has been investigated at
SPring-8 to develop a low-emittance and short-bunch
injector for the linac. We commenced this R&D with asingle-cell cavity in which the inner copper wall wasused as a photocathode. This cavity has an output port
for extracting a part of the RF power and the loaded Q islowered. This enables to shorten the filling time andachieve a higher-gradient field.
Using this cavity, we have examined dependences ofbeam characteristics on RF, solenoid fields and laser

As shown in Fig. 1, the test bench is located in
Machine Laboratory building, which can be connectedwith the linac building at the L1 beam transport line (250
MeV) by removing a concrete plug. Therefore, in the
future it will be possible to inject the electron beam
produced by the photocathode RF gun into the 1-GeV
linac.

Figure 1: Location of new RF test bench. (a: Clean room for driving laser system, b: Radiation shielded accelerator
room, c: Klystron and modulator)#ihcuinat@spring8.or.jp

Available online at http://www.JACoW.org

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Figure 2: Layout of 30-MeV linac with photocathode RF gun.
A 3-m travelling wave structure has been added after
the RF gun and the approved maximum beam energy has
been increased from 4.5 MeV to 30 MeV. The thicknessof the concrete shield has been increased from 0.5 m(partly 1.0 m) to 1.4 m, while the floor area of theaccelerator room has been expanded to make it threetimes larger. This test bench will be used not only forthe photocathode RF gun R&D but also for high-gradienttests in collaboration with other institutes and highpower tests of RF components before installation in the
1-GeV linac and so on.
There are two accelerators in the radiation shield. One
is a 30-MeV linac with the photocathode RF gun and theother is a standalone RF gun for photocathodeexperiments. The latter includes experiments for
cartridge-type electric tube with Cs2Te cathodes [3].
The layout of the 30-MeV linac is shown in Fig. 2.
The RF source is an 80 MW klystron (Toshiba E3712),
and the RF power is distributed into two RF gun cavities
and a 3-m long travelling wave accelerating structure,
which is the same one as is used for the SPring-8 1-GeV
linac.
As shown in Fig. 3, the high-power RF distributing
system comprises magic-tees, 3-dB directional couplers,
phase shifters, dummy loads, RF windows and so on. A
combination of a magic-tee, a phase shifter and 3-dB
directional coupler divides RF power into two
waveguides in an arbitrary ratio. Therefore, the RF
power and phase for the two RF gun cavities and thetravelling wave structure are variable in this distributing
system.

A feature of this system is that there is no circulator toprotect the klystron from the reflected RF power because
the loaded Q value of the RF gun cavity is lowered to
one fourth of that for typical standing wave cavities byextracting some of the power, and then the reflected
power is much smaller -- like travelling wave structures.
Regarding the driving laser system, a highly stabilized
and profile-controlled system has been underdevelopment in a new clean room with a cleanness ofclass 1000 [4]. The total floor area of the clean room
becomes 2.7 times larger than the previous one. The airtemperature near the laser table is stabilized within 0.6
degree and the humidity is kept at around 55% R.H. tominimize the charge-up and avoid damages on the
optical elements. The down-flow of the air is dispersed
to decrease the fluctuation of the laser path. To maintainthe cleanness of the air, the previous clean room is used
as an anterior chamber of the new one.

RECENT PROGRESS
Following the installation of the accelerator system,
automated RF conditioning for waveguides and RF
cavities was performed successfully.
We tested a chemical etching method for surface
treatment of the RF gun cavity to improve the quantum
efficiency (QE) and high-gradient performance qualities
such as the RF breakdown rate and dark currents. As aresult, the conditioning time was clearly shortened,achieving a maximum QE of 8.6 x 10-3 % for our cathodeand a maximum field gradient on the cathode of 183
MV/m [5].
Beam acceleration was also successful, and an
emittance measurement by using the quad-scan method
was tested for a 24.5-MeV beam [6].
R&D concerning the driving laser system is focusedon laser pulse shaping in both the spatial and temporaldimensions which is required for the emittance reduction.
A deformable mirror system for spatial shaping and a
spatial light modulator based on a fused-silica plate fortemporal shaping, are under development [4].

MULTI-CAVITY RF GUN
Figure 3: High-power RF distribution system. (G1: RF
gun cavity #1, G2: RF gun cavity #2, KLY: 80 MW
klystron, ACC: 3-m travelling wave structure)

TUPOS18

We are currently investigating an RF gun system that
can attain lower emittance in higher-charge regions. In

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T.T. Taniuchi et al. / Proceedings of the 2004 FEL Conference, 431-434

order to reduce space charge induced emittance growthat higher bunch charge while maintaining a high-gradientacceleration using our low-Q cavity, an addition of RF
cavities after the current cavity has been investigated.
The acceleration by single-cell cavities will also be
effective for the emittance reduction because a field
gradient can be higher than that of the disk-loaded
accelerating structures. In the following subsections, theresult from a computer simulation, a design of the RF
cavity and a new configuration of the high power RF
distributor are described.

Simulation
The beam dynamics in a two-cavity RF gun have been
investigated by using a simulation code PARMELA. As
a result of an optimization for the RF phase and fieldstrength, it was found that the beam emittance could belowered to 2.4 πmm•mrad at a charge of 1.4 nC/bunch,which is lower than that of current single-cell cavity
system. Fig. 4 shows an example of the beam emittancealong the beam line.

Qext for input port

3,160

Qext for output port

3,950

Loaded Q

1,580

Shunt impedance for β=1

5.3 MΩMaximum accelerating field gradient

100 MV/m

High-power RF system
We are currently investigating the two-cavity system,
but simulation results indicate an effectiveness of threecavity system for the emittance reduction. Therefore, ahigh power RF distributor for the three-cavity RF gun
has been designed. If we adopt the low-Q type cavity,
the required total RF power will exceed the maximum
power of the klystron, i.e., 80 MW. One option forsolving this problem is to install an RF compression
system such as SLED. However, we selected anothersystem that utilize the output power from our low-Q typecavity and minimizes the cost. However, the filling timeof the first cavity becomes longer. Fig. 5 illustrates thehigh-power RF distribution system for the three-cavity
RF gun.

Figure 4: Simulated result for emittance in a twocavity RF gun.

Design of RF cavity
In the simulation, optimum RF phase and fieldstrength for the two cavities are obtained. Then arealistic RF cavity for the second one was designed using
a 3D field solver code, MAFIA.
To maintain high-gradient performance and employ
the present RF distribution system, a low-Q type cavity
is adopted. The external Q value for the output port wasdetermined considering the RF distribution systemdescribed in the next subsection. Relevant parameters
for the second cavity are listed in Table 1.
Table 1: Design parameters for second and third cavities.
Radius of beam pipe

10 mm

Curvature radius of cavity nose

5 mm

Cavity length

38 mm

Q0

15,800Figure 5: High-power RF distribution system for thethree-cavity RF gun system. (C1~C3: Three-cavity RF
gun, G2: RF gun cavity #2, KLY: 80 MW klystron,
ACC: 3-m travelling wave structure)
This system can divide the RF power and feed it into
the second and third cavities in any arbitrary ratio. The
output power from the second and third cavities aresubsequently recombined in a power distributor and fed
into the first cavity, which requires the highest RF powerof all three cavities. Use of this system enables the RF
power and phase for the three cavities being tuneable.
For a fast switching between the experiments using the30-MeV linac and that using RF gun #2, we will install avacuum-type waveguide switch in the waveguide before
the second cavity.

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CONCLUSION
The construction of the new test bench for thephotocathode RF gun R&D has been completed, and the30-MeV linac and the standalone RF gun for the cathodedevelopment are now ready for further experiments.
We are planning to measure and optimize theemittance of the beam that is produced from the RF gun
and accelerated up to 30 MeV. The optimization
includes a shaping of laser pulses in both the spatial andtemporal dimensions, RF phase and field strength of eachcavities, solenoid fields and so on.
To attain practical use of a photocathode RF gun, a
new cavity system is under development that is designed
to lower the beam emittance in higher-charge regions
exceeding 1 nC. Presently a multi-cavity RF gun is a[4] H. Tomizawa et al., “Development of Adaptive
Feedback Control System of Both Spatial andTemporal Beam Shaping for UV-Laser Light Source
for RF Gun”, LINAC’04, Lübeck, August 2004, (tobe published).
[5] H. Tomizawa et al., “Effects of Chemical Etching as
a Surface Treatment for Accelerating Structures

TUPOS18

promising candidate for the above requirement withsimulation work and RF design continuing.

REFERENCES[1] H. Dewa et al., Proc. of ICFA Workshop, “ThePhysics and Applications of High Brightness
Electron Beams”, Chia Laguna, July 2002, p. 28.
[2] T. Taniuchi et al., “Characteristics of a PhotocathodeRF Gun in Higher Field Gradient”, LINAC’02,
Gyongju, August 2002, p. 683.
[3] J. Sasabe et al., “Photocathode RF gun using
cartridge-type electric tubes”, FEL’03, Tsukuba,
September 2003, Nucl. Instr. and Meth. A 528(2004) 382.
Made of Copper”, Proc. of the 29th Linear
Accelerator Meeting in Japan, Funabashi, Japan,
August 2004, p. 147.
[6] H. Dewa et al., “Photocathode RF Gun Designed as aSingle Cell Cavity”, EPAC’04, Lucerne, July 2004,(to be published).

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T. Tanaka / Proceedings of the 2004 FEL Conference, 435-438

FEL SIMULATION CODE FOR UNDULATOR PERFORMANCEESTIMATION
Takashi Tanaka
RIKEN/SPring-8, Koto 1-1-1, Mikazuki, Sayo, Hyogo 679-5148, Japan
Abstract
An FEL simulation code called SIMPLEX is introduced,
which has been developed to investigate the effects of theundulator field error on the FEL gain. It can perform FEL
simulations with the magnetic field distribution actually
measured along the undulator axis so as to check the performance of the undulator as an FEL driver. Basic equations are derived that enable the numerical implementationof the FEL equations with the error fields taken into account. Practical examples for investigation of the undulator
field error are also presented.

is the horizontal component of the beam current density, µ0
the permeability of vacuum. Averaging over the period ofradiation, T = 2π/ω, and integrating by part, we have



1 ∂
ω ∂
+
Ẽ
∇2 + 2i
c ∂z
c ∂t
N

=
with

ψj (z) = ku z +INTRODUCTION
The undulator is one of the most important components
of an FEL. In particular, a quite large number of periods isrequired to achieve saturation in SASE-based x-ray FELs.
Because the permanent magnets in the undulator are not
perfect, the undulator field has necessarily error components. Needless to say, the tolerance on the undulator fielderror is more severe for larger number of periods. It is thus
important to check the performances after construction ofan undulator by measuring the magnetic field and calculating optical properties with it.
As a spontaneous-emission synchrotron radiation (SR)source, the performances of an undulator are in general
specified by a quantity called the phase error. It is also
possible to compute the intensity of SR by Fourier transforming the electric field generated by an electron moving
in the undulator field. On the other hand, it is not easy tocheck the performances of the undulator as an FEL driver.
The most promising way is to perform simulations of the
FEL processes driven by the undulator with error fields.
We have recently developed an FEL simulation code called
SIMPLEX that can perform FEL simulations with the magnetic field distribution actually measured along the undulator axis. The details of which are described in the following
sections.

FEL EQUATIONS
The amplification process in the FEL is represented bythree equations, i.e., the wave, energy and phase equations.
The wave equation of the radiation field under the paraxial approximation is written as



1 ∂
∂jx
ω ∂
+
Ẽ + c.c. = µ0,eiω(z/c−t) ∇2 + 2i
c ∂z
c ∂t
∂t
where Ẽ is the complex amplitude of the radiation field, jx

Available online at http://www.JACoW.org

iµ0 ωe βjx eiku z e−iψj δ(r − r j ),
T j=1

ω
c


z−

 z

dz 
β⊥j (z  )

(1)


,

where λu = 2π/ku is the periodic length of the undulator,
N is the number of electrons existing in the averaging area,and β j , r j , and ψj are the velocity, position and phase of
the j-th electron, respectively. The phase equation can be
modified as
2− K 2 /2dψj
∆ω γj2 β⊥j
2∆γj
= ku
, (2)
−
−
dz
γ0
ω0
1 + K 2 /2with
∆γj = γj − γ0 , ∆ω = ω − ω0 ,where γj is the energy of the j-th electron, γ0 is the averageenergy of the electron beam at the undulator entrance, ω0 is
the fundamental energy of the undulator radiation, and K
is the deflection parameter of the undulator.
The energy of each electron changes by interaction withthe radiation field, which is described by the equationdγje=(βjx e−iku z eiψj + c.c.).
dz
mc2

(3)

The differential equations (1) ∼ (3) can be solved numerically with a certain longitudinal step ∆z. In most FEL
simulations, a multiple length of the undulator period λu
is chosen for ∆z. This is because the electric field Ẽ andelectron energy γj do not change drastically over such alength, and the equations can be averaged over ∆z with theperiodic condition of the magnetic field for ideal undulators. For real undulators, however, the periodic condition
cannot be applied to modify the FEL equations because of
the field error intrinsic to the real undulators.

NUMERICAL IMPLEMENTATION
The most straightforward way to solve precisely the FEL
equations with the field-error effects taken into account is

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T. Tanaka / Proceedings of the 2004 FEL Conference, 435-438

to adopt a fine integration step, i.e., ∆z  λu . Needlessto say, it takes a lot of computation time. Because Ẽ andγj are slowly varying functions compared to λu even in thecase with the real undulator, averaging is again a promising
way for practical simulation. It should be noted, however,that the averaging should be performed at every integration
step, i.e., z = ∆z, 2∆z, . . . , n∆z, . . .. In the following
sections, the FEL equations are modified to the forms thatare convenient for averaging.

Magnetic Field Model
In order to specify the electron trajectory in arbitrary
magnetic fields B, the equation of motion should be solved
with the Lorentz force taken into account, which needs 3dimensional field mapping. In the undulator line, however,
the electron trajectory can be decomposed into two components, which considerably simplifies the problem.
One is the the sinusoidal (or more generally, quasiperiodic) orbit that cause the interaction between the electrons and radiation field. For real undulators, it also contains random walks both in the horizontal (x) and vertical(y) directions due to error fields. In general, it hardly depends on the transverse coordinate of the injected electron
at the entrance of the undulator and is thus determined by
the magnetic field distribution B u measured along the undulator axis.
The other is the betatron oscillation induced by the focusing force on the electron beam generated by quadrupole
magnets and (natural) focusing in the undulator. It is reasonable to assume that the focusing field B f is uniform
over the distance occupied by each magnetic device asshown in Fig. 1.
Q. Magnet

Focusing

Undulator

Electron Motion
Now let us consider an electron travelling from z0 to z
with an initial condition β = β 0 and r = (x0 , y0 , z0 ) at
the longitudinal position of z0 . Assuming that the travelling
distance ∆z = z −z0 is much shorter than the period of thebetatron oscillation, the transverse position of the electron,
x and y, does not change significantly. Thus, the focusing
field Bf can be regarded to be constant. Then, the velocity
and position of the electron are obtained just by integrating
the field distribution along z axis
(4)
βx (z) = β0x + γ −1 [Iuy (z0 , z) + If y (z0 , z)],x(z) = β0x ∆z + γ −1 [Juy (z0 , z) + If y (z0 , z)∆z/2],
with=

If y (z0 , z)Juy (z0 , z)

=

z

z0

Iuy (z0 , z  )dz  ,and similar expressions for the vertical components βy andy.

Interaction Factor
In the differential equations (1) and (3), there exists an
identical factor βx eiku z e−iψ (and its complex conjugate),
which is regarded to be an efficiency of interaction between
the electrons and radiation field. It is easy to show that thisfactor is almost periodic with a period of λu /2. It is therefore necessary to average it over the distance of the integration step ∆z, which, in most cases, longer than λu /2. Inaveraging, we can omit the trajectory components related
to the betatron oscillation because the period of the betatron oscillation is much longer than λu , In other words, we
replace as follows
2
2
+ Iux
.
βx → Iuy /γ, (γβ⊥ )2 → Iuy

za zb

Longitudinal Position

Figure 1: Example of a magnetic device configuration andfocusing force distribution in the undulator line.
The above discussion arrows us to introduce an effective
magnetic field B eff that has no longitudinal components
and the form

In addition, we can neglect the terms ∆γ and ∆ω in thephase equation because they are nearly constant over ∆z.
Then, we haveβx eiku z e−iψ  = iwhich can be used to calculate the electron trajectory instead of the real field B. The field Bf (x, y, z) can be
regarded to be uniform with respect to z within a limited
range, e.g., za < z < zb as shown in Fig. 1.

Ja (z0 ) −iψj (z0 )
e
,
γ

with
Ja (z0 ) =B eff (r) = Bu (z) + Bf (x, y, z),

TUPOS19 zeBuy (z  )dz  ,mc z0e(z − z0 )Bf y ,=mc

Iuy (z0 , z)

1
i∆z

 z
z0

Iuy (z  ) exp
iku ρ(z0 , z  ),1 + K 2 /2

(5)

and
ρ(z0 , z) =

 z
z0

2
2
[Iuy
(z0 , z  ) + Iux(z0 , z  ) − K 2 /2]dz 437

T. Tanaka / Proceedings of the 2004 FEL Conference, 435-438

For ideal undulators without any field errors, Iux = 0 and
Iuy (z0 , z) = K sin ku z, thus we have

 


K 2 /4K 2 /4K
Ja (z) =
J0
−
J
.
1
2
1 + K 2 /2
1 + K 2 /2
Substituting this formula into (1) gives an ordinary wave
equation to describe the amplification process in the FEL
driven by an ideal undulator.

Electron Phase
Because the electron energy does not change significantly over ∆z, the electron phase can be calculated byintegrating equation (2) directly. Substituting (4) into (2)and integrating between z0 and z, we have2∆γ∆ω−ψ(z) = ψ(z0 ) + ku ∆zγ0ω02
ku (Rx + Ry − K ∆z/2),(6)+
1 + K 2 /2
with
Rx =

 z
z0

2
Iuy
(z  )dz  −2If y (z0 , z)
∆z

 z
z0

Juy (z0 , z  )dz +∆z[(γβ0x )2 + γβ0x If y (z0 , z) + If2y (z0 , z)/3]+2Juy (z0 , z)[γβ0x + If y (z0 , z)],(7)and similar expression for Ry . Note that the subscript j has
been omitted in the above equation for simplicity.

Processing of the Undulator Field Data
The above modifications on the FEL equations arrow us
to process the undulator field data convenient for numerical implementation, i.e., the entire undulator line is divided
into adequate integration steps and the quantities such as
Iuy , Juy and Ja are calculated in each step before starting the simulation. In most x-ray FELs, the gain length ismuch longer than the undulator period, which requires a
great number of periods to achieve saturation. Thus, longer
integration step is necessary to save the computation time.
The data processing scheme described here ensures a good
reproducibility of the electron motion and interaction efficiency regardless of the length of the interaction step, as far
as the electron energy and radiation field does not change
drastically within the step.
After the data processing, the FEL equations can besolved easily. The electron energy and phase can be calculated by substituting (5) and (7) into (2) and (3). The
wave equation (1) that describes the growth of the radiation field can be modified to a more convenient form fornumerical computation, by means of spatial and temporal
Fourier transforms [1].

above. Let us now show several examples of results to investigate the effects due to the undulator field error using
SIMPLEX. Accelerator and undulator parameters used in
the simulations are summarized in Table 1.
Electron Energy
Normalized Emittance
Energy Spread
Peak Current
Average betatron function
Undulator Period
Undulator Length
Undulator K Value
Wavelength
Gain Length

250 MeV
1πmm. mrad
2 × 10−4
2 kA
7m
15 mm
4.5 m
1.3
60 nm
0.16 mTable 1: Example of a magnetic device configuration andfocusing force distribution in the undulator line.

Performance of SCSS Prototype Undulator
SCSS stands for “SPring-8 Compact SASE Source” andaims at an X-ray FEL in the Angstrom wavelength region[2]. A prototype undulator for the SCSS project has been
constructed in 2003, the details of which are described in[3]. Here we check the magnetic performance of the prototype. Figure 2(a) shows the phase errors as functions of
the longitudinal position calculated with the magnetic fieldmeasured before and after the undulator field correction.
We can see a drastic improvement between the two. Inorder to check the actual performance as an FEL driver,
we performed FEL simulations, the results of which are
shown in Fig. 2(b) as the radiation power growth along
the undulator. As in the phase error, the FEL gain curve isimproved significantly by the field correction, and we can
expect the radiation power close to the ideal value with theconstructed undulator.

Effects due to the Ambient Field
The ambient field means weak and uniform magnetic
fields that cause a parabolic electron orbit. The main source
for this is the geomagnetic field and/or an offset voltage ofthe Hall probe that is usually used in the undulator fieldmeasurement. In addition, the electron beam injected into
the undulator with a vertical position offset with respect tothe undulator axis experiences a parabolic-like orbit due tothe natural focusing, which brings undesirable effects similar to those by the ambient field. The examples of the effects due to the ambient field ∆By in the vertical direction
are shown in Fig. 3 in terms of the electron trajectory andpower-growth curve. It is found that ∆By of 0.5 Gauss has
little effects on the FEL gain, while those of 1.0 Gauss are
not negligible.

EXAMPLES

Effects due to Inhomogeneous Demagnetization

An FEL simulation code, SIMPLEX, has been developed at SPring-8 using the numerical schemes described

It is well known that permanent magnets can be damaged by irradiation of the electron beam, which cause an

FEL Technology

438
60

(a)

50
40
30
20
0

(b)

100
10-1
10-2
10-3

Ideal
Before
After

10-4
10-5
-6

10

0.0

1.5

3.0

4.5

Distance from Undulator Entrance (m)Radiation Power (GW)

Horizontal Orbit(µm)

Figure 2: Magnetic performances of the prototype undulator for the SCSS in terms of the (a) phase error and (b)power-growth curve.
250
200
150
100
50
0
-50
-100
-150
101
0

10

(a)

1.000

(a)

0.998

0.5% demagnetization

0.996
0.994
1.0% demagnetization

0.992
0.990
101
100

(b)

10-1
10-2
10-3

Ideal
A=0.005
A=0.01

10-4
10-5
10-6

0.0

1.5

3.0

4.5

Distance from Undulator Entrance (m)∆By=1.0G

Figure 4: Effects of radiation-induced demagnetization onthe (a) field envelope and (b) FEL gain for two values ofthe maximal demagnetization fraction A.

∆By=0.5G

SUMMARY
(b)

10-1
10-2
10-3

Ideal
∆By=0.5G∆By=1.0G

10-4
10-5
10-6

Normalized Field Envelope

After(2.76)

10
-10
101

Radiation Power (GW)

imal fraction and typical depth of demagnetization, respectively. The examples are shown in Fig. 3 for two valuesof A. The depth D is fixed at 1.0 m in each simulation.
We find a significant gain degradation even for the 0.5 %demagnetization.

Before(17.4)

Radiation Power (GW)

Phase Error (degree)

T. Tanaka / Proceedings of the 2004 FEL Conference, 435-438

0.0

1.5

3.0

4.5

Distance from Undulator Entrance (m)Figure 3: Effects due to the ambient fields of 0.5 and 1.0
Gauss on the (a) electron trajectory and (b) FEL gain.
inhomogeneous field variation along the undulator. As an
example, let us consider the case when the magnetic field
distribution is given as
By (z) = B0 sin(ku z)F (z),The FEL simulation code, SIMPLEX, has been introduced. SIMPLEX has functions for FEL simulations
as follows: steady-state simulation with seeding; timedependent simulation with shot noise implementation for
SASE regime; wakefield implementation; error sources related to phase slippage between undulator segments, field
discrepancy, and trajectory straightness; graphical output.
SIMPLEX is freely available from the web site [4]. It isequipped with a full graphical user interface for pre- andpost-processing and does not need any other commercial
softwares or libraries. Because of the portability of thegraphical library used in SIMPLEX, it works on many platforms such as Microsoft Windows, Mac OS X, and unixbased OS such as Linux.

REFERENCES[1] T. Tanaka, H. Kitamura and T. Shintake, Nucl. Instrum. Meth.
A528 (2004) 172[2] T. Shintake, these proceedings

withF (z) = 1 − Ae−z/D ,being an field envelope function to describe the radiationinduced demagnetization, where A and D denote the max-

TUPOS19[3] T. Tanaka, K. Shirasawa, T. Seike and H. Kitamura, Proc. 8thInt. Conf. Synch. Rad. Instrum., 227 (2004)[4] http://radiant.harima.riken.go.jp/simplex

439

H. Hara et al. / Proceedings of the 2004 FEL Conference, 439-442

ELECTRON BEAM SIMULATIONS ON THE SCSS ACCELERATOR
T. Hara∗ , T. Shintake, H. Kitamura,
RIKEN/SPring-8, 1-1 Koto, Mikazuki, Sayo, Hyogo, 679-5148, JAPAN
Abstract
The SCSS (SPring-8 Compact SASE Source) is an X-ray
SASE-FEL project with a 6 GeV electron beam accelerator.
In the year of 2005, the construction of a 250 MeV facility
will be started as a preliminary step towards the X-ray radiation. One of the unique features of the SCSS is the use ofa pulsed high-voltage electron gun with a thermionic cathode. Meanwhile, the electron bunch should be compressed
properly at the injector in order to obtain sufficiently highpeak currents. In this paper, a layout of the 250 MeV accelerator is presented with the expected parameters of theelectron beam.

INTRODUCTION
The SCSS (SPring-8 Compact SASE Source) is an Xray SASE-FEL project based on a linear accelerator [1].
The full facility is planned to be constructed next to the 1
km beamline of SPring-8. In order to obtain 0.1 nm radiation, a low emittance electron beam with 6 GeV energy
is necessary in combination with 15 mm period in-vacuum
undulators [2]. As a preliminary step, we are planning toconstruct a 250 MeV facility to demonstrate SASE radiation in a VUV region and test the accelerator components
in the year of 2005.
One of the unique features of the SCSS accelerator is theuse of a pulsed high-voltage electron gun with a thermioniccathode [3, 4]. Main reason for this choice is its high stability and well developed technology relating to the gun.
However, the emission current of a theomionic DC gun
is small, typically a few amperes, comparing with the RF
photo-cathode guns employed in most of the X-ray FEL
projects such as LCLS or TESLA. Therefore the electron
beam should be properly compressed in the injector to obtain sufficiently high peak currents at the undulator section [1]. Figure 1 is the layout of the SCSS at the 250
MeV stage. In the following sections, the electron beam
parameters are estimated using the beam simulation code
”PARMELA”.

INJECTOR
The injector predominantly determines the quality of theelectron beam in linear accelerators. In order to make operate the SASE process, the electron beam with high brightness is required, meaning that low emittance, a high peakcurrent and a small energy spread. When the electrons
pass through the undulators, only the electrons in a sliceof the bunch can contribute to the amplification process of∗ toru@spring8.or.jp

Available online at http://www.JACoW.org

the SASE. The size of this slice is transversely determinedby a diffraction limit of emitted light and longitudinally bya slippage length at a maximum. Therefore the beam parameters of the sliced electron bunch are important rather
than total integrated or projected parameters of the wholebunch.
The initial condition of the simulation is given based on
the results of the emittance measurements carried out on
the electron gun. The measured profile in the phase space
is shown in fig. 2 (a) and its normalized emittance was 1.1
π mm-mrad with a emission current of 1 A [3, 4]. The endsof the measured profile have slightly curved tails due to thespace charge effect at the edge region of the round beam,and these tails increase the emittance in fig. 2 (a). Whenthe electron gun is installed in the injector, these tails will
be eliminated using a slit without loosing a major part ofthe charge. After eliminating the tails, the emittance of thecore beam can be estimated from the beam size and thedivergence at the beam center and it is about 0.6 π mmmrad in fig. 2 (a).
Since ”PARMELA” can not treat a DC electron gun, thesimulation can not fully reproduce the conditions of theemittance measurement. In the simulation, 500 keV energy is immediately given to the electrons at the start andno DC acceleration process is considered. Therefore, theinitial condition of the electron beam is determined so thatthe electron beam reproduces the core emittance of 0.6 π
mm-mrad and the same divergence at the beam center under the identical layout of the beam optics. The obtainedphase space profile by ”PARMELA” is shown in fig. 2 (b),in which the effect of the space charge is different from themeasured one (fig. 2 (a)) due to lack of DC acceleration in
the simulation. The measured and simulated divergences atthe beam center (x=0) are compared in fig. 2 (c).
A schematic layout of the SCSS injector is shown infig. 1. The emission current of the cathode is assumed
to be 3A in the simulation. The µsec cathode emission isimmediately accelerated by a 500 keV pulsed DC voltage.
At the chopper, an electron pulse with 1∼2 ns duration issliced out from the µsec emission as shown in fig. 3 (a).
Then in the 238 MHz SHB (Sub Harmonic Buncher), theenergy of the electrons is modulated as a function of theirlongitudinal position in the bunch (fig. 3 (b)). Since thisenergy modulation causes the velocity difference between
the electrons, it turns into a density modulation as they fly
through a drift space. The bunched electrons are accelerated to 1 MeV in a 476 MHz booster cavity and the lengthof the bunch is further compressed before arriving at thefirst S-band LINAC (fig. 3 (c)). In the first S-band LINAC,
the electrons are again compressed by placing the bunch atoff crest of the RF field. Finally at the exit of the injector,

FEL Technology

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H. Hara et al. / Proceedings of the 2004 FEL Conference, 439-442

500 keV Electron gun
3A, 0.5 πmm-mrad

Focusing coils
(b)

(a)

Quadrupoles(c)

238 MHz SHB 476 MHz Booster~210 kV~750 kVFirst S-band Second S-band

Beam chopper
Undulators(λu = 15 mm, 300 periods x 2 segments)

(e)

(d)

C-band (72 MeV x 4)

Injector
7m

Chicane (R56, max ~ 100 mm)

11 m

9m

11 m

~ 40 mFigure 1: Layout of the SCSS at the stage of 250 MeV beam energy. (a)∼(e) corresponds to the locations used in figs. 3
and 4
traveling wave disk loaded structure is assumed for the Cband LINACs. The RF fields of the cavities are calculatedby ”SUPERFISH” and 2-D axisymmetric fields are given
to ”PARMELA”.
Figures. 4 (a)∼(d) are the slice RMS emittance at the locations same as fig. 3. The length of the slice is 1 ps for
fig. 4 (a)∼(d), which is larger than the slippage length byrougly one order. The electron beam is focused by using
solenoid lenses in the injector and quadrupole magnets after the injector. The parameters of the focusing elements
are determined so as to minimize the slice emittance. With
the current injector parameters used in figs. 3 and 4, thebunch compression is stopped at each components so thatthe electrons are not over bunched to keep the emittancesmall. With the same configuration of the components as in
fig. 1, higher compression ratio can be obtained by slightly
changing the parameters of the SHB. However, the increaseof the peak current at low energy results in the degradationof the emittance due to the space charge effect.

dX (mrad)

3

2

0.3

0.4

1

0

0.9
0.6

-1

0.7

0.8
0.2

-2

0.5
0.1

-3
-4

-2

0

2

4

2

4

X (mm)(a)dX (mrad)

3

2

1

0

-1

-2

-3
-4

-2

0

X (mm)

Normalized intensity

(b)
1.4

PARMELA
Measured

1.2
1.0
0.8

EXPECTED PARAMETERS OF THE
ELECTRON BEAM

0.6
0.4
0.2
0.0
-1.0

-0.5

0.0

0.5

1.0

dx (mrad) at x = 0 mm(c)

Figure 2: Phase space profiles of the electron bunch, (a)measured [3] and (b) calculated by ”PARMELA”. The
measured and simulated divergences at the electron beam
center (x = 0 mm) is plotted in (c).
the peak current close to 100 A can be obtained with thebeam energy of 23 MeV (fig. 3 (d)).
In the simulation, APS (alternating periodic structure)
standing wave cavities are used for the S-band LINACs and

TUPOS20After the injector, the electron beam is accelerated to 250
MeV by four 1.8 m long C-band accelerator tubes. The
expected acceleration gradient is 35∼40 MV/m. Figures 3(e) and 4 (e) show the profile and slice emittance of theelectron bunch at 250 MeV. Expected paremeters of the 250
MeV electron beam are summarized in table 1.
In order to cut out a dark current from the accelerator
tubes, a chicane is installed between the C-band LINACs
and the undulators. The chicane is composed of four bending magnets and X-Y collimators will be installed between
the second and third magnets in the chicane. This chicane
is also necessary to inject laser light for the purpose of theundulator alignment [1] and FEL operation with seeding
light [6, 7].

441

H. Hara et al. / Proceedings of the 2004 FEL Conference, 439-442

100

60
40

0.2

20

0.0

0

40

0.5

20

0.0

0

40

0.0

0

3.0

120
100

2.0

80

1.5

60

1.0

40

0.5

20

0.0

0.0

3.0

120

2.5

100

2.0

80

1.5

60

1.0

40

0.5

20

0.0

0

(c)

20

80

10

40

0

0

(c)
3.0

120

2.5

100

2.0

80

1.5

60

1.0

40

0.5

20

0.0

0

0

200

200

100

100

0

0

80

100

3.0

120

2.5

100

2.0

80

1.5

60

1.0

40

0.5

20

0.0

0

0

10
Time (ps)6040Time (ps)15

Peak Current (A)300

Peak Current (A)

300

5

20

(d)

(d)

0

200

100

80

60
40
Time (ps)150
100Time (ps)Peak Current (A)120
Peak Current (A)

30

20

0

50

0

200
Slice emittance (π mm-mrad)

150
100
Time (ps)

800

(b)

Slice emittance (π mm-mrad)

40

0.4

0

400
Time (ps)Peak Current (A)

0.8

50

0

0

Peak Current (A)

80

800

2.5

800

400
Time (ps)

1.2

0

400
Time (ps)(a)

Slice emittance (π mm-mrad)

0.2

120

Beam energy (MeV)

60

1.0

Slice emittance (π mm-mrad)

Beam energy (MeV)80

Peak Current (A)

0.6
0.4

(b)

Beam energy (MeV)80

Peak Current (A)120

Beam energy (MeV)

2.0
1.5

0

(a)

0

120
100

800

400
Time (ps)

0

3.0
2.5

Peak Current (A)

80

0.4

Peak Current (A)Beam energy (MeV)

120

0.6

tance growth due to the CSR effect (Coherent Synchrotron
Radiation) is discussed in ref. [5] in case of a similar bunch
compressor design.

Slice emittance (π mm-mrad)

A saturation length corresponding to the parameters intable 1 is about 18 m. In order to obtain a shorter saturation
length, the peak current should be increased in the injector at the expense of the emittance, or in the chicane. The
current design of the chicane has the maximum R56 ≈ 100
mm and it can be used as a bunch compressor. The emit-

5

15
10
Time (ps)

20

20

(e)

(e)

Figure 3: Electron beam energy (blue lines) and peak current (red lines) as a function of longitudinal position (time)in the bunch. (a)∼(e) corresponds to the location marked in
fig. 1, at (a) chopper, (b) after SHB, (c) before first S-band
LINAC, (d) injector end (before first C-band LINAC) and(e) accelerator end (before chicane). The emission currentof the gun is set at 3A and the head of the electron bunchcorresponds to the time zero.

Figure 4: RMS normalized slice emittance (blue lines) andpeak current (red line) as a function of longitudinal position (time) in the bunch. (a)∼(e) corresponds to the location marked in fig. 1, at (a) chopper, (b) after SHB, (c)before first S-band LINAC, (d) injector end (before first Cband LINAC) and (e) accelerator end (before chicane). The
length of the slice is 1 ps for (a)∼(d) and 0.1 ps for (e). The
emission current of the gun is set at 3A and the head of theelectron bunch corresponds to the time zero.

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H. Hara et al. / Proceedings of the 2004 FEL Conference, 439-442

Table 1: Expected parameters of the electron bunch at theundulator of SCSS.
Electron Energy
Normalized Slice EmittancePeak Current
Slice energy spread
Undulator period
Nominal operation gap
K parameter
Radiation wavelength

250 MeV∼1.5π mm-mrad
100 A (before chicane)∼ 2 × 10−4
15 mm
3.5 mm
1.3
60 nm

SUMMARY
As a preliminary step to the X-ray SASE-FEL, a 250
MeV facility is planned to be constructed in the SCSS
project. The purpose of the 250 MeV facility is to demonstrate the SASE-FEL and test the accelerator components,
since the SCSS has unique features in its design, such as thethermal DC electron gun and in-vacuum undulators. The
electron beam parameters of the 250 MeV facility are estimated using the code ”PARMELA”. The design performance of the accelerator will be compared with measurements after the completion of the facility including a bunch
compressor.
Regarding the SASE operation at 60 nm with 250 MeV
electrons, we need to obtain a shorter saturation length thanthe expected one in this paper. After further optimizationof the beam parameters, particularly with the higher peakcurrent, the saturation length of ≈ 10 m is expected.

REFERENCES[1] T. Shintake, H. Matsumoto, T. Ishikawa and H. Kitamura,“The SPring-8 Compact SASE Source”, Proc. of the SPIE’s
46th Annual Meeting, San Diego, USA, June 2001.
[2] T. Tanaka, K. Shirasawa, T. Seike and H. Kitamura, “Development of the short-period undulator for the X-ray FEL
project at SPring-8”, Proc. of 8th International Conference on
Synchrotron Radiation Instrumentation, San Francisco, USA,
August 2003, p. 227.
[3] K. Togawa, H. Baba, T. Inagaki, K. Onoe, T. Shintake,
T. Tanaka and H. Matsumoto, “Low Emittance 500 kV
Thermionic Electron Gun”, Proc. of 12th International Linear
Accelerator Conference, Lübeck, Germany, August 2004, p.
318.
[4] K. Togawa, H. Baba, T. Inagaki, K. Onoe, T. Shintake, T.
Tanaka and H. Matsumoto, “Emittance Measurement on the
CeB6 Electron Gun for the SPring-8 Compact SASE Source”,
in these proceedings.
[5] Y. Kim, T. Shintake, H. Matsumoto, H. Kitamura and
K. Sawada, “Beam Parameter Optimization for the PhaseI Stage of the SPring-8 Compact SASE Source (SCSS)
Project”, Proc. of EPAC 2002, p. 808.
[6] D. Garzella, T. Hara, B. Carré, P. Salières, T. Shintake, H.
Kitamura and M.E. Couprie, Nucl. Inst. Meth., A528 (2004),
p. 502.

TUPOS20[7] G. Lambert, B. Carré, M.E. Couprie, D. Garzella, Y.
Mairesse, P. Salières, A. Doria, L. Giannessi, T. Hara, H. Kitamura and T. Shintake, “Seeding High Gain Harmonic Generation with Laser Harmonics Produced in Gases”, in theseproceedings.

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REDUCING BACK-BOMBARDMENT EFFECT USING THERMIONICCATHODE IN IAE RF GUN#

T. Kii, K. Hayakawa, K. Masuda, S. Murakami, H. Ohgaki, T. Yamazaki, K. Yoshikawa, H. Zen
Institute of Advanced Energy, Kyoto University, Uji, Japan

Abstract
We have studied the improvement in electron beammacropulse properties from a 4.5 cell thermionic RF gun.
Energy spectrum, macropulse duration and emittance,
were measured with a 2 mm diameter slim thermionicdispenser cathode. The effect of a transverse magnetic
field reducing back-streaming electrons was studied
experimentally. The effect of non-flat RF power tocompensate decreasing beam energy during macropulse
due to a back-streaming electrons has also been studied.

INTRODUCTION
Compact and simple FEL machines will be importantfor various applications such as material processing,
medical, bio science, and so on. A thermionic RF gun
seems to be a good choice for such compact machines,
because it is compact, easy to operate, and can produce
high brightness electron beams. However, backbombardment problem is limiting the macropulse
duration.
We evaluated the effect of back-streaming electrons
quantitatively, using an IR thermometer and numericalsimulations[1,2], and the effect of transverse magnetic
fieldoncathodesurfacequantitatively[3],[4].
Furthermore, we have estimated the effect of a
combination of slim cathode and transverse magnetic
field[5], and concluded that the combination is effective
to suppress a temperature rise during macro pulse.
In this study, the effect of slim cathode and transverse
magnetic field is studied experimentally. Effect of a nonflat RF input to compensate for decreasing beam energy
during macropulse due to a back-bombardment effect isstudied.

EXPERIMENTAL SETUP
Fig. 1 shows the experimental setup. A dispenser
cathode of disk like shape with 2 mm diameter ismounted in the first half cell of our 4.5 cell RF gun.
Initially the surface temperature of the cathode is kept ataround 1020 °C. To reduce back-streaming electrons,
transverse magnetic field is applied by a dipole magnet,
which is located just behind the RF gun. The amplitude of
the magnetic field on the cathode surface is 29 gauss.

D2

FC1

Slit
Dipole magnet
D1
CT2
Thermionic
RF Gun

FC2
CT1

SC1

Fig. 1 Experimental setup
RF power fed to the RF gun is controlled by changing
reactance in a pulse forming network (PFN) of modulator
during operation by controlling remotely the reactors withstepping motors. By using the variable reactor system, we
can modulate the RF amplitude up to about 20%.
The performance of the modulator is shown in table 1.
Table 1 Performance of the modulator NKLY-170-10u(manufactured by Nissin High Voltage)
Pulse voltage
170 kV
Pulse current

140 A

Pulse duration

10 µs

Maximum repetition

10 ppsExtracted beam properties are measured using current
transformers (CT1 and CT2), Faraday cups (FC1 andFC2) and a fluorescent screen (SC1).

RESULTS
Beam properties
Effect of the slim cathode and the transverse magnetic
field on the cathode surface was checked by measuring
maximum electron macro pulse width after the bending
magnet (D1). Results on a previous cathode with 6 mmdiameter and on the slim cathode are shown in table 2.

___________________________________________#

kii@iae.kyoto-u.ac.jp

Available online at http://www.JACoW.org

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6 mmφ without magnetic field
Tcathode = 1000 °C
Pin=7.4 MW<500 nsec

6 mmφ with magnetic field
Tcathode = 1000 °C
Pin=7.4 MW

500 nsec

2 mmφ with magnetic field
Tcathode = 1020 °C
Pin=5.0 MW

3.0 µsec

As shown in table 2, pulse width has been improved byusing the slim cathode and the transverse magnetic field,
but this is still not sufficient for the FEL experiment[6].
Emittance with / without the transverse magnetic field
were also measured using the fluorescent screen (SC1)and quadrupole magnet (Q1). Projected images on thescreen are analyzed with tomographic method using
algebraic reconstruction technique[7,8]. The measured
geometric emittance are shown in table 3.
Table 3 Beam emittanceCondition

Emittancecompensate for the decrease of the beam energy during
macro pulse by controlling input RF waveform.
When flat RF power was fed to the RF gun as shown infig. 3 by open circles, peak energy decreases rapidly as
shown in fig. 4 by dotted line. Thus, pulse width after thebending magnet (D1) is limited to about 3.0 µsec asshown in fig. 5 by open circles. To compensate the energy
decrease, amplitude of the input RF power was modified
as shown in fig. 3 by solid line. As shown in fig. 4, thepeak energy was successfully kept constant up to 3.5 µsec.
Pulse width is improved and peak current increases asshown in fig. 5 by solid line and total charge in amacropulse increases up to about twice that with the flat
input. The effect of the amplitude modulation method issummarised in table 4.

7

Non-Flat RF pulse

6Power (MW)Table 2 Maximum macro pulse width
Condition
Pulse width

543Flat RF pulse

2

2 mmφ without magnetic field

1.96 πmm-mrad

1

2 mmφ with magnetic field

1.79 πmm-mrad

0
-2

10
with magnetic field Bx=29 Gauss
without magnetic fielddI/dE (a.u.)

8
6

0

1

2

3

4 5 6 7 8energy (MeV)

9 10 11

Fig. 2 Energy spectra

Energy compensation
For the FEL experiment, a macro pulse longer than 3µsec will be required. For this purpose, we tried to

TUPOS21

9.5
9.0
8.5

-2

0

8

10.0

Flat RF pulse
Non-Flat RF pulse

7.5

2

6

10.5

8.0

4

2
4
Time (µs)

Fig. 3 Flat/non-flat RF power fed to the RF gun

Energy (MeV)As shown in tables 2 and 3, the transverse magnetic
field can reduce back-streaming electrons withoutchanging beam emittance.
Energy spectra were also measured with / without themagnetic field. As shown in fig. 2, the energy spectrum is
not changed by the transverse magnetic field.

0

-1

0

1

2 3 4
Time (µs)

5

6

7

8

Fig.4 Time evolution of the peak energy during macro
pulse

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T. Kii et al. / Proceedings of the 2004 FEL Conference, 443-446

Table 5constant

100

Current (mA)80

Non-Flat RF pulse

Required RF power to keep beam energy

Current density [A/cm2]

Required power [MW]

60

15.9

8.88

40

31.8

8.99

20

47.8

9.13

63.7

9.24

79.6

9.42

95.5

9.60

111.4

9.81

127.3

9.90

143.2

10.03

0
Flat RF pulse

-20
-2

0

2
4
Time (µs)

68Fig. 5 Wave form of the beam current, measured using
CT2

Table 4 Effect of non-flat RF input
Flat RF pulse

Non-Flat RF pulse

Pulse width

3.0 µs

4.2 µsPeak current

40 mA

90 mA

Total charge

97.7 nC

205.8 nC

Power (MW)10

ANALYSIS
To establish the energy compensation method using
amplitude modulation, we have estimated the effect of
this method with a particle simulation code PARMELA(version 3.30)[9]. As a first step, current density during
macro pulse on the cathode surface was evaluated. Timeevolution of the current density on the cathode is shownin fig. 6
160

2

Current (A/cm )

8
6
4
2
0
-2

-1

0

1

2 3 4
Time (µs)

5

6

7

8

Fig. 7 Ideal RF wave form to extract electron beams
with constant energy.

According to the results, in case for the maximum
modulation of 19% of our power modulator, more than
1000% change of the current density is acceptable to keep
the peak energy constant. In this case, estimated width ofthe macro pulse is longer than 5.5 µsec, but it is notconsistent with the experimental results.
The reason of the inconsistency may be due to atransient phenomenon of the RF cavity and difference
between matched loading and real beam loading.

140
120
100
80
60
40
20
0
-2

12

-1

0

1

2 3 4
Time (µs)

5

6

7

8

Fig. 6 Time evolution of current density during
macropulse
Next, we evaluated the RF power required to accelerate
up to the same energy as that for the initial current density.
The required power is shown in table 5. Thus, the ideal
RF wave form is derived as shown in fig. 7.

SUMMARY
To improve electron beam properties, a slim cathodeand transverse magnetic field are used. We could produce
longer macro pulse, but it was not enough for FEL
experiment, because beam energy is decreasing in themacro pulse due to the back-streaming electrons.
Thus, we fed non-flat RF to the 4.5 cell thermionic RF
gun to compensate for the decrease of the beam energy byadjusting the reactance of the PFN. As a result, we

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T. Kii et al. / Proceedings of the 2004 FEL Conference, 443-446

succeeded in producing high-brightness electron beamwith 4 µsec macropulse duration.
The effect of the energy compensation using thistechnique was numerically studied also. In the case of our
4.5cell thermionic RF gun, it was found that theamplitude modulation of 19% could keep the peak energy
constant even when the current on the cathode surfacechanged by more than 1000%. To understand thediscrepancy, transient analysis in the RF gun seems to benecessary.
For the future application of the FEL experiment, phasestability of electron micro bunches and beam emittance
are also very important. These parameter will bemeasured and checked to see whether the extracted beamis acceptable for the FEL experiment.

TUPOS21

REFERENCES[1] T. Kii, et al., Nucl. Instr. And Meth. A 475 (2001)
588[2] T. Kii, et al., Nucl. Instr. And Meth. A 483 (2002)
310[3] C.B. McKee and John M.J Maday, Nucl. Instr. And
Meth. A296 (1990), 716[4] T. Kii, et al., Nucl. Instr. And Meth. A 507 (2003)
340[5] T. Kii, et al., Nucl. Instr. And Meth. A 528 (2004)
408[6] H. Ohgaki et al., Nucl. Instr. And Meth. A 507(2003) 150[7] C. B. McKee et al., Nucl. Instr. and Meth., A358
(1995) 264; X. Qiu et al., Phys. Rev. Let. 76 No.20(1996) 3723
[8] H. Ohgaki et al., Nucl. Instr. And Meth. A 528(2004) 366[9] L.M. Young, J.H. Billen, PARMELA, LA-UR-961835, 2001

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T. Kii et al. / Proceedings of the 2004 FEL Conference, 447-449

RENEWAL OF KU-FEL FACILITY#

T. Kii, K. Hayakawa, S. Murakami, H. Zen, K. Masuda, H. Ohgaki, K. Yoshikawa, T. Yamazaki,
Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 611-0011, Japan

Abstract
We have started construction of new FEL facility(Kyoto University FEL: KU-FEL) which will be used forresearch on energy science. In the past, we havedeveloped the KU-FEL parasitically at a sharedexperimental facility. Thus construction time was quite
limited, and we had no space for future applications of the
IR-FEL. Therefore we decided to renew an old
experimental hall. In this paper, status of construction andfuture plans are described.

INTRODUCTION
Users demands in the area of energy-related science toa high-power tunable IR lasers are increasing in Japan,such as basic study of high-efficiency solar cells,
generation of sustainable energy source of alcohol and/or
H2 from polluted gas, and separation of DNA and/or RNA.
To satisfy these demands, we decided to renew our FEL
facility to be more user friendly and to operate more
flexibly.

DESIGN
Experimental hallConstruction and fundamental studies on the KU-FEL
have been carried out parasitically at a building belonging
to the Institute of Chemical Research where a few otheraccelerators were operating. Therefore, available machinetime for our experiments was quite limited. We decided
recently to move the KU-FEL to our own building andreconstruct the machine. The building used to be forplasma experiments and there was no provision forradiation shielding. We modified the room by adding
concrete walls of 2-m thickness and some space for users.
A Schematic drawing of the experimental hall is shownin fig.1. The room with the shielding was completed in
June, 2004. We decided not to use a costly shielding door
by use of stairs to step up to the top of the shielding walland down to the accelerator room. Concrete blocks can beremoved temporarily when large equipment is to be
carried in.

Fig. 1 Experimental hall___________________________________________#

kii@iae.kyoto-u.ac.jp

Available online at http://www.JACoW.org

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T. Kii et al. / Proceedings of the 2004 FEL Conference, 447-449

Initial plan
As a first step, we are planning to construct a compact
IR-FEL system, which consists of a 4.5 cell thermionic
RF-gun, a 3 m accelerator tube and 1.6 m Halbach typeundulator. Schematic view of the system is shown in fig.
2.

because the undulator is an old one which used to be used
for a different system and not adequate to the present
system.

Future plans
A 1.6 cell photocathode RF-gun system will be added
to the system in the near future and it will be usedalternately with the present thermionic RF-gun according
to the demands of users. The photocathode material will
be Cs2Te.[5]Fig. 3 shows a schematic view of the photocathodeupgrade.

Fig.2 4.5 cell gun and linac
The electron beam of about 30 MeV will be provided
by the thermionic RF gun and the linac. The configuration
has been already designed to achieve a FEL lasing from 4
to 13 µm [1,2], and acceleration test has been carried out
at the previous experimental hall.[3, 4]
All devices were moved to the new hall in July, 2004.
We hope to resume the operation of the linac in fall of
2004. The FEL is expected to lase next year. However,the lasing wavelength will be limited to around 13 µm

Fig. 4 Future upgrades

TUPOS22

Fig.3 Photocathode upgrade
After the photocathode upgrade, we will install anenergy recovery system using a normal conducting
accelerator tube.[6] This upgrade is mainly to reduceshielding duty to the radiations from used electrons.

T. Kii et al. / Proceedings of the 2004 FEL Conference, 447-449

Some experiments on material science and bio science
will need polarized laser light, and a helical undulator will
be needed to satisfy some users’ demands. APPLE-II typeundulator[7] or Onuki type undulator[8] is considered atpresent. Two-stage FEL system to increase the FEL
power[9] is also planned for the future. Generation of
FEL-Compton backscattering x-rays is also planned. Inorder to compensate for the low yield of this method, theIR FEL in a cavity will be directly used. The expected xray energy is from 2 keV to 20 keV by using 32-MeV
electron beam and 10-100 µm FEL. FIR radiation is alsoplanned using thermionic RF gun.
These upgrades are shown in fig. 4.

SUMMARY
We have renewed an experimental hall for FEL
experiments. The accelerator and the IR-FEL system will
be installed shortly. The building is completed, and beamcommissioning will be started in this year.
After lasing in the 10 µm wavelength region, we areplanning to upgrade our facility to satisfy users’ demands.
By using various types of radiations (e. g. FIR radiation,

449

IR FELs, Compton X-ray), material and bio/chemical
science will be studied.

REFERENCES[1] T. Yamazaki, et al., Nucl. Instr. And Meth. A 483 II(2002) 13.
[2] H. Ohgaki, et al., Nucl. Instr. And Meth. A 507(2003) 150.
[3] S. Murakami, et al., Proceedings of the 1st Annual
Meeting of Particle Accelerator Society of Japan andthe 29th Linear Accelerator Meetings in Japan, (2004)
599[4] K. Masuda, et al., in these proceedings[5] H. Ohgaki, et al., in these proceedings[6] K. Masuda, et al., Nucl. Instr. And Meth. A 507(2003) 133.
[7] A. Bhowmik et al., Nucl. Instr. And Meth. A272
(1988) 183.
[8] H. Onuki et al., Appl. Phys. Lett. 52 (1988) 173.
[9] O. Chubar et al., J. Synchrotron Rad. (1998) 5, 481.

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BEAM PROPERTY MEASUREMENTS ON THE KU-FEL LINAC
K. Masuda*, K. Hayakawa, T. Kii, S. Murakami, H. Ohgaki, T. Yamazaki, K. Yoshikawa, H. Zen,
Inst. of Advanced Energy, Kyoto Univ., Gokasho, Uji, Kyoto 611-0011, Japan
Abstract

INTRODUCTION
An infrared FEL facility, KU-FEL[1,2], is underconstruction for researches on advanced sustainableenergies, such as bio-energy, solar energy. An electron
beam of 30 MeV has been obtained by an S-band rf gun
with a thermionic cathode and a recently installed
accelerating tube. In this paper, we will describe
measurements of the beam properties on the KU-FEL
linac, such as transverse emittance, energy spread, andbeam current. Comparison with PARMELA[3]simulations will be also presented.
One of the critical R&D issues on our KU-FEL linac isthat of reducing and/or compensating the adverse effectdue to back-streaming electrons onto the cathode, andtime-varying beam-loading and accordingly time-varying
output beam energy during a macropulse [4], inherent inthermionic rf guns. The introduction of transverse dipole
magnetic fields along the cathode surface [5] has beenfound effective against this back-bombardment effect inour rf gun [6], while effects of the induced transverse
beam deflection on the output beam transport through thelinac as well as the beam emittance have not been
evaluated. In this paper, we will discuss comparisons of
the beam properties with and without the transverse Bfield in the vicinity of the cathode.

EXPERIMENTAL SETUPThe KU-FEL linac consists of an S-band 4.5-cell rf gun
with a thermionic cathode, a 3-m accelerating tube, and abeam transport system, shown schematically in Fig. 1.
The typical output energy by the gun is 9 MeV. An
energy analyzer consisting of a 45-degree bending magnet
and a horizontal slit is located between the gun and theaccelerating tube. The energy analyzer is followed by 3_________________________________________* E-mail: masuda@iae.kyoto-u.ac.jp

TUPOS23

FC2

O

Q1
S1

G

250

SC1 B1

25
0

Q8

SC2
C2 B3

FC3

250

180-degree
ARC

F C1

710

RF GunAccelerator Tube
630

630

DSl it

G B2

250

E
-L

710

An infrared FEL facility, KU-FEL, is underconstruction for advanced energy researches. An S-band
rf gun and an accelerating tube has been installed.
Measurements of beam properties have been carried out.
An energy spread below 1 % at 50 mA current has beenobtained. The normalized emittances were measured to be
78 π mm mrad in horizontal and 70 π mm mrad in verticaldirections by the tomographic technique. A dipole sweep
magnet was set for sweeping the back-streaming electrons
vertically out of the cathode in the rf gun. It is found thatthe magnet does not affect the beam emittance, but resultsin poor current transmittance through the linac.
PARMELA simulation suggests the use of a horizontal
Sweep magnet instead of the vertical one.

1500

FC4

Undulator
to be installed

Figure 1: Schematic view of the KU-FEL linac.
quadrupole magnets and another dipole which comprisean achromatic transport system (Dog-Leg section in Fig.
1) to the accelerating tube. The designed maximum beamenergy is 40 MeV, which will be led through the 180degree arc section into the undulator to be installed to
produce 4-13 µm IR-FEL [7].
On one hand a thermionic rf gun has advantageous
features over a photocathode one, such as low cost, easy
operation, and high average current. On the other hand it
inherently has some disadvantages such as current andenergy fluctuations during a macropulse due to beamloading and back-streaming electrons hitting the cathode.
To cope with the last problem, we have set a dipole
magnet (called ‘Sweep magnet’ hereafter) to sweep out
the back-streaming electrons by providing horizontaltransverse B-field along the cathode surface [5]. In order
to compensate the resultant vertical beam deflection withrespect to the gun axis, a steering dipole magnet set at the
gun exit (S1 in Fig. 1) was used.
Also, aiming at a further reduction of back-streaming
electrons, use of a cathode with smaller diameter in
combination with the Sweep magnet is being studied [8].
In the present measurements, a tungsten dispenser
cathode of 2 mm diameter was used instead of thecathode of 6 mm diameter previously used [9]. The
cathode surface temperature was measured by an IR
pyrometer and was fixed to 1473 K. The corresponding
current density on the cathode surface is 38.1 A/cm2.
Throughout the measurements, the macropulse durationof rf input to the gun was fixed to 2 µsec in order tominimize the degradation in the projected beam’s
properties owing to the time-variation during themacropulse. The rf input powers to the gun and theaccelerating tube were 7 and 10 MW respectively. In thispaper, the magnetic flux density by the Sweep magnet in
the vicinity of the cathode was fixed to 29 gauss.

RESULTS AND DISCUSSIONSBeam properties at the gun exit
Measurements of beam currents, transverse emittances,and energy spectra at the gun exit were carried out with

Available online at http://www.JACoW.org

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K. Masuda et al. / Proceedings of the 2004 FEL Conference, 450-453

1.0

p.
ex

0.6

calc
.

dI/dE (a.u.)

0.8

0.4

0.2

0.0
8.0

8.5

9.0

9.5

10.0

10.5

11.0

Energy (MeV)

Figure 2: Energy spectra at the gun exit by themeasurement (dashed line) and by the simulation ( solidline). The dotted lines indicate the energy acceptance ofthe following energy slit (B1 and Slit in Fig. 1).

Y' (mrad)

5

0

-5

-5

0

5

Y (mm)(a)Y' (mrad)

5

0

-5

-5

0

Y (mm)

5(b)
Figure 3: Vertical phase space distribution in the verticaldirection, (a) reconstructed by the tomographic techniquefrom the observed images in SC1 in Fig. 1, and (b) by thesimuration. The black circles in (b) show particles within
the major high energy component indicated in Fig. 2.

and without the Sweep magnetic field. The tomographic
method described in [9] was applied for themeasurements of the transverse phase space distributions
and corresponding emittances, with a quadrupole magnet(Q1 in Fig. 1) and a phosphor screen (SC1). The energy
spectra were taken with a bending magnet (B1) and a
Faraday cup (FC2). The energy resolution was found tobe ∆E/E = 13 % by a PARMELA run.
Introducing the Sweep magnet, the beam current,
measured with a Faraday cup (FC1 in Fig. 1), was seen to

Table 1: Unnormalized emittances at Q1 downstream thegun exit (see Fig. 1). The emittances by the simulation
take only the high energy component indicated in Fig. 2
into account, while those in the parentheses include allparticles.
[π mm mrad]measurement
simulationwithhorizontal
1.9
0.23 (0.18)
Sweep
vertical
1.8
0.23 (1.25)
magnetw/ohorizontal
1.8
0.21 (0.22)
Sweep
vertical
2.0
0.14 (0.23)
magnetdecrease from 460 mA to 400 mA. No degradation in thetransverse emittances in both horizontal and verticaldirections was observed, while a slight improvement in
the energy spread was seen, as stated in [8]. The
experimental results in the case without the Sweep
magnet are shown in Figs. 2 and 3, together withPARMELA results for comparisons.
The energy spectra are shown in Fig. 2. The difference
between the measured and the calculated energy spreads
in the figure, may be due the time-dependent beamloading effects during the macropulse which are ignoredin the simulation. In the measurements downstream the
Dog-Leg section, the energy acceptance of the energy slit
was fixed to 10.0 ± 0.6 MeV, which is indicated in Fig. 2
by the dotted lines.
Figures 3 (a) and (b) show the phase space images inthe vertical direction, and the corresponding emittances.
Both the beam emittances with and without the Sweep
magnet are listed in Table 1. The rotational angle in thephase space shown in fig.3, is reproduced well by thesimulation, although appreciable differences in thecorresponding emittances can be observed. As before thisdifference can be due to time dependent effects along themacropulse, and also to the broad energy spread in thereconstruction process in the tomographic measurement,
which are neglected in the simulation, though extremely
low energy component must be swept out of the phosphor
screen (SC1) in the measurement also.

Beam properties at the accelerating tube exit
The beam without the Sweep magnetic field applied in
the vicinity of the gun cathode was transported throughthe Dog-Leg section to the accelerating tube. The beam
properties were measured at the accelerating tube exit,
with a quadrupole magnet (Q8 in Fig. 1) and a screen
monitor (SC2) for transverse emittances, and with abending magnet (B2) and a Faraday cup (FC4) for theenergy spectra.
For the SC2, either a 1-mm thick phosphor (chromiumdoped alumina) or an aluminium plate can be used atexactly the same position. As it is seen in Fig. 4, thefluorescence profile from the phosphor screen is foundbroader than the transition radiation profile from thealuminium plate. The broadening was around 35 % inboth horizontal and vertical directions, depending neither

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K. Masuda et al. / Proceedings of the 2004 FEL Conference, 450-453

Table 2: Beam currents [mA], from the gun down to the accelerating tube exit.
gun
accelerating tube
accelerating tube
exit
entranceexit
w/o Sweep magnet
460
60
48
experimentswith Sweep magnet
400
46
<5*
w/o Sweep magnet

633

197

with Sweep magnet

520

105
20
*average over macropulse durationon the incident beam angle of 0 and 45 degrees nor on the
beam size of 2.2 and 1.6 mm in FWHM. Although thisbroadening with phosphor screen would result in an
overestimate in the emittances, we used the phosphor
screen, characterized by a much higher signal to noise
ratio.
Reconstructed images by the tomographic technique inthe transverse phase spaces are shown in Figs. 5(a) and(b). The resultant geometric emittances were 1.3 π mm
mrad in horizontal and 1.2 π mm mrad in vertical,
corresponding to normalized emittances of 78 and 70 π
mm mrad.
Then we tried to transport the beam with the Sweep
magnetic field applied, by changing the strength of thequadrupole magnets and of the steering magnet at the gun
exit (S1 in Fig. 1). In contrast with the case without the
Sweep magnet, the beam could hardly be transported
through the accelerating tube, although, as presented in
the previous section, almost no degradation in the beam
properties were seen at the gun exit either in themeasurement or the PARMELA simulation. So far, wehave obtained beam currents listed in Table 2 from thegun exit to the accelerating tube exit. The tendency of apoor transmittance in the case with the Sweep magnet canbe also seen in PARMELA results as summarized in thetable.
Figure 6 shows the measured energy spectra with andwithout the Sweep magnet, both normalized as their peaks
are unity. Although the energy resolution and signal tonoise ratio were poor for the case without the Sweep
magnet, the energy spread with the Sweep magnet was
found 1.5 % (FWHM), and was found to be broader thanthe one obtained without the Sweep magnet (less than0.7%). We can see this tendency more clearly in the
PARMELA results in Fig. 7, showing that the energy
spreads (FWHM) with and without the Sweep magnet
were 2.4% and 0.49% respectively, which seem to agreewith the experimental ones. From the simulations in Fig.
7 we can see that the sharp peak in the energy spectrum
without the Sweep magnet was almost lost with respect tothe case with the Sweep magnet.
As shown in the evolution of the beam envelope by the
PARMELA simulations in Figs. 8 (a) and (b), we could
hardly compensate the effects due to the verticaldeflection induced by the Sweep magnet in the gun, evenwith an additional steering magnet between the gun and

TUPOS23

1.2

Normalized Intensity

simulation

65

Phosphor Fluorescence
Transition Radiation

1.0
0.8
0.6
0.4
0.2
0.0
-3

-2

-1

0

1

2

3

X (mm)

Figure 4: Comparison between the horizontal profiles ofthe fluorescence from the phosphor plate, and thetransition radiation from the aluminium plate.

(a)

(b)
Figure 5: Transverse phase space distributions at theaccelerating tube exit obtained with Q8 and SC2 in Fig. 1
in (a) horizontal and (b) vertical directions.
the following quadupole magnet (Q1). Then we
performed PARMELA runs with a horizontal Sweep
magnet instead of the vertical Sweep. In this case,because horizontal dispersion can be controlled in thequadrupole magnets in the Dog-Leg section, we could

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K. Masuda et al. / Proceedings of the 2004 FEL Conference, 450-453

find a set of the magnet parameters showing a bettertransmittace to the end as shown in Fig. 9. As a result, thecalculated current at the accelerating tube exit was 181
mA.
with Sweep Magnet
w/o Sweep Magnet

1.0

20mm(H)

Horizontal beam envelope

Gun

Dog-leg

Accelerator Tube

Normalized Signal

0.8

Vertical beam envelope
0.6

20mm(V)

0.4

Total Length 7.54m

Figure 9: Calculated evolution of the horizontal andvertical beam envelopes with a horizontal Sweep magnet
instead of the vertical one.

0.2

0.0
28

29

30

31

32

CONCLUSION

Energy (MeV)

Figure 6: Measured energy spectra with and without the
Sweep magnet, both of which are normalized to theirpeaks.
120

Particle Number

100

with Sweep Magnet
w/o Sweep Magnet

80

60

40

20

0
28

29

30

31

32

Energy (MeV)

Figure 7: Energy spectra by the simulations with andwithout the Sweep magnet.

We have measured the electron beam properties,
namely energy spread, and transverse emittances at the rf
gun exit, and at the exit of the accelerating tube where theenergy was measured to be 30.7 MeV. A beam withenergy spread of less than 1 % and 48 mA current was
obtained. The normalized emittances were measured to be
78 π mm mrad in horizontal and 70 π mm mrad in verticaldirections by the tomographic technique with a phosphor
screen.
A dipole (Sweep) magnet was set for sweeping theback-streaming electrons vertically out of the cathode in
the rf gun. The induced beam deflection in the vicinity of
the cathode was found not to degrade the output beamemittances in the present case. However, the verticaldeflection by the Sweep magnet resulted in poortransmittance down to the accelerating tube exit. The
simulation predicts that much better transmittance can beachieved by use of a horizontal Sweep magnet instead of
the vertical one in our layout.

20mm(H)

Horizontal beam envelope

Gun

Dog-leg

Accelerator Tube
Vertical beam envelope(a) 20mm(V)Total Length 7.54m

20mm(H)

Horizontal beam envelope

Gun

Dog-leg

Accelerator Tube
Vertical beam envelope(b) 20mm(V)Total Length 7.54m

Figure 8: Calculated evolution of the horizontal andvertical beam envelopes, for the case (a) with and (b)without the Sweep magnet.

REFERENCES[1] T. Yamazaki, et al., Proc. of 23rd Int’l FEL Conf.
(2002) II13.
[2] T. Kii, et al., “Renewal of KU-FEL facility” in theseproceedings.
[3] L. M. Young, J. H. Billen, PARMELA, LA-UR-961835.2001.
[4] K. Masuda, et al., Nucl. Instr. and Meth. A 483(2002) 315.
[5] C.B. McKee and J.M. Maday, Nucl. Instr. Meth. A
296 (1990) 716.
[6] T. Kii, et al., Nucl. Instr. And Meth. A 507 (2003)
340.
[7] H. Ohgaki, et al., Nucl. Instr. And Meth. A 507(2003) 150.
[8] T. Kii, et al., “Reducing back-bomdardment effectusing thermionic cathode in IAE rf gun” in theseproceedings.
[9] H. Ohgaki, et al., Nucl. Instr. and Meth. A 528(2004) 366.

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H. Ohgaki et al. / Proceedings of the 2004 FEL Conference, 454-457

UPGRADE DESIGN OF KU-FEL DRIVER LINAC USINGPHOTO-CATHODE RF-GUN
H. Ohgaki#, K. Hayakawa, S. Murakami, H. Zen, T. Kii, K. Masuda, K. Yoshikawa, T. Yamazaki
Institute of Advanced Energy, Kyoto University
Gokasho, Uji, Kyoto 6110011, JAPANINTRODUCTION
An infrared FEL (4-13 µm) facility for energy science
is under construction at the Institute of Advanced Energy,
Kyoto University[1]. The electron beam of 30 MeV has
been successfully accelerated by a linac system which
consists of a 4.5-cell thermionic RF gun, a ‘dog-leg’transport system, a 3m s-band linac, and a 180-degree arc
for bunch compression[2]. Figure 1 shows the schematic
view of the linac system which includes the upgrade planview. To reduce the back-bombardment effect in the 4.5cell RF gun, several attempts have been made, and themacro pulse duration of 3 µs has been achieved[3].
However, there still needs several efforts are needed toextend the macro pulse duration to reach the FEL
saturation[4]. Upgrade from the present thermionic RF
gun to a photocathode RF gun is one of promising ways,
because a photocathode RF gun is free from backbombardment. Thus, a design work for the system
upgrade of the linac system from gun to FEL has been
performed. At first, we evaluate the beam parameters of
the existing 4.5-cell RF gun which is operated as aphotocathode. Then the FEL gain is compared with the

4.5-CELL RF GUN
The 4.5-cell RF gun has been used for a thermioniccathode in the original system[4] and successfully
generated several hundred mA, 10 MeV electron beam[5].
The maximum electric field at the cathode surface is 32
MV which is limited by 7 MW output power of the RF
source. We fixed the maximum electric field to be 32 MV
during the calculation. The driver laser assumed here is apicosecond UV laser, i.e. the SHI type one[6,7], whose
beam profile is 0.7 mm at the cathode surface and thepulse duration is 6.0 ps. The Gaussian shapes are also
assumed both for the transverse(1mm cut-off) and for thelongitudinal(12 ps cut-off) distribution to simplify the
a)
2.0

1.5

1.0

0

10

20

30

40

50

60

50

60

R F P hase (deg)
2.5

b)

2.0

1.5

1.0

0.5

Accelerator Tube710180-degree
ARC

0.0

0

10

20

30

40

R F phase (deg)710Beam Dump

original design. Next, the beam parameter and the FEL
gain with a 1.6-cell photocathode RF gun are also
evaluated.

N orm alized Em ittance (πm m -m rad)Upgrade design of KU-FEL driver linac has been
carried out to obtain a stable oscillation in the infrared
FEL. The existing 4.5-cell thermionic RF gun will be
operated with a photocathode to enhance the FEL gain.
The numerical evaluation of beam properties is carriedout from gun to FEL by using PARMELA and TDA3D.
The evaluated peak current is 4 times and the expected
FEL gain is 10 times as high as those with the thermioniccathode. A 1.6-cell photocathode RF gun dedicated tophotocathode operation is also examined to obtain an
excellent electron beam. Expected FEL gain is more than
2 times as high as the gain with the 4.5-cell photocathodeRF gun.

dE/E (%)

Abstract

Undulator

Fig. 1 Schematic view of the KU-FEL driver linac.
___________________________________________#

Fig.2 Transverse RMS emittance(a) and energy
spread(b) of the electron beam from the gun as afunction of the laser injection timing.

ohgaki@iae.kyoto-u.ac.jp

TUPOS24

Available online at http://www.JACoW.org

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H. Ohgaki et al. / Proceedings of the 2004 FEL Conference, 454-457

120

a)

7.4

100

P articles/0.5 deg

N orm alized Em ittance (πm m -m rad)

a)

7.2

7.0

6.8

80

FW H M = 4.0 deg

60
40
20

6.6
-100

-90

-80

-70

0
-5

-60

0

5

b)

1.2

P articles/20 keV

1.0

dE/E (%)

10

15

P hase (deg)R F P hase (deg)

0.8
0.6

150

100

dE/E=0.36%
50

0.4
0.2
-100

-90

-80

-70

-60

R F phase (deg)

0
33.2

33.3

33.4

33.5

33.6

33.7

33.8

Energy (M eV )Fig.3 Transverse RMS emittance(a) and energy
spread(b) of the electron beam from accelerator tube.

Fig.4 Phase(a) and energy(b) spectrum at the entranceof the undulator.

calculation. Figure 2 shows the transverse RMS
emittance(a) and energy spread(b) of the electron beamfrom the gun as a function of the laser injection timing.
PARMELA is used for calculations. It is clear that theelectron beam with the transverse RMS emittance below
2 πmm-mrad and the energy spread below 1% can be
expected with the 4.5-cell photocathode RF gun. On theother hand, the transverse RMS emittance of 4 πmm-mrad
and the energy spread of 22% have been calculated withthe thermionic RF gun[4]. The beam charge of 250 pC,
which is obtained with normal operation in the existing
gun, is assumed. The laser timing of 30 degree, where thebest energy spread is obtained in fig.1, is used for thefollowing calculations.
It should be noted that the thermionic RF-gun needs anenergy compressor and/or an energy filter for its’ broad
energy distribution. Therefore, the original design of thelinac system employs a ‘dog-leg’ transport system for theenergy filter[4]. Although, we can omit this section for thephotocathode RF gun for its’ narrow energy spread, we
will keep the ‘dog-leg’ section for the thermionicoperation of the RF-gun which is preferable forexperiments which need high total power beam. We mayomit the 180-degree arc section because of a short bunch
beam from the photocathode RF-gun. However, since weare planning to extend our system to the energy recovery
one for the future[8], we will keep the 180-degree arc inthis calculation, too. The beam transport system isdesigned by TRACE3D to satisfy the achromaticcondition in ‘dog-leg’. Figure 3 shows the transverse
RMS emittance(a) and energy spread(b) from theaccelerator tube as a function of the RF-phase of theaccelerator tube. It is clear that the transverse emittance isalmost constant (-7 πmm-mrad), although the energy
spread varies with the RF-phase. The smallest energy
spread, 0.2%, is obtained with -80 degree which is used in
the following calculations. We found that the transverse
emittance is mainly enlarged by the ‘dog-leg’ section.
The achromatic 180-degree arc section is set both forthe matching condition of the undulator parameter and forthe bunch compression condition with matrix element,
R56, by using TRACE3D. The phase spectrum and theenergy spectrum at the entrance of the undulator are
shown in figure 4. Consequently, a beam with peakcurrent of 150 A and an energy spread of 0.36% beam canbe generated by using the 4.5 cell photocathode RF gun.
The normalized emittance is calculated to be 7.0 πmmmrad in horizontal and 11 πmm-mrad in vertical. On theother hand, a beam with 40 A peak current and 0.4 %energy spread beam with a normalized emittance of 11πmm-mrad in horizontal and 10 πmm-mrad in vertical has
been obtained with the thermionic RF gun[4]. As a result,almost 4 times large peak current can be expected withthe photocathode RF-gun. However, the beam emittanceand the energy spread are not so improved from those ofthermionic system. The main reason of this emittance

FEL Technology

H. Ohgaki et al. / Proceedings of the 2004 FEL Conference, 454-457

growth is a slight difference between PARMELA andTRACE3D.
The expected FEL gain is calculated with the evaluatedelectron beam parameters by using TDA3D. The
undulator parameter used is shown in table 1. We
assumed that the Rayleigh length and the position of thebeam waist are fixed at centre of the undulator, 0.8 m. K
parameter, 0.95, is also fixed. The calculated FEL gain inwavelength of 6.86 µm is 310% with the electron beam
generated with the 4.5-cell photocathode RF gun. On theother hand, the FEL gain with the 4.5-cell thermionic RF
gun is 32% at the same conditions as in the photocathode.
Consequently, the expected FEL gain with the 4.5-cell
photocathode RF gun is almost 10 times as high as thatwith the original design. This enhancement in FEL gain ismainly due to the enhancement of the peak current. The
round-trip development of the FEL gain is also calculated
by using modified TDA3D code assuming 10% loss perround-trip. The result shows that the gain saturation canbe observed from about 35 round-trips, 0.4 µs. Here weassume the optical cavity length of 3.78 m which isadjusted to the mode-lock frequency of the laser, 79.34
MHz. On the other hand, 175 round-trips is required forthe thermionic RF gun. As a result, the FEL saturation
will be easily achieved and stable FEL will be expectedby the 4.5-cell photocathode.

1.6-CELL RF GUN
Although the existing 4.5-cell RF gun can be operated
both as a photocathode and as a thermionic one, as shownin previous section, the estimated emittance is enlarged bythe ‘dog-leg’ beam transport system. However, thethermionic operation is still preferable for a high total
charge operation. Thus we plan to introduce a new RF
gun dedicated to the photocathode operation into oursystem to obtain an excellent electron beam. The BNL
type 1.6-cell photocathode RF gun, which is widely used
for generation of a high brightness electron beam[9] and 1πmm-mrad with 1 nC electron beam has been generated,
is presently considered as a photocathode RF gun. As isshown in figure 1, the 1.6-cell photo-cathode RF gun will
be placed just upstream of the accelerator tube. The RF
system will be shared with the existing RF gun.
The beam evaluation for the 1.6-cell RF gun is also
carried out with the maximum electric field of 100 MV at
the cathode surface. Figure 5 shows the transverse RMS
emittance(a) and energy spread(b) of the electron beamfrom the RF gun as a function of the laser injection
timing. It is clear that the transverse RMS emittance of
1.5 πmm-mrad and energy spread of 0.25% can begenerated at the 30 degree. These values are almost same

TUPOS24a)N orm alized Em ittance (πm m -m rad)

Table 1 Main parameter of the undulator
Period40 mm
Number of period
40
Total length
1600 mmGap
26-56 mm
K value0.95-0.17

3.0

2.5

2.0

1.5

1.0

0

10

20

30

40

50

60

R F Phase (deg)
2.5

b)
2.0

dE/E (%)

456

1.5

1.0

0.5

0.0

0

20

40

60

RF Phase (deg)Fig.5 Transverse RMS emittance(a) and energy
spread(b) of the electron beam from the gun as afunction of the laser injection timing.
as the 4.5-cell photocathode RF gun. The solenoid field
for the emittance compensation[10] is also taken into
account. The solenoid field used is the same geometricconfiguration of reference[11]. The field distribution is
calculated by using POISSON. We choose the maximum
field of 1800 Gauss, where the smallest transverse
emittance, 2.4 πmm-mrad, is obtained from theaccelerator tube. Figure 6 shows the transverse RMS
emittance(a) and energy spread(b) of the electron beamfrom the accelerator tube as a function of RF phase of theaccelerator tube. RF-phase of 65 degree, where thesmallest energy spread is obtained in figure 6, is used in
the successive calculations. It should be noted that thetransverse emittance slightly growths in the solenoid field
and further optimization of the solenoid field will be
required for our configuration. Figure 7 shows the phase
spectrum and the energy spectrum at the entrance of theundulator with a matched 180-degree arc which also
works as a bunch compressor. Finally, a peak current of
180 A and an energy spread of 0.31% electron beam canbe generated by the 1.6-cell photocathode RF gun. The
normalized emittance is calculated to be 10 πmm-mrad inhorizontal and 1.7 πmm-mrad in vertical. Consequently,
by using 1.6-cell photocathode RF gun, we can expect an
improved transverse emittance and a higher peak current
electron beam.than that from 4.5-cell photocathode RF
gun.

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H. Ohgaki et al. / Proceedings of the 2004 FEL Conference, 454-457

Transverse Em ittance (πm m -m rad)

a)

2.41

2.40
40

50

60

70

80

90

80

90

1.5

1.0

0.5

0.0
40

50

60

70

R F P hase(degree)

Fig.6 Transverse RMS emittance(a) and energy
spread(b) of the electron beam from the accelerator
tube.

P articles/0.5 deg.

a)

250

200

σ=1.4 deg

150

100

50

0

REFERENCES

16

18

20

22

24

26

28

30

32

34

P hase (deg.)b) 200P articles/20 keV[1] T. Yamazaki, et al., Free Electron Laser2001(2002),II-13.
[2] K. Masuda, et al., to be presented in FEL2004.
[3] T. Kii, et al., to be presented in FEL2004.
[4] H. Ohgaki, et al., NIM A507 (2003) 150.
[5] H. Ohgaki, et al., NIM A528 (2004) 366.
[6] F. Sakai, et al., Proceedings of the PAC1999 (1999)
2036.
[7] J. Yang, et al., NIM A491 (2002) 15.
[8] K. Masuda, et al., NIM A528 (2004) 134.
[9] e.g. D. Palmer, et al., Proceeding of the PAC1995(1995) 2432; R. Alley, et al., NIM A429 (1999) 324;
Y. Aoki, et al., Proceedings of the PAC1999 (1999)2018.
[10] R.E. Carlsten, NIM A285 (1989) 313.
[11] F. Sakai, et al., Jpn. J. Appl. Phys., Vol.41 (2002)
1589.

2.42

b) 2.0

CONCLUSION
Upgrade design of KU-FEL driver linac has been
carried out to obtain a saturated FEL in the infrared region.
The existing 4.5-cell thermionic RF gun will be operated
with a photocathode. The numerical evaluation is carriedout from gun to FEL by using PARMELA and TDA3D
codes. The expected FEL gain is 10 times larger than thatof original system. A 1.6-cell photocathode RF gun
dedicated to photocathode operation is also considered toobtain an excellent electron beam. The FEL gain with the
1.6-cell photocathode RF gun is more than 2 times as highas that with the 4.5-cell photocathode RF gun. Further
studies are needed to optimize the final upgrade design
both for the photocathode operation and for thethermionic cathode operation which is still attractive forhigh average current.
The authors would like to thank F. Sakai (SHI) for his
help for this work

2.43

R F P hase (degree)dE/E (%)

The expected FEL gain can be calculated with thenumerical evaluation. The undulator parameter used is thesame as 4.5-cell RF gun (table 1) except for the FEL
wavelength, because the electron energy(28 MeV) is
different from that of 4.5-cell photocathode system(34MeV). The calculated FEL gain in wavelength of 9.8 µm
is 810%. On the other hand, the FEL gain with the 4.5cell photocathode RF gun is calculated to be 320%. It
should be noted that the same electron beam parameter asin the previous section is used for the 4.5-cell
photocathode RF gun except for the beam energy. Morethan 2 times larger FEL gain will be obtained with the
1.6-cell photocathode RF gun. This enhancement in FEL
gain is both due to the enhancement of the peak current
and improvement in the transverse emittance. The roundtrip development of the FEL gain is also calculated as thesame manner as the previous section. The result showsthat the gain saturation can be observed from about 10
round-trips. As a result, the FEL gain will be further
enhanced by using the 1.6-cell photocathode RF gun.

150

dE/E=0.31%

100

50

0

27.8

27.9

28.0

28.1

28.2

28.3

28.4

Energy (M eV )Fig.7 Phase(a) and energy(b) spectrum at the entranceof the undulator.

FEL Technology

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S.K. Kashiwagi et al. / Proceedings of the 2004 FEL Conference, 458-461

FIRST MODEL OF THE EDGE-FOCUSING WIGGLER FOR SASE
S. Kashiwagi#, K. Kobayashi, T. Noda, R. Kato, G. Isoyama,
ISIR, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka, JapanS. Yamamoto and K. Tsuchiya
Institute of Materials Structure Science, KEK, 1-1 Oho, Tsukuba, Ibaraki, Japan
Abstract
The first model of the edge-focusing (EF) wiggler,which produces the strong transverse focusing field
incorporated with the normal wiggler field, has been
fabricated to evaluate its performance. It is a five-period
planar wiggler with an edge angle of 2 degrees and a
period length of 60 mm. The magnetic field in the wiggler
is measured using Hole probes at four different wiggler
gaps. It is experimentally confirmed that a high field
gradient of 1.0 T/m is realized along the beam axis in the
EF wiggler.

INTRODUCTION
A conventional planar wiggler of the horizontal
oscillation type focuses the electron beam in the verticaldirection, but does not focus in the horizontal direction. If
the beam is injected to the wiggler with the matchingcondition in the vertical direction, the vertical beam size
will remain constant as it moves along the wiggler. In thehorizontal direction, however, no focusing force exists
and the beam size will increase and diverge if the external
focusing force is not provided. Various schemes havebeen proposed or investigated to provide the focusing
force in the both directions in the wiggler for SelfAmplified Spontaneous Emission (SASE) in the shortwavelength region so that the beam size is kept small over
the whole length of the very long wiggler [3-9]. In theseschemes, either pole faces are shaped or permanent
magnet blocks are added in the wiggler gap, in order toproduce the field gradient for focusing the beam. The
magnet gap of the wiggler is sacrificed in some of thesemethods or the good field region is limited in the othermethods.
As a new method for the integrated-focusing, we
proposed the Edge-Focus (EF) wiggler, which can
produce the high magnetic field gradient superimposed on
the normal wiggler field [1,2]. The EF wiggler has anadvantage that the strong field gradient can be producedwith no obstacles in the wiggler gap and the good fieldregion is as large as that of the normal wiggler field. It
can be used not only for SASE experiments but also for
FEL in order to enhance the gain. As a next step of our
proposal, we have fabricated the first experimental modelof the EF wiggler. In the fabrication process of this model
wiggler, we developed a new method to make a low-error
wiggler without adjustment of the magnetic field by trial
and error, and reported at the preceding FEL conference[2]. The wiggler parameters of the first model have been___________________________________________#

E-mail: shigeruk@sanken.osaka-u.ac.jp

TUPOS25

chosen to meet requirements from our SASE experimentin the far-infrared region being conducted at the Instituteof Scientific and Industrial Research (ISIR), Osaka
University [10,11]. In this paper, we will describe the firstmodel of the EF wiggler and report results of themagnetic field measurement for the EF wiggler.

FIRST MODEL OF THE EDGEFOCUSING WIGGLER
The EF wiggler is basically a Halbach type wiggler
made only of permanent magnet blocks, but their shapes
are not rectangular parallelepipeds. The magnet blocks ofthe EF wiggler with vertical magnetization have a
trapezoidal shape with an edge angle φ, while those withlongitudinal magnetization have a parallelogram shapewith the same angle (shown in Figure 1). The average
focusing force of the EF wiggler can be calculated using
the simple model with the edge angle for the bending
magnets. In the simple model based on transfer matrices,
the focusing force in the EF wiggler (horizontal
oscillation type) is approximately given bykx =1  dBy  4e B0 φ=×Bρ  dx  m0c γ λw
2

(1)
2

8 − π  e   B0    − kx
k y = k0 − k x =3π  m0c   γ (2)where k0 is the natural focusing force of the wiggler forthe vertical direction and k0= kx+ ky. From Eq. (1), thefield gradient is given by

dB y
dx

=4

B0 .
φ

λw

(3)

The field gradient is approximately proportional to theedge angle and hence the focusing force along the wiggler
can be easily adjusted with the edge angle φ.
The first model of the EF wiggler consists of fiveperiods with the period length λW = 60 mm and the edge
angle φ = 2 degrees. The main parameters of the model
wiggler are listed in Table 1. The magnetic gap ismechanically fixed, but it can be easily changed bychanging columns supporting the upper magnet array.
The permanent magnet is Nd-Fe-B with the residual
induction of 1.32 T, and the standard dimensions of themagnet blocks are 2a × 2b × 2c = 100 × 20 × 15 mm3. The
peak magnetic field of the wiggler at g = 30 mm is

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S.K. Kashiwagi et al. / Proceedings of the 2004 FEL Conference, 458-461

Figure 1: Magnet array of the first model of the EF
wiggler. The vertical magnetization magnet blocks have a
trapezoidal shape, while those with longitudinalmagnetization have a parallelogram shape.

Figure 3 shows the vertical magnetic field By(z)measured at the 30 mm gap along the wiggler axis from –300 mm to +300 mm . We calculate the three-dimensional
magnetic field in the EF wiggler numerically with themagnetic charge method [12] and compare the calculated
values with the measured ones. The calculated values
agree quite well with the measured values except for theabsolute value. The measured magnetic field at the middleof the wiggler axis (the peak magnetic field) is
approximately 4200 Gauss. This value is about 2%
smaller than a calculated value. This small difference
seems to come from short and shallow steps at the bothends of the magnet blocks for mechanical clamping tofolders, which are not taken into account in thecalculation.
To obtain the field gradient (dBy/dx) of the model
wiggler, we measure the magnetic field along theTable 1: Main parameters of the model EF wiggler
Block size (2a×2b×2c)
100×20×7.5 mm3
Gap
30 mm
Number of periods
5 periods
Residual induction of magnet
Br = 1.32 T
Peak magnetic field (analytical) B0 = 0.43 T
Edge angle
φ = 2.0 °Averaged field gradient (φ= 2°) dBy/dx = 1.0 T/m
calculated using a 3D program to be 0.43 T [12]. The
field gradient of the model wiggler averaged over a
wiggler period is about 1 T/m at 30 mm gap and the edge
angle of 2 degrees. This edge angle is chosen so that the
double focusing is realized in both the vertical and thehorizontal directions for the 11.5 MeV electron beam.

Figure 2: Photograph of the setup for the magnetic fieldmeasurement of the EF wiggler at KEK.
5000

By = 4206.9 Gauss

In order to evaluate performance of the EF wiggler, themagnetic field has been measured at the High Energy
Accelerator Research Organization (KEK), using amagnetic sensor with two Hole probes for simultaneous
measurement of the vertical and the horizontal fieldcomponents, which is mounted in a small oven to control
the temperature of the sensor. Owing to the temperature
control, an accuracy of the magnetic field measurement isachieved to be about 0.1 Gauss. The Hole probes were
calibrated using NMR. The magnetic sensor is mounted
on a 3-axis linear stage, with which it is scanned along the
wiggler axis and its transverse position (x-y position) is
adjusted. Figure 2 shows the experimental setup for themagnetic field measurement of the EF wiggler. We
measure the magnetic field simultaneously in thehorizontal and the vertical directions using thismeasurement system and make the field mapping in the
wiggler.

By [Gauss]

FIELD MEASUREMENT OF THE
WIGGLER

0

-5000
-300

-200

-100

0

100

200

300

z [mm]

Figure 3: Measured vertical magnetic field By(z) along
the central wiggler axis.

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y = 4205.5 - 7.887x R= 0.99865

By [Gauss]

4250

4200

4150

4100
-10

-5

0
x position [mm]510Figure 4: Measured magnetic field By(x, y=0) as afunction of the horizontal position at the middle of the
wiggler.

TUPOS25

λw = 60 mm, φ= 2deg.

dBy/dx11

By0 [T]

longitudinal axis at several transverse positions. Figure 4
shows the measured vertical magnetic field along the xaxis (horizontal) at the middle of the model wiggler,where the vertical magnetization block is located. The
vertical magnetic field changes linearly with thehorizontal position over the width of the wiggler and theslope is steep. The field gradient is derived with linear
fitting of the data points as shown in Figure 4. The
electron beam receives the focusing force produced bythis large field gradient.
We measure the magnetic field at wiggler gaps g = 30,
40, 50, and 60 mm by changing columns supporting theupper magnet array and derive the transverse field
gradient as a function of the wiggler gap. The field
gradient averaged over the wiggler periods is shown in
Figure 5, together with the peak magnetic field. The solid
circles and open circles show the measured peak magnetic
field and the averaged field gradient of the EF wiggler,
respectively. The solid line and the dashed line show thepeak magnetic field and the averaged field gradientcalculated with the 3D program, respectively. The
measured values are in good agreement with thenumerical calculation as shown in Figure 5. The peakmagnetic field of the wiggler decreases exponentiallywith increasing the wiggler gap and the averaged field
gradient also decreases exponentially as shown in Figure
5, but the slope for the field gradient is gentler than thatfor the peak magnetic field. The peak field at the gap 60
mm decreases to one fifth of the value at 30 mm, whereas
the field gradient at 60 mm decreases to only a half of thevalue at 30 mm. This behaviour is favourable in the viewof the beam dynamics in the wiggler.
The simple model based on transfer matrices fails to
explain this behaviour, because the field gradient of the
EF wiggler given by Eq. (3) is proportional to the peakmagnetic field. We think that this is because the variationof the fringe field with the wiggler gap is not taken into
account in the simple model calculation for the field
gradient of the EF wiggler. This indicates that the fieldmeasurement and the 3D magnetic field calculation of the
wiggler are important to understand the field distribution
in the wiggler.
The EF wiggler can produce the high field gradient in
the wiggler and the sum of the vertical focusing force andthe horizontal one is constant and equal to the natural
focusing force, as shown by Eq. (2). The electron beam issimultaneously focused in the both directions with the
weak focusing scheme if the horizontal focusing force
generated by the edge angle is smaller than the natural
focusing of the wiggler, which is realized when theelectron beam energy is low and the peak magnetic fieldof the wiggler is high as well as the edge angle is not verylarge. If the horizontal focusing force of the EF wiggler islarger than the natural focusing, the defocusing force isprovided in the vertical direction. In this case, the strong
focusing scheme can be applied to focus the electron
beam in the both directions, using two kinds of EF
wigglers with positive and negative edge angles. The peakfield decreases exponentially with increasing themagnetic gap and accordingly the natural focusing force
also decreases exponentially. When the wiggler field
becomes weak, the double focusing condition may not be
fulfilled at larger gaps. It is, therefore, important tocarefully choose the focusing scheme, either the weakfocusing or the strong focusing. As an example of the
double focusing, the square roots of the betatron functionsin the 2m-long conventional planar wiggler with the edge
angle = 0 deg. and in the EF wiggler with the edge angleof 1 degree are shown in Figure 6. The EF wiggler can
produce focusing forces in the both directions and thedBy/dx (average) [T/m]

4300

By

0

0.1

0.1

25

30

35

40

45 50
gap [mm]

55

60

65

Figure 5: Peak magnetic field and the field gradient of
the EF wiggler as a function of the wiggler gap. The
solid circles and the open circles show the measured
peak magnetic field and the average field gradient over
the wiggler period, respectively. The solid and thedashed lines show calculation using the 3D program.

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S.K. Kashiwagi et al. / Proceedings of the 2004 FEL Conference, 458-461

Edge angle = 0 deg

favourable in view of the beam focusing in the wiggler.
We experimentally evaluated the performance of the EF
wiggler with the magnetic field measurement. We plan tofurther study characteristics of the EF wiggler.

ACKNOWLEDGEMENT
Edge angle = 1.0 deg

Figure 6: Square root of the betatron function for theconventional planar wiggler with no edge and the EF
wiggler with the edge angle of one degree. The solid andthe dashed lines show the horizontal and verticalbetatron functions, respectively.
betatron functions can be made small and almost constantthrough the wiggler, using the matching conditions. For
the conventional planar wiggler, the horizontal focusing
force has to be provided with external quadrupole
magnets and hence the beam cannot be focused as small
as it is in the double focusing scheme. The EF wiggler
can be used to enhance the gain of SASE and FEL.

CONCLUSION
In order to advance the development of the EF wiggler,which we had proposed, we fabricated the first model ofthe EF wiggler. The magnetic field in the wiggler wasmeasured using Hole probes at four wiggler gaps. It was
experimentally confirmed that a high field gradient of
about 1.0 T/m was realized along the beam axis in the EF
wiggler, which was superimposed on the normal wiggler
field. We obtained the relation between the magnetic field
gradient and the magnetic gap of the EF wiggler. The
field gradient decreases with increasing the magnet gap
more slowly than the peak magnetic field does, which is

The authors would like to thank Mrs. T. Koda and K.
Okihira of NEOMAX Co., Ltd. for their help on the
fabrication and the magnetic field measurement of the EF
wiggler. This research was partly supported by the Joint
Development Research at the High Energy Accelerator
Research Organization (KEK), 2003-17, 2003 and theMinistry of Education, Science, Sports and Culture,
Grant-in-Aid for Exploratory Research, 15654036,
2003&2004.

REFERENCES[1] G. Isoyama et al., Nucl. Instr. and Meth. A 507 (2003)
234[2] S. Kashiwagi et al., Nucl. Instr. and Meth. A 528(2004) 203[3] J. Pfluger and Yu. M. Nikitina, Nucl. Instr. and Meth.
A 381 (1996) 554[4] M. Takabe et al., Nucl. Instr. and Meth. A 331 (1993)
736[5] Y. Tsunawaki et al., Nucl. Instr. and Meth. A 304(1991) 753[6] M. Shiho et al., Nucl. Instr. and Meth. A 304 (1991)
141[7] A. A. Varfolomeev and A. H. Hairetdinov, Nucl. Instr.
and Meth. A 341 (1994) 462[8] A. A. Varfolomeev, et al., Nucl. Instr. and Meth. A
358 (1995) 70[9] Ross D. Schlueter, Nucl. Instr. and Meth. A 358(1995) 44[10] R. Kato, et al., Nucl. Instr. and Meth. A 407 (1998)
157[11] R. Kato, et al., Nucl. Instr. and Meth. A 445 (2003)
164[12] G. Isoyama, Rev. Sci. Instrum., Vol. 60, No. 7(1989) 1826

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UPGRADE OF THE L-BAND LINAC AT ISIR, OSAKA UNIVERSITY
FOR A FAR-INFRARED FEL
R. Kato#, S. Kashiwagi, T. Yamamoto, S. Suemine, G. Isoyama,
ISIR, Osaka University, Mihogaoka, Ibaraki, Osaka 567-0047, Japan
Abstract

INTRODUCTION

high-intensity single-bunch beam for pulse radiolysis, but
not optimized for development of FEL. Though theduration of the rf pulse could be extended to 4 µs, themaximum macro-pulse length of the electron beam islimited to 2 µs, since the filling time of the accelerating
structure is 1.8 µs. As a result, the FEL could not reachpower saturation because the number of amplification
times was limited.
Recently, the linac has been extensively remodelled torealize high operational stability and reproducibility foradvanced studies in beam science and technology. Almost
all the power supplies, including the main rf power source,
are replaced with new ones. At this opportunity, the linac
is also made suitable for FEL. The electron beam with amacro-pulse up to 6 µs can be accelerated, so that the
FEL will reach power saturation. The modification of thelinac has been completed and commissioning is now inprogress. In this paper, we will report performance andcharacteristics of the linac after the modification.

We are developing the far-infrared free-electron laser(FEL) using the L-band electron linac at the Institute of
Scientific and Industrial Research (ISIR), Osaka
University. The first lasing of the FEL was obtained atwavelengths from 32 to 40 µm in 1994 [1], and thewavelength region has been extended up to 150 µm [2].
The linac was designed and constructed for producing the

The schematic layout of the L-band linac is shown in
Figure 1.The linac consists of a thermionic gun, threestage sub-harmonic buncher (SHB) system, a pre-buncher,a buncher, and a 3 m long accelerating tube. The
thermionic gun (Eimac, YU-156) is a dispenser type with

The L-band linac at the Institute of Scientific andIndustrial Research, Osaka University, has been renewed
in order to realize high stability of the electron beam andeasy changes of operation modes for various kinds ofexperiments. In the modification, it was included thereplacements of the klystron and the pulse modulator for
it to provide the rf power with the pulse duration up to 8
µs to realize power saturation of the FEL. The
modification of the linac has been completed andcommissioning is now in progress. The intensity
fluctuations of the beam intensity in the transient and thesingle-bunch modes were decreased to one-tenthcompared with previously measured values before theremodelling. The fluctuation of the beam energy in the
single-bunch mode was less than 0.1% in standard
deviation.

NEW LINAC SYSTEM

QM
ACC

Chicane

QM

QM

QM

QM

QM
WIG

QM

QM

QM
QM
QM

Exp. Room 2

Figure 1: The schematic layout of the L-band linac. E-GUN: Electron gun, SHB1: 108MHz SHB cavity #1, SHB2:
108MHz SHB cavity #2, SHB3: 216MHz SHB cavity, PB: Prebuncher, B: Buncher, ACC: 1.3 GHz accelerating
tube, BM: Bending magnet, QM: Q-magnet, AM: Analyser magnet, WIG: Wiggler, BCM1-4: beam current
monitors, BPM1: beam position monitor.
____________________________________________#

kato@sanken.osaka-u.ac.jp

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R. Kato et al. / Proceedings of the 2004 FEL Conference, 462-465

1500

Std. dev. : 0.15 [%]Stability of the beam current in the transient
mode

500

97

99

101

103

Normarized beam intensity [%]Figure 2: Histogram of the electron beam intensity
extracted from the cathode. The intensity wasmeasured with BCM1 at the entrance of the first SHB
cavity.

105
Acc

100

105

95

100

Exp. Room 2
90

BEAM STABILITY
Stability of the beam current from injector
A histogram of the electron beam intensity extracted
from the cathode is shown in Figure 2. The beam intensity
was measured with a current transformer, BCM1 at theentrance of the first SHB cavity. A sampling period is 0.5

110

0

1000

2000

3000

4000

Beam Intensity at Exp. Room 2 [%]the cathode diameter of 3.0 cm2 and the operating voltage
is 100 kV. The cathode voltage and the cathode heater are
stabilized with regulated AC power sources (Behlman,
BL1350; Takasago, ARH500). The SHB system iscomposed of two 108 MHz and one 216 MHz standing
wave cavities, and each cavity is independently driven
with a 20 kW rf amplifier. The pre-buncher, the buncher,and the accelerating tube have travelling wave typestructures with the accelerating frequency of 1.3 GHz
driven with one 30 MW klystron (Thales, TV-2022E) anda new pulse modulator, while they were driven with two
klystrons before the remodelling. The new klystronsystem has two operation modes with different pulse
durations. One is called the normal mode, in which theflat top is 4 µs long and the peak power is 30 MW. The
other is the long pulse mode for FEL experiments, inwhich the pulse duration is 8 µs but has the peak power is
25 MW. The maximum reputation rate is 60 Hz in thenormal mode, while it is reduced to 30 Hz in the longpulse mode. The pulse height fluctuation of the output
voltage of the modulator is measured to be less than
0.1 % (peak-to-peak) and the undulation of the flat top tobe below 0.2 % (peak-to-peak). In a test experiments, theflatness of 0.1 % was realized over a 5.5 µs time region
on the flat top.

The transient mode is most frequently used in the Lband linac. In this operation mode, the SHB system isswitched off. Since the single rf power source is used forthe three rf structures, the beam stability deteriorated
mainly by the fluctuation of the rf amplitude in the shortperiod. In the long period, it becomes worse due to thetemperature drift of the electron gun cathode, as well as
the periodical temperature change of the cooling water
system and the air-conditioner.
The beam intensities measured with time in this modeare shown in Figure 3. They were measured with BCM2
at the exit of the accelerating tube and with BCM3 at thebeam port in the 2nd experimental room. The sampling
period is 0.5 seconds and the measurement time is 4,500
seconds. The intensities are normalized with theirrespective average values. Figures 4 and 5 showrespective histograms of the beam intensities derived
from the data shown in Figure 3. In addition tofluctuations of the beam intensities in short periods, it canbe seen that the intensities slightly decrease with time.
The long-term drift per ten minutes is 0.04 % for the
beam intensity at the exit of the accelerating tube and it is0.08 % for that at the beam port of the 2nd experimental
room. These long-term drifts were subtracted from thedata and then the intensity distributions were calculated.
The standard deviation is 0.25 % for the beam intensity atthe exit of the accelerating tube as shown in Figure 4 andit is 0.34 % for the beam intensity at the beam port of the
2nd experimental room. These values are as small as onetenth of previously measured values before theBeam Intensity at Acc [%]Counts1000

0seconds and the measurement time is 1,500 seconds. The
intensity is normalized with the average. The standard
deviation is 0.15 %.

95

Time [sec]Figure 3: The beam intensities measured with BCM2
at the exit of the accelerating tube (red lines) and with
BCM3 at the beam port in the 2nd experimental room
(blue lines).

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1500

Std. dev. : 0.25 [%]Counts1000

Stability of the rf power

500

0
97

99

101

103

Normarized beam intensity [%]Figure 4: Histogram of the beam intensity measured
with BCM2 at the exit of the accelerating tube in thetransient mode.
1500

Std. dev. : 0.34 [%]As mentioned previously, the variation of the rf phase
does not significantly affect the beam intensity in thetransient mode. We, therefore, simultaneously measured
the beam intensity and the rf power with time. Figure 6
shows the rf power measured at dummy loads for thebuncher and the accelerating tube. They are normalizedwith respective average values. The fluctuation of the rf
power is 0.14 % (standard deviation) for the buncher and0.11 % (standard deviation) for the accelerating tube.
Since the single rf power source is used for buncher andthe accelerating tube, both of the rf power shows similarfluctuation pattern.

Stability of the single-bunch beam
The single-bunch mode is used in the SASE-FEL
experiments. In this mode, the SHB cavities are driven
with the independent rf sources. Since the number of therf sources is four in the single-bunch mode, which should
be compared with one in the transient mode, influences ofphase jitters of the sources are added to the beam. Figure
7 shows the beam intensities measured with BCM2 at theexit of the accelerating tube and with BCM4 at theentrance of the wiggler with time. The measurement timeis 730 seconds and the sampling period is 0.73 seconds.
The intensities are normalized with respective averagevalues. The long-term drift per ten minutes is 0.76 % forCounts

1000

500

0
97

horizontal position changes there and portion of theelectron beam scraped out, so that the beam intensitychanges. This is the reason why the standard deviation of
the beam intensity measured with BCM3 is larger thanthat measured with BCM2. Similarly, the standard
deviation of the beam intensity measured with BCM2,
0.25 %, is larger than that measured with BCM1, 0.15 %,because a part of the beam is lost in the bunching process
due to the fluctuation of the rf power.

99

101

103

102

101

Normarized beam intensity [%]TUPOS26

Buncher RF Power [%]remodelling. The fluctuation of the beam intensity islarger at the beam port in the 2nd experimental room,
0.34%, than at the exit of the accelerating tube, 0.25 %.
The transverse position of the electron beam isdetermined by the energy of the electron beam, which is acharacteristic of the electron beam, and by the dispersion
function, which is a characteristic of the beam transport
line. At the exit of the accelerating tube, the dispersion
function is zero, so that the beam does not move evenwhen the energy changes. For the beam port in the 2nd
experimental room, on the other hand, the beam line islong and there are some regions where the dispersion
function is not zero. If the electron energy fluctuates, the

100

101

99

100

Acc RF Power [%]Figure 5: Histogram of the beam intensity measured
with BCM3 at the beam port in the 2nd experimentalroom in the transient mode.

Buncher

Acc
98

0

1000

2000

3000

4000

99

Time [sec]Figure 6: The rf power measured with time at dummyloads for the buncher and the accelerating tube.

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R. Kato et al. / Proceedings of the 2004 FEL Conference, 462-465

105

110

0.3

105

95

100

0.2

Energy Fluctuation [%]100

Beam Intensity at Wig. [%]Beam Intensity at Acc. [%]

Acc

0

100

200

300

400

500

600

700

0
-0.1
-0.2

Wig
90

0.1

95

-0.3

Time [sec]the beam intensity at the exit of the accelerating tube andit is 0.77 % for that at the entrance of the wiggler. The
standard deviation of the beam intensity without the longterm drift is 0.40 % at the exit of the accelerating tube,
while it is 1.00 % at the entrance of the wiggler. These
values decreased one-tenth in comparison with previously
measured values before the remodelling, too. However,since the stability of the SHB system is not enough, it isthought that there is still room for improvement in thesystem.
Figure 8 shows the beam energy measured with BPM1
on the beam transport line to the FEL system in the
single-bunch mode. The sampling period is 0.73 seconds
and the measurement time is 730 seconds. The standard
deviation of the beam energy was 0.08 % as shown in
Figure 9. Since almost energy fluctuation is included
within the limit of ±0.15 % from the centre energy,
wavelength shift caused by the energy fluctuation isestimated to be less than ±0.3 %.

SUMMARY
We evaluated the beam stability of the transient and thesingle-bunch modes after the remodelling. In the bothmodes, the current stability was improved drastically, thefluctuation of the beam intensity decreased to one-tenthcompared with measured values before the remodelling.
Since the fluctuation of the beam energy for the singlebunch mode was less than 0.1% in the standard deviation,
the FEL oscillation can be expected to be more stable.
Next we will evaluate the beam stability of the long pulse
mode for the FEL oscillation experiment.

0

100

200

300

400

500

600

700

Time [sec]Figure 8: Temporal fluctuation of the beam energy
measured with BPM1 on the beam transport line to the
FEL system.
60

Std. dev. : 0.08 [%]50
40CountsFigure 7: The beam intensities measured with BCM2
at the exit of the accelerating tube (red lines) and with
BCM4 at the entrance of the wiggler (blue lines) in the
single-bunch mode.

30
20
10
0
-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Energy Fluctuation [%]Figure 9: Histogram of the beam energy fluctuation
measured with BPM1 on the beam transport line to the
FEL system.

REFERENCES[1] S. Okuda, et al., Nucl. Instr. and Meth. A 358 (1995)
244.
[2] R. Kato, et al., Nucl. Instr. and Meth. A445 (2000) 169.

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DEVELOPMENT OF COMPACT SOFT X-RAY SOURCEBASED ON LASER UNDULATOR *R. Kuroda#, D. Ueyama, T. Saito, S. Minamiguchi, K. Hidume, M. Washio,
Waseda University, Tokyo, JapanS. Kashiwagi, Osaka University, Osaka, Japan,
J.Urakawa, H.Hayano, KEK, Ibaraki, Japan
Abstract
A compact soft X-ray source is required in various
research fields such as material and biological science.
The laser undulator based on Compton backward
scattering has been developed as a compact soft X-ray
source for the biological observation at Waseda
University. It is performed in a water window region(250eV - 500 eV) using the interaction between 1047 nm
Nd:YLF laser and 4.6 MeV high quality electron beam
generated from rf gun system. The range of energy in thewater window region has K-shell absorption edges of
Oxygen, Carbon and Nitrogen, which mainly constitute ofliving body. Since the absorption coefficient of water ismuch smaller than the protein’s coefficient in this range, adehydration of the specimens is not necessary. As apreliminary experiment, about 370 eV X-ray generation
was carried out. In this conference, we will report resultsof experiments and our future plan.

INTRODUCTION
Short-pulse X-ray source is required in various research
fields, such as material and medical science. To meetthese demands, R&D on the next-generation light source
has been initiated at several laboratories in the world. Oneof the most promising approaches to short-pulse X-ray
sources is the laser undulator, which is based on Comptonor Thomson backward scattering [1, 2].
The Compton backward scattering, in which a photon
reverses its on colliding head-on with an electron, hasbeen proposed as a way to generate X-rays with opticallaser beam and low energy electron beam either throughthe spontaneous emission or the free-electron laser (FEL)
mechanism[3]. The mechanism is closely related toundulator radiation so that the laser field acts as anelectromagnetic undulator generating up-shifted radiationin the X-ray regime. In this case, it is easily to generatepicosecond X-ray using the recent developments of thelaser and the accelerator technologies because the pulse
length of the generated X-ray is roughly obtained fromthe electron and the laser pulse lengths.
On the other hand, Soft X-ray with the energy in “water
window” region, which is 250 eV – 500 eV (2.5 nm – 5nm), can be extensively applied to biological studies,because the absorption coefficients of proteins in thisregion are larger than that of water. Dehydration of
biological specimens can be avoided in both studies in___________________________________________*707 HRC: High Tech Research Project, MECSST#
rkuroda@waseda.jp

TUPOS27

vivo and in vitro. K-shell absorption edges of O (532 eV),C (284 eV) and N (400 eV), which are main elements ofliving bodies, exist in “water window” region [4]. The
monochrome X-ray with energy between these edges canbe employed for the intrinsic contrast imaging in hydrated
samples. The compounds containing these elements in thesample can be highlighted. The laser undulator possesses
so many features including its wide energy tunability andits compactness of instruments X-ray with narrow energy
bandwidth and good directivity can be selected by cuttingout with the scattered angle.

HIGH QUALITY ELECTRON BEAM
GENERATION SYSTEM
RF gun system
The rf gun system is composed of the BNL type 1.6 cell
S-band rf cavity with Cu photocathode, a set of solenoid
magnets for emittance compensation [5, 6, 7], a stabilized
laser and rf power source. Figure 1 shows the total beamline which is within 2 × 2 m2 as a table-top size. The
photocathode surface of the rf gun cavity was polishedusing diamond powders. Present quantum efficiency of
Cu cathode has been achieved about 5 × 10-5 without laser
cleaning. High accelerating field is effective to reduce anemittance growth due to space charge effect for a highcurrent beam. However, we will suffer the increase ofdark current due to field emission in the high gradient
operation. Therefore, in order to reduce the dark current, adiamond turning method has been applied for a finemanufacturing of the rf gun cavities.

Figure 1: The view of the total beam line
Main parts of rf source consists of 10 MW S-band
klystron (Tomson: TV2019B6) and a small pulse
modulator (Nissin Electric Co., Ltd.). The pulse

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Dr. Kuroda et al. / Proceedings of the 2004 FEL Conference, 466-469

modulator has good stability and flatness of the output
pulse.

Laser system
All solid state picosecond Nd:YLF laser system(PULRISE-V), which was developed by SHI (Sumitomo
Heavy Industries, ltd.), is used not only for the irradiation
onto potocathode to generate the electron beam, but also
for the soft X-ray generation using the laser undulator.
The laser system has an active timing and intensity
stabilization systems against a temperature change andtiming jitter from a reference rf signal. Fluctuation of airand vibrations of mirrors on the laser optical path affectthe laser intensity and pointing stability on thephotocathode. The laser system is put inside theaccelerator room to achieve short optical path length tothe photocathode. The timing and amplitude fluctuation
due to an electro-magnetic noise and radiation had been
investigated using time domain demodulation techniquebetween a seed laser and the reference rf signal [8,9]. As aprevious result, the timing jitter was measured less than
0.5 ps and the effects of the electromagnetic noise andradiation were negligible for the laser stability. It issufficiently small timing fluctuation for the soft X-ray
generation.

Additional laser amplification
Our all solid state Nd:YLF laser system (PULRISE-V)
can provide about 1 mJ/pulse at fundamental wavelength.
However, our requirement for the soft X-ray generation
experiment and the pulse radiolysis experiment is larger
than 10 mJ/pulse. Therefore, a flush lamp pumped 2-passlaser amplification using Nd:YLF crystal (65 mmφ ×90mm) has been installed. The maximum gain of theamplifier is about 102 at 900 V flushing voltage. The
optimum laser energy can be arbitrary obtained bychanging the flushing voltage. High power laser beam
was obtained by amplifying the residual fundamental
laser beam (IR: 1047 nm) to collide with the electron
beam for the laser undulator.

Electron beam status
High quality electron beam is produced by aphotocathode rf gun system. The 4th harmonic laser (UV:
262 nm) which is irradiated onto the photocathode of therf gun is obtained from a Nd:YLF fundamental laser (IR:1047 nm) by passing through two beta barium borate(BBO) crystals in the PULRISE-V laser system. The
electron bunch charge and beam energy was measured asa function of rf phase. The typical results are shown in
Fig. 2. The bunch charge of 1 nC is achieved at the beamenergy of 4.6 ± 0.1 MeV. UV laser to drive the rf gun andIR laser for the applications were generated from a sameseed oscillator, so that it was easily to makesynchronization between them. Figure 3 shows the block
diagram of the synchronization system.

Figure 3: Block diagram of the synchronization system
The beam emittance and the bunch length
measurements were carried out using slit scan method andtwo-frequency analysis technique, respectively [10].
Comparing between results of experiments andsimulations, these were agreed well [11].

SOFT X-RAY GENERATION
Analysis
A simple approach to analyze the Compton scatteringin a general configuration is to notice the similarity
between the role of a laser beam and a static magnetic
undulator in inducing a sinusoidal motion of theelectrons[1, 12]. The wavelength of the up-shifted
radiation as the X-ray can easily be calculated fromenergy and momentum conservation asλ≅λ0 (1 + K 2 / 2 + γ 2θ 2 ),2γ 2 (1 − cos φ )(1)where the Compton shift has been neglected. Here, γ isthe Lorentz factor, K the wiggler strength, θ the angle ofobservation, φ the angle of the laser propagation toward
the electron beam and λ0 the incident laser wavelength.
The wiggler strength is expressed by

K = eA0 / me c 2 ≈ 0.85 × 10 −9 λ0 I ,Figure 2: The charge and energy of the electron beam
as a function of the rf phase.

(2)

where I [W/cm2] and λ0 [µm] are the intensity and thewavelength of the incident laser, respectively. Here, c isthe light velocity, e the elementary electric charge, me theelectron rest mass, A0 the vector potential of the incident
laser.

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Figure 4: Experimental layout including the rf gun system and the laser system

Soft X-ray generation experiment
Figure 4 shows the experimental layout for the laser
undulator. Our system is a table-top size within 2 × 2 m2
including the rf gun system and Nd:YLF laser system.
The electron beam parameters and the laser beam
parameters in this experiment are given in Table 1 and 2,
respectively.
Table 1: Electron beam parameters
Electron beam
Ave. beam energy
4.6 MeV
Beam charge
0.60 nC/bunch
Bunch length
10 ps (FWHM)
Beam size σx
280 µmBeam size σy
250 µmRepetition rate
5 Hz

emitted by electron beam passing through a 5 mmthickness glass plate and reflected by an Al mirror with asmall pinhole at the collision point, so that the Cherenkov
light can be guided toward the same direction of the laser
beam to make time and spatial coincidence between them.
The laser beam passes through the pinhole and both thelaser beam and the Cherenkov light are guided to a streak
camera. The generated X-ray is separated from theelectron beam using the analyzer magnet and guided to an
X-ray detector. The detector is a circular microchannel
plate (MCP) (F4655-10: HAMAMATSU PHOTONICS K.
K.) with high speeded response that has about a gain of 5
× 106 and the quantum detection efficiency of the MCP isabout 10 % at 370 eV X-ray [13]. The distance between
the collision point and the detection point is about 840
mm and the effective diameter is 15mm. The X-ray
scattered within about 8.9 mrad was detected.

Table 2: Laser beam parameters
Laser beam
Wavelength
1047 nm
Energy / pulse
10 mJ
Pulse length
10 ps (FWHM)
Beam size σx
80 µm
Beam size σy
80 µm
Repetition rate
5 Hz
In this experiment, Short-pulse soft X-ray generation
using the laser undulator based on the Compton backward
scattering between a 4.6 MeV electron beam and a 1047
nm laser beam at 160 deg of the laser propagation angle φtoward the electron beam has been successfully
performed. A spatial overlap between the electron beamand the laser beam is confirmed by observing both beam
images on the identical phosphor screen located at thecollision point using a CCD camera. Cherenkov light is

TUPOS27

Figure 5: The typical X-ray signals
Figure 5 shows the typical X-ray signals detected by
the Microchannel plate (MCP) by changing the timing
between the electron beam and the laser beam. The total
number of the detected photons is obtained from theDr. Kuroda et al. / Proceedings of the 2004 FEL Conference, 466-469

469

amplitude of the maximum X-ray signal using its gain andthe quantum detection efficiency. The amplitude of X-ray
signal that is about 380 mV corresponds to the number ofdetected photons about 1.9 × 102 /pulse. In this case, thetotal number of generated photons is analyticallyestimated to be approximately 1.9 × 104 /pulse This X-ray
has maximum energy of about 370 eV with 0.2 % energy
bandwidth that is between the K-shell absorption edges of
N and C. It is expected that this soft X-ray will have many
application to the biological observation.

SUMMARY
Soft X-ray generation in “water window” region basedon the laser undulator have been successfully performed
using the rf gun system with Nd:YLF laser system which
is a table-top size within 2 × 2 m2. This X-ray has
maximum energy of about 370 eV and the total number ofgenerated photons is analytically 1.9 × 104 photons/pulse.
Out of total generated X-ray, the useful soft X-ray thathas energy between the K-shell absorption edges of N and
C is analytically about 4.0 × 103 photons/pulse within
about 50 mrad scattered angle that correspond to about
5.2 % energy bandwidth and we can select such usefulsoft X-ray by cutting out within the scattered angle. It is
expected that this X-ray will have many application to
many wide research fields such as biological observation.
As next step, soft X-ray optics with zone plates or an Xray CCD camera was proposed for the soft X-ray
microscopy to apply to the biological observation.

ACKNOWLEDGEMENT
Authors would like to express sincere thanks to Mrs. T.
Takatomi and Y. Watanabe of KEK for their deep help on
manufacturing the rf gun cavity. We would like to express
our gratitude to Dr. K. Ushida of RIKEN for manytechnical supports and insightful discussion for its
application. We would like to express great thank Drs. A.
Endo and Y. Aoki of SHI and FESTA group for theirexpert technical support about laser system.

REFERENCES[1] W. Leemans et al., Proc. PAC ‘95, p. 174 (1995).
[2] S. Kashiwagi et al., NIM A455, 36 (2000).
[3] A. Ting et al., NRL preprint NR/MR14790-92-6973(1992).
[4] B. L. Henke et al., Atomic Data and Nuclear Data
Table 27 (1982).
[5] X. J. Wang et al., Phys. Rev. E 54-4, 3121 (1996).
[6] X. Qiu et al., Phys. Rev. Lett. 76 20, 3723 (1996).
[7] D. T. Palmer et al., Proc. PAC ‘97, p. 2843 (1997).
[8] T. Oshima et al., Proc. PAC 2001, p. 2400 (2001).
[9] H. Tsuchida, Optical Lett., 23, 286 (1998).
[10] R. Kuroda et al., Jpn. J. Appl. Phys. (2004) in press.
[11] K. Sakaue et al., Proc. EPAC 2004 (2004).
[12] K.-J. Kim et al., NIM A341, 351 (1994).
[13] G. W. Fraser et al., NIM A195, 523 (1982).

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C.A.J. van der Geer et al. / Proceedings of the 2004 FEL Conference, 470-473

REPETITIVE BUNCHES FROM RF-PHOTO GUN RADIATECOHERENTLY
C.A.J. van der Geer, S.B. van der Geer, M.J. de Loos,Pulsar Physics∗ , Soest, The Netherlands
D.A. Jaroszynski, University of Strathclyde† , Glasgow G4 0NG, Scotland, UK
Abstract
We consider injecting the plasma wake field acceleratorof the Alpha-X project [1] by a sequence of low charge pancake shaped electron bunches. This solves the problem of
undesired expansion due to space-charge forces of a single
high charge bunch. To this end the photo-excitation laser
pulse of the RF-photo-injector is split into a sequence of
sub-pulses. The inter-bunch distance can be chosen suchthat the sub-bunches fall into successive ponderomotive
wells of the plasma accelerator. In this way the total radiated output is kept as high as possible. The repetitive photogun can be tested, at low energy, by injecting its output into
an undulator and monitor the radiation. This programme isinformed by results of new GPT simulations [2].

INTRODUCTION
In the ALPHA - X-project an ultra-short electron bunch,of the order of 30 µm (100 fs) will be accelerated in a laser
driven plasma wake-field accelerator and then subsequently
sent through an undulator [3] to produce useful radiation.
The main purpose of the experiment is to demonstrate thepossibility of constructing a table top FEL.
As with conventional accelerators, the first problem toattack is the production of electron bunches which are
sufficiently short to inject into the accelerating potential.
The ponderomotive wavelength of the wake-field accelerator is of the order of 40 µm for a plasma density, ne =7 · 1017 cm−3 . The RF-photo-injector used will deliver
5 MeV, 30 µm, bunches of several hundreds pC, but due
to the space-charge forces, such bunches can not be transported over the inevitable space required for other beamline components between the gun and the accelerator. Evenpancake-shaped bunches of this size with only 100 pC total
charge will expand considerably.
In order to keep the total accelerated charge to an acceptable level while maintaining the bunches short we propose
to split the bunch into a number, say ten, sub-bunches andto fill not one, but 10 successive buckets of the ponderomotive wave in the plasma wave accelerator. This bunch
splitting is obtainable via Fourier plane filtering of the laser
pulse illuminating the photocathode. The generated sequence of sub-bunches will have a total length of ≈ 1 mm,still corresponding to a small fraction in the RF-cycle of
the gun ( 3 GHz) and thus the resulting sub-bunches canbe considered almost identical. In this paper we fill every∗ http://www.pulsar.nl† http://tops.phys.strath.ac.uk

TUPOS29

other bucket of the PMW, to ease interpretation. This results in a total length of ≈ 2 mm, still short with respect tothe 3 GHz cycle.
As the plasma wave accelerator is already a quite complicated device on its own, it is useful to test the generationof sub-bunches separately. At 5 MeV, the midrange of theRF-photo gun, the ponderomotive wavelength of the generated light in the undulator is quite close to that of thewake-field accelerator. If successive PMW-well’s in the undulator are filled with sub-bunches, the output radiation isin phase and adds coherently. This can be monitored witha spectrometer or THz-detector [5], and so, the repetitive
photo gun can be tested with the undulator alone.
In this paper we calculate the output of the undulator fora single bunch when the bunch length is varied, and for asequence of sub-bunches when the inter sub-bunch distanceis varied.
The simulations are carried out with GPT. The electron
bunch and undulator parameters used in this paper are compiled in tables 1 and 2.
Table 1: Electron bunch parameters
EnergyE0 = 5 MeV
Emittancen = 3 µm
Sub bunch Charge
qb = 10 pC
Total bunch Charge Qb = 100 pC
Sub bunch length
σz = 30 µm (Gaussian)
Total bunch length
Lb ≈ 2 mm
Tranverse size
σr ≈ 1 mm

Table 2: FEL parameters
Undulator per.
Nu = 96λu = 15 mm
Krms = 0.71
Magnet strength Bu = 0.72 T
Gap width
G = 3.5 mm
Slot dim.
w = 5 mmd = 1 mmwaveguide dim. a = 4 mm
b = 4 mmrad. wavelength λs = 98.5 µm λpmw = 97.9 µm

EXPANSION OF THE ELECTRON BUNCH
The longitudinal expansion of a 30 µm bunch, in the
beam line between the gun and the accelerator, is shownin fig. 1 for two values of the bunch charge, 100 pC and
10 pC respectively. The transverse dimensions of the bunch

Available online at http://www.JACoW.org

471

C.A.J. van der Geer et al. / Proceedings of the 2004 FEL Conference, 470-473

Ey

= 0

50

Ez

= −

40

80

30

60

Qbun  10 pC

40

20
10

20

0
0

0.2

0.4
0.6
z, m

0.8

1

Figure 1: Longitudinal expansion of a short bunch due tothe space-charge forces in one meter drift space. The bunchenergy is 5 MeV, the bunch length is initially 30 µm. The
bunch charge is indicated. Its transverse size in both cases,
is kept at ≈ 1 mm with a solenoid, the field of which isshown as dotted lines.
are kept at σr = 1 mm using a solenoid lens, the Bz component of which is shown as a dotted line in the figure. The
one meter drift space is necessary for beam line components between the gun and the plasma wake-field accelerator. It is also the approximate length of the undulator. A
100 pC bunch becomes more than 5 times longer, while theexpansions of a 10 pC bunch is acceptable. Hence, in order
to fill one bucket of the plasma wake field accelerator thebunch charge should be maintained at or below 10 pC.

COMPUTER MODELkx
cos(kx x)sin(ky y)cos(ωt − kz z)
kzwith kx = n π/a, ky = m π/b, k 2 = kx2 + ky2 + kz2 .

The interaction is calculated via the innerproduct v · E
for each particle at each time step for each mode without
any averaging. This model is very general, includes spontaneous and stimulated emission and covers FEL-interaction
from start-up to the saturated regime. The undulator field is
calculated with RADIA and introduced into GPT via a field
map.

RADIATION FROM ONE (SUB)-BUNCH
The shorter the bunch the stronger the spontaneous radiation from that bunch. The total radiated power decreases
rapidly when the bunch length increases.[5] Fig. 2 gives
the total radiated power as a function of the (initial) bunch
length expressed in Joule per Coulomb squared for a bunchcharge of 10 fC and for a bunch charge of 10 pC. We seethat the radiation is proportional to the square of the bunchcharge, which is typical for spontaneous emission of extremely short bunches.
101015 J C2

100

Wrad

Σz Μm

120

60

B mT

Qbun  100 pC

140

8
6

Qb 
Qb 

10pC
10fC

4
2
0

Codes
RADIA subdivisions
GPT field map divisions
Number of modes
No of particles

RADIA, GPT, MATHEMATICA

3,3,3
0.5, 0.5, 0.375 mm
100 < Nm < 1000
1000 < Np < 10 000

Table 3: Simulation parameters
3D particle tracking simulations have been carried out
with the General Particle Tracer Code (GPT), in the combined field of radiation, undulator and space charge. The
radiation is self consistently calculated with a custom
model, similar to the one presented at EPAC[4]. The mode
frequencies used in the model were chosen to be multiples
of an imaginary gun repetition frequency, such that the radiation pattern repeats itself after a distance which is much
longer than the electron bunch or sequence of bunches.
This way the set remains complete with a reasonable number of modes.
The modes used are the HEnm modes with n = m = 1
of a corrugated waveguide without losses.
Ex= sin(kx x)sin(ky y)sin(ωt − kz z)

0.2

0.4
0.6
Lb Λpmw

0.8

Figure 2: Radiated Energy per square Coulomb versus
bunch length for a single sub-bunch. For bunch length
smaller than half the PMW-length, the total radiated power
is proportional to the square of the bunch charge.
The spectral evolution from ”high” and low bunchcharge has the same profile and is shown in fig. 3 for abunch length of 30 µm (0.3λpmw ). The 3D representation eases interpretation, while below the calibrated contour plots give contours of constant power per mode. The
bunch position in the undulator (and in time) increases frombottom to top. For the low bunch charges, the final level(green) is reached at the end of the undulator, while thislevel is already reached only after a few cm for a high bunchcharge.

RADIATION FROM SEQUENCE OF
BUNCHESThe total energy radiated by a sequence of sub bunches
depends on the inter sub-bunch spacing. It is maximum

FEL Technology

472

Qbun  10 pC

Ln WradQbun  10 fC

J C2  

C.A.J. van der Geer et al. / Proceedings of the 2004 FEL Conference, 470-473

35
34
33

Qsb  10pC
Qsb  10fC

32
1.6

z m

z m

1.2

1.2

0.9

0.9

0.6

0.6

0.3

0.3

2.8
3.
3.2
Freq . THz

1.8

2
2.2
DbbΛpmw

2.4

Figure 4: Total power radiated by a sequence of ten subbunches as a function of the distance between them. Whenthe charge per sub-bunch is low, the maximum radiation occurs when Dbb is around a multiple of the PMW. However,at the nominal bunch charge of 10 pC per sub-bunch thisdependence almost disappears due to stimulated emission.
see peaks at both the second and third harmonic of 3 THz
but at low bunch charge these peaks are much narrower andmore distinct.
2.8
3.
3.2
Freq . THz

CONCLUSION
Figure 3: Spectral evolution for a single bunch of 30 µm
for the indicated bunch charge. The upper plots are on alinear scale to help interpretation of the contours of constant intensity on a logarithmic scale. The contour distanceis 3 dB.
when the individual bunches radiate in phase, which iswhen Dbb = n λpmw with an integer value for n. This isshown in fig. 4, which shows the total radiated energy at theend of the undulator as a function of the ratio Dbb /λpmw .
This dependence can be used to measure the inter bunch
distance. At a higher bunch charge, however, the pronounced peak at Dbb = λpmw disappears, because of stimulated emission.
The evolution of the spectrum radiated by a sequence of
10 sub-bunches is given in fig. 5 for the case that the interbunch distance Dbb = 2 λpmw . The bunch charge Qsb is
10 fC in the plots at left and 10 pC in the plots at right. The
plots are similar to those in fig. 3, however, in this case
we see that at higher bunch charge the generated spectrum
broadens and the power level flattens in the second half of
the undulator.

HIGHER HARMONICS
The short bunches not only radiate at the first harmonic
but also produce significant radiation at higher harmonics. Fig. 6 shows the spectra generated by the sequence of
30 µm sub bunches with Dbb = 2.05 λs for 0.1 pC and forthe nominal 10 pC charge per sub-bunch. In both cases we

TUPOS29

The plasma wake field accelerator of the Alpha-X
project requires extremely short injected bunches in order to deliver a reasonable low energy spread at its output. These bunches are produced by a RF-photoinjector
but expand rapidly due to their space-charge, in the space
between the gun and the wakefield accelerator. If, however, this bunch is split into a sufficiently large number of
equidistant sub bunches, fitting into the buckets of the accelerating field, this problem can be solved. It is shown
that, for a typical sub bunch of 5 MeV, 10 pC, 30 µm(100 fs) the parameters of the bunch sequence can be tested
without the plasma wave accelerator by monitoring the radiation that it produces in the undulator.

REFERENCES[1] D.A. Jaroszynski and G. Vieux, Lasers and Particle Beams,(2003) Coherent spontaneous emission.
[2] S. B. van der Geer, M. J. de Loos, The General Particle
Tracer Code, Thesis TU Eindhoven 2002, ISBN 90-3861739-9;
Pulsar Physics, General Particle Tracer, http://www.pulsar.nl[3] B.J.A Shepherd and J.A. Clark, ”Magnetic Design of a focusing undulator for Alpha-X”, proceedings EPAC 2004.
[4] M. J. de Loos, C. A. J. van der Geer, S. B. van der Geer,
3D Multi-Frequency FEL Simulations with the General
Particle Tracer Code, EPAC 2002, Paris, France, pp.849;[5] D.A. Jaroszynski et al. PRL 71, (23), 3798-3801 (1993)

C.A.J. van der Geer et al. / Proceedings of the 2004 FEL Conference, 470-473

Qsb  10 fC

Qsb  10 pC

Qsb  10 fC

Qsb  10 pC

z m

z m

1.2

1.2

0.9

0.9

0.6

0.6

0.3

0.3

2.6

473

2.6

2.8
3.
Freq. THz

2.8
3.
Freq. THz

Figure 5: Spectral evolution from a sequence of ten subbunches separated by 2.05 λpwm , the position of the peakin fig. 4. On the left are the results for Qsb = 10 fC, whileon the right Qsb = 10 pC. The 3D plot aids interpretation.
The contour distance is 3 dB.

PmodedBm

0
Qb10. pC

20
40
60
80

Qb0.1 pC

100
3

4

5

6
7
Ν THz89Figure 6: Spectra generated by a sequence of 10 subbunches, each with the indicated charge.

FEL Technology

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H. H. Lu et al. / Proceedings of the 2004 FEL Conference, 474-477

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FEL Technology

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H. H. Lu et al. / Proceedings of the 2004 FEL Conference, 474-477

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FEL Technology

478

Y. T. Ding et al. / Proceedings of the 2004 FEL Conference, 478-480

STUDY ON THE PLANAR UNDULATOR SCHEME WITH FOCUSINGPROPERTIES FOR PKU-FEL*
Yuantao Ding#, Jia’er Chen, Senlin Huang, Yuangang Wang, Kui Zhao, Jiejia Zhuang
IHIP, Peking University, Bejing, 100871, China
Abstract
An IR range SASE FEL test facility will be built at
Peking University. The project is designed to get the
SASE FEL at 7 micron driven by a superconducting
accelerator. A hybrid planar Nd-Fe-B undulator isemployed and the optimization of the external focus
system for the undulator is studied. In the PKU-FEL
facility, the electron energy is about 30-40 MeV. The
combined function undulator with FODO lattice imposesquite stringent tolerances on the strength of the quads. To
solve this problem, the weak natural focusing of theundulator in the vertical plane together with horizontally
focusing quads, is proposed to supply the focusing in thefacility. The combined function undulator of FOFO latticeand FF lattice in the horizontal plane are studied.
Compared with the FODO lattice, the FOFO and FF
lattice make the saturation a bit longer and therequirements of the field accuracy for the focusing system
are much reduced.

INTRODUCTION
Short-wavelength FELs are primarily directed toward
x-ray regime at wavelength down to 1 Å. Such a source ofcoherent laser-like x-rays would have many applications[1]. SASE mode is one of the best methods to get shortwavelength FEL.
Table 1 The main parameters of PKU-FELElectron beam
Energy20-40MeV
Peak current
200A
RMS emittance
5mm.mradRMS energy spread
80keV
Bunch duration~ 1ps
Undulator
Period length
27mm
K parameter
1.5
Undulator length
5m
FEL
Wavelength
7μm
Saturation length~4.5m
Saturation power~80MW
PKU-FEL facility is an ideal platform to study thephysical and technical issues of single pass SASE FEL
and high average power FEL. Peking University
Superconducting Accelerator Facility (PKU-SCAF) [2],which comprises a superconducting RF photoinjector and___________________________________________* Work supported by Chinese department of Science and Technology
under the National Basic Research Projects No. 2002CB713600.
#
dingyt@pku.edu.cn

TUPOS33

superconducting main linac, will be used to drive FELs.
The main coupler and cryostats are designed to work at
CW mode. At the first stage, SASE FEL experiment atwavelength of 7 µm will be studied [3]. In this paper, theundulator focusing structure is studied.

THE COMBINED FUNCTION
UNDULATOR
Undulator is the most prominent FEL specificcomponent. Given electron beam and undulator
parameters, the radiation wavelength is determined by aresonance condition

λ = λw (1 + aw 2 ) / 2γ 0 2
where aw = K /2 for planar undulator, γ 0 is related tothe average beam energy. The undulator has to provide asinusoidal magnetic field so that FEL process can takeplace, and it also has to keep the beam size small over thewhole undulator length. A planar hybrid permanent
magnet undulator combined with a superimposed periodic
quadrupole lattice structure (Four Magnet Focusing
Undulator, 4MFU[4]) is adopted at PKU SASE FEL[5].
321

Figure 1: The scheme of combined function
undulator, 1: magnets for undulator field; 2: poles;
3: focusing magnet arrays
We optimized the undulator parameters according to thefitting numerical solutions of the coupled MaxwellVlasov equations [6]. The electron beam parameters I, εn,σe are fixed at nominal values given in table 1. The beta
function is used the optimized value.
For this undulator used in the IR range FEL, the weaknatural focusing in the vertical plane can be used. For
example, while the energy of the electron beam is 35MeV,
the average beta function in the vertical plane is about

Available online at http://www.JACoW.org

479

Y. T. Ding et al. / Proceedings of the 2004 FEL Conference, 478-480

FODO scheme
First the focusing magnet arrays were calculated as
FODO structure. According to the optimization, the
FODO period length is 8λw with focusing field gradient of
17T/m and dispersing field gradient of 14T/m at x
direction. With this FODO lattice and natural focusing of
the planar undulator, average beta functions of 26cm atboth x and y direction are obtained. Figure 2 shows theelectron beam rms size along undulator in x and y
direction. The average beam sizes are almost equal in thetwo directions [7]. Figure 3 gives the FEL power along
undulator. The undulator field is assumed to be ideal, andthe influences of different rms quadrupole offsets to the
FEL saturation are also shown in Figure 3.

FOFO scheme
The FODO lattice in the undulator keeps the transverse
beam dimensions within a well specified variation. But
the alignment precision of quadrupole is high. Since thenatural focusing keeps the beam dimension small in thevertical plane, we put the external focusing quadrupole
only in x direction. So the external focusing system is a
FOFO structure. The optimized parameters are that thefield gradient is 2T/m. The length of the focusing
quadrupole is 2λw and the the drift length is 10λw. With
this structure, the average transverse beam size at x
direction is bigger than that of at y direction, as showed in
Figure 4. From Figure 5, we can see that the influences of
the quadrupole offsets to the FEL saturation power are
much decreased, and the saturation length is about 4.2m.
electron beam size (m)30cm. In the design of the external focusing structure, thenatural focusing in the vertical plane will be included. The
FODO, FOFO and FF structure is calculated with
GENESIS1.3 in steady state mode in this paper.

rms electron beam size (µm)

180
170
160

2.6x10-4

2.4x10-4

2.2x10-4

2.0x10-4

1.8x10-4

1.6x10-4

1.4x10-4

1.2x10-4

1.0x10

-4

-1

150

0

1

2

3

z (m)

4

5

6

7

Figure 4: The transverse rms electron beam sizewith FOFO focusing scheme. The solid black line
shows the beam size at x direction, the dashed redline shows that at y direction.

140
130
120
110

8

10

2

z (m)

3

4

A
B
C

7

10

5

6

10

Figure 2: The transverse rms electron beam sizewith FODO focusing scheme, the solid black line
shows the beam size at x direction, the dashed
red line shows that at y direction.

5

10

power (W)

1

4

10

8

1x10

7

9x10

3

10

A:
B:
C:

7

8x10

7

2

7x10

10

7

6x10

1

10

8

1x10
8

10

7

9x10

7

7

D
E
F

7

8x10

5x10
4x10

0

10

7

3x10

7

7

10

7x10

-1

7

2x10

10

7

6x10

7

1x10

7

5x10
6

10

4x10

0

7

Power (W)

3x10
5

10

3.5

-2

10

7

7

1

2

4.0

3

z (m)

4.5

4

5.0

5

6

2x10

7

1x10

2.5

3.0

3.5

4.0

4.5

5.0

4

10

Figure 5: The influences of the rms quadrupole
offsets to FEL gain with FOFO focusing scheme.
The undulator field is assumed to be ideal. The lines
marked with A, B, C mean that the quadrupole
offsets are 0, 100µm, 200µm respectively.

3

10

D
E
F
G

2

10

1

10

0

10

0

1

2

z (m)

3

4

5

Figure 3: The influences of the rms quadrupole
offsets to FEL gain with FODO scheme. The
undulator field is assumed to be ideal. The lines
marked by D, E, F, G mean that the quadrupole
offsets are 0, 30µm, 50µm and 80µm
respectively.

To get a round beam size in the transverse section, we
can increase the strength of the field gradient of the
FOFO structure. When the field gradient is increased to
4.5T/m, the average beam size is nearly round. In thiscase, the alignment precision of quadrupole is muchstricter than that in Figure 5. To make the gain reduction

FEL Technology

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Y. T. Ding et al. / Proceedings of the 2004 FEL Conference, 478-480

less than 10%, the quadrupole offsets have to be smaller
than 70µm.

FF scheme
In fact, the FOFO scheme can be transferred to FF
scheme. That is, the focusing magnet arrays are put in thefull length of x direction. There is no drift length inexternal focusing period. According to the optimization,
the focusing field gradient is 0.8T/m. The rms transverse
beam size is shown in Figure 6. It is nearly round in thetransverse section. The FEL power along the undulator isshown in Figure 7, with different quadrupole offsets. To
get the gain reduction of FEL power less than 10%, thequadrupole offsets have to be smaller than 150µm.

SHORT BUNCH EFFECT
For the IR range FEL, the short bunch effect has muchinfluence at this facility. With the electron beam rms
bunch duration of 1ps, the SASE FEL process was
simulated in the time-dependent mode using GENESIS
1.3 code. There is only a single temporal spike in the FEL
radiation pulse. The radiation FEL pulse has fulltransverse and longitudinal coherence. The fluctuation of
the FEL power and saturation length is large. With thetime-dependent mode simulation, the average saturation
length of the SASE FEL is about 30cm longer than the
result from steady state mode.

SUMMARY-4

Electron beam size (m)1.9x10In this paper, the focusing properties of the 4MFU used
for IR SASE FEL were investigated. For IR range FEL,
the natural focusing in vertical plane and the external
focusing quadrupoles in horizontal plane control theelectron beam transverse dimensions along the undulator.
With the FF focusing scheme, the average beta function isabout 38cm. The design and measurement of an undulator
model with 10 periods have been finished at BFEL lab.
The measurement results agree well with the design
values.

-4

1.8x10-4

1.7x10-4

1.6x10-4

1.5x10

0

1

2

3

4

5

6

Z (m)

Figure 6: The transverse rms electron beam sizewith FF focusing scheme, the solid black line
shows the beam size at x direction, the dashed
red line shows that at y direction.

.

REFERENCES
[1]

8

10

A
B
C

7

10

6

10

5

Power (W)

10

4

10

8

1x10

7

9x10

3

10

7

8x10

A
B
C

7

2

7x10

10

7

6x10
1

10

7

5x10

7

4x10

0

10

7

3x10

7

2x10

-1

10

7

1x10
-2

10

0

1

2

3.5

4.0

3

4

4.5

5

5.0

6

Z (m)

Figure 7: The influences of the rms
quadrupole offsets to FEL gain with FF
focusing scheme, the undulator field isassumed to be ideal, the lines marked with A,
B, C mean that the quadrupole offsets are 0,
100µm, 200µm respectively.

TUPOS33

Patrick G. O’Shea and Henry P. Freund,
Science,2001, 292:1853-1858.
[2] Zhao Kui, Quan Shengwen,Hao Jiankui et al, Nucl.
Instr. & Meth. In Phys. Res. ,2002, A483:125-128[3] Ding yuantao, Huang Senlin, Zhuang Jiejia, Wang
Yugang, Zhao Kui, Chen jiaer, Nucl. Instr.& Meth.
In Phys. Res. 2004, A528, 416-420;[4] Plufger J., Nucl. Instr. & Meth. In Phys. Res. , 1996,
A381:554-559.
[5] Lu Huihua et al, HEP & NP, 2004, 28:902-907[6] Xie Ming, Nucl. Instr. & Meth. In Phys. Res. ,2000,
A445:59-66.
[7] Yuantao Ding, Senlin Huang, Jiejia Zhuang et al,
Nucl. Instr. & Meth. In Phys. Res. ,2004, A528:416420.

481

S.L. Huang et al. / Proceedings of the 2004 FEL Conference, 481-483

BEAM LOADING TESTS ON DC-SC PHOTOINJECTOR AT PEKING
UNIVERSITY*
Senlin Huang, Jia'er Chen, Xiangqiang Chu, Yuantao Ding, Jiankui Hao, Fei Jiao, Lin Lin,
Xiangyang Lu, Shengwen Quan, Guimei Wang, Lifang Wang, Rong Xiang, Binping Xiao, Datao
Xie, Limin Yang, Baocheng Zhang, Kui Zhao# , Feng Zhu , SRF Laboratory,
Institute of Heavy Ion Physics, Peking University, Beijing 100871, China
Abstract
Since the beginning of commissioning in February
2003, lots of tests on the DC-SC photoinjector test
facility have been performed. At present, Q0 of the
1+1/2-cell superconducting cavity has reached 2×108 (at4.2 K) and the average gradient was about 3.5 MV/m inoperation. The DC gun can provide stable electron
beams. When the power of output laser went up to
100mW (266 nm), the average beam current reached 500µA. Beam tests at 4.2 K have been carried out, andsuperconducting acceleration was achieved. Average
current of electron beams was about 100 µA after
acceleration.
Beam loading tests at 2 K will be carried out soon. At
the same time, further investigations are in progress toimprove diagnostics system and to measure theemittance, energy spread and pulse length of electron
beams.

INTRODUCTIONA FEL facility (PKU-FEL [1]) is under construction at
Peking University. Based on PKU-SCAF [2], asuperconducting accelerator facility, PKU-FEL has thecharacteristics of high stability and high average power.
PKU-FEL will run in IR (5~10 µm) and THz (100~3000µm) region. The facility can also provide high-quality
electron beams for experimental studies in some relative
fields such as nuclear physics experiments and so on.
Figure 1 gives a schematic layout of PKU-FEL facility.
One of the most important features is that asuperconducting photoinjector - DC-SC photoinjector [3]is selected to supply electron beams with high average
current and outstanding beam quality.

Figure 1: Schematic Layout of PKU-FEL facility.
As has been reported before, in January 2003, the DCSC photoinjector test facility was constructed. After ayear of commissioning and testing, we haveaccomplished the first successful step. The DC gun can
provide stable electron beams and when the power of
output laser went up to 100 mW (266 nm), the average
beam current reached 500 µA. However we found thatthe 1+1/2-cell cavity had a relatively low Q0 value andmultipacting was encountered frequently which could
not be easily eliminated. For some time low Q0 andmultipacting troubled us so much that we almost could
not go on. To improve the quality of the 1+1/2-cellcavity,sputtering
technology
was
employed.
Experiments show that Q0 of the 1+1/2-cell cavity hasreached 2×108 (at 4.2 K). Moreover, multipacting could
be easily eliminated, and when eliminated at low input___________________________________________* Supported in part by Chinese Ministry of Science and Technology
under the National basic Research Projects (No.2002CB713602)#
kzhao@pku.edu.cn

Available online at http://www.JACoW.org

power (~ mW), multipacting would not appear at higher
input power any more.

QUALITY IMPROVEMENT OF
SUPERCONDUCTING CAVITY
Earlier experiments indicated that the Q0 of the 1+1/2cell cavity was about 107. Furthermore multipacting was
encountered from time to time during experiments. It
seemed that the inner surface of the cavity was not goodenough and earlier mechnical polishing and BCP did notwork well. To improve the quality of the cavity, a dryprocessing method - DC sputtering - was employed.
(Figure 2). DC sputtering has several effects. Fisrt, local
annealing. Through controlling the working pressure,sputtering could take place in different areas. The second
effect is surface polishing. (Figure 3) Sputting could
eliminate small emitters and contaminants. The
improvement of inner surface leads to the improvement

FEL Technology

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S.L. Huang et al. / Proceedings of the 2004 FEL Conference, 481-483

of superconducting performance and also increases themultipacting threshold.

superconducting acceleration was observed through RFphase shift. A curve of electron beam current vs. phasedifference between RF and laser is shown in figure 4.
Acceleration effect could also be observed obviously
from the difference between beam spots at fluorescence
before and after acceleration. (Figure 5 and Figure 6)
Photocurrent Measured from Fluorescence Screen

14

12

10

8

6

4

2

0
-50

0

50

100

150

200

250

300

350

400

450

500

Phase Difference Between RF and Laser (Degree)

Figure 2: DC sputtering device for post-treatment of
1+1/2-cell cavity.

Figure 3: 1+1/2-cell cavity after DC sputtering.
The post-treatment of the 1+1/2 cavity was carried out
step by step, including mechanical polishing, cleaning,
DC sputtering, BCP, HP rinsing with ultrapure water andcleanroom assembly. Main parameters of DC sputtering
were as following: background pressure was 10-6 Pa;
sputtering current was about 2 A. High-purity Ar served
as sputtering gas and working pressure was 17~20 Pa.
Time for DC sputtering was 2 hours.
Experiments after post-treatment validated that DC
sputtering worked remarkably. Q0 of the 1+1/2-cellcavity reached 2×108. Moreover, multipacting could be
easily eliminated, and when eliminated at low input
power (~ mW), it would not appear at higher input power
any more.

BEAM TESTS
Beam loading tests have been carried out at 4.2 K, andwe have succeeded in superconducting acceleration. In
experiments Eacc of the cavity was about 3.5 MV/m (at4.2 K), and energy of electron beams after acceleration
was about 300 keV (after the B-Magnet). Evident

TUPOS34

Figure 4: Electron beam current vs. phase difference
between RF and laser.

Figure 5: Beam spot at fluorescence target, about 2 mapart from photocathode (before acceleration by
superconducting cavity).

Figure 6: Beam spot at fluorescence target, about 2 mapart from photocathode (after acceleration by
superconducting cavity).
Energy gain of the electron beams through thesuperconducting cavity is about 270 keV, which is quite
lower than expected. The reason lies in the relative lower

S.L. Huang et al. / Proceedings of the 2004 FEL Conference, 481-483

Eacc of superconducting cavity. In the operation Eacc ofthis cavity was 3~4 MV/m, and it was hard to enhance
Eacc at 4.2 K. Therefore 2 K beam loading tests isunderway to improve Eacc and thus to reduce phaseslippage in multi-cell cavities.

UPGRADE OF DC-SC PHOTOINJECTOR
DC-SC photoinjector was designed for PKU-FEL,
which aims at high average power FEL. Throughexperiments on the DC-SC photoinjector test facility, we
have validated that the DC-SC photoinjector is a good
choice to provide moderate average current electron
beams with low bunch charge and very high repetition
rate.
Table 1: Parameters of the new photoinjector
2+1/2-cell cavity
Eacc
15 MV/mDrive laser
Pulse length
Spot radius
Repetition rate

10 ps
2 mm
81.25 MHzElectron bunch
Charge/bunch
EnergyEnergy spread (rms)
Emittance (rms)<60 pC
3.72 MeV
1.68%
2.0 mm-mrad

Experiments on the test facility also indicate that tofulfil the requirements of PKU-FEL to the injector, it isnecessary to upgrade the core elements of photoinjector-

483- DC gun and superconducting cavity. Voltage of the DC
gun will rise to 150 keV, and accordingly, the structureof high voltage terminal will be improved which willlead to some changes in the structure of cryostat. A
2+1/2-cell cavity will be employed for the new injector.
Design and optimization have been accomplished.
Stamping technology and electron beam welding
technology will be used to fabricate the new cavity.
High-purity Nb plates from Ningxia of China will bechosen for the 2+1/2-cell cavity. Parameters of the newphotoinjector are list in Table 1.

SUMMARY
We have found a new and simple method to processsuperconducting cavities. Through this method, DC
sputtering, the quality of cavity improves remarkably in a
dry way.
Beam tests (at 4.2 K) on DC-SC photoinjector test
facility have been carried out. The results of beam tests
agree with those of simulations. At present 2 K beam
tests are in progress.

REFERENCES[1] Kui Zhao, et al., Proceedings of APAC 2004,
Gyeongju, Korea.
[2] Zhao Kui, et al., Nucl. Instr. and Meth. A 483 (2002)
125.
[3] Zhao Kui, et al., Nucl. Instr. and Meth. A 475 (2001)
564.

FEL Technology

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X. Lu et al. / Proceedings of the 2004 FEL Conference, 484-486

THE DRIVE LASER SYSTEM FOR DC-SC INJECTOR*
Xiangyang Lu#, Lin Lin, Fang Wang, Shengwen Quan, Kui Zhao
Institute of Heavy Ion Physics, Peking University, Beijing 100871
Abstract
PKU-SCAF has developed a photoinjector which adopt
a 1+1/2 cell super conducting cavity and DC electron gun.
We also developed a low cost drive laser system for thephotocathode DC gun to provide high average beam
current. This laser system include a commercial highrepetition rate, ps, all solid-state laser, the home madeSHG and FHG, Fourier relay optics and the uniform
illumination optics. The test results shows the output
power at 266 nm of the laser system is more than 1.2W
and got more than 500 µA beam current from CsTe
cathode from the DC gun.

INTRODUCTIONFEL needs high quality electron beam. For theadvantages of laser driven photo-electron gun, manylaboratories choose this approach. In general, the beam
design requires the drive laser should be operated withhigh pulse energy stability, short pulse duration and hightiming precise for a long term. Some of the applications
need high peak power and for high average current needs
the high average power. The drive laser system became
complex under those requirements. That means both thelaser cost is high and it needs experts to keep the daily
maintenance.
A photo-injector which adopts a 1+1/2 cell super
conducting cavity and DC electron gun has beendeveloped at Peking University for years [1], [2]. This
design is very good for average current acceleration.
Peking University RF superconducting acceleration study
group is a relative small team. For this reason, we need agood drive laser system to operate, develop this injector,
which should be low cost, low maintenance. To study thecharacters of the injector and exam the physic
conceptions, the drive laser also have to fit some special
requirements, such as to provide the uniform beamprofile.
After investigating the laser market, we choose GE100-XHP, TBWP, Switzerland, laser as the main part ofour drive laser system. According to the requirement ofcathode material, CsTe, we develop the second and fourthharmonic generator, beam transport system and designed
the beam shaping device. Now, this system is daily
operated in the laboratory and the output of the photoelectron gun reaches more than 500 µA with the homemade CsTe cathode. In this paper, authors describe thedrive laser system and its specifications.
___________________________________________* supported by NSFC (Grand No: 10299021&50132010) and National
Basic Research Program (973) (Grand No: 2002CB713602).
#
xylu@pku.edu.cn

TUPOS35

LASER AND SHG/FHG
The Series GE-100-XHP are passively mode-locked
diode-pumped
solid-statelaser
systemsusing
semiconductor saturable absorber mirrors (SESAMs). The
GE-100-XHP is combined of a semiconductor pump laserand saturable absorber and yields very clean picosecond
pulses with exceptional amplitude and phase noise
performance. The detail descriptions refer to TBWP
documents [3].
There is a built-in nanosecond-response photodiode at
the laser head back panel which not only allows the user
to confirm pulsed operation but also provides the signal
for feedback control. In our system, the CLX-1100 timing
synchronization with the phase-locked-loop feedback isused.

Fig. 1 The drive laser system for DC-SC injector.
In the fig, f = 100 mm f ’ = 3400 mm,“1” is the special flattener, “2” is the cathodeThe working function of CsTe requests lightwavelength should be shorter than 270 nm. For thisreason, we developed SHG and FHG system. Second
harmonic generation (SHG) is realized with a criticallyphase-matched Potassium Titanyl Phosphate harmonic

Available online at http://www.JACoW.org

485

X. Lu et al. / Proceedings of the 2004 FEL Conference, 484-486(KTiOPO4 or KTP) crystal. The fundamental laser (1064nm) is focused by a lens (focus length is 200 mm) thenpass into a 7×7×10 mm KTP crystal cut in the x-y plane
for type II. A second lens (focus length is 100 mm) is
positioned after the KTP crystal to realize a 6f system tocollimate the 532 nm, second-harmonic beam. The
fundamental and second harmonic beam are separated by
a 45° harmonic separator which reflecting more than 98%
1064 nm light and transmitting more than 95% 532 nm
light.
Table 1: The parameters of the laser system
Wave length
(nm)

1064

532

266

Power
(W)

10

>4

> 1.2

Pulse Width
(ps)

9.9

Fig. 2 The two elements beam shaping system

Repetition
rate (MHz)

81.25

Power
Stability~ 1%

Timing jitter
(ps)

< 0.5

The beam spot size on the cathode surface is required
from 2 to 5 mm. If the beam spot is too small, the highpower density will damage the cathode. If beam spot is
too large, the electron beam profile will be also too larger.
To solve this problem, the Fourier relay technique is used.
This approach could also maintain a clean transverse
mode and improve the beam spot pointing stability.
The primary aperture position is chosen at the beam
waist of the fundamental beam, before the SHG crystal.
The first lens of focal length 200 mm is placed the
distance 200 mm after the primary aperture and 200 mm
before the KTP crystal. As the description above, lens L1and L2 are in 6f relation. Then the other lenses are placedin 4f relation. The final is a composite lens of focal lengthof 3400 mm. By tuning the gap between the convex andconcave lens, the beam spot size could be adjusted. The
typical UV beam spot size is about 3 mm.

Spot size on
Target (mm)~3

The resulting second-harmonic beam passes through alens (100 mm) that focuses it into a 6×5×15 mm CLBO
crystal (θ = 62.5°, ϕ = 90°, type I). A Pellin Broca prism
separates the unconverted 532 nm light from the UV
beam. To avoid the CLBO crystal damaged by water
vapor, it is installed in a home made heating oven. Theoven temperature is keen in 105°C.
The maximum 1064-532 nm conversion efficiency isabout 50%. After adjusting the tilt of KTP crystal, themaximum UV power has been reached 1042 mW and the
532 nm beam was at 4.35 W. It should be noted that theUV transmission of the AR coating at each surface of thelens is 90% and the UV losses of the Pellin Broca prism
are about 10%, a total UV power of more than 1.4 W
should be generated . If there is an AR coating of 266 nm
on the CLBO crystal surface, the measured power also
should be higher.

LASER BEAM TRANSPORTATION AND
BEAM SHAPING
The distance from our laser room to the cathodeposition is about 8 m. The fundamental laser beam
divergence is about 1 mrad. After SHG and SHG, thebeam divergence is even more, e.g., the walk-off of
CLBO is about 1.2°. So, when the drive laser reaches thecathode, the beam spot size will be larger than 100 mm.

Fig. 3 The single element beam shaping and thesimulation result

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X. Lu et al. / Proceedings of the 2004 FEL Conference, 484-486

Beam dynamic simulation result shows that if laser
beam spatial profile were uniform, the accelerated beamemittance would be smaller. To prove this achievement,
we like to add a spatial flattener in our system. There arenumbers approach could produce the uniform beamprofile [4], [5]. We have designed both two elements andsingle element beam shaping system. The simulation
results are shown in Fig.2 and Fig.3. From the simulation,
there is not much different between two approaches. After
further study, we will decide to adopt which one.

CONCLUSIONS
We use a commercials laser, GE-100-XHP, as the mainparts to set-up our drive laser. The home made SHG and
FHG performed high efficiency. This is a compact andlow maintenance system. By use of the Fourier relay
technique, the laser transportation is well and the typicalbeam spot on target is about 3mm. With this system, we
have got electron beam current more than 500 µA fromthe home made TeCs cathode.
We also designed beam shaping system to get theuniform beam profile. The simulation shows both single
and two elements system can generate good beam profile.

TUPOS35

If the spatial flattener is adopted, the Fourier relay systemshould be redesigned.

REFERENCES[1]. Kui Zhao, Jiankui Hao, Yanle Hu, et al., Research on
DC-RF superconducting photocathode injector for highaverage power FELs, Nucl. Instr. Meth. A475 (2001)
564-568.
[2] http://apac04.postech.ac.kr/[3] http://www.tbwp.com/Time_Bandwidth/[4] David L.Shealy ,“Theory of Geometrical Methods
for Design of Laser Beam Shaping System,” San Diego,
2 August 2000 SPIE’s 45 th Annual Meeting, Laser Beam
Shaping Conf., 4095-011[5] J.A.Hoffnagle and C.M.Johnson, “ Design andperformance of a refractive optical system that converts a
Gaussian to a flattop beam, ” Appl.Opt.39,54885499(2000)[6] S. Zhang, G. Neil and M. Shinn, “Single-element
laser beam shaper for uniform flat-top profiles” OpticalSociety of America

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Chen Nian. Chen et al. / Proceedings of the 2004 FEL Conference, 487-489

SIMPLIFIED METHOD FOR EXPERIMENTAL SPECTRAL RATIOCALCULATION OF CHG-FEL*
Nian Chen#, Pengfei Zhang, Duohui He, Ge Li, Shancai Zhang, Yuhui Li
National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, China

Abstract
Coherent harmonic generation free-electron laser(CHG-FEL) acts as a harmonic amplifier of the seedlaser. The spectral ratio, which is defined as the ratio of
coherent radiation intensity and incoherent radiation
intensity in infinitesimal bandwidth and solid angle
aperture, can evaluate the performance of CHG-FEL. In
the experiment, we can only get the experimental integral
ratio integrated over the actual bandwidth and solid angle
aperture of the radiation measurement system. Because
the coherent radiation and incoherent radiation are very
different in the spatial and spectral structure, theexperimental integral ratio is greatly influenced by themeasurement system and can not be directly used toevaluate the performance of CHG-FEL. So we must
calculate the experimental spectral ratio according to theexperimental integral ratio, the bandwidth and solid angle
aperture of the measurement system and the parameters of
CHG-FEL. And our work is to give a simplified method
for the calculation of experimental spectral ratio.

INTRODUCTION
Coherent harmonic generation free-electron laser(CHG-FEL) is one way of storage ring FEL [1-3]. The
main component of CHG-FEL is optical klystron (OK),which consists of three sections - two undulators
separated by a dispersive section. In the first undulator(modulator), an energy modulation is imposed on theelectron beam by interaction with a seed laser. The energy
modulation is converted to a coherent spatial density
modulation as the electron beam traverses the dispersion
section which is a single-period wiggler with strong
magnetic field. The second undulator (radiator), tuned toa higher harmonic n0 (n0=1, 2, 3…) of the seed laser
wavelength λs, causes the micro-bunched electron beam toemit coherent radiation whose fundamental wavelength is
λs/n0. CHG-FEL acts as a harmonic amplifier of the seed laser.
It becomes high-gain harmonic generation free-electron
laser (HGHG-FEL) if the radiator is long enough for
amplification until saturation is achieved [4].
In CHG-FEL experiment, we can obtain, on axis, thecoherent (with seed laser) and incoherent (without seedlaser) radiation at the wavelength λs/n0nr (nr=1, 3, 5…)from radiator and the incoherent radiation at the
wavelength λs/nm (nm=1, 3, 5…) from modulator. The aimof CHG-FEL is to gain the coherent radiation at the
wavelength λs/n0nr. For example, in the experiment of___________________________________________*This work is supported by Foundation of National Key Program for
Basic Research of China (2001CCB01000), National Natural Science
Foundation of China (20173055), Natural Science Foundation of Anhui
Province (01046202).
#
chnian@mail.ustc.edu.cn

Available online at http://www.JACoW.org

CHG-FEL on the ACO storage ring at Orsay of France,
they have obtained the 3rd and 5th harmonic coherent
radiation of the seed laser wavelength 1064nm using asymmetrical OK (n0=1, nr=3, 5) [3]. And for our
experiment, the OK is unsymmetrical, which benefits the
HGHG study. It has two working modes: first, to obtainthe 2nd harmonic coherent radiation of the seed laser
wavelength 532nm (n0=2, nr=1); second, to obtain the 3rd
harmonic coherent radiation of the seed laser wavelength
1064nm (n0=1, nr=3) [5].
The performances of different CHG-FELs can beeffectively evaluated by the experimental spectral ratio
R’spe which can be approximately calculated byexperimental integral ratio R’int and the ratio of theoretical
spectral ratio Rspe and theoretical integral ratio Rint:''
Rspe= Rint× Rspe Rint .
(1)
R’int can be directly measured in experiment, and Rspe/Rint
can be calculated according to the bandwidth and solid
angle aperture of the measurement system and theparameters of CHG-FEL.
We give a simple method to calculate the Rspe/Rint inthis paper. In the following discussion, the variables with
subscript u, m, d and r represent parameters of any
undulator, modulator, dispersive section and radiator
respectively.

UNDULATOR RADIATION
When an electron beam traverses the periodic magnetic
field provided by an undulator, it emits radiation at thewell-known resonant wavelength λ and its nth odd
harmonics λ/n. λ is defined asλ=λu(1 + K u2 2 ) .
2nγ 2

(2)

Here, λu is the undulator period, γmc2 is the electron beamenergy, m is the electron mass, c is the light speed,
Ku=eB0λu/(2πmc)=93.37B0λu is the undulator parameter, e
is the charge on the electron, and B0 is the maximum onaxis magnetic field strength of the undulator.
The radiation energy by a single electron per unit solid
angle (dΩ) and per uint wavelength (dλ) is given by [6]:22πi ( cτ − n⋅ x (τ ) )
+∞
d2I
e2
dτ , (3)=n × ( n × v (τ ) ) e λ
2 ∫−∞dλ dΩ 1e-1 4πε 0cλwhere ε0 is permittivity of vacuum, n=(sinθcosφ, sinθsinφ,cosθ) is the unit vector from the point of emission to theobserver, v=(vx, vy, vz) is the electron velocity, and x=(x, y,z) is the electron trajectory. The magnetic field in an ideal
planar undulator isgiven by By(z)=B0cos(2πz/λu), for0≤z≤Nuλu, with Bx(z)=Bz(z)=0, Nu is the period number.
The electron velocity and trajectory can be calculated
according to B(z), and then with equation (3), the

FEL Technology

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Chen Nian. Chen et al. / Proceedings of the 2004 FEL Conference, 487-489

radiation energy can be calculated at any solid angle andwavelength. Here, we only give the single-electron
radiation intensity on axis at the resonant wavelength:θ = 0, λ = λd2 Idλ dΩ 1e−1=

e 2 n 2 N u2γ 2 K u2

4πε 0 c (1 + K

2
u

2)

2

Fn2 ( K u ) ,

(4)

with




kK u2
kK u2
 − J k +1  , (5)Fn ( K u ) = J k −1 
2
2




2  4 (1 + K u 2 ) 
2  4 (1 + K u 2 ) here Jn(x) is the Bessel function of nth order.
For a bunch with Ne electrons whose distribution is ρ(x,y, z), according to equation (3), the radiation intensity ofthe electrons is given as follows:
d2 I
d2 I
=
dλ dΩ N e−1 dλ dΩ 1e-1e
2 . (6)× ∫∫∫ ρ ( x, y, z ) e

−i

2π

λ

(θ cos ϕ ⋅ x +θ sin ϕ ⋅ y + z )dxdydz

INCOHERENT RADIATION OF CHG-FEL
The incoherent radiation at measured wavelength
λs/n0nr, not only comes from radiator but also frommodulator when n0 is an odd number. From the principleof CHG-FEL and resonant relation (1), we obtainλr(1+Kr2/2)=λm(1+Km2/2)/n0. And combining this equation
with equation (4), the relation between the single-electron
radiation intensity on axis at the wavelength λs/n0nr frommodulator d2Im/dλdΩ and that from radiator d2Ir/dλdΩ canbe calculated as follows:θ = 0, λ =d2 Im
dλ dΩ 1e−1

λs
n0 nr

θ = 0, λ =

= P×

d2 Ir
dλ dΩ 1e−1

n0 nr

,

(7)

 λm2 N m2 K m2 Fn20 nr ( K m )n0 = 1,3,5, 7L. (8)P =  λr2 N r2 K r2 Fn2 ( K r )
r
0
=
2,
4,
6,8
n
L
0

Without seed laser, the energy and spatial density ofelectrons are not modulated. Thus, electrons can be
regarded as uniformly distributed over the radiation
wavelength and the radiation fields of two individual
electrons are incoherent. The incoherent radiation
intensity is proportional to the number of electrons in thebunch, we getλsθ = 0, λ =2n0 nr
d 2 I inc
2 d Ir= N e (1 + P )dλ dΩ N e−1dλ dΩ 1e−1

λs
n0 nr

. (9)

e

The bandwidth and solid angle aperture of incoherent
radiation are far larger than those of the measurement
system. So, within bandwidth and solid angle aperture of
the measurement system, the incoherent radiation
intensity can be regarded as invariable which is equal tothe value on axis at the wavelength λs/n0nr.

TUPOS36

With seed laser, the distribution of electrons is nolonger uniform after the energy and spatial density
modulation. The initial distribution of electrons can beapproximately expressed as Gaussian distribution:
ρ0 ( x, y, z ) =

−

Ne

32
( 2π ) σ xσ yσ z

e

x2
2σ x2

−

y2
2σ 2y

−

z2
2σ z2

,

(10)

where σx and σy are transverse sizes of bunch, σz is thelongitudinal size of bunch. The distribution of electrons at
the exit of the dispersive section can be expressed as∞ 2nπ  
ρ ( x, y , z ) = ρ0 1 + ∑ 2J n ( nη ) f n cos z   , (11) λs   n =1
with η=4π(Nm+Nd)∆γm/γ and fn=exp{-8[nπ(Nm+Nd)σγ/γ]2},
where Nd is the parameter of dispersive section, 2πNd
represents the dephasing created by the dispersive section
between an electron and the seed laser wave,∆γm/γ=eNmλmKmEsF1(Km)/(2γ2mc2) is the maximum
relative shift of the electron induced by the seed laser, Es
is the electromagnetic wave amplitude of seed laser, σγ/γ
is the energy spread of the electron beam [1]. As aconsequence of Equations (6) and (11), we get thefollowing expression for the coherent radiation intensityof CHG-FEL:
d 2 I coh
= N e2 J n20 nr ( n0 nrη ) f n20 n r
dλ dΩ N e−1
e

−

4π 2

×e λ

2

−4π

2

×e

λs

with

θ = 0, λ =COHERENT RADIATION OF CHG-FEL(θ cos ϕσ +θ sin ϕσ )
2

2

2
x

1 n n σ z2  − 0 r  λ λs 

2

2

2
y

.

(12)

2

2

d Ir
dλ dΩ 1e−1

According to the above equation, we give thebandwidth ∆λcoh and solid angle aperture ∆Ωcoh ofcoherent radiation:
ln2 2
λ2∆λcoh =λ , ∆Ω coh =.
(13)
2πσ xσ yπσ zWithin bandwidth and solid angle aperture of themeasurement system, the coherent radiation intensity can
not be regarded as invariable because ∆λcoh and ∆Ωcoh arevery small.

EXPERIMENTAL SPECTRAL RATIOCALCULATION
According to equations (9) and (12), we can get thetheoretical spectral ratio as follows:θ = 0, λ =λsθ = 0, λ =

λs

n0 nr
n0 nr
d 2 I cohd 2 I inc
Rspe =:
dλ dΩ N e−1dλ dΩ N e−1
.

=

e

1

(1 + P )

2

e

Ne J

2
n0 nr

( n0 nrη ) f

(14)

2
n0 nr

From equations (9) and (12), we can also get thetheoretical integral ratio in bandwidth ∆λ and the solid
angle ∆Ω of the measurement system. Here, we skipped489

Chen Nian. Chen et al. / Proceedings of the 2004 FEL Conference, 487-489

the rather tedious details of the integral and reported thefinal result only as equations (15)-(17): d2 I∫∆λ ∫∆Ω  dλ dcohΩ −1  dΩ dλNe e 

Rint == Rspe I ∆Ω I ∆λ , (15)
2
d I

inc
∫∆λ ∫∆Ω  dλ dΩ −1  dΩ dλNe e 
where2(λ n n )I ∆Ω = s 0 r
4πσ xσ y ∆Ω4π∆Ωcos 2 ϕσ x2 + sin 2 ϕσ y2 )− (16)2(
 σ xσ y 2π e ( λs n0 nr )dϕ × 1 −
2
2
2
2
∫
0
2π
cos ϕσ x + sin ϕσ y





and
I ∆λ =( λs n0 nr )2πσ z ∆λ22 πσ z ∆λ

∫

−

τ

2

( λs n0 nr )2e 2

2πσ z ∆λ2π−

( λs n0 nr )2

dτ .

(17)

Here, we list four particular cases and give theirapproximate expressions.
If ∆λ>∆λcoh and ∆Ω>∆Ωcoh, then:4( λs n0 nr );(18)
Rint = Rspe
8π 3 2σ xσ yσ z ∆λ∆ΩIf ∆λ>∆λcoh and ∆Ω<<∆Ωcoh, then:2(λ n n )Rint = Rspe s 0 r ;2 πσ z ∆λ
If ∆λ<<∆λcoh and ∆Ω>∆Ωcoh, then:(19)

Rint = Rspe

( λs n0 nr )24πσ xσ y ∆Ω

;

(20)

If ∆λ<<∆λcoh and ∆Ω<<∆Ωcoh, then: Rint=Rspe.
For our experiment, the reference [7] gives a set of its
parameters: σx=0.518mm, σy=0.051mm, σz=11.3mm,
n0=2, nr=1, λs=532nm and λ=266nm. According toequation (13), ∆λcoh=0.0017nm, ∆Ωcoh=0.43×10-6rad2. For
theactualmeasurement
system,∆λ=0.15nm,∆Ω=0.12×10-6rad2, we can get Rspe/Rint=192 using
equation (15)-(17). If ∆λ=0.15nm, ∆Ω=1.2×10-6rad2,
Rspe/Rint=478 using equation (18) and Rspe/Rint=678 using
equation (15)-(17). If we have measured the experimental
integral ratio R’int, then, using equation (1), we cancalculate the experimental spectral ratio R’spe.

REFERENCES[1] J.M. Ortega, Y. Lapierre, B. Girard, et al. IEEE
Journal of Quantum Electronics. QE-21 (1985) 909.
[2] R. Prazeres, J.M. Ortega, C. Bazin, et al. Nucl Instrand Meth. A 272 (1988) 68.
[3] R. Prazeres, P. Guyot-Sionnest, J.M. Ortega, et al.
Nucl Instr and Meth. A 304 (1991) 72.
[4] L.H. Yu, M. Babzien, I. Ben-Zvi, et al. Science. 289(2000) 932.
[5] Chen Nian, Xu Hong-liang, Liu Jin-ying, et al. HighPower Laser and Particle Beams. 15 (2003) 524.
[6] J.D. Jackson. Classical Electrodynamics (wiley, New
York, 1965) p.480.
[7] J.Y. Liu, C.Z. Diao, D.H. He, et al. Proceedings of the2003 Particle Accelerator Conference. Portland:
2003.968.

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Chen Nian. Chen et al. / Proceedings of the 2004 FEL Conference, 490-493

MULTI-OBJECTIVE OPTIMIZATION FOR PURE PERMANENTMAGNET UNDULATOR MAGNETS ORDERING USING MODIFIEDSIMULATED ANNEALING *Nian Chen#, Duohui He, Ge Li
National Synchrotron Radiation Laboratory, University of Science and Technology of China, Hefei, Anhui 230029, China

Abstract
Undulator filed errors influence the electron beam
trajectories and lower the radiation quality. Angulardeflection of electron beam is determined by first field
integral, orbital displacement of electron beam isdetermined by second field integral and radiation quality
can be evaluated by rms field error or phase error.
Appropriate ordering of magnets can greatly reduce theerrors. We apply a modified simulated annealing
algorithm to this multi-objective optimization problem,
taking first field integral, second field integral and rms
field error as objective functions. Undulator with small
field errors can be designed by this method within areasonable calculation time even for the case of hundredsof magnets (first field integral reduced to 10-6T·m, second
integral to 10-6T·m2 and rms field error to 0.01%). Thus,
the field correction after assembling of undulator will begreatly simplified. This paper gives the optimizing
process in detail and puts forward a new method toquickly calculate the rms field error and field integrals.

INTRODUCTION
Undulators and wigglers are the main components ofthird-generation synchrotron radiation sources and freeelectron lasers [1]. Undulators are mostly built of
permanent magnets with iron poles (hybrid undulators) orwithout iron poles (Pure Permanent-Magnet undulators or
PPM undulators). The unavoidable remanence
inhomogeneities of these magnets and construction errors
cause the undulator magnetic field errors [2], which affectthe trajectories of the electron beam and lower theradiation quality of undulator or FEL [3]. Angulardeflection of electron beam is determined by first field
integral along the beam axis, orbital displacement ofelectron beam is determined by second field integral
along the beam axis, and radiation quality can beevaluated by rms field error or phase error [4]. To reduce
the undulator magnetic field errors, we need a sufficiently
precise mechanical construction and a certain method to
overcome the influence of remanence inhomogeneities.
That is, we should not only provide a precise method tomeasure the individual permanent magnets and assemble
them to form undulator [5], but also provide anappropriate ordering of undulator magnets before
assembly. And the sorting procedure of ordering is mainly
based on “Simulated Annealing” [6] although “genetic
algorithms”
have also been used [7] and it is widely___________________________________________*This paper is supported by Foundation of National Key Program for
Basic Research of China (2001CCB01000), National Natural Science
Foundation of China (20173055).
#
chnian@mail.ustc.edu.cn

TUPOS37

applied to the PPM undulator where linear superposition
can be used.
We apply a modified simulated annealing algorithm tothis multi-objective optimization problem, taking first
field integral, second field integral and rms field error as
objective functions. And we put forward a new quick
method to directly calculate the rms field error and field
integrals according to remanence and positions ofindividual magnets. Illustrations are drawn from thereconstruction of the first undulator (modulator of optical
klystron) of CHG-FEL for National Synchrotron
Radiation Laboratory.

OBJECTIVE FUNCTIONS
Figure 1 shows the structure of undulator. The
undulator consists of three configuration magnets, which
are horizontal (“H”) magnets with the main remanence inthe horizontal direction, vertical (“V”) and terminal (“T”)
magnets with the main remanence in the vertical direction.
“T” magnets differ from “V” magnets only in width andtheir width is half those of “V” magnets. X, Y, Z are
length, height, width of the magnet. And g is the gap ofundulator magnetic field.

Figure 1: Structure of undulator.
For purposes of discussion, we assume a rectangularcoordinate system with the electron propagation axis in
the z direction, the principal component of the magnetic
field By in the vertical y direction, and the x-z plane being
thus the plane of the electron sinusoidal motion.

Measurement and Calculation of Magnets
To measure all the magnets equivalently, we define areference position with the main component in the
upward vertical y direction. Therefore, for a magnet, theAvailable online at http://www.JACoW.org

491

Chen Nian. Chen et al. / Proceedings of the 2004 FEL Conference, 490-493

remanence components Br1, Br2, Br3 are in the x, y, z
direction respectively. For ideal magnets, Br1=Br3=0. For
real magnets, in general, |Br1|:|Br2|:|Br3| approximately
equals 1:1000:10.
After measurement of individual magnets, we canobtain the values of Br1,n, Br2,n, Br3,n, and here n is theserial number of magnets from 1 to Ntotal (the total numberof all the magnets). We choose N magnets among the Ntotal
according to Br2,n and arrange them to assemble theundulator.
If the magnet is used in the “V” or “T” configuration,
Br1 corresponds to Brx, Br2 to Bry and Br3 to Brz. If themagnet is placed in the “H” position, Br1 corresponds toBrx, Br2 to Brz and Br3 to Bry.
Take the centre of the magnet as the origin of thecoordinate, and the magnetic field in y direction By(x,y,z),
generated by this system outside the magnet, is given by
the following expression:
By ( x, y,z ) = b ( X,Y,Z ) - b ( -X,Y,Z ) - b ( X,-Y,Z )+b ( -X,-Y,Z ) - b ( X,Y,-Z ) +b ( -X,Y,-Z ) (1)+b ( X,-Y,-Z ) - b ( -X,-Y,-Z )For ideal “V” and “T” magnets,
 X  Z   Y 
x -  z -   y - B2  2  
2b ( X,Y,Z ) = r tg -1 
2
2
2 
4π
  x - X  + y - Y  + z - Z  
 
 

 
2 
2   2  
(2)

For ideal “H” magnets,
2
2
2−B  X X  Y  Z b ( X,Y,Z ) = r ln  - x+  x -  + y -  + z -   (3)4π  2 2   2   2  
By of individual magnets can be calculated using
Equations (1), (2) and (3). For calculating rms field errorof undulator, we should record the values in the positions
whose distances from the centre of the magnet are integer
times of Z. “V” magnets are recorded as BV0, BV1, BV2,BV3…. And for “H” magnets, they are BH0, BH1, BH2,
BH3....

Figure 2: Distribution of magnetic field By, 1st integral and 2nd
integral of individual magnet (remanence Br=1T).

Figure 2 shows the distribution of magnetic field By (a),first integral (b) and second integral (c) of individual
magnets (remanence Br=1T).
To get the first integral of individual magnet I1, we
integrate By along the z-axis from –∆z to ∆z, where ∆z isthe distance between the centre of the magnet and themeasured position. Integrating By twice, we can get thesecond integral I2. For magnets with unit remanence (1T),“V” magnets: I1= K1, I2= K1∆z; “T” magnets: I1= K1/2 andI2= K1∆z/2; “H” magnets: I1= 0 and I2= K2. When ∆z is
big enough, K1 and K2 are constants, decided by X, Y, Z, x,
y. In our illustration, X=100mm, Y=23mm, Z=23mm, x=0,
y=Y/2+g/2, ∆z=600mm, K1=2.4143mm, K2=170.78mm2,
Bv0=0.0904T, Bv1=0.0246T, Bv2=-0.0034T, Bv3=-0.0043T;
BH0=0T, BH1=0.0505T, BH2=0.0106T, BH3=-0.0012T.

Field Integrals Calculation of Undulator
For nth real magnets, field integral is given as:
If it is “H” magnet (n=3, 4, 4i-1, 4i...),
 n-1 INT n I1,n = ( -1)  4  ( -1) K1 Br 3 ,n(4)
 n-1 INTn
 I 2 ,n = ( -1)  4  ( -1) K1 Br 3,n ∆ zn + K 2 Br 2 ,n 
If it is “V” magnet (n=5, 6, 4i+1, 4i+2…),
 n-1 INT  I1,n = ( -1)  4  K1 Br1,n(5)
 n-1 INTn-1
 I 2 ,n = ( -1)  4   K1 Br1,n ∆ zn + ( -1) K1 Br1,n 
If it is “T” magnet (n=1, 2, N-1 and N), n-1 INT n
 I1,n = ( -1)  4  ( -1) K1 Br 3 ,n
 n-1 

K
n K1
INT 
 (6)
 
Br 3,n ∆ zn + 2 Br 2 ,n 
 I 2 ,n = ( -1)  4  ( -1)
2
2



For undulator, the first field integral I1 and second field
integral I2 are given as:
N

I1 = ∑ I1,nn=1

N

I 2 = ∑ I 2 ,n

(7)

n= 2

Rms Field Error Calculation of Undulator
The peak values of magnetic field appear at the centreof “V” magnets. So the total number of peak values in theundulator is INT(N/4)-1. The peak value is given as:
Bi = BV 0  Br 2 ,( 4i+1 ) + Br 2 ,( 4i+2 ) 
+ BV 1  Br 3 ,( 4i-1 ) - Br 3 ,4i - Br 3 ,( 4i+3 ) + Br 3,( 4i+4 ) 

+ BV 2  -Br 3 ,( 4i-3 ) - Br 2 ,( 4i- 2 ) - Br 2 ,( 4i+5 ) - Br 2 ,( 4i+6 ) 

+ BV 3 -Br 3,( 4i-5 ) + Br 3 ,( 4i- 4 ) + Br 3 ,( 4i+7 ) - Br 3,( 4i+8 )  (8)+ BH 1  Br 2 ,( 4i-1 ) + Br 2 ,4i + Br 2 ,( 4i+3 ) + Br 2 ,( 4i+4 ) 

+ BH2  Br 3,( 4i-3 ) - Br 3 ,( 4i- 2 ) - Br 3 ,( 4i+5 ) + Br 3,( 4i+6 ) 

+ BH 3  -Br 2 ,( 4i-5 ) - Br 2 ,( 4i- 4 ) - Br 2 ,( 4i+7 ) - Br 2 ,( 4i+8 ) 

Here, i=1,2,…, INT(N/4)-1, is the serial number.
For undulator, the rms field error is given as:

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492

σB B =

Chen Nian. Chen et al. / Proceedings of the 2004 FEL Conference, 490-493

1B

1INT ( N 4 ) - 4

INT ( N 4 ) - 2∑
i= 2(B - B)

2i(9)

MULTI-OPTIMIZATION MODIFIED SA
Simulated annealing (SA) is a technique used to findgood approximate solutions for combination optimization
problem. We apply a multi-optimization modified SA
algorithm (with heating procedure and the best movestrategy based on standard SA) to optimize the problem of
PPM undulator magnets ordering [8]-[9].
The multi-objective functions are (s is a solution):
f1(s): the rms field error of undulator;
f2(s): the absolute value of first field integral;f3(s): the absolute value of second field integral.

Preliminaries• A weighting function S(s) is chosen:
f (s)
f (s)
f (s)
S ( s ) = w1 1
+ w2 2+ w3 3f1 ( s0 )f 2 ( s0 )f 3 ( s0 )(10)Here, w1, w2 and w3 are weighting factors, andw1+w2+w3=1.
• Parameters of the heating procedure are initialized as:h (the heating factor) and Hstep ( the heating length).
• Parameters of the cooling procedure are initialized as:
T0 (initial temperature, calculated in modified SA,
but given in standard SA), α (the cooling factor <1)
and Nstep (the cooling length of temperature step).
• Two stopping criteria are fixed: Tstop (the final
temperature) and Nstop (the maximum number of
iterations without improvement).
• A neighborhood N(s) of feasible solution in thevicinity of s is defined.

Procedures• Initialization. Initialize w1, w2, w3, h, Hstep, α, Nstep,
Tstop and Nstop, set m=n=Hcount=Ncount=0; Draw at
random an initial solution s0, and evaluate f1(s0),f2(s0), f3(s0) and S(s0); Set a list of potentiallyefficient solutions PE.
• Heating procedure. Draw at random a solution s’N(sn), and evaluate f1(s’), f2(s’) and f3(s’) and S(s’); If
S(s’)>S(sn), we accept the new solution: s’→sn+1,
Hcount= Hcount+1, else, sn→sn+1. Update the list PE
with the solution s’, and set n=n+1. If n=Hstep, thenbreak and set T0=h×Hcount, else, iterate.
• Cooling procedure. Randomly draw K solutions fromthe N(sn), and evaluate f1, f2, f3 and S of them. Let thebest solution among the generated K solutions be s’;Replace sn by s’ with probability: S ( sn ) − S ( s ' )  
p = min 1, exp 
(11)

Tm

 

If s’ is accepted s’→sn+k, Ncount=0, else, sn→sn+k,
Ncount= Ncount+K. Update the list PE with the solutions’; Set n=n+K. m=m+K. If m/Nstep is an integer, then

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Tm=αTm-k, else Tm= Tm-k; If Tm< Tstop or Ncount=Nstop,then stop, else, iterate.

OPTIMIZATION RESULTS
We use the following parameters: w1=0.6, w2=0.2,
w3=0.2, h=1.0, Hstep=100, α=0.9, Nstep=200, Tstop=0.0001,
Nstop=500, K=10.
We initialize 10 orderings of magnets, and optimize
each ordering by five methods, including modified SA,
modified SA only with heating procedure (K=1), standard
SA, Local Search (T→0) and Exhaustion approach. It
takes approximately 100 seconds for each process (CUP
2.0G).
Table 1 shows the optimization results of modified SA
and some other methods after 10 calculations of each. We
can see that the ordering of magnets provided by SA canreduce the undulator field errors much more greatlycompared with the results of other methods listed in thetable. And modified SA is better than other SA
Algorithms with smaller mean value and rms divergence.
Table 1: Optimization results of Modified SA and other methods
Algorithm

Rms field
error (10-4)

1st integral(10-6T·m)

2nd integral(10-6T·m2)

Initial solution

58.6±9.7295±239312±251

Modified SA

1.71±1.12

1.18±1.91

0.71±0.87

1.82±1.14

1.55±1.40

3.22±4.67

Standard SA

2.13±1.28

1.13±1.59

0.42±0.47

Local Search

3.15±1.87

3.89±7.09

0.64±1.54

Exhaustion approach

31.9±3.826.1±23.5

17.4±17.9

Modified SA (onlywith heating procedure)

In order to demonstrate the precision of the quick
method in calculation of undulator field errors, we designa very precise three-dimensional program in which we
first calculate undulator field according to remanence andpositions of individual magnets, and then analyze theundulator. From Table 2, we can see the two results arevery close (can be ignored considering the construction
errors), but actually the time used by our quick method isover 1000 times less than the latter.
Table 2: Calculation results of objective functions by quick method
and three-dimensional program (in parentheses)

Rms field error σB/B
st

-6

nd

-6

1 integral (10 T·m)
2

2 integral (10 T·m )Rms phase error σφ

Beforeoptimization

After
optimization

0.653%(0.634%)

0.103‰(0.099‰)-463.4 (-464.9)-1.33 (-2.01)-566.5 (-568.3)-0.79 (0.23)/(13.11)/(0.78)

Figure 3 shows the trajectory of electron beam before
and after optimization. Angular deflection ∆x’and orbital
displacement ∆x of electron beam are given as:
300 I1300 I 2∆x ' =∆x =(12)
E[ MeV ]E[ MeV ]Chen Nian. Chen et al. / Proceedings of the 2004 FEL Conference, 490-493

493

Optimization of the magnets ordering can also save thetime for field measurement and correction after
assembling.

REFERENCES

Figure 3: Electron trajectory before and after optimization

Figure 4 shows the spectrum of spontaneous emission
before and after optimization.

Figure 4: Spontaneous emission spectrum before and optimization

CONCLUSION
The optimization results exposed in this paper showthat the undulator field errors can be greatly reduced (rmsfield error reduced to 0.01%, first field integral to 106
T·m, second integral to 10-6T·m2 and rms phase error to 1
degree). The field after assembly will inevitably differ
from predictions from the optimization results due to theconstruction errors, and because of this reason, we don’t
consider the multipole field errors and set the weighting
factors 0.6 for rms field error, 0.2 for first integral, 0.2 forsecond integral [5].
Once the magnets have been constructed and measured,
the remaining errors can be overcome by swapping
magnets, or more commonly by “shimming” [10].

[1] P.G. O'Shea, H.P. Freund. Free-electron lasers: status
and applications. Science. 292 (2001) 1853.
[2] B.M. Kincaid. Analysis of field error in existing
undulators. Nucl Instr and Meth. A 291 (1990) 363.
[3] E. Esarey, C.M. Tang, W.P. Marable. The effects offield errors on low-gain free-electron lasers. IEEE
Journal of Quantum Electronics, 27 (1991) 2682.
[4] B.L. Bobbs, G Rakowsky, P. Kennedy, et al. In searchof a meaningful field-error specification for wigglers.
Nucl Instr and Meth. A 296 (1990) 574.
[5] R.A. Cover, G Rakowsky, B.L. Bobbs, et al.
Undulator design for synchrotron radiation source
using simulated annealing. IEEE Journal of Quantum
Electronics. 31 (1995) 664.
[6] M.E. Couprie, C. Bazin, M. Billaron. Oprimization of
the permanent magnet optical klystron for the superACO storage ring free electron laser. Nucl Instr andMeth. A 278 (1989) 788.
[7] R Hajima, F Matsuura. Advanced optimization of
permanent magnet wigglers using genetic algorithm.
Nucl Instr and Meth. A 375 (1996) 19.
[8] H Ishibuchi, S Misaki, H Tanaka. Simulated annealing
with modified generation mechanism for flow shop
scheduling problems. European Journal of Operational
Research. 81 (1995) 388.
[9] J. Teghem, D. Tuyttens, E.L. Ulungu. An interactive
heuristic method for multi-objective combinatorial
optimization. Computers & Operations Research. 27(2000) 621.
[10]J Chavanne, P Elleaume. Undulator and wiggler
shimming. Synchrotron Radiation News. 8 (1995) 18.

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J. Jia et al. / Proceedings of the 2004 FEL Conference, 494-497

DESIGN OF UNDULATOR FOR THE SHANGHAI DUV-FEL
Jia Qi-ka, Zhang Shancai, Lu Shengkuan, He Duohui
NSRL,University of Science and Technology of China, Hefei,China
Zhou Qiaogen, Cao Yun, Dai Zhimin, Zhao Zhentang
SSRF, Shanghai Institute of Nuclear Research, Shanghai, China
Abstract
The design study of the undu1ator for Shanghai deep
ultra violate free electron laser source (SDUV-FEL) is
presented. The optimum undulator parameters for the
FEL performance have been studied. The scheme offocusing and segmentation is discussed. The requirementsof undulator magnet field and main technical demand are
given.

selection range of λu and K are not large. Overall
consideration gives the undulator parameters as Table 2
Table 1 Main parameters of the SDUV-FEL
FEL Wavelength (nm)88Electron beam Energy (MeV)

269

Bunch charge (nC)1

INTRODUCTION

Peak Current (A)400

The project SDUV-FEL [1] was proposed by Shanghai
Institute of Applied Physics (SINAP), National
Synchrotron Radiation Laboratory (NSRL), and Instituteof High Energy Physics (IHEP) in 1998. The design andthe relevant R&D of the SDUV-FEL facility have been
under way since 2000. The aim of the project is toprovide a high-brightness stable narrow-bandwidthcoherent deep ultra-violet (DUV) source, and promote an
R&D activity oriented to the development of a coherent
X-ray source in China.
The SDUV-FEL project plan implement HGHG
research in DUV wavelength ， for the first step the
SASE experiment study will be carried out in the spectral
region about 260nm. The undulator system includes a
modulator section, a dispersive section and a multisegmented radiator. In this paper, the design study of theradiator undu1ator is presented. The optimisation ofmodulator and dispersive sections with the HGHG
experiment will be given in a separate paper.
.

εN(mm-mrad)

4

Local energy spread (%)

0.1. Table 2 Main parameters of the Undulator
type

hybridGap(mm)10

Period (mm)25

Peak magnetic field (T)0.6

Section number

6

Section length (mm)1512.5Drift between sections (m)0.1

Average beta function (m)

~3.0

K

1.4

PARAMETER OPTIMIZEDFOCUSING AND SEGMENTATION

The long undulator with high precision, small gap andtransverse focusing is key technology for high gain shortwave length FEL. Design and optimization of theundulator is impartible with design and optimisation ofwhole FEL experiment. The main design parameters of
SDUV FEL are listed in the Table 1.
The design target of high gain FEL is to reach the
maximum saturation power by the minimum saturation
length. In principle the period of undulator should be as
short as possible. But owning to wakefield effect,
radiation damage and the practical condition limit, theundulator gap cannot be decreased along with thedecreasing of undulator period. Therefore when theundulator period is decreased too much, the undulator
parameter K will be too small and radiation power will be
too
weak.
For
our
case,
given
radiation
wavelength (88nm) and electron energy (~300MeV)，theThe radiator undulator is about 10 meter long. In orderto reach the best couple of electron beam and radiation
the electron beam must be properly focused.
There are several schemes of focusing. For natural
focusing the beta function βy0 (cm)=0.241γ/Bu(T) (withparabolic pole face: βn=√2βy0 ) is constant, the segment
length can be chosen arbitrary. Natural focusing is weak
and suitable for longer wavelength FEL. For integrate
focusing which combine the focusing quadrupole magnet
into the undulator, the technology is complex. The costfor long undulator is too much.
Separate focusing is a relatively simple scheme, which
was adopted on the storage rings widely. But thesegments length can’t be chosen arbitrary. The breaklength restricted by the quadrupole magnet (and beam
monitor) can’t be too short. The FEL performance isaffected by the “filling factor” of undulator.

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495

J. Jia et al. / Proceedings of the 2004 FEL Conference, 494-497(2)λ FD is FODO period length, L i and l d is the undulator
segment length and break length respectively. f isquadrupole focusing length. From expression (2) it cansee that with shorter segment length a larger range of theaverage beta function can be available.
To make variation of e-beam envelope small, thevariation of β should be small, namely

1 + λ FD ( 4 f )βM=βm
1 − λ FD ( 4 f )2.0σγ/γ=0.2%
εn=6µ

1.8

Ip=0.3KA
4µ,0.4KA ,0.1%

Lg (m )

1.6
1.4
1.2
1.0
0.8
0.6
0.0

0.5

1.0

1.5

2.0

2.5

3.0

β

Fig.1 optimized β function by Xie Ming’s formula
1.40

natural focusing

90 cm
125 cm150 cm180 cm200 cm220 cm

1.35

1.30

1.25

(3)

should be small. It requires λFD (4 f ) << 1 , this also means
prefer shorter segment length.
But the shorter segment length, the less “filling factor”
of undulator is. That will cause the FEL saturation power
to decrease greatly.
Average beta function, quadrupole focusing length,
FODO period length and undulator segment length andbreak length satisfy the relation:
λ(4)
β > 2 f >> FD ≥ Li >> ld
2
According the fitting formula of Xie Ming [3], theoptimized average beta function is βopt =1.26m (Fig.1),
and ρ=2.87*10-3, Lg=76cm, ZR=1.37m, σ⊥=0.098mm forthe parameters of Table 1. The gain length dependence on
emittance, energy spead and beam peak current are also
given in Fig.1. The result demand Li+ld < β /2=0.6m, thatis too short. In the formula of Xie Ming, the undulator“filling factor” is not considered.
To get more accurate result, the 3D simulation code
GENESIS is used. The break length is included in thesimulation, which is kept as 20cm long. The electron
beam is matched into the undulator. The average beta
function is varied by varying the quadrupole magnet fieldstrength. The natural focusing effect is also included.
From the simulation results (Fig.2 and Fig.3) 1.2m to
1.5m long segmentation is good choice for shorter gain
length, higher saturation power and good control of beam
size. So the segment is chosen as 1.5m long with a

1.20

1.15

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

β(m)

Fig.2 Gain length versus β
for different segment length
natutal focusing

180

160

140

Psat(MW)λFD = 2(Li +ld ) ≤ β ≤ βnsymmetric configuration and the optimal beta function isabout 2.8m.

Lg(m)The selection of focusing scheme is connected with theaverage beta function. For a given emittance, a smaller
average beta function means a smaller beam size, a larger
pierce parameter ρ , i.e. a shorter gain length. But asmaller average beta function also means larger angularspread at the same time. That makes the gain length
longer. Therefore an optimal average beta function exists.
The optimal beta function tie up with ε、σγ、and Ip, thechoice shouldn’t be too sensitive to the electron beam
parameters.
To accumulate experience for future development ofshorter wavelength FEL and considering complexity oftechnica, separate focusing scheme with FODO lattice isadopted.
For the FODO focusing, in the thin lens approximation,
average beta function can be given as [2]:
2 f
(1)
β =
≥ λ FD
1 − ( λ FD 4 f ) 2

120

90 cm
125 cm150 cm180 cm200 cm220 cm

100

80

60

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

3.2

3.4

β(m)

Fig.3 Saturation power versus β
for different segment length

All undulator segments should be in good consistency.
The segments in succession must be well matched. The

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J. Jia et al. / Proceedings of the 2004 FEL Conference, 494-497

phase matching and break length have the relation as
follow

K2 
 − [z u + (Li − z d )] −l d = Mλu 1 +
2 

2

(5)


 e   
 2   ∫z  ∫z Bu dz '  dz + ∫− ∞  ∫− ∞ Bu dz '  dz  mc   d 

∞

2

∞

zu

z

2

Effects of quadrupole offsets
The misalignment of quadrupole will cause the FEL
saturation length growth and power degradation. From thesimulation result (Fig.5 and Fig.6), the tolerance on
quadrupole offsets is ∆x<20µm ， ∆x'<13µrad ， thecorresponding field integral is 2nd <18T*mm2，1st <120
G*cm.

where the M is an integer. The arrangement of undulators
is shown as Fig.4. Where the quadrupole magnet is placedin the break length.

8

FEL Saturation Power (W)

2.0x10

Fig.4 arrangement of undulator

λFEL=88nm
8

1.5x108

1.0x107

5.0x10The correctors will be used to correct trajectory,
quadrupole offset and match phase. The end poleconfiguration is being carefully optimized to erase edge
field’s effect.

0.0
0.00
0.02
0.04
0.06
0.08
0.10
Transverse Displacement of Quadrupoles (mm)Fig.5 Effects of quadrupole offsets
on the saturation power

MAGNETIC FIELD REQUIREMENTWe demand the gain bandwidth due to angular spreadto be smaller than natural bandwidth, i.e.
∆x'< 2λs ρ λu . This gives the requirement for the field
first integral

I (G .m ) < 17 ρ (1 + K 2 2 )(6)For K=1.38，ρ=2*10 ，it has I ≤ 1G*m，it’s not too
difficult to achieve.
For the field 2nd integral we demand the transverse
offset of electrons in the undulator to be smaller than theundulating amplitude of undulator. It gives:-3σ II ( G .m 2 ) <λ u ( cm ) K
12 π

(7)

FEL Saturation Length (m)50Field integral

λFEL=88nm

40

30

20
0.00
0.02
0.04
0.06
0.08
0.10
Transverse Displacement of Quadrupoles (mm)Fig.6 Effects of quadrupole offsets
on the saturation length

For K=1.38 ， ρ=2*10-3 ， we have σII<9T*mm2,
corresponding σx<10µm，it is not easy to achieve.

Peak field error

TECHNICAL DESIGN

Also from gain bandwidth requirements, it gives

1
1 ∆λ
∆B
<( + 2) s ≈ ρ
B
2 K
λs

(8)

For our condition, it is about 0.002 and is rather difficult.

Phase error
Phase error will increase FEL gain length. [4,5].
σ φ2

Lg → Lg e 3(9)∆Lg/Lg≅σϕ /3

(10)

2

For σϕ=10°, the gain length variation is ∆Lg/Lg≅1%, it iseasy to realize.

TUPOS38

Considerations of Hybrid vs. PPM
For the pure permanent magnet (PPM) undulator thedesign and analysis is convenient, but the magnet block
requirement is stringent，it needs more workload. For
hybrid undulator the design and analysis is rather
complicate. It can give higher peak field than PPM ones
when g/λu < 0.4 (Fig.7), but the harmonic component may
be larger, the field is highly affected by the pole shape.
The segments matching problem is more serious forhybrid structure. The radiation damage problem is more
serious for PPM structure. For our case (g/λu∼0.4), either
one can be used. The hybrid structure is chosen.

J. Jia et al. / Proceedings of the 2004 FEL Conference, 494-497

497±9.9mm. The worst demagnetizing field is adjacent to theend corner of pole and just above the chamfer.

Mechanical design

2

B0

Bhyb

Bppm
1

0.1

0.2

0.3

0.4

0.5 0.6 0.7 0.80.9 1

g/λu

Fig. 7，Peak field versus gap/period
The peak field of hybrid undulator can be calculated by
the following empirical formula−g

B0 = 0.95ae λu

( b−c

g

λu

)

0.07≤g/λu≤0.7 (11)a = 0.55 Br + 2.835
b = −1.95 Br + 7.225
c = −1.3B + 2.97r

where Br is the remanent field strength of permanent
magnet. The permanent magnet material we choose
NdFeB N38SH for it has enough high coercivity. The
magnet pole, we choose vanadium permendur for its
higher saturation field.

Pole geometry optimization
The goal of pole dimension optimization is that with
sufficient field strength on the axis insured the field in thepole is far from saturation, the demagnetizing field in
magnet block is not large, and magnet material isminimized [6].
Thickness (electron moving direction) ： with the
thicker permanent magnet the larger field can be achieved,
but the harmonic field may be larger too. The thickness
rate of pole and magnet block usually is zp/zm~1/2.
The height (gap direction) of magnet and pole is chosen
as ym/yp~1.2. [7]The width (undulating direction) of magnet and poleare determined by good-field-region requirement(∆B/B<ρ in sufficient wide range). Usually ym/xm~0.9 ischosen. The final geometry dimension is as follow:
For the magnet: zm=8±0.011mm, ym=45±0.05mm,
xm=60-0.10mm, perpendicular of magnet：±0.02 mm
For the pole: zp=4.5+0.012mm, yp=38±0.012mm,
xp=40-0.050, -0.089mm.
To avoid saturation of the pole, the all edges of poleand magnet facing toward gap are chamfered.
The numerical simulation by OPERA-3D show that the
maximum field is 0.64T, the good field for ∆B/B0=0.1% is
about ±8.5mm. And good field for ∆B/B0=0.2% is about

A C type girder support structure is chosen. A fixed
gap is adopted to simplify the fabrication. The magnetic
force between poles is 710Kg. The main mechanicalrequirements and specifications are:1) The beam parallelism：0.02mm2) Pole gap tolerance ±0.05mm.
3) Neighbour pole gap difference tolerance ±0.03mm4) Pole displacement in “z” direction (top and bottom)±0.10mmMinor adjustment can be done individually for eachpole to tune the field. The base of undulator can bevertically and horizontally adjusted. The alignment
precision for horizontal direction is about 5µm, and forvertical direction is given by:λu∆ B < 0.25mm
(12)
∆y =
π
2B
Now a two periods prototype of undulator is underconstruction. The optimal design of undulator end part isunder way. The much more detail work will be continued.

REFERENCE[1] Z.T.Zhao et al., Nucl.Instr. & Meth. A528,pp591594,2004[2] TESLA Technical Report Part V, Eds.:G.Materlik,
T.Tschentscher, DESY Report 2001-XX, Chapter
4(2001)[3] M.Xie, Proc. PAC95, 183(1995)[4] Kwang-Je Kim, Nucl.Instr. & Meth.A445 (2000) 24[5] Jia Qi-ka, High Power Laser and Particle Beams,
Vol.14, No.2, ( 2002) pp165-168[6] LCLS Conceptual Design Report Chapter 8 (2002 )[7] R.D.Schlueter, China Accelerator Physics School(1998)

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x. Xiao et al. / Proceedings of the 2004 FEL Conference, 498-500

STUDY OF CONTROL GRID THERMIONIC CATHODE RF GUN
Xiao Jin#, Xinfan Yang, Ming Li, Yanan Chen, Xumin Shen, Jie Liu, Zhou Xu,
Applied Electronics Institute, CAEP, China
Abstract
In this paper, the beam loading effect in the thermioniccathode RF Gun was studyed. To minimize the energy
spread in macropulse of RF Gun, a design of Control Grid
Thermionic Cathode RF Gun was given. In numericalsimulation, the result of this kind RF Gun is: electron
beam energy is 2MeV, transverse emittance is
23πmm.mrad, micropulse width is 25ps, micropulse beam
current is 12A. The primary experiments has been done.
For 1% electron beam energy spread selected by α
magnet, the beam current can get 400mA.

1 INTRODUCTION
The thermionic RF-gun has been widely used in FEL
experiment. The main problem of thermionic RF-gun iselectrons back bombardment.
At CAEP, a L-band thermionic RF-gun was used forthe 100um FEL device. To produce 4us macropulse
electron beam, the micropulse current in 2% energy
spread is limited by effect of back bombardment to 5A.
The electron back bombardment change the beam load ofthermionic RF-gun, and increase the electron energy
spread in beam macropulse. To increase the beam current,
the effect of back bombardment must be controlled.

2 EFFECT OF BACK BOMBARDMENT
The standing wave accelerator includes RF generator,
circulator, coupler, and cavity (Fig. 1). And its equivalentcircuit can be drawn as figure 2.

∆U = CVc (Vmax − Vc )∆t

Where Vmax is the maximum voltage of cavity without
electron

beam,

Vc

is

the

voltageofcavity,U = (1 2)CVc is the stored energy, and τ is the2resonance time constant.
For the steady-state of cavity, the average electron
beam power Pb equals to the increasing of stored energyof cavity.

Pb = CVc (Vmax − Vc )

1

(2)

τ
We express τ = 2Q ω and Q = ωU ( Pex + Pc ) ,where Pex is the external power dissipated, Pc is thepower dissipated in cavity wall. Substituting these
expressions into Eq. 2, we can get

Vc = Vmax

Pex + Pc
Pex + Pc + Pb

(3)

So, the change of cavity voltage can be written as

dVc
1
dPb
=−
P +P
Vc
1 + ex c Pb
Pb

(4)

For the accelerator design, the waveguide-to-cavity
coupler is always set to critically coupled with thedesigned beam current. So Eq. 4 can be written as

dVc
1
dPb
=−
P
Vc
2 + 2 c Pb
Pb
Figure 1: RF system of the standing wave accelerator[1].

(1)

τ

(5)

When the beam power is larger compared with theaverage power dissipated in cavity wall, the change ofelectron beam load will remarkably influence the beamenergy. Figure 3 shows the electron beam waveform of
thermionic RF-gun in CAEP.

Figure 2: The equivalent circuit of the standing wave
accelerator[1].
By the equivalent circuit of accelerator, the stored
energy of cavity is___________________________________________#

xiao_jin@hotmail.com

TUPOS39

Figure 3: Electron beam waveform of thermionic RFgun(<ch1>).

Available online at http://www.JACoW.org

499

x. Xiao et al. / Proceedings of the 2004 FEL Conference, 498-500

The first cells of the RF-gun act as a bunching segment
too. The bunching segment makes the electron and themicrowave synchronize better and more electron will be
captured. The SUPERFISH CODE and the GPT CODE
has been used to calculate the electron beam. The currentof the cathode is 2A. The field ratio of the second cell to
the first cell is about 4, the electrons get energy mainly
from the second cells.
The simulation result (energy spread 1%) is: beamenergy is 2MeV, emittence is 23pi mm*mrad, micropulse
width is 25ps, micropulse current is 12A. Somesimulation results show in figure 6 and figure 7.
time=2.9e-009
5.06
5.04
5.02

G

In FEL experiment, the electron beam energy spreadmust be controlled strictly (always less than 1%). So themain problem of thermionic RF-gun is the effect of backbombardment. The process of the back bombardment is:• Electrons back bombardment• The temperature of cathode increasing• The electron beam current increasing• The electric field of cavity reducing• Electron beam energy reducing
So there are many methods to minimize the effect ofback bombardment.
• To control the electrons back bombardment, we
can carefully design the cavity, use the cathodewith a hole in center, use the magnetic field, et al.
• To control the temperature of cathode, a laser canbe used to heat the cathode.
• To control the electron beam current, we can use
the control grid electron gun.
• To control the electric field of cavity, the power ofmicrowave is needed to be controlled.
• To control electron beam energy, a external
electrical source can be used to change theelectrical potential of cathode.
In our design of the new RF-gun, the control gridelectron gun was used. To minimize the emittence of theelectron beam, the grid was put into the first cell. Figure 4
shows the position of the grid and the cathode. The space
between grid and cathode is about 0.9mm, the voltage ofcathode is 600-1000V. Figure 5 shows the structure of the
new RF-gun cavity. .

4 SIMULATION RESULT

5.00
4.98
4.96
0.648

0.650

0.652

0.654

0.656

0.658

z

Figure 6: Electron beam energy distribution at the exit.
time=8.6e-009
500
400

G_cntbar

3 CONTROL GRID THERMIONIC RFGUN DESIGN IDEA

300
200
100
0

4.85

4.90

4.95

5.00

5.05

G_hisbar

Figure 7: Electron beam energy spectrum.
Figure 4: Structure of the RF-gun near the cathode.

5 EXPERIMENT RESULTThe characteristic parameters of the control grid RFgun are measured by net work analyzer: The resonant
frequency of the π/2 mode is 1300.16MHz, the coupling
coefficient of the wave guide to the cavity is 5.2. The
klystron microwave source is 3.5MW. The voltage
between grid and cathode is 400V. The macropulse width
is 4µs, the beam current at the a magnet exit during themacropulse up to 400mA. Fig.8, Fig.9, and Fig.10 show
some pictures of the new RF-gun and some experimentresults.
Figure 5: Structure of the RF-gun cavity.

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x. Xiao et al. / Proceedings of the 2004 FEL Conference, 498-500

Figure 8: Picture of control grid electron gun.
Figure 10: Electron beam waveform of the new RFgun(<ch1>).

6 CONCLUSIONSThe thermionic cathode RF gun is a kind of excellent
electron source. In this work, the control grid electron gun
has been used to reduce the effect of back bombardment.
The experiment results show that these methods work
efficiently. But we also found that the beam emittence islarger than simulation result.

REFERENCES
Figure 9: Picture of the new RF-gun.

TUPOS39[1] Wangler T P, Principles of RF Linear Accelerators,
New York, J. Wiley & Sons Inc., 1998

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C.S. Hwang et al. / Proceedings of the 2004 FEL Conference, 501-503

SUPERCONDUCTING UNDULATOR WITH VARIABLY POLARIZED
LIGHT
C. S. Hwang*, P. H. Lin, W. P. Li, C. H. Chang, T. C. Fan
NSRRC, 101 Hsin-Ann Road, Hsinchu Scien Park, Hsinchu 30077, Taiwan
AbstractThis
study
investigates
planarin-vacuo
superconducting elliptically polarized undulators withperiodic length of 5 cm (SEPU5) producing linearly andcircularly polarized infrared rays or x-rays source. The
vertically wound racetrack coil is chosen for the coil andpole fabrication of the SEPU5. When the up and down
magnetic pole arrays with alternative directions rotatedwires in the horizontal plane, an elliptical field radiates
elliptically polarized light in the electron storage ring, thefree electron laser (FEL), and the energy recovery linac(ERL) facilities. Meanwhile, an un-rotated wire magnet
array is constructed together with the rotated wire magnet
array on the same undulator is used to switch the linear
polarization in horizontal and vertical, as well as theright- and left-circular polarization radiation. This
investigation describes the main factors of the planar andhelical undulator design for FEL and the concepts
concerning the magnet array structures of thesuperconducting undulators.

INTRODUCTION
The circular polarization mode of the ellipticallypolarized undulator provides the high gain and high fluxin the FEL scheme. Several schemes [1-4] have beendeveloped to generate the function of linear and helically
distributed fields, using electromagnets with copper coils,
and hybrid or pure structures with permanent magnets invarious configurations. These schemes, either with helicalgeometry, which combines separate horizontal andvertical devices, or with planar geometry with a variable
phase, yield variably polarized light. A planar
superconducting elliptical polarization undulator [5] with
5 cm period length (SEPU5) produces a helical field inthe storage ring, and in the FEL or ERL accelerator
facilities are developed. This magnet provides more
intense right- and left-circularly polarized light, and islinearly polarized in the horizontal and vertical direction.
Combining two magnet arrays with (inner magnet array)
and without (outer magnet array) pole rotation in the samestructure creates various tunable polarizations. The
vertical-winding racetrack coil structure for the in-vacuo
superconducting undulator [6] is chosen for therequirements of the tunable polarizations function.
Therefore, given a periodic length of 5 cm and a gap of 13mm and 23 mm for the outer and inner magnet array,
respectively, the maximum magnetic flux densities in thehelical undulator are Bz = 2.7 T and Bx = 0.54 T when thewires are rotated by 35o[7]. When the SEPU5 operated
with 100 MeV energy of the linac accelerator, the SEPU5___________________________________________*cshwang@nsrrc.org.tw

Available online at http://www.JACoW.org

provides 1-10 µm circular polarization IR wavelength in
the FEL facility for the user requirements in Taiwan.
Additionally, the SEPU5 can also provide horizontal andvertical linear polarization in the energy ranges of 1-100µm and 1-10 µm, respectively. This study describes
concepts related to the elliptical, helical and linear
polarization mode in the same undulator, and presents thedesign of the magnet array structures of the ellipticalsuperconducting undulators. The use of two different
excitation currents to generate the mechanism of thepolarization switching in the right- and left-circularpolarization radiation and linear polarization is discussed.
Furthermore, the features of magnetic field and photon
spectra on the in-vacuo superconducting ellipticalpolarization undulators are also elucidated. Finally, thephoton flux in different polarization mode and themechanism of the switching polarization radiation are
discussed.

DESIGN CONCEPT OF THE SWITCHING
POLARIZATION MECHANISM
Two planar magnet arrays with period length of 5 cmcomprise the superconducting elliptical polarization
undulator (SEPU5) structure. The outer magnet array has
a rotated pole [5,8] that the rotation angle is 35o and theinner magnet array does not have a rotated pole [9]. The
two magnet arrays are combined as in Fig. 1. According
to this SEPU5 structure, the maximum magnetic force
between the two magnet arrays is about 4.5 kg. However,each coil in every pole was divided by four parts toanalysis the force in the local coil between the twomagnets arrays. The maximum force is 10 kg in the local
coil parts. Hence, the force between the local parts is not
an issue on the magnet operation. The total energy of thismagnet is 56 kJ. Table I lists the main design parametersof the superconducting elliptical polarized undulator.
Depending on the IRFEL requirement in NSRRC, theRayleigh range ZR is 1 m and the maximum optical beam
waist w0 = (ZRλ/π)1/2= 1.75 mm in the photon wavelength
between 1-10 µm. Therefore, the undulator minimum gap
was estimated as gmin= 5 w0 + 2t = 13 mm. Where tdenotes the thermal shielding and redundancy factor forthe superconducting magnet operation. The excitation
current Ji and Jo on the superconducting coil of the innerarray and outer array is independent. In this structure, thepolarization can be switched via different combinations of
the two-excitation currents. Table II lists the features inthe six types of polarization mode by different
combinations of the two-excitation currents in the
superconducting elliptical polarized undulator. The
polarization modes are changed by the different

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C.S. Hwang et al. / Proceedings of the 2004 FEL Conference, 501-503

polarization with field strength of Bz = 1.8 T and Bx = 0.
Table II lists the relationship between the polarization
mode and the excitation current combination.

SPECTRA FEATURES OF THE
SUPERCONDUCTING ELLIPTICALUNDULATOR

Table 1: Design parameters and features of thesuperconducting elliptical polarization undulator.
Number of poles

80

Periodic length λu (cm)5

Magnet gap g of inner (outer) array (cm)

1.3 (2.42)

Physical length L (cm)220

Inner pole rotation angle θ (deg)35

Outer pole rotation angle θ (deg)0Field strength on coil Bs (T)4.6
2

Maximum excitation current Ji (A/mm )678

Maximum excitation current Jo (A/mm2)

850

Total energy (kJ)

56.04

Force between magnet arrays {Fx,Fy,Fz}(Kg){1, 1, 4.5}

TUPOS40

10

15

15

10

Linear polarization in horizontal

10

circular polarization
elliptical polarization
Linear polarization in vertical

14

1(Phot/s/0.1%bw/0.4A)

combination of the two-excitation currents. (1) When the
inner and outer magnet array is excited by Ji =678 A/mm2
and Jo =0, respectively, the SEPU5 produces an ellipticalfield with field strength of Bz = 1.34 T and Bx = -0.5 T.
This operation mode is a right elliptical polarization mode.
In this mode, high-energy photon is radiated by means of
the higher harmonic spectra. (2) If the current Jo = -398
A/mm2 was also excited on the outer magnet array, thenthe elliptical field becomes the helical field with the fieldstrength of Bz = -Bx = 0.5 T. In this operation mode
provide a right circular polarization. (3) If the current
continuously increases to Jo = -620 A/mm2, then the rightcircular polarization becomes the vertical linear
polarization with the field strength of Bz = 0 T and Bx = 0.5 T. (4) If the current continuously increases to Jo = -750
A/mm2, the vertical linear polarization becomes the left
elliptical polarization with field strength of Bz = -0.3 T
and Bx = -0.5 T. (5) If the current continuously increases
to Jo = -850 A/mm2, the left elliptical polarization becomesa left circular polarization with field strength of Bz = Bx =-0.5 T. (6) If the excitation current was set at Ji = 0, Jo =678 A/mm2, then the SEPU5 produces horizontal linear

Flux (Phot/s/0.1%bw/0.4A)

Figure 1: 3D schematic drawing of the superconducting
elliptical undulator structure. The pole of the innermagnet array rotated 35o and the outer magnet array
displays no pole rotation.

The SEPU5 operates in a 100 MeV linac to provide theinfrared source between 1-10 µm. Figure 2 shows the
spectra features of the SEPU5 operated on a different
polarization mode in the 100 MeV electron accelerator
energy. The high radiation gain and flux occurs in thecircular polarization mode that only exists in the firstharmonic spectrum, Fig. 2 only showed the flux in thecircular polarization mode and in the first harmonic
spectra of the elliptical and linear polarization modes.
However, in the storage ring or ERL accelerator facility,
the higher harmonic spectra can be extended to higher
energies. Figure 2 reveals a higher flux in the right- andleft-circular polarization mode, and demonstrates that theenergy spectrum range is between 1-8 µm. However, toextend the spectrum energy range, the ellipticalpolarization mode was selected to provide the energy
range of 1-30 µm. However, the circular polarization rate
is reduced in the elliptical polarization mode, and thephoton flux is smaller than the circular polarization modein the same energy range. Additionally, Fig. 2 shows that
the SEPU5 also provides the horizontal and vertical linear
polarization mode. If the SEPU5 was operated in thevertical (horizontal) polarization, the spectrum energy
range will be located in the range 1-6 (1-60) µm.
However, the photon flux is also slightly smaller than thatin the elliptical polarization mode. If the higher harmonic
spectra radiates from the SEPU5 in the 3 GeV storage
ring or ERL, the energy can reach up to 4 keV. Figure 3
shows the higher energy photon in the soft x-ray region
was radiated in the 3 GeV accelerator facilities.

14

10
10

Photon Energy (µm)

Figure 2: Spectra distribution of various polarization
modes in the superconducting elliptical polarization
undulator (SEPU5) was obtained in the 100 MeV electron
linac.

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C.S. Hwang et al. / Proceedings of the 2004 FEL Conference, 501-503

Table 2: Combination of the excitation current for different polarization mode on the superconducting ellipticalpolarization undulator. Six polarization modes exist that are operated in the electron energy 100 MeV: Right Elliptical
Polarization (REP), Left Elliptical Polarization (LEP), Right Circular Polarization (RCP), Left Circular Polarization(LCP), Vertical Polarization (VP) and Horizontal polarization (HP).
REP

LEP

RCP

LCP

VP

HP

Excitation current Ji (Jo) (A/mm )678 (0)678 (-750)

678 (-398)

678 (-850)

678 (-620)

0 (678)Magnetic flux density Bz (Bx) (T)

1.3 (-0.5)-0.3 (-0.5)

0.5 (-0.5)-0.5 (-0.5)

0 (-0.5)

1.8 (0)Flux @ 1(6) µm (p/s/0.1%bwx10 )

1.7 (2.3)

1.9 (2.9)

2.2 (3.3)

2.2 (3.3)

1.7 (2.0)

1.7 (2.0)

Spectrum energy range (100 MeV) (µm)

30 – 1

7–1

8 – 0.96

8 – 0.96

6 – 0.99

60 – 1

Deflection parameter Kz (Kx)

6.3 (2.3)

1.3 (2.3)

2.3 (2.3)

2.3 (2.3)

0 (2.3)8.4 (0)

2

15

16

10

15

10

14

14

10

10

3 GeV
circular polarization
elliptical polarization
Linear polarization in vertical

Flux (Phot/s/0.1%bw/0.4A)

Flux (Phot/s/0.1%bw/0.4A)

REFERENCES
15

10

Linear polarization in horizontal
13

13

10

10
100

1000

10000

Photon Energy (eV)Figure 3: Spectra distribution obtained in the 3 GeVelectron energy on various polarization modes.

CONCLUSION
It is possible and feasible to radiate the circular andlinear in horizontal and vertical polarization light in an invacuo superconducting elliptical undulator. For the
infrared ray FEL in a 100 MeV electron linac, thesuperconducting elliptical undulator with period length of
5 cm radiates the energy range between 1-30 µm in theelliptical polarization light or between 1-60 µm in thehorizontal linear polarization light. The switch between
all polarization modes does not involve mechanicalmovements and simply tunes the excitation current on the
inner and outer magnet array. In addition, the in-vacuo
superconducting elliptical undulator can also operate in
the medium-accelerator storage ring or the ERL facility
with shorter period length, and can use the higher
harmonic spectrum to extend the energy range to the hard
x-ray range.

ACKNOWLEDGEMENTS
The authors would like to thank the National Science
Council of Taiwan for support of this research underContract No. NSC93-2112-M-213-001. Mr. H. H. Chen
and M. H. Huang are appreciated for discussing
mechanical structure of the elliptical undulator.

[1] K. Halback,” Physical and optical properties of rareearth cobalt magnets”, Nucl. Instrum. Methods Phys.
Res., Sect. A 187, 109 (1981).
[2] H. Onuki,” Elliptically polarized synchrotron
radiation source with crossed and retarded magnetic
fields”, Nucl. Instrum. Methods Phys. Res., Sect. A
246, 94 (1986).
[3] S. Sasaki, ” Analysis for a planar variable-polarizing
undulator”, Nucl. Instrum. Methods Phys. Res., Sect.
A 347, 83 (1994).
[4] R. P.Walker and B. Diviacco, “ Studies of insertion
devices for producing circularly polarized radiation
with variable helicity in ELETTRA”, Rev. Sci.
Instrum. 63, 332 (1992).
[5] A. Bernhard, B. Kostka, R. Rossmanith, et al.,“ Planar and planar helical superconducting
undulators for storage rings: state of the art”, 9thEuropean particle accelerator conference (EPAC
2004), 5-9 July 2004, Lucerne, Switzerland.
[6] C. S. Hwang, W. P. Li, P. H. Lin, C. H. Chang,“Comparison of Predesign Parameters for Mini-Pole
In-Vacuo Superconducting Undulators”, IEEE Trans.
On Appl. Supercon. (in press).
[7] C. S. Hwang, P. H. Lin, “Comparison of two
superconducting elliptical undulators for generating
circularly polarized light”, Phys. Rev. ST Accel.
Beams. (in press).
[8] S. Sasaki, “ Concept design for a superconducting
planar helical undulator”, presented in the Workshop
on Superconducting Undulators & Wigglers,Grenoble, June 30 – July 1, 2003.
[9] Andreas Geisler, Achim Hobl, Detlef Krischel,Robert Rossmanith, and Michael Schillo, “First fieldmeasurements and performance tests of asuperconductive undulator for light source with aperiod length of 14 mm”, IEEE Trans. On Appl.
Supercon. 13, No. 2, 1217 (2003).

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COMMISSIONING OF STRONG TAPERED UNDULATOR DEVELOPEDFOR IFEL ACCELERATOR
S.V. Tolmachev#, A.A. Varfolomeev, A. Varfolomeev Jr., T.V. Yarovoi,
RRC “Kurchatov Institute”, Moscow 123182, Russia,
P. Musumeci, C. Pellegrini, J. Rosenzweig,
UCLA, Los Angeles, CA 90085, USA
Abstract
Here we describe the manufactured KIAE-2p planar
undulator designed for the Inverse Free Electron Laser
experiment at the University of California in Los Angeles.
New technology enabled to fabricate the installation
responding to the stringent requirements on mechanicalconstruction accuracy and magnetic field strong tapering.
Results of the magnetic field measurements by different
methods are given. The obtained magnetic field maps
were used for final simulations of the acceleration
process. It is shown that for nominal electron beam andlaser beam parameters up to 30% of electrons can be
captured and accelerated from initial 14 MeV up to 52
MeV. Special analysis of the undulator acceptances forthese parameters is made. It is shown that the accelerationis possible up to energies >30 MeV for rather wide rangesof laser pulse energy, Rayleigh length and e.b. emittance.

Figure 1: Photo of the melted block systems: 1 – nonmagnetic side blocks; 2 – permendure central block; 3 –magnets fixation.

INTRODUCTION
The KIAE-2p undulator was designed andmanufactured for the UCLA – Kurchatov Institute IFEL
project [1,2]. Physical requirements for the undulator andsimulations results of the design were given earlier [3].
The main particularity of the undulator is strong taperingof both magnetic field periods and strength of the fields aswell. This tapering is required since the projected Inverse
FEL should be driven by a high power CO2 laser beamfocused inside the undulator by a lens with rather small
focus distance. The nominal Rayleigh length (3.6 cm) isrelatively small in comparison with the size of the IFEL
installation so diffraction of the laser beam should betaken into account. This diffraction dominated regime wascarefully investigated in a series of numerical simulations[4–7] results of which were used in the designing of theundulator.

UNDULATOR CONSTRUCTION
Technical problems followed from the undulator
requirements could not be solved without newtechnologies unusual for routine undulator production. To
make the problem of magnets and poles supports lesscomplicated a new type of support construction was
suggested and used (Fig. 1). The basic array of poles ismade as a frame from titanic (non magnetic) side blocks(2) and profiled permendure (magnetic) central block
melted in one block. Windows between poles were cut out___________________________________________#

tsv@kiae.ru

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Figure 2: Common view of the KIAE-2p undulator with
the Hall probe stepmotor driver.
by electroerrosion method, enabling to provide therequired high accuracy of the shaped construction.
Higher fields in comparison with routine hybrid
undulators were needed. Enhancement over Halbah limitsof the fields was required. For this purpose new cone
shape of poles (2) were used. Not equal magnetic field
fluxes of two neighbouring magnet cells required bystrong tapering were achieved by using coneshaped sidemagnets with specific support systems. Common view of
the assembled two section undulator is shown in Fig. 2.
Two sections of the undulator were mounted on tube
rails as a support. Alignment of the two sections mounted
on the rails was performed with using a granite table.
Small slopes have been got. The first section axis gives
deviation <0.012 mm on the total section length. The
second section was aligned up to <0.003 mm and theslope between two undulator section axes gives <0.003
mm misalignment.

Available online at http://www.JACoW.org

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505

Figure 3: Magnetic fields directly measured by the Hall probe (a) and following from (a) the first (b) and the second (c)field integrals of KIAE-2p undulator (left graph). Deviations from projected ones respectively (right graph).

MAGNETIC FIELD TESTS
During tuning and commissioning the undulator
magnetic fields were measured with high accuracy and bydifferent methods. Some special measures were used toget high precision. A unit was manufactured for automatic
scanning by the Hall probe. So it was possible to makemeasurements in many (from 60 to 200) points per one
period length. For the same reason of getting highprecision very small Hall probe crystal was used
(0.5×1.0×0.38 mm3) with very high (10–5) stability of thecurrent supply. Hall probe voltage was measured withaccuracy ±0.1 µV. Calibration of the Hall probe was madewith using a special reference magnet. As a result the Hall
probe mean response ratio was found to be 7.9 µV/G. For
more higher precisions corrections on nonlinearity of this
response has been taken into account. The Hall probe was
fixed on a special nonmagnetic carriage which could be
moved by a stepmotor driver (Fig. 2) along the undulator
axis in the gap keeping the Hall probe just on theundulator axis. Total accuracy of the magnetic fieldmeasurements ±0.1 G was achieved. Tuning of theundulator fields was made by moving side magnets or
small moveable pieces of the poles. In extreme cases thebasic magnets and (or) side magnets interchanged
positions in the frames what gives some kind of sorting.
After the first stage of tuning magnetic field profiles
became similar to that found in simulations [7] within±0.08%. At the same time for the second integral of the
field deviations were not so small. An additional tuning

was needed to improve the field integrals. It was made byadmitting some larger field deviations. The final results ofthe field tuning using Hall probe are given by Fig. 3.
Deviations of the measured magnetic fields, first andsecond field integrals from the projected ones are also
given. The field deviations here are ±0.4%, and grow up
to 4% in the intersection gap caused probably by small
geometrical changes in this gap. The second integralscoincide with the theoretical ones within 5%.
For the final testing of the second field integrals andfocusing ability of the undulator the pulsed wire method
was used. A BeCu wire of 50 µm diameter and 1.6 m long
was used. Special optical detector provided sensitivity
247 µm/V at working range 60 µm. To get information
about the focusing properties of the undulator the wire
should be positioned parallel to the undulator axis intransverse (x or y) direction [8]. Fig. 4 shows
measurement results for both the horizontal and verticalplanes respectively. It is seen, that for the horizontal wire
displacement curves remain parallel to the undulator axis
showing absence of the defocusing in x-z plane. For thevertical wire displacement curves are inclined to theundulator axis showing that focusing in y-z plane takes
place.

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Figure 4: Illustration of the horizontal (left graphs) and vertical (right graphs) focusing properties of the KIAE-2p
undulator measured by pulsed wire method.

ACCEPTANCE FOR THE LASER BEAM
PARAMETERS PROVIDED BY THE
UNDULATOR
As a final test of the tuned magnetic fields a new
simulation of the acceleration process was made withusing the measured magnetic field map (Fig. 3).
Calculations of the maximum accelerated electronsenergy γmax and the capture ratio χ were made fordifferent deviations from nominal ones in laser pulse
energy, Rayleigh length zr and laser focus position zf.
Results are summarized in Table 1.
Table 1. Simulation results
Laser and e-beam
parameters

Laser power, GW
250
300
400
Nominal regimezr = 3.6cm, zf = 0 cm
γmax=105,
γo =28.5, ε =10 mm·mrad
χ=34%
Not nominal regimezr = 1.8cm, zf = 0 cm
γmax=42, γmax=53, γmax>95,
γo =28.5, ε =10 mm·mrad
χ=0%
χ=1%
χ=3%;
γmax>90,
χ=4%;γmax>85,χ=6%
zr = 1.8cm, zf = -2.0 cm
γmax=50, γmax>85, γmax>85,
γo =28.5, ε =10 mm·mrad
χ=0%
χ=2%;
χ=2%;
γmax>80, γmax>80,
χ=8%;
χ=8%;
γmax>75, γmax>75,
χ=9%
χ=23%

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Figure 5: Energy distribution of the output electrons forthe nominal regime.

Figure 6: Energy distribution of the output electrons forthe not nominal regime (zr = 1.8 cm, zf = -2.0 cm).

S.V. Tolmachev et al. / Proceedings of the 2004 FEL Conference, 504-507

507

Figure 7: Photo of the IFEL beamline.
Maximum electron energy for nominal parameters isequal to 52 MeV (γ=105). Corresponding energy
spectrum of the output electrons is shown in Fig. 5. Total
capture ratio equals to 34±1%. All these data are adequate
to the IFEL project requirements. The histogram of theoutput electrons energy for not nominal regime is shownin Fig. 6. Not nominal regime date given by Table 1
shows strong sensitivity of the whole acceleration process
to the laser beam parameters (shape, power and focus
position). On the other hand these data can be considered
as rather wide acceptances for these parameters notstoping the acceleration process in the first undulator
section.

* * *After commissioning undulator was placed in thespecial vacuum box. The box was installed on the IFEL
beamline (see Fig. 7). Alignment of all beam line
elements was made with accuracy 0.1 mm by using areference laser.

REFERENCES[1] P. Musumeci, C. Pellegrini, J. Rosenzweig, A.
Varfolomeev, S. Tolmachev, T. Yarovoi. “On the IFEL
experiment at the UCLA Neptune Lab”. Proc. of the
PAC2001, June 18-22, 2001, Chicago, IL, p.p. 40084010.
[2] P. Musumeci, C. Pellegrini, J.B. Rosenzweig, S.
Tochitsky, G. Travish, R. Yoder, A. Varfolomeev, S.
Tolmachev, A. Varfolomeev Jr., T. Yarovoi “Status of the

Inverse Free Electron Laser Experiment at the Neptune
Laboratory”. Proc. of the PAC2003 Conference, May 1216, 2003, Portland, Oregon, USA, p.p. 1867-1869.
[3] A.A. Varfolomeev, S.V. Tolmachev, T.V. Yarovoi, P.
Musumeci, C. Pellegrini, J. Rosenzweig. “Undulator withnonadiabatic tapering for IFEL project”. Nucl. Instr. andMeth. A483 (2002) 377.
[4] A.A. Varfolomeev, S.V. Tolmachev, T.V. Yarovoi.
“First approach to simulations of the undulator for the
IFEL project of UCLA”. Int. report CRL 01-01, 2001,
Moscow.
[5] A.A. Varfolomeev, S.V. Tolmachev, T.V. Yarovoi.
“Beam acceptances for UCLA IFEL project estimatedalong with special undulator design simulations.” Int.
report CRL 02-01, 2001, Moscow.
[6] A.A. Varfolomeev, S.V. Tolmachev, T.V. Yarovoi.
“Simulations with the purpose to optimize IFEL undulator
design for UCLA-RRCKI project.” Int. report CRL 0301, 2001, Moscow.
[7] S.V. Tolmachev. “Design of the undulator
construction with taken into account technologicalcapabilities of its fabrication”. Preprint IAE-6237/2, 2001,
Kurchatov institute, Moscow (in russian).
[8]. N.S. Osmanov, S.V. Tolmachev, A.A. Varfolomeev.
“Further development of the pulsed wire technique formagnetic field and focusing strength measurements inlong undulators”. Nucl. Instr. and Meth. A407 (1998)
443.

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FEL AND LIBERA BOTH PUSH PERFORMANCE INTO NEW FRONTIERS
R. Ursic, B. Solar, Instrumentation Technologies, Slovenia
Abstract
Free Electron Lasers and Libera electron beam position
processor share a common vocation – they both pushperformance into new frontiers. Advances in electron
accelerator technology that enabled FELs to fulfill theirearliest days promises have also been due to the recent
developments in the beam instrumentation. Libera thathas till now been successfully employed in the lightsources projects promises to become an indispensable tool
also in the FEL field. The three main advantages of
Libera are: all-in-one, customization and connectivity.
All-in-one is the concept of unification of various
building blocks and thus various functionalities in one
product. The customization is enabled by the product’s
reconfigurability that allows it to grow and support new
requirements and application without changing hardware.
The consequence of the two is the capacity of the single
instrument to perform a variety of tasks that before weresplit among different devices. Connectivity improves thecommunication between controls and beam diagnostics,
brings out-of-the-crate-freedom and opens unforeseen
possibilities for feedback building, inter-accelerator
cooperation and remote technical support.

INTRODUCTION
FELs are often called the fourth generation lightsources. Even if they are quite different from storagerings there is one goal they certainly have in common: ahigh quality beam. For FELs the quality of the electron
beam is measured by the brightness, where is it not only
necessary to create a bright electron beam but it is also
necessary to preserve the brightness as the electron isaccelerated and transported to the laser. From the earliest
days of FELs, it was clear that they were capable toovercome the limitations of the previous generations lightsources in the field of very high average power and very
short wavelengths. But it is only the recent developments
in electron accelerator technology that enabled FELs tostart to fulfill their earliest day promises.
With a practical example of Libera we would like toshow that the revolutionary design of this beam position
processor could with success be employed to improve thequality of beam. We start with the description of the firstmember of the Libera product family, the electron beam
position processor, which is an all-in-one, customizableproduct with rich connectivity options. It is intended for
demanding beam position monitoring and local and global
feedback applications on the light sources.
However, a Libera common, reconfigurable hardware
platform allows expanding the number of family
members. Developing a new Libera member, which
would cover the specific needs of pulsed machines likefree electron lasers is certainly an option, which wedemonstrate with some preliminary measurements in the

TUPOS45

final paragraph. Each user can customize various
attributes of the system to its needs, yet at the same time
benefit from the portability of the core all-in-one
encapsulated software. Flexible software architecture
allows rapid adaptation to multiple applications. Byleveraging “commodity” technologies, this flexibility is
actually achieved at reduced cost. The use of “openstandards” for intra- and inter-system communication
simplifies integration within the lab, feedback building,and enables a broader view of integration between
research facilities

LIBERA ADVANTAGES
Libera electron beam position processor is the firstmember of the Libera family. Its advantages are as
follows:

All-in-One
All-in-one is the concept of unification of various
building blocks and thus various functionalities in one
product. Libera is an all-in-one solution that enables
accurate beam position monitoring, trouble-freecommissioning, and local and global feedback building.
The timing and housekeeping functions do not span
across multiple boards in different racks, but are allcontained in a single module.

Customization
Customization is a capability that allows adaptation offunctionality of the device to specific requirements
without changing hardware. For the purpose of this paper
we identify three types of customization:
The parametric customization allows adjustment of
performance by simply changing parameters, without
affecting architecture of the programmable hardware.
Examples are analog board gain control and FIR filter
bandwidth by changing tap settings.
The architectural customization involves changes oflogic configuration (FPGA firmware, DSP code and othersoftware) to optimize performance for a particularpurpose. It allows building specific logical and signal
processing blocks, data-flow paths and algorithm
implementations.
The customization of communication interfaces
involves communication interfaces that can facilitate
implementation of different communication standards
without changing hardware.

Connectivity
Fast serial interconnect technologies provide a brandnew perspective on the process of developing highavailability and next-generation accelerator control andfeedback systems.

Available online at http://www.JACoW.org

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In general, individual modules may have their own
processors, operating systems and memory and cancommunicate independently with other modules. Because
nodes are operating-system agnostic, integration is nolonger required at the driver/backplane level but ascends
to the network and transport layers, using standard
protocols, which means significant time savings andsimpler design models.

LIBERA BUILDING BLOCKSIn the following part of the paper we discuss details
about the Libera electron beam position processor. A 1U
19” enclosure with a power supply accommodates analog
and digital boards, which are supported by software thatis easily adjustable to customer needs.

Analog Board
The analog board consists of a quasi-crossbar switch,
four identical RF channels, four analog-to-digitalconverters, and an interface to the digital board.
The innovative patent-pending quasi-crossbar switch
matrix unites the benefits of both the multi-channel andthe multiplexed system, and at the same time compensates
for the disadvantages of the two. We achieve
reproducibility and good “beam vs. current” dependence,
which are multiplexed system characteristics and – using
a multi-channel approach – we ensure a broader band ofoperation facilitating position measurements on a turn-byturn basis. Specifically, the switch facilitates redirectionof any of the four input signals to any of the four RF
channels.

Figure 1: Analog board block diagram.

Digital Board
Core building blocks of the Digital Board are the
FPGA (Free Programmable Gate Array), SBC (Single
Board Computer) and Memory. The board has also a veryrich set of interfaces.
The Virtex II Pro FPGA with two IBM PowerPC™
405 processors from Xilinx is the core of the digitalboard. It is a system-on-chip (SoC) solution, whichfacilitates the following functionalities: digital signal
processing, communication, formatting, timing, andhousekeeping. This architecture allows replacement ofsome hard-wired DSP functionality with more flexible
procedural description of algorithms. Another powerfulfeature of the Virtex-II Pro FPGA is integrated up to
3.125 Gbps Rocket IO transceivers. The transceivers
address all existing connectivity requirements as well as
emerging high-speed interface standards.
The SBC (Single Board Computer) built around aStrongArm-based Intel Xscale PXA255A processor, is amezzanine board. It provides application software,bootstrap for the configurable FPGA logic, configuration,
diagnostics and maintenance of Libera. Programming of
the FPGA via SBC is extremely efficient and it takes
approximately 1 second. The SBC downloads the FPGA
code via LAN, facilitating easy configuration of a BPM
system consisting of many Liberas. The embedded Linux
operating system with networking capabilities simplifies
integration into an accelerator control system. Fast
Ethernet is a native networking solution.
High capacity Memory enables the storage of a large
amount of data. The basic Libera electron beam position
processor configuration allows storing 32 Mbytes of dataor 1 million turn-by-turn samples.
The SFP (Small Form Pluggable) widely supported
open standard enables hot swap of various types of fiber
optic and copper-based transceivers into host equipment.
This provides the user with the flexibility to choose
between different protocols. Applications include: Gigabit
Ethernet, Fibre Channel, and Infiniband.

Figure 2: Digital board block diagram.

Software
The software is composed of system software andapplication software. The application software is limited
to the SBC. System software, on the other hand, spans
FPGA with embedded PowerPC processors, in addition to
the SBCThe System Software can be roughly divided into theoperating system component, covering GNU/Linux andthe embedded, digital signal processing (DSP) component
on the FPGA. The key elements of the latter are various
filtering and decimation algorithms. These can be tuned tothe end-user’s requirements so that BPM data is available
on a precise time scale, with desired bandwidth and

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estimate bunch charge we took sensitivity of a typicalstorage ring button pickup and assumed that current
sensitivity of a typical stripline is ten times higher.
0.1

Resolution / mmaccuracy. Additionally, fast feedback can be implemented
upon the end user's request. The GNU/Linux operating
system on the SBC provides a flexible and capable
platform for such tasks as networking, maintenance andcustomization.
The Application Software enables seamlessintegration of Libera into various accelerator control
systems. It allows users to interface Libera across a
network, deploy custom applications on Libera and use
Libera in fields or for tasks previously not envisioned, yet
in a way that is consistent and well defined. The Control
System Programming Interface (CSPI) is a high-level
programming interface that allows separating control
system-dependent knowledge from logic and details
related to Libera. The CSPI is effectively shielding
applications from intricacies and changes in theunderlying system software and hardware. Implemented
as a library, the CSPI facilitates accessing full Libera
functionality in a consistent and documented way.

0.01

0.001
0.1

1

10

Charge per bunch / nC

Figure 4: Laboratory measurement of pulsed to pulse
position fluctuation for a typical stripline pickup withposition sensitivity of 0.1 mm-1.

CONCLUSIONS

Figure 3: Software block diagram.

COVERING THE NEEDS OF THE
PULSED MACHINES
The performance of the first Libera family member was
optimized for the 3rd generation light sources, which are
based on storage rings and where signals originating fromthe pickups are periodic in nature. However, we also
encouraged our users to put Liberas in their Linacs andtransfer lines. The motivation for that is very practical: tohave a uniform BPM system installed on the wholeaccelerator facility. This approach simplifies system
integration, commissioning and maintenance, which inturn significantly lowers system life-cycle cost.
One of the most challenging aspects of measuring beam
position on FELs is pulse to pulse position measurement
fluctuation, which limits measurement resolution. In orderto evaluate how well Libera covers the needs of FELs, we
performed laboratory measurements of Libera electron
beam position processor. Individual pulses weregenerated using a step recovery diode. Figure 4 shows
measurement resolution as a function of bunch charge. To

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Libera is a product family, which open architecture
provides solid foundation for building different family
members, each optimized to satisfy specific beam
instrumentation needs. In this article we have explained
all-in-one, customization and connectivity advantages of
Libera family. We have also demonstrated that alreadythe first member of the Libera family, the electron beam
position processor, is showing excellent performance.
Despite being optimized for storage rings, it may satisfy
also the FEL beam position monitoring needs.
Developing a new Libera member especially for the FEL
machines, we are confident to be able to significantly
improve the performances.

ACKNOWLEDGEMENTS
We would like to express our gratitude to theInstrumentation Technologies colleagues, who to a great
extend contributed to the Libera design and development.

REFERENCES[1] S.V. Benson, “Free –Electron Lasers Push into New
Frontiers”, 2003, Optic&Photonic News[2] http://www.i-tech.si[3] R. Ursic, R. De Monte, “Digital Receivers Offer New
Solutions to Beam Instrumentation”, 1999 Particle
Accelerator Conference, New York, USA[4] R.
Ursic,“Reconfigurable
Instrumentation
Technologies, Architectures and Trends”, Beam
Instrumentation Workshop, 2002, Upton, USA[5] R. Ursic, B. Solar, “Holy trinity of Instrumentation
Development”, Beam Instrumentation Workshop,
2004, Knoxville, USA

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511

OPTICAL SYSTEMS FOR THE FOURTH GENERATION LIGHT SOURCE,
4GLS
F. M. Quinn, M. Bowler, M. D. Roper, M. MacDonald,
CCLRC Daresbury Laboratory, Synchrotron Radiation Department
Abstract
4GLS is a multi-user, multi-source facility proposed forconstruction at Daresbury Laboratory in the UK. By
exploiting super-conducting linac technology with energy
recovery, it will combine three free electron lasers and arange of conventional synchrotron radiation sources
covering the THz to SXR region. The facility will provide
femtosecond pulses at high repetition rate, with the FELs
delivering GW peak power in the VUV and XUV region.
This paper discusses the options and challenges for the
optical systems associated with the suite of photon
sources. The beamlines will need to operate both
independently and in flexible, synchronised combinations.
Together with the requirements for preserving the ultrabright, fast pulse properties, this places unique demandson the design, layout and operational modes. The paper
summarises current technical achievements and identifies
the research and development necessary before detailed
design of the 4GLS optical systems.

INTRODUCTION
The Fourth Generation Light Source, 4GLS, wasconceived as an optimal solution to the needs of the low
energy photon-based research community in the UK [1].
Funding for a research and development phase wasawarded in 2003; this includes production of a conceptual
design and the construction of an ERL-prototype.

The 4GLS suite of light sources

deflection angle. Hence the XUV FEL is shown on a
bypass arm of the electron beam transport system. Thislayout will evolve during the conceptual design process.
Table 1: 4GLS sources and existing relevant systems
4GLS source
XUV FEL10-100eVVUV FEL3-10eVIR FEL
0.02-0.4eV
CBS
KeV-Mev
THz CSR<0.01eV
Undulators
1-400eV
Bendingmagnets<3000eV

Examples of relevant existing
systems
One user facility in second phase
commissioning:
Tesla Test Facility, 10-200eV[2]phase 2 due October ‘04
Several experiment projects:
EUFELE, 3.5-6.5eV [3]
DUV-FEL BNL [4]
NIJI IV [5]Several user facilities:
FELIX [6] 0.25-0.005 eV
Jefferson Lab [7]
CLIO 0.012 - 0.4[8]Purpose built facility for medical
applications:
Vanderbilt FEL Centre [9]Several FEL based experiments [10]Demonstration experiments:
For example, BESSY II [11],Jefferson lab [12], ALS [13]examples on 3rd generation storagerings with longer pulse lengths
examples on 2nd and 3rd generation
storage rings with longer pulse
lengths

Figure 1. A scheme for the layout of 4GLS and its
proposed FEL and spontaneous sources.
The uniqueness of 4GLS is due to combining
superconducting energy recovery linac technology for
production of high quality electron beams with a varietyof free electron lasers, undulators and bending magnet
sources.
Figure 1 shows a scheme for the layout of the suite ofsources. A driver for this layout is the aim to direct
multiple sources onto a user experiment; this isconstrained to varying degrees by the usable optical

Available online at http://www.JACoW.org

Figure 2. Estimated peak brightness for the 4GLS suite ofphoton sources. Also shown are the calculations for the
ERL prototype currently under construction

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Determination of required research and development
during the design phase depends on the current
operational experience with sources similar to those
proposed for 4GLS. Table 1 lists the 4GLS suite of FELs
and other sources and identifies the most comparable,
existing facilities; the calculated peak brightness is shownin Figure 2. While the potential of FEL sources is being
explored in several projects, only IR FELs havesignificant operational experience as user facilities.

ISSUES AND OPTIONS FOR THE
PHOTON BEAMLINES
The optical systems for 4GLS need to match theproposed science programme and to preserve the uniqueproperties of the source. As the conceptual design phasestarts, it is important to understand the current state of theart and to highlight key technological challenges.

XUV FELThe XUV FEL will operate in single pass mode with noconstraints due to cavity optics. The design parameters
are still to be determined, but pre-design goals are shownin Table 2.
Table 2. Goals for XUV FEL performance.
parameter
range
energy/pulse
Pulse length
Micro-pulse
Macro-pulse
Average power
bandwidth
divergencePre-design values
10-100eV
2mJ
20-100fs
Repetition rate 65Mhz, 650 pulses
Repetition rate 60Hz
80W
3-6 x 10-4
30 – 150 µrad

The proposed experimental programme will require
both monochromated and direct FEL beams with microfocussing options, covering the first and higher harmonics
of the radiating undulator.
The most challenging source parameters for the XUVFEL beamline design are the energy per pulse which is
sufficient to cause component damage and the ultrashortpulse length goal which will place optical path difference
and stability constraints on the mechanical design.
No operational experience is available for pulse
energies at this photon energy or pulse length; the only
similar source is the Tesla Test Facility VUV FEL,
currently in phase 2 commissioning and due to take beamin October 2004. Significant research has been done onlaser ablation and damage thresholds, mostly driven by
micromachining requirements [14]. These show thatseveral damage mechanisms exist such as ablation, latticedamage, and photoemissive stress [e.g. 15] which dependon the energy deposited per unit area, the surface
condition, absorption efficiency in the material, the pulse
length and the photon energy. Schemes to mitigate theeffects are proposed in design studies for Tesla X-FEL[16], LCLS X-ray FEL [17] and TTF VUV FEL [18].

TUPOS47

These are based on using grazing incidence geometries
and low Z materials to reduce flux density and absorption.
More exotic schemes such as multifaceted reflectors, gas
optics, and renewable mirrors have also been proposed[15, 19].
The most relevant values for laser damage thresholds(LDT) come from research carried out at TTF phase 1
showing that LDT ranges from 0.03 J/cm2 for bulk Si to
0.06 J/cm2 for bulk carbon [20]. Using the LDT for
carbon and the estimated energy density per pulse for the
4GLS XUV FEL, a grazing incidence optic would need to
be at a minimum distance of 30m to give a safety marginof 1/10 of the LDT. While this has been accommodated
easily in the layout of TTF phase 2 which is a single
source entering an experiment building via a long tunnel,
it could have a significant impact on the layout of 4GLS.
The use of low Z materials will also affect the output
spectrum of the optical system, giving undesirable
absorption edges in the XUV and SXR range; forexample, carbon mirrors would affect the exploitation ofhigher harmonics.
However, the available data are very limited as they
only give values for ablation from a few bulk materials
whereas SR optics traditionally exploit thin coatings on
substrates (frequently dielectrics). Also, the accumulated
effects during long term exposure at different repetition
rates are not known. Gratings may have specific issues
due to the surface profile. More measurements are
required to ensure appropriate optical engineering
designs.
It is expected that apart from the instantaneous heatload considerations, designs similar to existing 3rd
generation SR beamlines can be adapted for use on 4GLS
[21]. Ultrafast pulse length and stability preservation will
demand isochronous photon beam design; optical path
differences experienced by a 200 fs pulse as it transits abeamline will need to be less than 10 microns (compared
to several mm for 3rd generation storage ring pulses of~10 ps). Vibration and thermal drift also need to beconsidered at this level.
A schematic layout is shown in Figure 3 which
incorporates an expansion space to reduce the power
density on the beamline optics and a pair of deflection
mirrors to select use of either the direct or monchromatedbeam. To cover the full harmonic photon energy range of
10 to 500 eV with a higher resolving power than the FEL
bandwidth may need two optimised monochromator
modules. The expansion space could usefully contain gas
phase filtering, intensity attenuation and photon
diagnostics similar to the systems developed for TTF
phase 2 [22].

Expansion
space

XUV FEL
Diagnostics
and filtering
modules

Deflection
mirrors

ent
Experimomator
MonochrExperiment
Monochromator

Direct beam

Experiment

Figure 3. Schematic layout for XUV FEL beamline.

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M. Quinn et al. / Proceedings of the 2004 FEL Conference, 511-514

Table 4. Goals for IR FEL performanceVUV FEL
The proposal for the VUV FEL is based on an optical
klystron; the pre-design goals are shown in Table 3. Suchsystems have operated successfully on storage ringfacilities [23] with the highest energy so far, 6.5 eV, 190
nm, demonstrated by EUFELE at Elettra [24].
Table 3. Goals for VUV FEL performance.
parameter
range
energy/pulse
Pulse length
repetition
Average power
bandwidth
divergencePre-design values
2-10eV
15 µJ
200-1000 fs
Repetition rate 6.25 MHz
100W<4 x 10-4
150-400 µrad

Again, both monochromated and direct FEL beam will
be required with a range of post focussing options.
Designs evolved for 3rd generation storage ring sources
utilising near normal incidence optics can be used. While
the average power loading is non-trivial, it is withincurrent experience. The instantaneous power loading ismuch reduced from the XUV FEL case but may yet
restrict the acceptable mirror incidence angles.
The most critical issue is that of cavity optics receiving
the full radiation load at normal incidence from the laser
cavity while needing to maintain very high reflectivity tosustain lasing. Outcoupling this power also requires either
significant transmission or a holed resonator. These
technical issues are currently limiting the lasing andtuning range of cavity FELs to less than 6.5eV[25]. In
order to reach the pre-design goal of 10 eV, 4GLS will
exploit the enhanced gain due to higher bunch charge andshorter electron bunches. This reduces the requirement forcavity mirror reflectivity from the extremely high value of>95% required for storage ring FELs. Even with thisrelaxed criterion, cavity mirror technology working overlong periods above 6.5 eV still needs to be proven. Recent
experimental results for capped aluminium mirrors give abest reflectivity of 75% at 10eV [26]. Damage thresholds
for these are now needed.
An alternative scheme would exploit high gain
harmonic generation and remove the need for an opticalcavity. Lasing has been achieved at 4.6 eV (266nm) at the
Brookhaven DUV FEL with 80-100 µJ per pulse [27].
The third harmonic has been used for experiments at 13.9
eV (88 nm) with measured power of 0.3 µJ per pulse [28].

IR FELThe IR FEL is based on an optical cavity design; thepre-design goals are given in Table 4. In the infra-red, awide variety of optical systems is possible and asignificant operational experience is available from IR
FELs and dedicated laser facilities [29].

parameter
range
energy/pulse
Pulse length
repetition
Average power
divergencePre-design values
0.4 – 0. 017 eV
75 µJ
100 fs – few ps
10 MHz900 W
0.4 – 7 mrads

Compton Backscattering source
Recent assessment has shown the potential of using
Compton backscattering on 4GLS to generate ultra-short
X-ray pulses. Existing projects cover the use of CBS in
medical imaging and extending the applications of IR
FEL facilities [9, 10]. The average flux ranges from 109 to
1012 ph/sec thus the primary optical difference from 3rdgeneration storage ring sources is mainly in the pulse
duration. Pulse lengths below 300fs become shorter inphysical length than the extinction lengths of Bragg
crystals affecting the diffraction process. This problem isbeing addressed by the research and development
activities for LCLS and TESLA X-FEL[16, 17].

Coherent Synchrotron Emission (THz)
Coherent radiation is produced in accelerators when theelectron bunch length is becomes less than the
wavelength of the radiation [12], giving flux
enhancements of the order of 109. Emitted power levels
up to 1 Wcm-1 have been measured [30]. As with the IR
FEL, there are no specific challenges for optics in thisregion.

Spontaneous sources
4GLS will also provide a suite of undulator andbending magnet sources; the primary operational mode
may need to have pulse lengths of ~1 ps to reduce thelikelihood of SASE and CSR emission. The proposed
devices will be high flux and brightness sources covering
IR to SXR with variable polarisation and the flexible
pulse characteristics of the ERL. The absorbed heat loadon the undulator beamlines will be substantially reduced
from devices on existing 3rd generation machines, whileproviding a peak brightness two orders of magnitude
higher. As with the FEL beamlines, existing opticalconcepts will be transferable to 4GLS, requiring only theadditional consideration given to preserving the fast
timing characteristics of the emitted photon pulses. The
exploitation of IR and visible light will be simplified by
the ease of extracting large apertures from the smaller,
more flexible ERL ring architecture.

CONCLUSIONSIn summary, the progress from 3rd generation storage
ring to 4th generation ERL and FEL photon sources bothbrings new optical challenges and removes others.

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The greatest challenge will be finding suitable opticalmaterials which can withstand the instantaneous heatload, particularly from the XUV FEL, reducing theconstraints on the optical design to more optimal levels.
A further need is to find cavity mirror optics which
deliver the desired tuning range for the VUV FEL.
General optical systems mechanical design has topreserve the fast pulse properties for all the 4GLS
sources. This is likely to be most acute for large opticalsystems (high performance XUV monochromator andbeamline can extend over 30m) or for optics requiring
significant cooling.
The ease of extracting large apertures will remove
difficulties experienced by IR and visible beamlines on
storage ring sources. The low electron beam energy also
removes the average power load issue for low energy
undulators sources.
Research into optics resilient to high instantaneous andaverage heat load will be part of the next stage of the
4GLS project.

REFERENCES[1] W. Flavell, E. A. Seddon, P. Weightman, M. A.
Chesters, M. W. Poole, F. M. Quinn, D. T. Clarke, J.
A. Clarke, M. J. Tobin, J. Phys.: Condens. Matter 16(2004) s2405-12[2] DESY report ‘TESLA-FEL 2002-01’[3] R. P. Walker et al, NIM A 467(2001) 34-37[4] L. DiMauro et al, NIM A 507 (2003) 15-17[5] K. Yamada et al, NIM A 475 (2001) 205-10[6] A. F. G. van der Meer, NIM A 528 (2004) 8-13
[7] G. R. Neil et al, Phys. Rev. Lett. 84 (2000) 6622
[8] R. Prazeres, F. Glotin, J. M. Ortega, NIM A 528(2003) 83-87[9] F. E. Carroll, American J. of Roentgenology 179(2002) 583; F. E. Carroll et al, SPIE 3614 (1999)
139-46[10] J. R. Boyce et al, Proc. Of the 2003 Particle Accel.
Conf. P938; F. Glotin et al, Phys. Rev. Lett. 77(1996) 3130; I. V. Pogorelsky et al, Phys. Rev.
Special Topics; Accel. and Beams 3 (2000) 090702[11] E. J. Singley et al, Phys. Rev. B 69 (2004) 092512;
M. Abo-Bakr et al, Phys. Rev. Lett. 90 (2003)
094801[12] G. P. Williams, Phil. Trans. R. Soc. Lond. A, 362(2004) 403-14[13] J. M. Byrd et al, Euro. Part. Accel. Conf. 2004
LBNL-55688[14] R. M. Wood, ‘Power and Energy Handling
Capability of Optical Materials’ TT60, SPIE Press(2002); J. K. Chen et al, Int. J. Solids and Struct. 39(2002) 3199; F. Stiez et al, App. Surf. Sci. 127-9(1998) 64; B. C. Stuart et al, Phys. Rev. B 53 (1996)
1749; J. Holfield et al Chem. Phys. 251 (2000) 237;
P. B. Corkum et al Phys. Rev. Lett. 61 (1988) 2886;
J. Gudde et al App. Surf. Sci. 127-9 (1998) 40

TUPOS47[15] R. Tatchyn, SLAC publication SLAC-PUB 6064
(2001)[16] Tesla Technical Design Report, Part V (2001)[17] LCLS Conceptual Design Report, SLAC-R 593(2002)[18] ‘Sase FEL at the Tesla Facility; Phase 2’ TESLAFEL 2002-01[19] D. Ryutov and A. Toor, SPIE 4500 (2001) 140-55[20] A. Andrejczuk et al, Hasylab Annual Report Part 1(2001) 117[21] H. Petersen et al, Rev. Sci. Instr. 66 (1995) 1; J. H.
Underwood in ‘Vacuum Ultraviolet Spectroscopy II’,ed. J. A. Samson and D. L. Ederer, Academic Press(2000) Chapter 3[22] K. Tiedtke et al, AIP Conference Proceedings 705(2003) 588; M. Richter et al, App. Phys. Lett., 83(2003) 2970
[23] M. E. Couprie, NIM A 393 (1997) 13; W. B. Colson
NIM A 429 (1999) 37[24] M. Trovo et al. NIM A 483 (2002) 157[25] D. Garzella NIM A 507 (2003) 170-4; A. Gatto et al
NIM A 483 (2002) 357-62[26] F. Bridou et al, Proc. SPIE vol 5250 (2003) 627[27] L. H. Yu et al, NIM A 528 (2004) 436-42[28] W. Li et al, Phys. Rev. Lett. 92 (2003) 083002[29] S. V. Benson, NIM A 483 (2002) 1-7; H. A.
Schwettman, NIM A 528 (2004) 1-7; R. Prazeres etal, NIM A 528 (2004) 83-87[30] G. L. Carr et al, Nature 420 (2002) 153

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A CONCEPT FOR Z-DEPENDENT MICROBUNCHING MEASUREMENTS
WITH COHERENT X-RAY TRANSITION RADIATION IN A SASE FEL*
A.H. Lumpkin#, W.M. Fawley†, and D.W. Rule‡
Advanced Photon Source, Argonne, Illinois 60439 USA†
Lawrence Berkeley National Laboratory, Berkeley, California 94720 USA‡
NSWC, Carderock Division, West Bethesda, Maryland 20817 USA
Abstract
We present an adaptation of the measurements
performed in the visible-to-VUV regime of the zdependent microbunching in a self-amplified spontaneousemission (SASE) free-electron laser (FEL). In theseexperiments a thin metal foil was used to block the more
intense SASE radiation and to generate coherent opticaltransition radiation (COTR) as one source in a two-foil
interferometer. However, for the proposed x-ray SASE
FELs, the intense SASE emission is either too strongly
transmitted at 1.5 Å or the needed foil thickness forblocking scatters the electron beam too much. Since xray transition radiation (XTR) is emitted in an annulus
with opening angle 1/γ = 36 µrad for 14.09-GeV
electrons, we propose using a thin foil or foil stack to
generate the XTR and coherent XTR (CXTR) and anannular crystal to wavelength sort the radiation. The
combined selectivity in angle and wavelength will favor
the CXTR over SASE by about eight orders of magnitude.
Time-dependent GINGER simulations support the zdependent gain evaluation plan.

INTRODUCTION
Previously, measurements in the visible-to-VUV
regime of z-dependent e-beam microbunching in a selfamplified spontaneous emission (SASE) free-electron
laser (FEL) have provided important information about
the fundamental mechanisms [1-3]. In those experimentsa thin metal foil was used to block the more intense SASE
radiation and to generate coherent optical transition
radiation (COTR) as one source in a two-foil
interferometer.
However, for the proposed Linac
Coherent Light Source (LCLS), the intense SASE
emission is either too strongly transmitted at 1.5 Å or theneeded foil thickness for blocking scatters the electron
beam too much. On-axis crystals used in Bragg or Laueconfigurations are also subjected to the intense x-rays and14.09-GeV electron beams. In order to extend the COTR
techniques to the x-ray regime, we have evaluated a novel
concept that takes advantage of the fact that x-raytransition radiation (XTR) is emitted naturally into anannulus with opening angle 1/γ = 36 µrad for 14.09-GeV
electrons. This angle corresponds to a projected annularradius of 850/425 µm at a distance of 24/12 m (where
12 m is the LCLS diagnostics station interval). We____________________________________________* Work supported by the U.S. Department of Energy, Office of Basic
Energy Sciences, under Contract Nos. W-31-109-ENG-38 and DEAC03-76SF0098.
#
lumpkin@aps.anl.gov

Available online at http://www.JACoW.org

propose using a thin foil or foil stack to generate the XTR
and coherent XTR (CXTR). Additionally, if the foil stack
is designed appropriately, resonant XTR (RXTR) would
be emitted with enhanced angular brilliance. We would
use an annular crystal to wavelength-sort the radiation.
The high-power e-beam, incoherent spontaneous emission
radiation (SER), and SASE would each go through theon-axis hole in the crystal. Importantly, at the CXTR
angular location of 24 m, the SASE and SER are red
shifted and would not be Bragg-reflected into theconverter crystal and detector. The combined radial
position and wavelength selectivity will favor CXTR over
SASE by at least eight orders of magnitude. A mosaic
crystal would be needed to cover the expected CXTR
normalized bandwidth of 0.1%. For the LCLS, timedependent GINGER simulations indicate that sufficientcoherent microbunching and concomitant detectable
CXTR occur by z ~ 20 m. This should allow anevaluation of the z-dependent gain and microbunchingfrom this point onward. We believe this to be more viable
than sorting the on-axis SER and SASE before the z =40m point.

BACKGROUND AND PHYSICSCONSIDERATIONS
One of the major issues is the survivability of foils or
crystals put into the intense x-ray and electron beams.
Based on assessments done previously [4], it is actually
the absorption of a significant fraction of the x-ray powerthat is the larger challenge. The nominal particle beam
parameters of a 1.5 π mm·mrad normalized emittancebeam of 1-nC charge and 14.09-GeV energy are projected
to result in x-ray power of 10 GW at 1.5 Å.
Issues related to performing a z-dependent gain
measurement using intraundulator diagnostic stations aredaunting. In particular:
1. The high absorption of x-ray power for the fulloperating conditions is projected to melt any
material at 15 Å and all above carbon at 1.5 Å.
2. The beam energy jitter of 0.1%, or 0.2% inwavelength, compared to the natural bandwidth of
10-5 for a diamond crystal monochromator creates amismatch.
3. The high level of SER for a 3% bandwidth (BW)was projected to mask the SASE radiation in thefirst 40 m of the undulator string. Of course, in
0.3% BW the SASE would be apparent sooner in z.
We propose that critical information on the FEL
performance could be obtained by tracking XTR as it

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evolves into significant intensities of CXTR. We takeadvantage of the fundamental angular distribution of XTR
that is annular, in contrast to the on-axis SASE. This is
schematically illustrated in Fig. 1.
The features of the diagnostic technique aresummarized below. We assume that a low-z foil (carbon
or Be) can survive in the 1.5-Å regime as reported, or alower-power commissioning scheme might be used. In
fact, this might be the selective emittance spoiler concept
described by Emma et al. [5] to produce fs x-ray pulses
with GW peak power, but much lower average power than
the full LCLS mode.

Conversion Mechanism
The transition radiation generated at the boundary of amaterial and the vacuum as the e-beam transits theinterface is the basis of this technique. Although thephoton yield is lower in the x-ray regime than in thevisible light regime, there are still detectable photons. Fora single foil we have two interfaces producing x-rays inthe forward direction. The signal scales as the square of
the number of interfaces if the thickness is an integral
phase step.
The foil could be inserted at the
intraundulator stations at 0 m, 12 m, 24 m, etc. We
estimate there would be about 104 photons in a 1% BW at~8 keV from a carbon foil and 1-nC beam.

Resonant X-ray Transition Radiation (RXTR)
To boost the XTR signal, we propose evaluating the
RXTR technique developed by a number of laboratories a
decade or more ago [6,7] to make an x-ray source basedon relativistic e-beams transitioning a foil stack consistingof M foils. They demonstrated that by choosing the
thickness and separations in integral phase steps, they
could enhance the radiation angular density by a factor of
M2. We need to evaluate if one can scale the beamenergies up by 50 and still make a realistic (compact)radiator at 8 keV. The sharpness of the annulus of RXTR
depends partly on M, and intensity peak angle (θopt)

depends on 1/γ and the material plasma frequencies. Evena simple nonresonant stack of five to ten foils would
increase the XTR by five to ten over a single foil.

Coherent X-ray Transition Radiation (CXTR)
In addition, the microbunching of the e-beam in the
SASE process would enhance the CXTR signal at 1.5 Åby a few orders of magnitude by the 100-m point. As
shown in Fig. 2, the spectral content is already narrowedby the 18.5-m point as predicted by GINGER simulations.
In Fig. 3, the z-dependent growth of the microbunchedfraction of nearly 32% is shown. With high bunching
fraction in mind, we now consider a calculation based on
extending the model described in a companion paper on
coherent optical transition radiation [8,9]. The CXTR
spectral-angular distribution is given by a product offunctions as shown in Eq. (1):d 2 N1d 2N(1)=
F (k ) ,dω dΩ dω dΩwhere the single particle TR distribution is given by
d 2 N1in the case of a single foil, and the coherencedωdΩfunction F (k ) is given by

F (k ) = N + N B (N B − 1) H (k ) ,2(2)

the bunching fraction
fB = NB Nandρ(k )H (k ) == g x (k x ) g y k y Fz (k z ) is the FourierQtransform of the charge form factors with Q = Ne = total
charge of the micropulse. The transverse form factors are
1 −σi2 ki2 2modeled as Gaussian g i (k i ) =e, i = x,y. In
2π
particular we consider g x (k x ) for the paraxial beam
2π
trajectories with θx << 1, where k x ≈ kθ x and k =λwith λ the radiation wavelength of 1.5 Å. In Fig. 4 we
where

( )

Figure 1: A schematic of the competing beams of SASE, SER, electrons, and XTR in the bore of the FEL vacuum
chamber. The thin foil that generates XTR/CXTR and the annular crystal are shown as separated by 24 m in thisexample. The CXTR angle is expected to fall well inside of the XTR angle due to coherence function factors.

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500 microbunches would be coherent at 1.5 Å. In thiscase we assumed that the foil-induced scattering or energy
straggling will not drastically reduce the microbunching
fraction. This aspect needs to be evaluated in more detail.

Detection Concept

Figure 2: A GINGER simulation of the LCLS showing
the microbunching spectral content at z =18.5 m.

At a downstream position (+24 m from the foil for
14.1-GeV energy), we would use an annular crystal tointeract with the off-axis XTR concentrated in a ring ofradius 850 µm (the CXTR, Fig. 4, will be at a smaller
angle/radius due to the coherence function). This crystal
would Bragg-select the 1.5 Å x-rays to be directed withhigh efficiency in its BW (~2 × 10-4 for Ge or Si) to the xray detector. A mosaic crystal might increase the BW to
0.1%. The on-axis SASE, SER, and e-beam would eachgo through the on-axis hole in the crystal. The off-axis
SASE or SER would be red shifted ~1.3% by the γ2θ2term (at 10 µrad) of the FEL resonance condition given in
Eq. 1 for the generated wavelength λ,λ  K2(3)
λ = u2 1 ++ γ 2 θ2  ,


2
2γ 

where γ is the Lorentz factor, λu is the period of theundulator (3.0 cm), K=3.5 is the undulator parameter, andθ is the angle relative to the beam axis. Unlike CXTR,
these red-shifted photons will not satisfy the Bragg’s law
condition at 1.5-Å wavelength. The x-rays would bedirected to an area x-ray detector or possibly converted tovisible light with a YAG:Ce converter screen. The visible
light would be detected by an area detector or an
intensified camera.

GINGER Simulations

show that CXTR falls well within the 1/γ cone of XTR for
an assumed projected radius σx = 5 µm. This assumes
some substructure on this length scale in the electronbeam transverse phase space such as occurred in our
visible-UV COTRI experiments. The vertical axis isphoton intensity per steradian-µbunch-0.1% BW. Since
we estimate that 500 microbunches are in a coherence
length, the incoherent curve intensity would be multipliedby 500 while the CXTR part would be multiplied by 5002.
The lobes are peaked in the 5-µrad angular regime andwould move out in angle for smaller effective beam sizes.
We analytically show the effects of a bunching fraction of
0.1, 0.2, and 0.3 as well in Fig. 4. In concept we do havethe annular cone versus the on-axis SASE, but we needsufficient CXTR at an angle where the SASE radiation isred shifted out of the crystal bandwidth.
Details of the coherence length and the effective
number of electron/microbunches radiating coherently
need to be addressed. For a 0.1% BW we estimate that

4.0e+7dN/dΩ [photons / sr-µbunch-0.1% BW]

Figure 3: GINGER simulation predictions for the zdependent microbunching fraction over the wavelength
region shown in Fig. 1.

Additional information on the source strengths
competing in the off-axis location is provided by
GINGER simulations of the predicted LCLS
performance.
Based on 1.2 mm mrad normalized

3.5e+73.0e+7bunching fraction
0.3

2.5e+72.0e+7
1.5e+70.2

1.0e+70.1
5.0e+6
incoherent
0.0

-50

-40

-30

-20

-10

0

10

20

30

40

50

θx (µrad)Figure 4: Calculated angular distribution for XTR and
CXTR for an effective projected radius of σx = 5 µm and14.1-GeV beam on a graphite foil. The incoherent
intensity and those at bunching fractions of 0.1, 0.2, and
0.3 are shown.

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emittance, the FEL power saturates at 85 m at a level of~20 GW and has a power gain length of ~4.4 m as seen in
Fig. 5. The peak of the time-averaged microbunchingoccurs at z = 85 m.
Using a GINGER diagnostic of microbunching phaseand amplitude, one can calculate the instantaneous
microbunching spectrum b(ω) at a given z. By z =15.7 m, the coherent signal-to-noise ratio in 0.6% BW isbetter than 10:1. Another aspect is the strength of the
SASE at the off-axis location. One analytically estimatesthat the intensity is down by a factor of 10-4 at a distanceof 4σ for a Gaussian function, which is corroborated by
the GINGER simulation at r = 200 µm for z = 42.81 m as
seen in Fig. 6. This effect, combined with the Bragg
angle selectivity, explains why we expect to see the
CXTR detection favored by eight orders of magnitude
over SASE.

SUMMARY
In summary, we have described for the first time anexperimental technique to measure the electron-beam zdependent microbunching in an x-ray SASE FEL. We
propose taking advantage of the fundamental annularangular distribution of CXTR as compared to the on-axis
SASE radiation and the spectral red shift of the SASE todetect the CXTR at the fundamental x-ray wavelength.
Initial experiments on XTR generation are being proposed
on SLAC’s Sub-Picosecond Pulse Source (SPPS) in thenext year.

ACKNOWLEDGMENTS
We thank B.X. Yang for useful discussions on x-ray
issues, and also M.J. Hogan and P. Krejcik of SLAC on
FFTB and SPPS issues, respectively. We also
acknowledge the support of H.-D. Nuhn (SLAC) and S.V.
Milton (ANL).

REFERENCES

Figure 5: A GINGER prediction of the x-ray SASE
power showing the z-dependent gain.

Figure 6: A GINGER simulation of the x-ray SASE FEL
showing the SASE radiation intensity as a function ofradial position. The intensity has already dropped by 10-4
at r = 200 µm for z = 42.8 m.

TUPOS48[1] A.H. Lumpkin et al., Phys. Rev. Lett., 86(1), 79,
January 1, 2001.
[2] A.H. Lumpkin et al., Phys. Rev. Lett., 88(23),234801, June 10, 2002.
[3] A.H. Lumpkin et al., “First Observations of COTR
due to a Microbunched Beam in the VUV at 157
nm,” Nucl. Instrum. Methods (in press 2004).
[4] R. Bionta et al., “Report of the LCLS Diagnostics
and Commissioning Workshop,” SLAC-R-715 and
LCLS-TN-042, 2004.
[5] P. Emma et al., Phys. Rev. Lett., 92(10), 074801-1,
2004.
[6] M.L. Ter-Mikaelian, High Energy Electromagnetic
Processes in Condensed Media (Wiley-Interscience,
New York, 1972).
[7] M.A. Piestrup et al., Phys. Rev. A., 45(2), 1183,
January 1992.
[8] D.W. Rule and A.H. Lumpkin, Proc. of the IEEE
2001 Particle Accel. Conf., Chicago, IL, pp. 12881290 (2001).
[9] A.H. Lumpkin, R.J. Dejus, and D.W. Rule, “First
Direct Comparisons of a COTRI Analytical Model toData from a SASE FEL at 540, 265, and 157 nm,”these proceedings.

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FIRST DIRECT COMPARISONS OF A COTRI ANALYTICAL MODEL TODATA FROM A SASE FEL AT 540, 265, AND 157 nm*
A.H. Lumpkin#, R.J. Dejus, and D.W. Rule†
Advanced Photon Source, Argonne, Illinois 60439 U.S.A.
†
NSWC Carderock Division, West Bethesda, Maryland 20817 U.S.A.
Abstract
We have been addressing fundamental aspects of the
microbunching of electron beams that are induced by the
self-amplified spontaneous emission (SASE) free-electron
laser (FEL) process using coherent optical transition
radiation interferometry (COTRI) techniques. Over thelast several years we have extended operations from thevisible to the VUV regime at the Advanced Photon Source(APS) low-energy undulator test line (LEUTL) project.
We have now performed our first direct comparison of theresults of an analytical model to COTRI experimental
data at 540, 265, and 157 nm.

INTRODUCTION
The interest in using coherent optical transition
radiation interferometry (COTRI) patterns to elucidate
self-amplified spontaneous emission (SASE) free-electron
laser (FEL) experiments has increased as we have
explored the technique’s sensitivities. In the past we had
only reported qualitative agreement on reproducing themain features of the far-field interferometric images [1-3].
As an exercise to develop our understanding and to test
our COTRI analytical model [4], test cases from the APS
SASE FEL data at wavelengths of 540, 265, and 157 nm
were evaluated. Although the beam energy is the main
parameter change, the relative angular pattern at thesethree wavelengths compared to the transform of theparticle distribution does help to probe the phenomena.
The direct comparisons reveal a number of details in theimages that are not matched by a simplifying assumptionof a single Gaussian transverse beam profile of the size
consistent with the incoherent OTR measurements.
Instead typically we need to use a split Gaussian with asmaller rms size to reproduce the fringe peak intensities inthe vertical plane and the asymmetry in the horizontal andvertical angles for the 540-nm and 265-nm cases. These
results indicate that there are localized transverse portionsof the beam distribution with a higher bunching fraction
than the mean. The different beam energies used inoperating at three wavelengths result in different overlapsof the Fourier-transformed bunch form factor and thesingle-electron OTR angular distribution for a two-foilgeometry. This aspect probes the model’s applicability
and sensitivities. We also provide evidence of the changes
in the effective microbunching transverse radius from theexponential gain regime into the saturation regime.
____________________________________________

Finally, we recognize that the experimental COTRI
patterns are not ideal, and that e-beam distributions andtrajectory/coalignment issues are also part of thephenomena.

EXPERIMENTAL BACKGROUND
The experiments were performed at the APS SASE FEL
facility. This facility includes the drive laser, S-band linac,bunch compressor, matching station, and the undulator
hall with the UV-visible and VUV-visible diagnostics
stations. Details have been reported previously [5] andmost recently in these proceedings [6]. The emphasis in
this paper will be on the description of the analyticalmodel in the next section and comparisons to data in thesubsequent section.

COHERENT OPTICAL TRANSITIONRADIATION MODEL
Optical transition radiation (OTR) is generated when acharged-particle beam transits the interface of two media
with different dielectric constants (e.g., vacuum to metal).
The techniques have been more widely employed withelectron beams, but so far only a few labs have looked atcoherent OTR (COTR) and used COTR interferometry.
Overall, the techniques provide information on transverse
position, transverse profile, divergence and beam
trajectory angle, emittance, intensity, energy, and bunch
length. There are coherence factors for wavelengths
longer than the bunch length and for microbunched beams
such as those induced by a SASE FEL process.
It is this latter process that we have explored with theconcomitant intense images. We use the model developed
previously [4] to show the first direct comparisons of our
COTRI data and calculations. The model describes thephenomenon in the spectral-angular distribution as a
product of several functions as shown in Equation (1):
2
2 d N
d 2N
1
= r⊥ ,||I (k )F (k ) ,
dω dΩ
dω dΩ

(1)

where r⊥,|| are the reflection coefficients, I (k ) is theinterference term, and F (k ) is the coherence function.
The single particle OTR distribution is()θ 2x + θ 2y
d 2 N1 e 2 1=dω dΩ hc π 2 ω γ −2 + θ 2 + θ 2

(

x

y

)

2

,

(2)

*Work supported by U.S. Department of Energy, Office of Basic Energy
Sciences, under Contract No. W-31-109-ENG-38.
#
lumpkin@aps.anl.gov

Available online at http://www.JACoW.org

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A. H. Lumpkin et al. / Proceedings of the 2004 FEL Conference, 519-522()

 kL − 2
γ + θ x2 + θ y2  ,(3))
I (k ) = 4 sin 2 4
where L = the foil separation and k is the wave vector.
The coherence function is given by

F (k ) = N + N B ( N B − 1) H (k )2,fB = NB N
andthe bunching fraction
ρ(k )H (k ) == g x (k x ) g y k y Fz (k z ) is the FourierQtransform of the charge form factors with Q = total chargeof the micropulse. The transverse form factors are
1 −σi2 ki2 2
g i (k i ) =e, i = x,y, and the longitudinal form
2π
1 −σ2Z k Z2 2factor for a microbunch is f (k Z ) =.
e
2π
The coherence function reduces to just the number ofparticles N when the number of microbunched particles
NB is zero. For the 540-nm case, we have fB at 10 to 20%
so the coherence enhancement of OTR is several orders ofmagnitude!
Besides tracking the z-dependent growth of COTR, the
540-nm COTRI patterns have an unusual sensitivity toelectron beam size compared to OTR as shown in Fig. 1
for 220-MeV beam and 0.2 mrad divergence. Here, thedifferent bunch form factors for 100-, 50-, and 25-µm sizeand 0.2% bunching fraction explicitly enhance different
peak fringes. The smallest beam size with largest form
factor in θ-space enhances the first three fringes compared
to only the inner lobes for the 50- and 100-µm sizes. The
sensitivity is less in the 100-, 150-, 200-µm regime asshown in Fig. 2, but there are still detectable differences.
Basically the OTRI fringe peaks act as a built-in metric.

( )Relative Intensity (arb. units)

1 .0

25 µm
50 µm

0.6

0.4

Incoherentcase

100 µm0.2

0.0-0.010-0.0050.000

Angle (radians)

0.005

0.010

Figure 1: Calculations showing the effects of beam sizesof 100, 50, and 25 µm on the COTRI fringe peak relative
intensities. A 220-MeV beam energy and 0.2 mrad
divergence were used.

TUPOS49

100 µm

0.8

150 µm
0.6

200 µm
0.4

0.2

(4)

where

0.8

1.0

Relative Intensity (arb. units)

where the angles θx and θy are measured with respect toe2= α is the finethe angle of specular reflection, andhc
structure constant.
I (k ) is given by

0.0-0.010-0.005

0.000

0.005

0.010

Angle (radians)

Figure 2: Calculations showing the effects of beam sizes
200, 150, and 100 µm on the COTRI fringe inner lobe
relative intensities. The cofactors are narrow in angularspace and only multiply the inner lobe distribution for thisparameter set.

COMPARISONS OF DATA AND THE
MODEL

540-nm Wavelength, Postsaturation Regime
The first case we wanted to study in more detail was the
far-field image taken from the saturation regime in z after
undulator 8 reported previously [2]. This particular image
is very rich in features as we noted at that time. The mostobvious effect after the reduced integrated intensity
compared to data after undulator 5, is the difference in theθx and θy structure seen in Figs. 3 and 4, respectively.
This is attributed to an elliptical e-beam and thecorresponding asymmetric transform of the bunch form
factor in θ-space. In the θy axis the presence of threefringe peaks versus the single inner lobe in θx is seen.
The data in the exponential gain regime late in z do notexhibit three fringe peaks in any plane, so larger effective
beam sizes are indicated.
The resulting calculations of the model using E = 220
MeV and σx′,y′ = 0.2 mrad are directly compared in Fig. 3
for θx and Fig. 4 for θy. As the beam form factor isadjusted, it is clear that the shape of the first lobe is also
sensitive to the effective beam size in the 50- to 100-µm
σx size.
In the θx plane (Fig. 3), beam sizes of 75, 85, and 95µm with a bunching fraction (BF) of 2% were evaluated.
The first fringe peak at about ±1 mrad is narrower thanthat of the first θy peak. This is due to the larger effective
σx, which transforms to a narrower bunch form factor inθ-space centered at θ = 0 so that only the inner side of thefirst lobe is involved in the products of Eq. (1).
When looked at closely, the vertical fringe patternimage has a slight tilt in the θx - θy plane so that our threecolumn-averaged profile does not hit the fringe peak at its
maximum for both +θy and -θy values (Fig. 4). Attempts
to match the asymmetry in peak intensities were made,but it appears that while σy = 20 µm works for fringe

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A. H. Lumpkin et al. / Proceedings of the 2004 FEL Conference, 519-522

peaks 1, 3, and 4 at negative θy, the second fringe peak isoverestimated. A σy = 25 µm value seems to give thecorrect height for peak #2, but it then misses theintensities for peaks 3 and 4.
1.0
x-rms=75 microns
85 microns
95 microns

0.9

1.0
0.9

0.7

0.8

0.6

0.7

Intensity (arb. units)

Intensity (arb. units)

0.8

For this run, the effective beam size at this location
seems to be elliptical with the major axis now on the yaxis. This results in only seeing the two inner peaks with avalley depth between them consistent with σy′ = 0.1 mrad,
BF = 2%, and σy = 35 µm as shown in Fig. 7.

0.5
0.4
0.3
0.2

0.6
0.5
0.4

0.2
-10

-5

0

5

10

15

θx (mrad)0.1

Figure 3: A direct comparison of model results with σx =75, 85, and 95 µm and 2% bunching fraction andexperimental θx data for the saturated regime case at
540 nm.

0.0
-10

0

5

10

Figure 5: A comparison of the experimental θx and θydata for the 265-nm case.
1.0

ExperimentCalculation

0.9

-5

θ (mrad)

1.0

ExperimentCalculation

0.9

0.8

0.8

0.7

Intensity (arb. units)

Intensity (arb. units)θx profile

0.3

0.1
0.0
-15

θy profile

0.6
0.5
0.4
0.3

0.7
0.6
0.5
0.4
0.3

0.2

0.2
0.1

0.1
0.0
-15

-10

-5

0

5

10

15

θy (mrad)Figure 4: A direct comparison of model results andexperimental θy data for the saturated regime case at
540 nm. A split Gaussian with 20-25 µm was used.

0.0
-10

0

5

10

θ (mrad)Figure 6: A direct comparison of model results andexperimental θx data using the second harmonic
wavelength of 132.5 nm.

265-nm Case

1.0

ExperimentCalculation

0.9
0.8

Intensity (arb. units)

The image to be examined was previously published as
Fig. 3 of reference 7. The beam energy is now nominally
308 MeV.
The θx data are puzzling because although the two
peaks fit in the envelope of the θy peaks, they do notmatch, as seen in Fig. 5. However, the peak locations
match a calculation using the second harmonic
wavelength at 132.5 nm as shown in Fig. 6. The +θx size
is matched using σx = 20 µm, but the peak intensity
symmetry is not matched. We suspect this is a beamcoalignment or steering effect that is not in the model yet.
We do not believe our 265-nm bandpass filters would
pass the second harmonic, and furthermore, our camera isinsensitive at 132 nm. There has been a report of second
harmonic generation in a laser-field-accelerated electron
beam [8], and there may be some related physics issues.

-5

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0
-10

-5

0

5

10

θy (mrad)Figure 7: A direct comparison of model results at 265 nm
for σy = 35 µm and two divergences (0.2 and 0.1 mrad).
(The 0.1-mrad case has a deeper valley (red) like the data
(blue)).

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A. H. Lumpkin et al. / Proceedings of the 2004 FEL Conference, 519-522

157-nm Case

X Profile, VUV6, 157nm, Image #332, 03/07/03
exp. data
Profile thru center
50 µm - 50 µm
9/23/03
50 µm - 25 µm
40 µm - 25 µm
45 µm - 25 µm
43 µm - 25 µm

1.0
0.9

Intensity (arb. units)

0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

-3

-2

-1

0

1

2

3

θx (mrad)Figure 8: A direct comparison of the model results andexperimental θx data at 157 nm. A split-Gaussian beam
size is used to reproduce the asymmetry in the lobes andtheir peak positions.

SUMMARY
In summary, we have directly compared the results of a
COTRI analytical model and data ranging from 540 nm to
157 nm corresponding to beam energies of 220 to 400
MeV. We have found that we can interpret fringe peakasymmetry in θx - θy in terms of beam size asymmetry in x

TUPOS49

Rms beam size=50 µm
Rms beam size=60 µm
1.0
0.9
0.8

Intensity (arb. units)

The next wavelength regime used a new set of
diagnostic stations to detect VUV radiation [5]. All
optical transport is done with reflective optics. The beamenergy is now 400 MeV, and the spherical mirrors are
such that the camera only covers ± 2.5 mrad. At 400 MeV
and L = 63 mm we calculate that the second fringe peaklocations are at ± 2.0 mrad. This means that the majorityof the detected information is in the first fringe peaks. We
find that the bunch form factors and the narrower coneangle still result in sufficient sensitivity to beam size.
The image is somewhat like a four-leaf clover with four
lobes of comparable intensity at 90° to each other. The
fringe peak positions are different in θx and θy, and thiswe still attribute to the elliptical beam size. Only now thegame is played on the first peak shape, not the visibility ofthe second or third fringe. The θx profile is matched withan asymmetric Gaussian of 43 µm and 25 µm for negativeand positive angles, respectively, as shown in Fig. 8. The
first peak location at 0.75 mrad is matched with the lobe
width as well. There is a strong sensitivity of the lobe
intensity to beam size in the -θx data where 43 µm
matches better than 40 or 45 µm, but we probably also
have an alignment effect as well.
The θy profiles and fringe peak positions at ± 0.5 mrad
are matched with σy ~ 50 µm as seen in Fig. 9. The 40µm calculation has too large of a lobe width and the 60µm case mismatches the central minimum depth as wellas the peak position.

Y Profile, VUV6, 157nm, Image #332, 03/07/03
Profile thru center
exp. data
9/23/03
Rms beam size=40 µm

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

-3

-2

-1

0

1

2

3

θy (mrad)Figure 9: A direct comparison of model results for beam
sizes of 40, 50, and 60 µm and the experimental θy datafrom VUV-6 at 157 nm. Best fit is for σy = 50 µm.
and y. We also show that details involved in the ± θx or± θy asymmetry can be reproduced with a split-Gaussian
assumption for ± x or ± y beam profiles. COTRI has beenshown to be a sensitive diagnostic of electron microbunch
structure for the SASE process in the visible to VUVregimes. We expect that a similar formalism can beextended to the x-ray regime as discussed in another paperin these proceedings [9].

ACKNOWLEDGEMENTS
The authors acknowledge the support of Kwang-Je Kim
and the Advanced Accelerator Research Initiative at
Argonne National Laboratory.

REFERENCES[1] A.H. Lumpkin et al., Phys. Rev. Lett. 86, 79 (2001).
[2] A.H. Lumpkin et al., Phys. Rev. Lett. 88, 234801(2002).
[3] A.H. Lumpkin et al., “First Observations of COTR
due to a Microbunched Beam in the VUV at 157
nm,” Nucl. Instrum. Methods (in press 2004).
[4] D.W. Rule and A.H. Lumpkin, Proc. of the IEEE
2001 Particle Accelerator Conference, Chicago, IL,
pp. 1288-1290 (2001).
[5] P. Den Hartog et al., Nucl. Instrum. Methods A483,
407 (2002).
[6] A.H. Lumpkin et al., “Use of VUV Imaging to
Evaluate COTR and Beam-Steering Effects in a
SASE FEL at 130 nm,” these proceedings.
[7] A.H. Lumpkin et al., Nucl. Instrum. Methods A483,
402 (2002).
[8] S.D. Baton et al., Phys. Rev. Lett. 91(10), 105001-1(2003).
[9] A.H. Lumpkin, William M. Fawley, and Donald W.
Rule, “A Concept for z-dependent Microbunching
Measurements with Coherent X-ray Transition
Radiation in a SASE FEL,” these proceedings.

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A. H. Lumpkin et al. / Proceedings of the 2004 FEL Conference, 523-526

USE OF VUV IMAGING TO EVALUATE COTR AND BEAM-STEERINGEFFECTS IN A SASE FEL AT 130 NM*
A.H. Lumpkin**, Y.-C. Chae, R.J. Dejus, M. Erdmann, J.W. Lewellen, and Y. Li
Advanced Photon Source, Argonne National Laboratory, Argonne, Illinois 60439, USA
Abstract
We report the first experimental data on coherent
optical transition radiation (COTR) at 130 nm as well as
first tests of the analytical model for single-kick-error
effects on gain in a SASE FEL. We use both near-field
and far-field imaging of the SASE radiation. We also use
the COTR near-field data to identify a calibration factor
error in the rf BPM system so that the SKE analysis isbased on the camera centroid positions and their relation
to those of the alignment laser only.

INTRODUCTION
We have continued to explore VUV operations on the
Advanced Photon Source (APS) self-amplified emission(SASE) free-electron laser (FEL) [1]. With installation ofa fifth VUV imaging station located after undulator 7 ofan eight-undulator series, we have performed our mostcomplete SASE gain curve measurements at 130 nm as
well as obtaining beam profile, position, and divergence
information. This is the shortest wavelength to date forour complementary coherent optical transition radiation(COTR) measurements [2]. We have also done the firstexperimental test of Tanaka et al.’s analytical model forthe effects of a single-kick error of the e-beam on gain
and microbunching in a SASE FEL [3]. In the course of
the experiments, we performed a direct comparison of thebeam position as determined by the local rf BPMs and the
VUV video cameras. An rf BPM calibration factor error
was determined so all steering data were evaluated using
the COTR near-field image centroids obtained from thecameras adjacent to and one undulator downstream of theselected horizontal corrector in the single-kick error tests.
In addition, we compared the e-beam image centroid
positions with those of the alignment laser at the available

cameras to sort out the effective trajectory and its effecton overall gain. The FEL performance was consistent
with GENESIS simulations of the experiment described indetail in a companion paper [4].

EXPERIMENTAL BACKGROUND
The APS injector system for the storage ring includes
an S-band linac that can be configured with thephotocathode (PC) rf gun to provide bright beams to the
FEL. The drive laser is a Nd:YLF oscillator with anamplifier, and the fundamental frequency is quadrupled toattain laser light at 266 nm. The PC gun was operated
with a Cu photocathode at the time of these experiments[5]. Typically, about 300 pC of charge were accelerated
and then bunch compressed in a chicane where the beamenergy is 150 MeV [6]. The normalized emittance εx,y =4.5/3.5 mm mrad was measured after the chicane, and thebunch length was measured with a zero-phasing rf
technique to be about 200 fs (rms). The beam is furthertransported to the low-energy undulator test line (LEUTL)
tunnel where eight, 2.4-m-long undulators are installed.
The gun, linac, and undulator system are schematicallyshown in Fig. 1, and the e-beam parameters are
summarized in Table 1.
Before and after each undulator station we have aquadrupole, steering correctors, rf BPMs, and visible light
imaging station. The quadrupole and horizontal andvertical correctors are located first in the drift space
followed by the rf BPM buttons. For the purpose of theseexperiments we used the five VUV imaging stations
installed after undulator numbers 2, 4, 5, 6, and 7 anddenoted as VUV-2, etc. As shown in Fig. 2, the station
included a first actuator that has a YAG:Ce screen, a thin
Al foil option, and pinhole reference target. At a

Figure 1: A schematic of the APS SASE FEL showing the PC gun, linac, bunch compression stage, three-screen
emittance matching station, and the undulator series with diagnostics.
___________________________________________* Work supported by the U.S. Department of Energy, Office of Basic
Energy Sciences, under Contract No. W-31-109-ENG-38.
**lumpkin@aps.anl.gov

Available online at http://www.JACoW.org

FEL Technology

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A. H. Lumpkin et al. / Proceedings of the 2004 FEL Conference, 523-526

Table 1: Nominal Electron Beam Parameters with the
PC-gun Beam Injected into the Undulators during theExperiments
Parameter
Beam Energy (MeV)
Emittance x,y (mm-mrad)
Peak Current (A)Bunch Length (ps rms)
Charge (pC)
Energy Spread (%)

Value
439
4-6
300 to 500
0.3300-400
0.1-0.2

performed and the integrated intensities in a prescribedregion-of-interest are determined. We also obtain the
projected profile centroids and sizes at FWHM.
The single-kick-error experiments were performed in
the undulator 5 region by turning off the quadrupole (Q5)and corrector (H5) after the undulator and using the H4
corrector before the undulator. The first test was toestablish the amount of steering strength by assessing the
rf BPM readings and the VUV-4 and VUV-5 camera
readings.

RESULTS AND DISCUSSION
The experiments were initiated with a z-dependent gain
scan following the tune-up through each of the five VUVstations. The near-field gain curve is presented in Fig. 3
which was not available during the experiment. From theselected VUV attenuators as a function of z, we assessedthat we were in the exponential gain regime at undulator 5
so we could test the model.

Figure 2: A schematic of the upgraded diagnostic stations
for VUV imaging after undulators 2, 4, 5, 6, and 7. The
quadrupole with H and V correctors, the rf BPM, the first
actuator stage, the 45° retractable mirror, and reflective
optics to the VUV camera are shown.
distance of 63 mm downstream a second pick-off mirror
is located on a stepper motor. In one position the mirror
surface is oriented to send optical radiation to the UVvisible cameras on the wall and the other position directs
radiation upward into the VUV transport. A fixed mirror
redirects the radiation to one of two selectable sphericalmirrors of focal length 900 and 2000 mm that provide
near-field and far-field imaging, respectively, for the
VUV CCD camera. A series of stepper motors locatedbetween the spherical mirror and camera control theselectable filter assemblies, which include visible lightbandpass filters, neutral density (ND) filters, VUVbandpass filters, and VUV regime attenuation. The CCD
camera is a Roper Scientific model with a 512 × 512 pixel
array sensor, which detects radiation from about 120 nm
through the visible regime [7] with a well depth of 105.
The camera is based on the Marconi VUV EEV57-10
back-thinned chip with no antireflection coating and cantransfer the full image at a maximum rate of 3 Hz. The
data are digitized by a 16-bit board and saved on a local
PC disk. Usually, we acquire 100 images for each zposition or angular kick position. The images aresubsequently transferred to the UNIX system andprocessed off-line with GIANT or J Data Miner [8], local
programs with an IDL base. Background subtractions are

TUPOS50

VUV Station

Figure 3: Results of the z-dependent gain measurement.
As part of the steering tests, the recorded rf BPM
positions before and after undulator 5 were tracked withsteering strength of H4. The results are shown in Fig. 4.
However, when we compared the deflections to the VUVimage centroids with H4 settings, we ascertained that the
rf BPM calibration factor was too low by a factor of six.
Since the VUV camera’s images were clearly moving
beam diameter distances and the calibration factor of thecamera had been confirmed by using the stepper motor tomove the pinhole target position a known amount, we
decided to rely on the VUV camera images. Examples of
the image position changes are given in Table 2, where
the calibration factor is 11 µm/channel, and in Fig. 5. The

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A. H. Lumpkin et al. / Proceedings of the 2004 FEL Conference, 523-526

effective kick angle is shown in Fig. 5 (bottom) with anaverage of ~0.3 mrad per Amp of corrector strength. We
also had recorded the alignment laser image positions ineach camera so we could reference the e-beam position to
the “straightline” of the alignment laser. The final results
indicate that in the undulator 5 region the beam trajectoryis actually fairly close to the alignment laser (within
50 µrad) so the analytical model should apply.

these conditions. Any offset, x0, is to be determined. In
addition, this model addressed a smearing of the
microbunching, which would cause a change in its gain
length Lg to
Lg′′ =

Lg
1− πx 2

, where Lg is the SASE gain length. (2)
VUV-5

VUV-4

Figure 4: Results of the rf BPM readings versus H4corrector strength. The reported deflections are found to
be too small compared to VUV image centroids.

Figure 5: Results of the VUV-4 and VUV-5 camera
image centroid shifts (top), the position difference in thetwo cameras (middle), and the effective kick angle(bottom) versus H4 corrector strength.

Table 2: Summary of Image Centroid Positions at
VUV-5 versus Corrector Setting (12-18-03)
Note: Foil in, ND0.0, Q5 off: H5 offDx*
Y c*File # Q4:V4 H4 (A) Xc*
4228 On-237--1204244 On
0
161
124
126
4249 On
2
290
129
117
4259 Off2
252
2244268 Off0
115-137 218
4278 Off-2(4)
229*Positions in channels (ch) at 11 µm per ch.

Dy*
6
-9

VUV-5
VUV-4

-6
11

Note: When turn off Q4/V4 with H4=0, the image moves-46 ch = -500 µm in x. V4 was at -1.7A in tuned state,
and we have a vertical motion down of 109 ch = 1100
µm.
The SKE model of Tanaka et al., [3] defines the new
SASE gain length L′g in terms of a critical angle,θ c = λ Lg , where λ is the wavelength of the SASE and

Lg is gain length at zero error. We can rewrite this as
Lg
L g′ =
where x = θ θ c ,
(1)
1− x2
and θ is the kick angle. The camera steering data are
given in Figs. 5 and 6. In Fig. 6 the ratio of P5/P4
represents the ratio of the VUV-5/VUV-4 image
intensities. By steering the beam close to one half thecritical angle, the gain is reduced by a factor of two under

Figure 6: The measured image intensities for VUV-4 andVUV-5 versus H4 corrector strength (top) and the basic
ratio P5/P4 of VUV-5/VUV-4 for the SASE undulator
light with far-field imaging (bottom).
The multiplier of π in the denominator on x2 causes amore rapid reduction in gain length versus θ, but the
curve is also only a bound on the inner θ limit. However,at the low gains at the time of the experiment the far-field
images were too weak and the near-field images may
have a contribution from the broadband UV-visible OTR
light.
We have repeated the experiments with rf
thermionic gun beam recently and will continue thisevaluation of microbunch smearing as detected by COTR
signals.

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SUMMARY
In summary, we have extended our COTR experiments
to 130 nm. The near-field images were used in the singlekick error tests to determine beam steering instead of the
rf BPMs whose calibration was found to be incorrect.
The comparisons of VUV SASE gain to steering error
were found to be in agreement with the model and
GENESIS simulations as described in more detail in acompanion paper [4]. The test of the microbunchingsmearing effect in the model was experimentally lessclear, and further experiments and analysis are warranted.

ACKNOWLEDGEMENTS
The authors acknowledge the support of Kwang-Je Kim
and the Advanced Accelerator Research Initiative at
Argonne National Laboratory.

REFERENCES[1] S.V. Milton et al., Science 292 (2002) 2037.
[2] A.H. Lumpkin et al., “First Observations of COTR
due to a Microbunched Beam in the VUV at 157
nm,” Nucl. Instrum. Methods (in press 2004).

TUPOS50[3] T. Tanaka et al., “Consideration on an Alignment
Tolerance of BPMs for SCSS Undulator Line,” Nucl.
Instrum. Methods (in press 2004).
[4] Y.-C. Chae et al., “An Experimental Study of the
Beam-Steering Effect on FEL Gain at LEUTL’s
Segmented Undulator,” (these proceedings).
[5] S. Biedron et al., Proc. of 1999 Particle Accelerator
Conference, New York, NY, 2024-2026 (1999).
[6] M. Borland et al., A.W. Chao (Ed.), Proc. of the 2000
Linac Accelerator Conference, Monterey, CA, SLAC
R561, 863 (2001).
[7] P. Den Hartog et al., Nucl. Instrum. Methods, A483,
407 (2002).
[8] B. Tiemann, J Data Miner analysis program, ANL,
(2003).

527

I.B. Vasserman / Proceedings of the 2004 FEL Conference, 527-529

TEST OF HORIZONTAL MAGNETIC FIELD MEASUREMENTS IN THE
PRESENCE OF A STRONG VERTICAL FIELD
Isaac Vasserman, Experimental Facility Division, Argonne National Laboratory, Argonne, Illinois
60439, USA
Abstract
Trajectory straightness is an important parameter in
defining the performance of free electron laser (FEL)
devices. Horizontal field measurements using Hall probes
were tested in 1997 in preparation for the tuning of theundulators for the FEL project at the Advanced Photon
Source (APS) [1]. This work is a continuation of the 1997
work, now for the demanding LCLS project. Tolerances
for the Linac Coherent Light Source (LCLS) FEL
undulator [2] specify a trajectory of <2 µm excursion inboth (horizontal and vertical) planes for a particle energyof 14.1 GeV, which means that measurements of a small
horizontal field in presence of strong (up to 1.5 T) verticalfield are required. Hall probe measurements under suchconditions are complicated due to the planar Hall probe
effect [3, 4]. The previous test done in 1997 showed thatthe 2-axis Sentron probe is a possible choice. Highsensitivity of horizontal field integrals to the vertical
position of the sensor was observed. By positioning theprobe accurately in the Y direction, this probe could be
used for fast measurements and tuning of devices for
LCLS undulator with a much larger magnetic field, thanfor the APS FEL project. Good agreement with reference
moving coil measurements was obtained. The Sentronprobe was recently used for LCLS prototype
measurements and tuning.

SUMMARY OF 1997 TEST
Test of horizontal field measurements, using different
types of Hall probes, was done in 1997 with a regularundulator A device, which is the main undulator type at
the APS storage ring [1]. Two Hall probes: the usual Belltype probe and the Sentron probe were used in this test.
The main challenge with horizontal field measurements is
a planar Hall-probe effect, which is associated with theangle between the vertical field and the axial probe
current flow direction. The main result from the 1997 testis that it is impossible to obtain the first and second field
integrals corresponding to reference measurements doneby moving coil. By adjusting the angle of the Bell Hall
probe around the horizontal (X) axis, either the first or
second field integrals could be made equal to thereference data but not both of them simultaneously. Suchan effect for the Sentron probe is rather small, as can beseen from Fig. 1. The Sentron probe is a new type of Hall
probe, a so-called vertical Hall device, which is sensitive
to the magnetic field parallel to the chip plane [5]. A
different effect contributes to the distortion of horizontal
field measurements in presence of a strong vertical field
for this probe: the field integrals dependence on vertical

INTRODUCTION
The very tight schedule for the LCLS project assumes
rather little time for tuning and measurements of the 33
devices comprising the undulator. So it is important tolimit the measurement technique options while tuning thedevice. A Hall probe is an essential part of this technique,which allows measurements and tuning of the field toobtain the best possible radiation performance of thedevice, including phase errors and trajectory straightness.
An important part of the tuning is reducing the first (J1)and second (J2) field integrals responsible for particle
trajectory angles and displacement to provide an overlapof radiation and particle beam. Measurements ofintegrated over device field integrals with help of rotationcoil and/or stretch wire is the most reliable way ofobtaining such data. The LCLS undulator consists of 3.4m-long sections with a 6.5 mm fixed gap, which makes
problematic the possibility of using such a technique,especially for horizontal field integrals measurements.
Improving the accuracy of the Hall probe measurementsallowing the use of the Hall probe for all tuning purposes
is a main goal of this work.

Available online at http://www.JACoW.org

Fig. 1 Sensitivity of Bell and Sentron Hall probes toangular positioning: first horizontal field Integral vs.
rotation angle around the X axis.
position (see Fig. 2). Results of the 1997 test showed arather small dependence of the angle but strong
dependence on vertical position. By choosing the proper
vertical position of the Sentron probe, both first andsecond horizontal field integrals are found to be very
close to the reference measurements done by moving coil,and such probe was used for tuning of the devices for the
APS FEL project.

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Fig. 3 Nonlinearity of a horizontal Sentron probe sensor
vs. vertical and longitudinal fields.

Fig. 2 Sensitivity of Bell and Sentron Hall probes tovertical position: ∆J1/∆Y≈350 (G-cm)/mm.

NONLINEARITY OF SENTRON 2-AXIS
HALL PROBE
The LCLS undulator has a much bigger verticalmagnetic field (up to 1.5 T) than does undulator A. To
check the possibility of using the Sentron probe in thiscase, a special test, using a LCLS prototype, was done. At
first, the nonlinearity of the horizontal field sensor in thepresence of strong longitudinal and vertical fields wasinvestigated. The Hall probe was placed in the APS
calibration magnet with a vertical field up to 1.5 T. To
create a horizontal component of the magnetic field, theprobe was inclined by a small (<1°) angle. The verticalfield was measured by a separate probe. The vendor’scalibration of the horizontal probe sensor shows a verysmall nonlinearity. The analog signal to the magnetic fieldratio for this probe is constant with an accuracy of 0.1%.
However, these measurements show that the presence of avertical field makes a difference. Results of suchmeasurements are shown in Fig. 3 (red crosses). The
horizontal field was calculated from the measured verticalfield:
Bx = B y * sin ϕ ,where ϕ is the inclination angle of the probe.

The vendor’s value for the analog-to-field ratio is 5 V/T.
The nonlinearity of the Hall probe in the region of thevertical field up to 1.0 T is about 6%. The amplitude of
the horizontal field for the LCLS prototype is < 10 Gauss,where the nonlinearity is small. Another, and muchstronger, source of errors is the contribution of thelongitudinal field. By rotating the probe around the axial
axis at 90°, a longitudinal component of the field wascreated. The results of the test are shown in Fig. 3 (blacksquares). There is a clear contribution of the longitudinalcomponent of the field, especially in the region of small(up to 300 Gauss) field, which is of most interest for us.
Results of the test with the LCLS prototype are described
below.

HORIZONTAL FIELD MEASUREMENTS
As was found in the test of 1997, there is a strong
dependence of horizontal field integrals on the vertical
position of the 2-axis Sentron probe. Sentron probe SN#367 was used for measurements of the LCLS prototype.
Results of the test show the same behavior of the integral
vs. vertical displacement dependence, as during 1997 test,with big quantitative difference: ∆J1/∆Y ~1330 (Gcm)/mm. Fig. 4 shows different trajectories calculated for
different vertical positions of the probe. As discussed
earlier [1], these results are related to measurement errors
associated with field vs. vertical displacement
dependence. What is the reason for such dependence?
From Maxwell’s equations, we have ∂By/∂x -∂Bx/∂y =0.
The results of measurements of the first vertical field
integral dependence on X, ∂Jy/∂x, made by moving coiland flipping coil, agree with Maxwell’s equation, while
the same measurements made by Sentron probe disagree.
Measurements of ∂By/∂x are close to each other fordifferent magnetic measurement techniques, including theHall probe. It means that horizontal field measurements,
made by an axial Hall probe, are not real and have someinduced error. A possible explanation could be associatedwith the existence of both longitudinal and verticalmagnetic fields. To find the correct vertical trajectory, aFig. 4 Vertical trajectories calculated from Sentron Hall
probe measurements at different vertical positions,
E=14.1 GeV.

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I.B. Vasserman / Proceedings of the 2004 FEL Conference, 527-529

reference test was done using the 81-mm-long moving
coil. A close match of the vertical trajectory was found for
the Hall probe, using the proper vertical position of theFig. 5 Comparison of vertical trajectories measured by a
Sentron probe and a moving coil.
probe. The result is shown in Fig. 5 for a particle energyof E=14.1 GeV. Comparison of moving coilmeasurements and Hall probe measurements of thevertical field was done as well and showed the same levelof agreement as for the horizontal field. No additional
adjustment was required in this case. Fig. 6 shows
horizontal field data measured with probea) in the case, where errors are defined by thelongitudinal field, we will have horizontal field distortion∆Bx=Bx(0.2mm)-Bx(-0.2mm)=0, when the longitudinal
field Bz=0 (pole centers);b) in the case, where only the vertical field is responsible
for the distortion, we will have ∆B=0, when the verticalfield By=0 (in-between the poles).
Taking this into account, we can conclude: the main
contribution to field errors is due to the Bz field (∆B=0
close to the pole centers). Two neighboring poles have thezero crossing point shifted in opposite directions, which
could be explained by the fact that the longitudinal field
has the same sign and vertical field has the opposite signin this location. It creates a DC component of thehorizontal the field and distortion of first and second field
integrals. Fortunately the effect of the vertical field israther small for this range of magnetic field, and it ispossible to find the proper Y, where the results ofmeasurements are close enough to reference
measurements, and the Hall probe could be used formeasurements and tuning of vertical trajectories.

CONCLUSION
Tests of horizontal field measurements done with the
LCLS prototype provided reliable results such that the
Sentron probe could be used for the LCLS project
horizontal field measurements and tuning. A test using acalibration magnet examined the nonlinearity ofhorizontal field measurements in presence of strong
vertical and longitudinal fields. The most probable reason
for horizontal field errors is associated with a strong
longitudinal Bz field for y≠0, and has to be taken into
account, especially in the case of devices with a strong
magnetic field. Some contribution of a strong verticalfield can be observed as well.

ACKNOWLEDGMENTS
This work is supported by the U.S. Department ofEnergy, Office of Basic Energy Sciences, under contract
No. W-31-109-ENG-38.

REFERENCES
Fig. 6 a: Horizontal field for y=-0.2 mm and y=0.2 mm; b:difference of the fields Bx (0.2mm) –Bx (-0.2 mm).
vertical offsets of ±0.2 mm and the difference between
these two measurements. From the data shown in Fig. 6b,
we can see that two types of nonlinearity exist: one is dueto the contribution of the longitudinal field, and another isdue to the vertical field. The undulator magnetic field in
the ideal case is determined by horizontal, vertical andlongitudinal components [6]:Bx=0
By=B0*cosh(ky)*cos(kz)
Bz=-B0*sinh(ky)sin(kz), where k=2π/λ, λ is an
undulator period.
We have two possible scenarios:[1] I. Vasserman, “Test of Horizontal Field
Measurements Using Two-Axis Hall Probes at the
APS Magnetic Measurement Facility,” Argonne
National Laboratory report ANL/APS/TB-32 (1998).
[2] Conceptual Design Report (CDR) for the Linac
Coherent Light Source Project, SLAC-R-593, April
2002, http://www-ssrl.slac.stanford.edu/lcls/cdr/[3] D. Swoboda, IEEE Trans. Magn. MAG-17, 2125
(1981).
[4] W. Poole and R. P. Walker, IEEE Trans. Magn.
MAG-17, 2129 (1981).
[5] B. Berkes, R.S. Popovich. “New type of a 3-axis
Hall Probe,” 9th International Magnet Measurement
Workshop, CEA/Saclay, France, June, 1995.
[6] H. Wiedemann, Particle Accelerator Physics II,
Springer, 1995.

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S.G. Biedron et al. / Proceedings of the 2004 FEL Conference, 530-533

DEVELOPMENT AND MEASUREMENT OF STRAIN FREE RFPHOTOINJECTOR VACUUM WINDOWS *Sandra G. Biedron1, Marcus Babzien2, Lahsen Assoufid3, Yuelin Li3, Greg Gill4, John W.
Lewellen1,3, Jun Qian3
1

Energy Systems Division, Argonne National Laboratory, Argonne, IL 60439 USA, 2Accelerator
Test Facility, Brookhaven National Laboratory, Upton, NY 11973 USA, 3Advanced Photon Source,
Argonne National Laboratory, Argonne, IL 60439 USA, 4Formerly of Insulator Seal, Division of
MDC Vacuum Products Corporation, FL 34243 USA
Abstract
RF photoinjectors produce the highest brightness
electron bunches only under nearly ideal illumination by adrive laser [1]. The vacuum window used to introduce thelaser beam is an essential element that may potentiallydegrade the distribution, making it difficult or impossible
to know the actual uniformity achieved at the cathode.
Because of the necessity to obtain ultrahigh vacuum near
the photoinjector, some restrictions are imposed on the
fabrication technology available to manufacture
distortion-free windows. At the UV wavelengths
commonly used for photoinjectors, it is challenging tomeasure and eliminate degradation caused by vacuum
windows. Here, we discuss the initial measurements of astrain-free, coated, UHV window manufactured by
Insulator Seal in collaboration with members of
Brookhaven and Argonne National Laboratories.

INTRODUCTION
The effectiveness of RF photoinjectors is dependent uponnear ideal illumination of the cathode by a drive laser.
Much progress has been made in developing laser systems
that meet the requirements imposed by photoinjectors andhigh-brightness experiments. These requirements include
precision control of intensity within the active region of
the cathode, a necessity for minimizing space-chargeinduced emittance growth. Most approaches involve
producing a uniform, or other mathematically simple,
laser intensity profile. However, laser diagnostics do not
typically extend into the vacuum system of thephotoinjector, and electron beam measurements to assessthe uniformity of the laser intensity distribution provide
very complex results. The vacuum window used to
introduce the laser beam is an essential element that may
potentially degrade any distribution, making it difficult or
impossible to know the actual uniformity achieved at thecathode. Because of the necessity to obtain ultrahighvacuum near the photoinjector, some restrictions are
imposed on the fabrication technology available tomanufacture distortion-free windows. At the UV
wavelengths commonly used for photoinjectors, it ischallenging to measure and eliminate degradation caused
by vacuum windows. Here, we discuss the initial
measurements of a strain-free, coated, UHV window

manufactured by Insulator Seal (ISI) in collaboration withmembers of Brookhaven National Laboratory (BNL) and
Argonne National Laboratory (ANL).

THE WINDOW
A class of laser input windows based on a newtechnological design has been fabricated for use withhigh-brightness, photocathode-rf gun systems. The ISIdesigned window is a special fused silica deep ultra violet
viewport with a dual-band or double “V” antireflection(AR coating) coating between 264 nm (<0.15%
reflectance from 250-270 nm) and 529 nm (<0.15%
reflectance from 515-535 nm for ease of alignment in thevisible) mounted on a 2.75” rotatable flange. We chose
this bandwidth of coating to accommodate both the ANL
Low-Energy Undulator Test Line (LEUTL) photocathoderf gun drive laser (fourth harmonic of Nd:Glass) [2] andthe BNL Accelerator Test Facility (ATF) photocathode-rf
gun drive laser (Nd:YAG). The window assembly was
designed to be parallel to within 10 arcseconds with asurface quality of 10-5 scratch-dig, and has a flatness of
0.1 wave at 632 nm.

MEASUREMENTS
The first set of measurements was performed at the ATF
at BNL using the frequency quadrupled Nd:YAG (266nm) photocathode-rf gun drive laser operating at 30
microjoules. The laser spot size at the window wasapproximately 5 mm diameter. The laser profile wasimaged at the cathode monument, a fluorescent target
which is at the conjugate image plane of the RF
photocathode surface, without and with the window in thepath. The window, when inserted, was placed unmounted(no vacuum equipment/flanges) perpendicular to the laserat ~ 1 meter upstream of the cathode monument. As
shown in Figure 1, there is only a slight change in the
beam profile in the comparison of the two cases. Although
the window could be installed as close as 0.2 meters fromthe cathode assembly, we believe this simple experimentand its positive result represents the behavior if thiswindow is mounted in the photocathode-rf___________________________________________*Corresponding author: biedron@anl.gov, Tel: 630 252 1162, Fax: 630
252 4886

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S.G. Biedron et al. / Proceedings of the 2004 FEL Conference, 530-533

531

Figure 1: Raw and enhanced laser profile of 30 microjoules of frequency quadrupled
Nd:YAG without (left column) and with (right column) the ISI window in its path.
\zooming onto their surfaces for maximum lateral
gun assembly. In fact, since the window can be mounted
resolution.
as close to ~0.2 meters from the cathode, any induced
Note that the optical AR coating is a three layer base ofphase distortion will not result in an intensity modulation.
The second set of measurements was performed at ANL SiO2 with a HfO2 coating of a proprietary to ISI thickness.
at the metrology laboratory of the Advanced Photon The index of refraction for Si02 is 1.47 and the index of
Source. We measured both unmounted and mounted refraction of HfO2 is approximately 2.25.
In Figures 2 and 3, respectively, the best fit withwindows to emulate the effect of the window actually
being attached to the photocathode-rf gun assembly. We spherical aberrations removed is presented for thealso measured the flatness profiles and present the raw mounted window. In Figures 4 and 5, respectively, theand best fit, with the spherical aberration removed. The best fit with the spherical aberrations removed isflatness is presented. Note that we refer to Window 1 as presented for the case of the unmounted window from one
that which is mounted on the vacuum cross and Window side. In Figures 6 and 7, respectively, the best fit with the
2 as the unmounted window. In the case of the mounted spherical aberrations removed is presented for the case of
window, the laser only passes the window from the most the unmounted window for the laser entering from theaccessible surface. In the case of the unmounted surface, opposite side. Both windows present very good surface
flatness measurements could be taken from laser flatness with values below the specification requirement
introduction on either side. The instrument used was a of 0.1 wv rms.
WYKO-6000 interferometer (WYKO Corp., 2650 East
Elvira Road, Tucson, AZ 85706, USA) that employs HeNe (λ=632.8 nm) laser test beam with 150 mm diam
aperture. The window measurements were done by

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Figure 2: Measured surface profile of the mounted
window #1. Here only tilt was removed. Unit: wv.

Figure 3. Measured surface profile of the mounted
window #1, with both the tilt and power removed. Unit:
wv.

Figure 6. Measured profile of the opposite surface of
window #2. Here only the tilt was removed. Unit: wv.

Figure 7. Measured profile of the opposite surface of thewindow #2, with the tilt and power removed. Unit: wv.

Figure 4. Measured profile of one surface of theunmounted window #2. Here only the tilt was removed.
Unit: wv.
a)b)c)
Figure 8: a) Input laser beam distribution before window
as imaged at cathode “monument”, b) cathode image fromexit port showing 5 mm diameter fiducial ring, c) cathodeimage with incident laser spot.

Figure 5. Measured profile of one surface of theunmounted window #2, with the tilt and power removed.:
Unit: wv.

TUPOS52

The third set of measurements was an experimental test
conducted at the ATF at BNL. The new window was
mounted on the entrance port of the gun, and the "old"standard style window without flatness consideration on
the symmetric port – referred to as the “output” port - on
the other side of the gun. There is a camera imaging thecathode on this output port that provides and excellent
real-time view of the UV on the cathode that also reveals
surface features. To assist with measurements, the ATF
has machined a 5 mm diameter fiducial groove onto thesurface of the cathode to assist in locating the precise
geometric center and provide a scale factor for the beam
image. The window appears to have added no distortion

S.G. Biedron et al. / Proceedings of the 2004 FEL Conference, 530-533

to the beam, and with the larger clear aperture, it isexpected that the cathode should be able to accept 4 mm
uniform laser spots. The cathode image and the laser
imaged on the cathode is shown in Figure 8. No
downstream measurements have been performed as ofyet, as there have been a number of challenges in thisreplacement gun’s commissioning.

CONCLUSIONS
Future plans include testing and characterization ofthese new technology laser input windows downstream of
the gun at the Accelerator Test Facility. Such work will be
critical to future photoinjector-based light source projects
such as the Linac Coherent Light Source (LCLS) [3] andthe high-average power free-electron lasers [4].

ACKNOWLEDGEMENTS
This work is supported by the US Department of Energy,
Office of Basic Energy Sciences under Contract No. W31-109-ENG-38 and by the Air Force Research

533

Laboratory and the Joint Technology Office of the HighEnergy Laser Program under funding source number JTO04-602-23. The work of M. Babzien is supported by theUnited States Department of Energy under contract DEAC-02-98CH10886. The work of G. Gill was supported
by Insulator Seal, a Division of MDC Vacuum Products.

REFERENCES[1] V. Yakimenko et al, NIM A, 483 (2002) 277-281[2] S.V. Milton et al., “Measured Exponential Gain and
Saturation of a Self-Amplified Spontaneous Emission
Free-Electron Laser,” originally published in Science
Express as 10.1126/science.1059955 on May 17, 2001;
Science, Vol. 292, Issue 5524 (2001) 2037.
[3] LCLS Design Group, LCLS Design Report, NTISDoc. No. DE98059292, April 1998 (Copies may beordered from the National Technical Information Service,
Springfield, VA 22162).
[4] G.R. Neil et al., Phys. Rev. Lett. 84, 662 (2000).

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S.S. Kurennoy / Proceedings of the 2004 FEL Conference, 534-537

COMPARISON OF PARMELA AND MAFIA SIMULATIONS OF BEAM
DYNAMICS IN HIGH CURRENT PHOTOINJECTOR
Sergey S. Kurennoy, LANL, Los Alamos, NM 87545, USA
Abstract

The emittance-compensating magnetic field in MAFIA
is calculated by the static solver S. Near the photocathode
this field vanishes due to properly adjusted currents in themain solenoid and the bucking coil. The comparison of
the fields computed by Poisson/SF and MAFIA ispresented in Fig. 2. The left graph shows the profile of thelongitudinal electric field on the cavity axis. The electricfield alternates its direction from one cell to the next, as itshould be in a π-mode. The fields in the third cell aredesigned to be lower than in the first two cells to reduce
the power density on the coupler irises in that cell. The
fields in the vacuum plenum are low. The right picture
shows the longitudinal component of the emittancecompensating magnetic field on the cavity axis. In
addition to vanishing near the photocathode, the field
decreases again far from it, where the beam is alreadyrelativistic and more rigid, so that the solenoidal focusing
is no more needed. Both the electric and magnetic fields
found by two different codes agree perfectly.
0

10

−0.1
5

−0.2

Bz, kGINTRODUCTION
The normal-conducting RF cavity of the high-current
CW photoinjector (PI) for high-power free-electron lasers
consists of 2.5 cells plus a vacuum plenum [1]. The cells
have an on-axis electric coupling through large beam
apertures. The PI has an emittance-compensating solenoidwith a bucking coil. After the first half-length cell, wherea photocathode will be housed, there are two full-length
cells, followed by a vacuum plenum with vacuum-pumpports. Two ridge-loaded tapered waveguides for RF input
are connected to the third cell. The vacuum-plenum cell
has its resonance at about 650 MHz, well below thefrequency 700 MHz of the working π-mode in the cavity.
The photoinjector RF cavity is practically axisymmetric
except for the RF couplers and vacuum pump ports. These
discontinuities create only small perturbations of thecavity RF fields, even though the coupler irises are thelocations of the highest power density of the wall ohmic
losses, see [1, 2]. Therefore, field calculations and beam
dynamics study in the cavity can be performed with good
accuracy using 2-D codes. The 2-D design of the cavity
and magnets was performed using the Poisson / Superfish(SF) codes [3] for field computations and Parmela [4] forbeam dynamics simulations.

Figure 1: 2.5-cell PI RF cavity layout used in MAFIA.
Dimensions are in m. The main solenoid (dark blue) andbucking coil (red) are surrounded by steel (green).

Ez, MV/m

A high-current RF photoinjector producing lowemittance electron beam is an important technology forhigh power CW FEL. LANL-AES team designed a 2.5cell π-mode 700-MHz normal-conducting RF photoinjector [1] with magnetic emittance compensation. Using
the electric field gradients of 7, 7, and 5 MV/m in thethree subsequent cells, the photoinjector will produce a
2.5-MeV electron beam with 3-nC charge per bunch and
7-mm-mrad transverse rms emittance. Beam dynamics inthe photoinjector has been modeled in detail. In addition
to the usual approach, with fields calculated by SuperfishPoisson and beam simulations performed by Parmela, we
also used MAFIA group of codes, both to calculate cavity
fields and to model beam dynamics with its particle-incell module TS. The second way naturally includes wakefield effects into consideration. Results of simulations andcomparison between two approaches are presented.

0

−0.3
−0.4

−5

−0.5

Parmela/SF
MAFIA
−10
0

10

20

30

40

50

60

70

0

MAFIA, corr
Poisson
10

20

30

40

50

60

70

z, cm

z, cm

Figure 2: Longitudinal electric field (left) and longitudinal
static magnetic field (right) on the cavity axis.

CAVITY FIELDS
The layout used for field computations in MAFIA [5]and the electric field of the working RF mode are shownin Fig. 1. Unlike the case of SF/Parmela, where the fields
calculated by SF are interpolated for Parmela, here wewant to use exactly the same mesh for both fieldcomputations and PIC simulations.

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WAKE FIELDS
Wake field effects can be, in principle, included into
Parmela beam dynamics simulations [4]. However,Parmela does not compute the wakes: they must be
calculated externally, by another code. Here is the maindifficulty of this particular problem: one has to calculate
wake fields in the photoinjector cavity, where the beam is

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S.S. Kurennoy / Proceedings of the 2004 FEL Conference, 534-537

accelerated from a non-relativistic, almost zero speed tothe speed of light, becoming relativistic only by thesecond cell. A standard numerical approach with ABCI or
MAFIA T-module, where a rigid bunch travels throughthe structure at the speed of light and the wakes behind it
are calculated, does not work in this case. In fact, there isno other way to calculate wake fields in such a problem
except using a self-consistent numerical solution of theMaxwell equations with account of particle motion, e.g., aparticle-in-cell (PIC) simulation. This is exactly what TScodes (TS2 for 2-D and TS3 for 3-D problems) in the
MAFIA suite do. Unlike that approach, Parmela applies
particle-push method using the RF and static fields
extracted from SF and Poisson, respectively, in the region
where the beam travels. It takes into account the beam
space-charge, as well as the image currents in thephotocathode plane, but does not calculate fields created
due to the beam charge interaction with the cavity walls,
i.e. the wake fields.

535

1.

2.

3.

BEAM DYNAMICS SIMULATIONS
TS2 PIC Simulations
An example of beam dynamics modeling with the
MAFIA TS2 PIC code is illustrated in Fig. 3. Snapshotsof the electric field (arrows) and particles (red dots) show
the bunch evolution during its acceleration in the cavity.
The injected 3-nC bunch has a uniform charge densitywith a longitudinal flat-top pulse shape of the total lengthof 6° RF, and its center is injected at the RF phase equal
to 15°. In TS2 the number of injected particles in thebunch is defined by the code, unlike the case of Parmela,and depends on the number of mesh points. The particles
can have different charges. For a typical TS2 run with
1.45 M mesh points in the whole 2-D region of Fig. 1,
including magnets and outside the cavity, the number ofparticles in the bunch of 1-cm radius is 6360 (only 10% ofparticles are plotted in Fig. 3). The mesh has the step sizes
inside the cavity ∆z≈∆r≈0.5 mm (it should behomogeneous in z inside the cavity for TS). The TS2 runwith this 1.45-M mesh takes 1.4 hours on a 3.2-GHz PC,
with a significant fraction of this time spent preparing theoutput file. For a finer mesh of 4.41 M points, with∆z≈∆r≈0.3 mm in the cavity, the same bunch consisted of
8040 particles, and the TS2 run took 3.6 hours.
For each frame in Fig. 3 (numbered in its lower left
corner), Table 1 gives the physical time and the value fora maximal arrow of the electric field in that frame. The
fields in the frames are scaled independently; enforcing
one global scale would not be useful here since the fieldvalues differ by almost two orders of magnitude. A few
frames in Fig. 3 show the RF field near its minima (RFphases are close to 0° or 180°), to emphasize the bunch
self-fields (space charge) and wake fields. In particular, inthe frames 3, 5, and 6, there are noticeable field arrows
near the bunch, which deviate from the RF field patternand correspond to the bunch self-fields. In the frame 8 one
can clearly see the fields left after the bunch (wakes) near
the cavity exit.

4.

5.

6.

7.

8.
Figure 3: Electric field and bunch evolution in the cavity.
Table 1: Time (ns) and max arrows (MV/m) in Fig. 3
Frame
1
2
3
4
5
6
7
8
Time
.12 .32 .67 .95 1.4 2.1 2.6 2.8
Emax
10 15 .53 14 .53 .53 13 .52
Figure 4 shows two snapshots of the electron bunch
shortly after injection. The bunch is very short and shaped
like a pancake. Its size rapidly increases due to spacecharge forces until it moves away from the photocathodeFEL Technology

536

S.S. Kurennoy / Proceedings of the 2004 FEL Conference, 534-537

where the magnetic field is getting stronger to prevent thebunch radial expansion. The bunch shape near the cavity
exit and the wakes are shown in Fig. 5 in detail, cf. Fig. 3(note different scales in Figs. 4-5; dimensions are in m).

the passage and at the cavity exit. This confirms that evenat a very high bunch repetition rate no noticeable wakeinfluence is observed.

Comparison of TS2 and Parmela results
We now will compare results of TS2 and Parmela beam
dynamics simulations of the photoinjector RF cavity.
Figures 6 show the beam transverse rms size, the beamtransverse rms emittance in the lab frame, and kinetic
energy as the function of the beam position in the cavity
for 3-nC charge per bunch.
5

3
Parmela
MAFIA TS2, 1.5M
MAFIA TS2, 2M mod
MAFIA TS2, 4.5M
Parmela sc3d, 100K

x

rms

, mm

4

Figure 4: Electron bunch near the photocathode (a. t=0.08
ns, Emax=5.3 MV/m; b. t=0.24 ns, Emax=9.4 MV/m).

2
1

Parmela sc3d, 800K, 643
0
0

10

20

30

40

50

60

z, cm

Lab frame ε

x,rms

a.

, mm.mrad

400

Parmela
MAFIA TS2, 1.5M
MAFIA TS2, 2M mod
MAFIA TS2, 4.5M
Parmela sc3d, 100K

350
300

3

Parmela sc3d, 800K, 64

250
200
150
100
50
0
0

10

20

Figure 5: Bunch and fields near the cavity exit (a. t=2.62
ns, Emax=1.1 MV/m; b. t=2.82 ns, Emax=0.63 MV/m).

TUPOS54

30

40

50

60

z, cm

b.

(b)

2.5
2

Ekin, MeV

From Figs. 3-5 we see that the 3-nC bunch is focusedwell by the external magnetic field and remains compact.
Its maximal transverse size at the cavity exit is below 7mm, smaller than the initial size of 1 cm. The bunch
length increases, of course, but remains below 1 cm.
Analyzing Figs. 3-5 and similar field snapshots, one canconclude that the beam space-charge electric fields are
below 1 MV/m, while the wake fields do not exceed 0.7
MV/m. These values are small compared to the maximal
RF field values of 10-15 MV/m.
We performed TS2 runs with a few (up to four)
identical 3-nC bunches separated in time by two RF
periods, which corresponds to 350-MHz bunch repetition
rate. Simulations show identical bunch parameters during

(a)

1.5
1
0.5
MAFIA TS2
Parmela
0
0

10

20

30

z, cm

40

50

60

(c)

Figure 6: Beam transverse rms size (a), emittance (b), andkinetic energy (c) versus beam position for a 3-nC bunch.

S.S. Kurennoy / Proceedings of the 2004 FEL Conference, 534-537

According to Figs. 6, TS2 and Parmela results agree
well. The kinetic energy curves from both codes justoverlap. The rms beam size predictions agree in general,but there are some differences accumulated by the cavity
end. The transverse emittance was calculated in the labframe, so the apparent emittance blow-up in the first cell
is simply due to the bunch rotation in the solenoidal field.
In Fig. 6b we see differences between two codes near the
point where the rotational part of the emittance reaches its
maximum. Investigating the reasons, we performed a few
code runs with modified parameters. In MAFIA, finer
meshes were used. In Parmela, we used optional 3-D
space-charge computations with spch3d instead of thestandard axisymmetric 2-D space-charge routine scheff[4]. These results are also plotted in Figs. 6. One can saythat the results obtained using 3-D and 2-D routines in
Parmela differ more than those of Parmela and TS2.
It is interesting to see how the results depend on thebunch charge. For that purpose, a few runs with bunchcharges of 10 nC and 1 nC have been performed, withoutchanging other parameters. Obviously, when the bunchcharge is varied without changing the magnetic field thatwas tuned for 3 nC, the bunch focusing is no longer
optimal. As one can expect, the beam is under focused for
10-nC bunch (Fig. 7), and over focused for 1-nC one. For
1-nC, the bunch becomes so tiny near the cavity exit
(below 2 mm transversely) that its self-field is getting
high, about 2.3 MV/m. The wake fields remain rather
weak. For the 10-nC case, the bunch is much larger bothtransversely (more than 1.5 cm) and longitudinally (about
2.5 cm) than for 3 nC. The self-field of 10-nC bunches is
not large because the charge density is reduced due to thebunch blow-up. There was also no noticeable wake-field
increase. More details can be found in [6].
8537

simulations, where both Parmela and TS2 have difficulty
computing space-charge fields of the thin pancake-likebunches accurately.
The transverse emittance values at the exit of the PI RF
cavity are between 7 and 10 mm·mrad. The bunch slices
in the phase space are not completely aligned yet after the
PI cavity. The design goal was to provide the lowest beamemittance at the wiggler. If we allow a 3-nC bunch to drift
after the PI cavity, its transverse emittance will reachabout 6 mm·mrad that corresponds to the best possiblealignment of the bunch slices. The design requirement forthe photoinjector was to have the beam transverse rms
emittance below 10 mm·mrad for 3-nC charge per bunch.

SUMMARY
The beam dynamics simulations of the high-current
photoinjector for high-power FEL using the MAFIA PIC
code TS2 are described. Results obtained from TS2 andParmela simulations agree well. Since the wake fields are
not taken into account in Parmela computations, thisagreement confirms that the wake-field effects in thephotoinjector RF cavity are negligible. The wakes are
weak not only for the design bunch charge of 3 nC, buteven for the higher bunch charge of 10 nC. The main
reason for that is the large size of the beam apertures in
the photoinjector RF cavity. The only noticeable wakefields are observed near the RF cavity exit, where theaperture radius is reduced to its smallest value of 2.5 cm.
However, the wakes die out before the next bunch arrival,even at the very high bunch repetition rate, 350 MHz, as
was confirmed by TS2 simulations with a few bunches.
For the design beam current of 100 mA, the bunch
repetition rate is 35 MHz.
The author would like to acknowledge useful
discussions with L.M. Young, J.H. Billen, F.L. Krawczyk,
and D.C. Nguyen.

7

REFERENCES

xrms, mm

6
5
4
3
2
1
0
0

Parmela
MAFIA TS2, 1.5M
MAFIA TS2, 4.5M
Parmela sc3d, 100K
Parmela sc3d, 800K, 643
10

20

30

40

50

60

z, cm

Figure 7: Transverse beam size versus beam position in
the cavity for a 10-nC bunch.
For all bunch charges, the kinetic energy plots are very
similar to that in Fig. 6c. As for other parameters, for 1nC bunches the agreement between the codes is excellent,but for 10 nC the differences are more noticeable than in
the 3-nC case. The reason is most likely in the strong
effects of the space charge at the initial stage of[1] S.S. Kurennoy, D.L. Schrage, R.L. Wood, et al.
“Normal-conducting RF cavity of high current
photoinjector for high power CW FEL”, these proc.
[2] S.S. Kurennoy, D.L. Schrage, R.L. Wood, et al.
“Development of photoinjector RF cavity for highpower CW FEL”, NIM A528 (2004) 392.
[3] J.H. Billen and L.M. Young. “SUPERFISH/Poisson
Group of Codes”, report LA-UR-96-1834, Los
Alamos, 1996 (rev. 2003).
[4] L.M. Young (documentation by J.H. Billen).
“PARMELA”, report LA-UR-96-1835, Los Alamos,
1996 (rev. 2004).
[5] MAFIA, v.4.107, CST GmbH (Darmstadt, Germany),
2002; www.cst.de[6] S.S. Kurennoy. “Simulation of beam dynamics inhigh-power CW photoinjector cavity with MAFIA PIC
code TS2”, tech note LANSCE-1: 04-012 (TN), Los
Alamos, 2004.

FEL Technology

538

D.H. Dowell et al. / Proceedings of the 2004 FEL Conference, 538-541

RF DESIGN FOR THE
LINAC COHERENT LIGHT SOURCE (LCLS) INJECTOR*
D.H. Dowell#, L. Bentson, R.F. Boyce, S.M. Gierman, J. Hodgson, Z. Li, C. Limborg-Deprey,J. Schmerge, L. Xiao, N. Yu, SLAC, Menlo Park, CA 94025, USA
GENERAL DESCRIPTION
OF THE INJECTOR

Abstract
The Linac Coherent Light Source (LCLS) will be theworld’s first x-ray free electron laser, and the successful
operation of this very short-wavelength FEL will require
excellent beam quality from its electron source.
Therefore a critical component is the RF photocathodeinjector. This paper describes the design issues of the
LCLS RF gun and accelerator structures. The injector
consists of a 1.6 cell s-band gun followed by two 3-meter
SLAC sections. The gun and the first RF section will
have dual RF feeds both to eliminate transverse RF kicks
and to reduce the pulsed heating of the coupling ports. In
addition, the input coupler cavities will be speciallyshaped to greatly reduce the RF quadrupole fields. RF
designs for the gun and the first accelerator section are
now complete. The work includes the gun’s new dual
coupler and full cell shape as well as the dimensions of
the L0-1 dual RF feed and coupling cell. Engineering has
begun on the L0-1 structure. These and other aspects ofthe gun and RF structure design will be discussed.

The Linac Coherent Light Source (LCLS) is a SASE
free electron laser using the last 1/3 of the SLAC two milelinac to produce 1.5 to 15 angstrom x-rays in a 120 meterlong undulator for use in a variety of x-ray science
experiments[1]. In order to satisfy the demanding
electron beam requirements, a new 135MeV photoinjector shown in Figure 1 will be built in an existing, offaxis vault at the 2/3 point of the main linac. The injector
accelerator consists of a modified BNL/SLAC/UCLA 1.6
cell S-band gun followed by two 3-meter long SLAC
accelerator sections. The 6MeV beam from the gun ismatched into the first accelerator section and accelerated
to 135MeV before injection onto the main linac axis witha 35degree bend [2]. Several modifications to the rf gun,linac and beamline as well as the inclusion of several
diagnostics have been incorporated into the injector
design to achieve the required 1.2micron projected andless than 1micron slice emittance at a charge of 1nC.

TCHA
MBE
R

VAC
UU
M
PUM
PS

TR
EAT
MEN

RF Gun &Solenoid

LON
ASSE GBEL
MBL LOY WSSPOSEA OLSL
FRO

Load Lock

CATH
ODE

U
GAHV ALLTE
VAL MET
VES ALPOR
HO CUPI
LDE
R NE

MVAL
VE

Gun Diagnostics

L0-1 & L0-2
3-m SLAC Sections
Laser Heater & Chicane
Transverse RF Cavity
Electro-Optic Diagnostic

Radiation Shield WallsOTR Emittance Diagnostics
35o Bend

SLAC Main Linac Beamline
Figure 1: Layout of the LCLS 135 MeV injector. The
injector length is approximately 20 meters from the gun to
the straight ahead spectrometer.

Straight Ahead Spectrometer___________________________________________*SLAC is operated by Stanford University for the Department of Energy
under contract number DE-AC03-76SF00515.
#
dowell@slac.stanford.edu

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Available online at http://www.JACoW.org

539

D.H. Dowell et al. / Proceedings of the 2004 FEL Conference, 538-541

Recently an inverse free electron laser, e.g. laser heater[3], has been included in the injector to increase theuncorrelated energy spread which suppresses the coherent
synchrotron radiation and longitudinal space charge
instabilities in the main accelerator and bunch
compressors [4].
This paper describes the RF design of the gun andaccelerator structures.

RF GUN DESIGN ISSUES
The design of the BNL/SLAC/UCLA s-band gun isbeing studied to meet the demanding beam requirementsfor LCLS. In general, the issues can be divided into two
types: thermal effects and RF field quality.

this is also the location of the largest dynamic stress due
to pulsed heating. The temperature rise per pulse iscomputed to be 137 degrees C for the original
BNL/SLAC/UCLA gun.
Both the static and dynamic stresses around thecoupling apertures are too large and would drasticallyshorten the gun lifetime at continuous 120Hz operation.
Therefore a new coupling-hole was designed with a pulse
temperature rise of 41 degrees C, well below 50 degrees C
which is considered acceptable for the NLC x-bandstructures [6]. Further analysis is required to confirm thebulk stress is similarly reduced.

Gun Thermal Design
The need for 120 Hz operation of this gun necessitates a
careful analysis of both the average and pulsed heating
thermal effects. ANSYS modeling of the gun was done toobtain the average temperature and stress distributions at
120 Hz. The gun temperature distribution is shown in
Figure 2 for the gun operating at 3.7kW of average power(120Hz, 3microsecond/pulse and 130MV/m peak cathodefield).

Figure 3: Mechanical stresses at 120 Hz operation. The
von Mise stress is given in Pascals.

RF Gun Dual Feed and Racetrack Design

Figure 2: Equilibrium gun body temperature distributionof the BNL/SLAC/UCLS operating at 3.7kW of average
power with an inlet water temperature of 20 degrees C
and a flow velocity of 16 fps. The temperatures are given
in degrees C.
The gun’s bulk distortion between ambient andoperating temperatures shown in Figure 2 shifts the pimode resonant frequency downward 1750 kHz.
Additional cooling and adjusting the water temperature tokeep the gun body temperature at 30 degrees C lowered
the pi-mode shift to an acceptable 100 kHz. This was for
4 kW average RF power and 13.9 degrees C inlet water.
[5] Therefore in the LCLS injector, the gun frequency will
be kept constant by regulating the gun temperature via thecooling water.
The mechanical stress distribution due to the averagethermal load is shown in Figure 3. The location ofgreatest stress is around the hole which couples the RFfrom the waveguide into the full cell. The maximum
static stress here is 14 ksi, which far exceeds the acceptedmaximum of 3-5 ksi for brazed copper.[5] In addition,

The electron source for the injector is the 1.6 cell, sband gun which will be modified to have dual RF feeds
and a racetrack shape for the full cell. The dual feed ismotivated by the desire to reduce the time-dependent
dipole field perturbation introduced by a single feed. In
the conventional BNL/SLAC/UCLA gun, the dipole fieldfrom the single feed is compensated with another unpowered, symmetric port opposite the power feed. In
addition, for the standard gun, the RF is coupled into thecell using θ-coupling which also reduces the dipole field[7]. However, even with the symmetric port and θcoupling, there remains a dipole kick due to the power
flowing into the cavity which dual feed eliminates.
Although the dual RF feed eliminates the dipole fields,
it increases the full cell quadrupole field. To study thiseffect the 3-D fields where computed using the parallelcode S3P developed by the Advanced Computation
Department of SLAC. These fully 3-D fields were used
to obtain the gun quadrupole strength as plotted in Figure
4. The original full cell cylindrical shape has a large
quadrupole strength which for a normalized electronenergy of 10 (5MeV) would have a quadrupole focal
length of approximately 300 cm. Although this is 20times weaker than the gun’s strong focusing (focal lengthof approximately 15 cm) due to the rotationallysymmetric radial fields at the ends of the cells, it
generates an asymmetric beam and emittance growth.

FEL Technology

540

D.H. Dowell et al. / Proceedings of the 2004 FEL Conference, 538-541-180 -130

racetrack cavity (lc=2.413cm)
with d=0.315cm
racetrack cavity (lc=2.413cm)
with d=0.356cm

-80

-30

20

70

120

170

rf phase (degree)

Figure 4: RF quadrupole kicks (γβ)r in the full cell withcylindrical and racetrack shapes.
In order to eliminate the quadrupole fields the full cellis made slightly elliptical with the long axis perpendicular
to the dual feed axis. The ideal elliptical shape is well
represented by offsetting two cylinders a distance d as
shown in Figure 5. The cylinder offset distance d isadjusted to eliminate the quadrupole field.

[Ez(radius) - Ez(on axis)] (MV/m)

Quadrupole ∆(γβ)r (1/m)

cylindrical cavity (lc=2.475cm)
8
6
4
2
0
-2
-4
-6
-8

2
r = 5 mmr = 3 mmr = 1 mm

1
0
-1
-2
-3
-4

0

5
10
distance from (cm)15

Figure 6: The difference of the off-axis and on-axis
longitudinal electric field along lines of constant radii,Ez(r,z)-Ez(r=0,z) for R=1,3 and 5 mm. Solid curves: S3P(3D), dashed curves: Superfish (2D).
The dependence of the radial electric field upon
distance from the axis is shown in Figure 7. These radial
fields have a linear dependence upon radius, indicating
little spherical aberration.

dr

10Er(r) (MV/m)

r

15

5
0
-5

r = 5 mmr = 3 mmr = 1 mm-10-15Figure 5: Racetrack shape of the full cell which cancels
the quadrupole field of the dual RF coupling holes. The
waveguide is above and below the cell. The optimal fullcell dimensions are r = 4.061cm cylinders offset a
distance d=0.340cm.

Other Gun Field Quality Issues
In addition to rotational field asymmetries, there arealso fields which depend upon the radius that are both
chromatic and geometric. One chromatic effect is shownin Figure 6, where the difference between the off-axis andon-axis longitudinal fields is plotted vs. z for radii of 1, 3
and 5mm. This radial field dependence is significant, forexample, integrating an electron from rest along a
trajectory at r=1mm has 2.7keV lower kinetic energy thanthe on axis electron. This energy spread contributes to theuncorrelated slice energy spread although initially it has aradius-energy correlation in the gun.
It is interesting to note that the measured uncorrelated
energy spread is a few keV[8], suggesting that asignificant portion of the uncorrelated energy spread isdue to the radial-dependence of the RF field and not only
to the space charge field.

TUPOS56

-20

0

5

10

15

distance from cathode (cm)Figure 7: The radial electric field along lines of constantradii: 1, 3 and 5 mm. Solid curves: S3P (3D), dashedcurves: Superfish (2D).

L0-1 STRUCTURE RF DESIGNThe 3-meter SLAC RF structures have known dipole
fields in both the input and output coupler cells due to thesingle-side feeds. In the original design the coupler cells
were offset transverse to the structure axis to compensate
for the amplitude part of the field, however the phase or
power flow term could not be canceled.[9] Our analysis
for the LCLS injector shows the remaining dipole andquadrupole fields lead to unacceptable emittance growth.
Therefore the coupler cell of L0-1 has been redesigned tohave a dual feed and a racetrack shape as shown in Figure
8.[10]

541

D.H. Dowell et al. / Proceedings of the 2004 FEL Conference, 538-541

Table I: Comparison of the original SLAC input coupler
with three dual feed coupler designs. Quadrupole headtail kick, ∆(⊥βγ)/m, is given for a 10 degree bunch at
5MeV.

Figure 8: The L0-1 structure coupler cell with dual RF
feed and racetrack shape. The optimal distance between
the cylinder centers is 13 mm.

Quadrupole ∆(γβ) r (1/m)

The integrated quadrupole kick as a function of RFphase (crest at 0 degrees) is given in Figure 9 for four
coupler configurations. The original single feed and thecylindrical dual feeds both have approximately the same
quadrupole kick. Both a cross dual feed and the racetrack
shape are effective at canceling the quadrupole field. We
have chosen the racetrack design for ease of fabrication
and because it introduces no additional penetrations in thecell walls.
original single-feedcylindrical dual-feedcross dual-feed
racetrack dual-feed

Head-tail angle∆θ (rad/m)

SLAC Single feed

0.78

0.078

Symmetric dual

0.63

0.063

Race-track dual

0.04

0.004

Cross Dual

0.20

0.020

SUMMARY AND CONCLUSIONS
A thermal analysis for the 120 Hz gun was performed
and the region of greatest heating and stress wasdetermined to be the RF coupling apertures in the full cell.
New apertures were designed with thicker copper andlarger radii to reduce the pulse temperature rise to 41
degrees C/pulse. This is considered acceptable based
upon NLC structure studies. The bulk thermal distortions
will be controlled by regulating the gun coolant to keep
the gun body at a constant temperature.
The designs of the RF gun and first accelerator section
were studied and found to have larger RF kicks than
acceptable for LCLS beam requirements. The RF
coupling cells for the gun and the L0-1 structure wereredesigned to have both dual feeds and racetrack shapes.
The dual feed eliminates the dipole fields and theracetrack shape cancels the quadrupole fields.
The RF design of L0-1 is finished and the engineeringof the dual feed accelerator structure has begun. The gundesign is nearing completion.

REFERENCES

rf phase (degree)

Figure 9: Change in transverse momentum as a functionof RF phase for various coupler cell geometries.
It is useful to compare the angular kicks with thenatural divergence of the beam. For an emittance of 1
micron, assume the beam is at a waist of radius 1 mm(rms). The beam divergence is thenσ x′ =∆(γβ⊥)/mεn= 100 micro − radiansβγσ xTable I gives the head-tail kick for a 10 degree (~10ps)
long bunch traveling though the L0-1 input coupler cell.
The head-tail angle for the original SLAC coupler is 78
micro-radians per mm. As this is nearly the same as thebeam’s natural divergence, the coupler field will increase
the projected emittance.
The racetrack dual feed
quadrupole field is 20 times smaller, producing negligible
emittance growth[1] Linac Coherent Light Source (LCLS) Design Study
http://www-ssrl.slac.stanford.edu/lcls/cdr/.
[2] C. Limborg et al., “Sensitivity studies for the LCLS
PhotoInjector Beamline”, Proceedings of the 2003
International FEL Conference.
[3] R. Carr et al, “Inverse Free Electron Laser Heater for
the LCLS,” EPAC’04, Luzern, July 2004.
[4] Z. Huang, et. al. “Suppression of Microbunching
Instability in the Linac Coherent Light Source,”
EPAC’04, Luzern, July 2004.
[5] R. Boyce et al., LCLS Tech Note LCLS-TN-04-4.
[6] D.P. Pritzkau and R.H. Seeman, Phy. Rev. ST Accel.
Beams 5, 112002(2002)[7] D.T Palmer et al., SLAC-PUB-95-6799.
[8] H. Loos et al., “Longitudinal Phase Space
Tomography at SLAC GTF and BNL DUV-FEL,”
Proceedings of the 2003 International FEL Conference[9] R.B. Neal ed., “The Stanford Two Mile Accelerator,”
W.A. Benjamin, 1968, pp. 144-148.
[10] Z. Li et al., “Coupler Design for the LCLS Injector
L0-1 Structure.” To be published as LCLS TechnicalNote

FEL Technology

542

T. Zwart et al. / Proceedings of the 2004 FEL Conference, 542-545

OPTIMAL RF SYSTEMS FOR LIGHTLY LOADED SUPERCONDUCTINGSTRUCTURES
T. Zwart#, D. Cheever, W. S. Graves, D. Wang, A. Zolfaghari,
MIT Bates Accelerator Center, Middleton MA 01949
W. North, Consultant
Abstract
Recent developments in the field of RF accelerators
have created a demand for power amplifiers that can
support very high accelerating gradients, 15-25 MV/m,in superconducting structures with extremely low
losses. Free electron lasers with modest beam current,
I<10 uA, or those based on energy recovery linacs may
have intrinsic power demands of less than 1 kW/m. We
present a design concept for an amplifier and external
tuner system that will efficiently meet this requirement.
A likely amplifier for this application is the Inductive
Output Tube (IOT) which offers high AC/RF
efficiency, flexible power output and switchingcapability without the need for external modulation.
The use of solid state amplifiers is also considered. The
external tuner circuit makes use of low loss RF
components, include waveguide, circulators and ferrite
phase shifters to create a moderate quality standing
wave between the amplifier and the superconducting
cavity. The potential effective Qext exceeds 3×107.
Plans for future work are presented.

INTRODUCTION
For emerging high gradient, low beam powersuperconducting (SC) accelerators, including energy
recovery linacs (ERL’s) and free electron lasers(FEL’s), the bulk of the generated RF power isreflected from the SC structure and absorbed in an
external load, connected to the reflected-power port ofa ferrite circulator. MIT is pursuing the design of asystem that would recycle this reflected RF power
while maintaining adequate phase and amplitudecontrol of the accelerating cavities. This will greatly
reduce the power needed from the RF amplifier, thus
substantially reducing the capital and operating costs
associated with these devices.
The intrinsic RF power required by an ERL or an
FEL can be quite low. For today’s state-of-the-art
superconducting structures with unloaded quality
factors (Q0) in excess of 1010 [1] the power to maintainthe cavity field amplitude is less than 50 W/m at
gradients of 25 MV/m. For average beam currents (orimbalanced currents in the case of an ERL) of less than
10 uA, the beam power is limited to 250 W/m at a
gradient of 25 MV/m. An ideal RF source coupled to a#zwart@rocko.mit.edu

TUPOS57

one meter cavity would therefore need to supply only
300 W to meet these demands.
Despite these low intrinsic demands, present
accelerator designs call for amplifiers with power
capabilities in excess of 5 kW/m [2]. This additional
power is necessary to compensate for small changes inthe superconducting cavity geometry due to mechanicalvibrations. This problem, known as microphonics, canbe addressed by spoiling the cavity quality factor with astronger coupling to the amplifier than would benecessary in the absence of the microphonicperturbation.
One strategy under development is to actively correct
the cavity geometry by means of a piezo-restrictive
tuner [3]. This tuner adjusts the length of the cavity tocompensate for the mechanical vibrations and maintainthe cavity center frequency. The device must be able tocorrect the micron scale deformations of the cavity at
frequencies between DC and a few hundred Hz.
Another approach is to make use of an external tuner
to apply a corrective phase shift to the reflected RF
wave and reintroduce it to the cavity structure [4, 5]. In
essence a second standing wave circuit of much lower
quality factor has been introduced into the RF system
between the amplifier and the superconducting
structure. The necessary external control (phase shift)
could be realized by means of low loss ferrite phaseshifters similar to those presently in use at the Bates
accelerator. Such phase shifters with very low insertion
loss (<0.7 dB), adequate range ( d ϕ > ±90°),
resolution ( dϕ < 1°), and high power handlingcapability (Pavg > 5 kW), are now available
commercially. Efforts are also underway at Fermilab
National Accelerator Laboratory to construct a device
with similar specifications for use in tuning individual
cavities of the TESLA Test Facility II Accelerator [6].

INTRINSIC RF POWER DEMAND
The power demand for an RF cavity can be divided
into two categories: power to maintain the cavity fields
and power to accelerate the beam. Equation 1 shows
the distribution of these power requirements:P=

β +1 
δω 2  (1)V2
2)⋅⋅ (1 + a + b ) + ( 2Qextω ( r / Q )Qext 4 β 

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T. Zwart et al. / Proceedings of the 2004 FEL Conference, 542-545

Here P is the power required by the RF amplifier, V
is the cavity peak voltage, r/Q is the cavity shunt
impedance, β is the coupling factor, a and b are
factors for the beam power at two distinct phases (theseterms almost cancel in the case of the ERL ) and δω
is a measure of the frequency variation of the cavity
due to uncontrolled sources. For superconducting
structures where β is much greater than unity andapplications with negligible beam loading equation 1
becomesP=δω 2 
V)⋅ 1 + (2Qext
4(r / Q)Qext 
ω 
2

(2)

Note that the power requirement due to the last termin equation 2 pertaining to the frequency variation of
the cavity would vanish if the RF source was able tovary its frequency to match the variation in the cavity
center frequency. Clearly this is not acceptable for an
accelerator where many 100’s of individual cavities
must be phase locked with respect to each other. In thiscase additional amplifier power is required tocompensate for a lower gain as the cavity frequency
fluctuates about the linac center frequency.
In the case where the beam power is small, the widthof the frequency variation determines the optimum
coupling and thus the power demand of the cavity.
Figure 1 shows the power demand at a beam current of
10 uA as a function of coupling factor for several
values of the frequency variation width.
20Power/m (kW)δf = 30 Hz

15

The approach considered here to reduce thefrequency variation of the system is by the introductionof an additional external oscillator of much lower Q.
Corrective phase shifts can be applied to the external
system which will reduce the frequency variation of thecoupled system.

a)
RF Amplifier(Klystron)

SC Cavity
Circulator

Load(Waster)b)

RF Amplifier(IOT or Solid State )Reactive Tuner
Directional Coupler~10 dBRF Recycling Loop
(Resonant Ring)
Loop loss <1 dB

Low Loss Ferrite Phase Shifters<P> = 10 kW
Insertion loss < 0.8 dB
τ < 50 us
dφ > ± 90°
Resolution < 1 °δf = 10 Hz

10Figure 2: Standard Amplifier Configuration (a) andreactive tuner/RF recycler configuration (b).

δf = 3 Hz
δf = 1 Hz

50
1.E+06center frequency by applying a correction directly tothe source of the perturbing influence, ie variations in
the cavity length. However the piezo also requires
operation at cryogenic temperatures and will have
limited access inside the cryomodule in the event of a
failure.
Further, the piezo device has its own
mechanical resonances which may interfere with
control system performance if the self-resonancefrequency overlaps with the microphonic excitation to
be controlled.

1.E+07

1.E+081.E+091.E+101.E+11

Q ext

Figure 1: Amplifier power demand vs external
coupling (Qext) for TESLA cavities at 1.3 GHz. All
curves assume a cavity voltage of 25 MV and a beam
current of 10 uA.
Notice that if the frequency variation could becontrolled at the level of 1 Hz the required power
would be reduced to less than one kW per RF
amplifier. The use of solid-state amplifiers rather thanvacuum tubes might then become possible.
Initial results using a piezo tuner indicate that insome environments microphonics can be controlled tovalues less than 50 Hz [Hof03]. The piezo tuner also
has substantial advantages in that it is a very low powerdevice and it has the potential to maintain the cavity

Figure 2 shows conceptually how a higher value of
Qext might be reached with the introduction of an
external tuner and resonant ring into the amplifier
cavity circuit. Figure 2a shows the standard
configuration where the amplifier output is delivered tothe cavity through a “protected” system, including
circulator and load. All reflected power from the cavity
is delivered to the load port of the circulator. In Figure
2b several new features have been introduced into theamplifier/tuner circuit. First, the klystron is replacedwith either an Inductive Output Tube or Solid Statepower amplifier. Second, the amplifier is coupled into a
resonant ring waveguide structure through a directional
coupler of -10 dB. The optimum value of the coupling
will depend on the losses in the resonant ring. The
phase of the traveling wave in the ring is adjusted bymeans of a low loss phase shifter which does not

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T. Zwart et al. / Proceedings of the 2004 FEL Conference, 542-545

Beam &
Circulator
Psource
Phase
Other
Total
Dir.
Power
Pring
CavityLoss
Shifter Loss
Loss
Loss
Coupler
Gain
Power
(kW)
(kW)
(dB)
(dB)
(dB)
(dB)
(dB)
(G)
240
0.00
0.00
0.00
0.16
14.4
27.3
10
<0.4
240
0.35
0.35
0.14
1.00
6.8
4.8
10
2.1
240
0.45
0.45
0.14
1.20
6.1
4.1
10
2.5
240
0.60
0.60
0.14
1.50
5.3
3.4
10
3.0
240
0.70
0.70
0.14
1.70
4.9
3.0
10
3.4
240
0.80
0.80
0.24
2.00
4.3
2.7
10
3.7
Table 1: Amplifier power requirements and resonant ring power gain for varying component insertion losses. The valueof the directional coupler is optimized for each different total loss. 20 MV/m, 10 uA beam current and Qext =107 areassumedrequire fast response time for CW beams as it will
respond to variations in the real component of thecavity power which should depend only on changes inthe dissipated power. Third, a reactive tuner has been
installed on the waveguide leg between the resonant
ring and the superconducting cavity. This tuner makes
use of a low loss ferrite phase shifter as it will require
operation at bandwidths significantly greater than thefrequency of the microphonic excitation. The
enhancement in field strength in the resonant structure
should exceed a factor of two and will depend criticallyon the losses in the phase shifter and circulator. Table 1
list the optimum coupling of the resonant ring as afunction of ring losses and indicates that amplifier
powers of only ~3 kW should be necessary to achieve
stable operation at gradients of 20 MV/m.

RF AMPLIFIER SELECTION
At an operating frequency of 1.3 GHz three distinct
amplifier types appear to have the potential to meet thepower needs of these lightly loaded SRF cavities. They
are the klystron, the inductive output tube (IOT) andthe solid-state power amplifier (SSPA). As describedabove the power demand is likely to fall in the range of
2-15 kW per meter of accelerating structure. The exact
power requirement will depend on the beam loading
and the degree to which the cavity center frequency canbe controlled. Both klystron and IOT offer power levels
in excess of 10 kW. The klystron is the moreestablished amplifier for accelerator applications, while
the IOT technology is presently in the prototype stage
at frequencies in the 1-2 GHz range. SSPA’s havelower power capability but may offer many systemadvantages in simplicity, size, cost, flexibility, andreliability and maintenance.
Prototype IOTs have recently become available atfrequencies of interest. The EIMAC Division (SanCarlos, CA) of CPI has built four devices at 1300 MHz
for accelerator applications, which have demonstrated
20 kW power output, 23 dB gain and over 50%

TUPOS57

efficiency (more is expected). In addition, THALES
has also developed a 1.3 GHz IOT and L3 Corp.
(formerly Litton Electron Dynamics) also produce
IOTs for UHF TV service and will have a prototype
IOT at 1300 MHz in few months.
IOTs are operated near Class B, approaching a
conduction angle of 180 degrees, and a maximum
theoretical efficiency of 78.5% (π/4). Practical UHF
IOTs have demonstrated efficiency above 70%.
Efficiency of an IOT operating at 1300 MHz is lessthan that of a lower-frequency device because ofincreased losses in the cavities and distortion of thecathode-current “discs” due to transit-time effects.
Nevertheless,computer-simulated
data
shows
conversion efficiency exceeding 68%, which has yet to
be demonstrated in the prototypes.
In addition to the advantage of high efficiency the
IOT offers a very flexible pulse structure and power
output. Unlike the klystron the IOT’s efficiency ismaintained across a wide dynamic range in power.
Further the IOT does not require external modulation.
Removal of the low power RF from the IOT grid turns
off the beam current in the tube. As the IOT iselectrically “short” it has a low phase pushing factor of
about one degree per percent relative voltage variation.
One drawback of the IOT as compared to the klystronis lower gain. The IOT offers ~23 dB where in the caseof the klystron gains in excess of 40 dB are readily
achieved. This lower power gain of the IOT will place
additional demands on the RF driveline distribution
system.
Although no SSPA can compete with either aklystron or an IOT at the 15 kW output level, thesuccessful realization of the tuning circuit describedabove would require amplifier power no greater than
~3 kW. A 1.3 GHz SSPA at 3 kW CW is quite
practical and has certain advantages, including lowvoltage operation and low phase and amplitude pushing
factors. At every frequency there is a “cross-over”
power level above which the relative advantages ofMicrowave Vacuum Electron Devices (MVEDs)

T. Zwart et al. / Proceedings of the 2004 FEL Conference, 542-545

545

exceed those of SSPAs. A power level of 3 kW isprobably below the “cross-over” point.

SUMMARY & RESEARCH PLAN
In the past year a team of MIT faculty andaccelerator physicists at the Bates laboratory haveproposed creating a Center for Accelerator Science andTechnology (CAST)at MIT. The core missions of thiscenter would be to educate students in the field ofaccelerator science and to promote the development of
cutting edge accelerator technologies. Under the
auspices of CAST MIT Bates has developed a threeyear plan to design, construct and qualify the highly
efficient RF amplifier, RF recycler and reactive tuner
system described above. The first phase will be devoted
to an analysis of the amplifier performance, component
requirements and engineering design. A preliminarymodel using the MATLAB Simulink platform will be
refined. Further measurements of the open and closed
loop characteristics of existing cavities at JLAB, TTF
and other labs will be performed. These results will be
evaluated to produce a set of specifications for theamplifier-tuner system which should yield an effective
coupling of Qext > 3×107 while still maintaining
adequate phase and amplitude control of the cavity. In
the final phase of this effort the system would beassembled at Bates and subsequently tested at one of
the laboratories with the appropriate SRF cavity
infrastructure

REFERENCES[1] TESLA Collaboration, “TESLA Technical Design
Report” DESY 2001-011, (2001) II 27[2] M. Liepe et al, “RF Parameter and Field Stability
Requirments for the Cornell ERL Prototype”,
Proceedings of PAC 2003 (2003) 1329
[3] S. Simrock et al., “First Demonstration of
Microphonic Control of a Superconducting Cavity
with a Fast Piezoelectric Tuner”, Proceedings of PAC
2003 (2003) 470[4] Y. Kang et al., “Reactive RF Tuning forCompensation of a Detuned Accelerating Cavity”,
Proceedings of Linac 2002 Gyeongju Korea (2002) 733[5] D.Horan, E.Cherbak, “Fast-Ferrite Tuner
Operation on a 352 MHz Single Cell RF Cavity at theAdvanced Photon Source”, Proceedings of PAC 2003
(2003) 1177
[6] S. Simrock, M. Huening Private Communication

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ELECTRON BEAM DIAGNOSTICS USING DIFFRACTION RADIATION∗
Bibo Feng† , William E. Gabella,
FEL Center, Vanderbilt University, Nashville, TN 37235, USA
Tamas R. Sashalmi, Steven E. Csorna,
Dept. of Physics, Vanderbilt University, Nashville, TN 37235, USA
Abstract
Diffraction radiation emitted from electron bunches has
the potential application as a non-intercepting electron
beam diagnostic. The electron longitudinal distribution
in a bunch can be obtained from the coherent diffraction
radiation spectrum; the transverse beam properties, suchas beam size, divergence and emittance, can be measured
through the analysis of the angular distribution of the coherent diffraction radiation. The design study and initial
experimental results at the Vanderbilt FEL facility are presented.

INTRODUCTION
Diffraction radiation (DR) is a promising technique forelectron beam diagnostic. DR technique can be developed
as a low cost, compact, and non-intercepting monitor which
can be very useful for free electron lasers and linear colliders. Electron bunch profile measurements have been conducted using coherent synchrotron radiation (CSR), coherent transition radiation (CTR), as well as coherent diffraction radiation (CDR)[1, 2, 3].
Diffraction Radiation is generated when a relativistic
electron passes through an aperture in a metallic plate. DR
intensity for N electrons can be described by
Itotal (ω) = I1 (ω)[N + N (N − 1)F (ω)],(1)

where I1 (ω) is the DR intensity at frequency ω from asingle electron, and F (ω) is the bunch form factor. DR,
like transition radiation, is emitted in the forward direction
along the electron path, and in the backward direction along
the direction of specular reflection from the metal screen.
CDR has a fixed phase relative to the electron bunches,
and the measurement of the coherent radiation gives thelongitudinal bunch form factor f (ω), thus providing information about the longitudinal bunch distribution function
S(z). The electron distribution in a bunch can be obtained
from the inverse Fourier transformation of the form factor.
CDR is a better choice for monitoring the electron beam
bunch shape as CDR perturbs the electron beam less thanCTR and CSR.
The use of diffraction radiation for measuring the transverse beam dimension is a new non-invasive technique.
There are a few experimental investigations at the present∗ Work is supported by the NSF and DOD through the MFEL program
under award No. F49620-01-1-0429.
† Corresponding author. Tel.:+1-615-343-6446; fax: +1-615-3431103. Email: bibo.feng@vanderbilt.edu

TUPOS58

time [4, 5, 6] . DR intensity is proportional to the squareof γ, and is distributed in angle as 1/γ, where γ =Ebeam /me c2 is the normalized electron energy; thus, boththe intensity and the angular distribution can be used to deduce the beam energy[7]. DR has the potential capability
to diagnose multiple beam parameters such as longitudinal
and transverse beam sizes, energy, position, divergence andemittance. DR technique can also be developed as a single
shot measurement.
Using the DR technique, one measures the spectrum andangular distribution in the frequency domain. High spatial
and time resolution are potentially possible, hence DR isable to satisfy the requirements of a linear collider facility. In addition, the angular distribution of the DR from anelectron passing through a slit in a metal foil has polarization properties because of the interference effects between
the two half-planes of the radiator. The polarization showsdifferent properties with the electric field parallel and normal to the plane of the slit. The electron beam transverse
dimension can be measured through the analysis of the angular distribution of the diffraction radiation.
In this paper, we present our initial results of bunch
length measurements using coherent diffraction radiationfrom a slit. Following this introduction, we give a description of the diffraction radiation from a slit and we show themethod of extracting the bunch length from the CDR interferogram in the time domain. We measured spectrum of
CDR from the slit and extracted the bunch length. As anapplication, we investigated the effects of changing linear
accelerator parameters such as phase and cathode heatingon the electron bunch length.

EXPERIMENTAL SETUP AND RESULTS
DR experiments were carried out at the Vanderbilt FELCenter on a Mark III type linear accelerator. The electron beam energy is variable between 25 and 45 MeV. The
electron beam macropulse duration is about 8µs, and theaverage beam current is about 150 mA. The pulse contains 23,000 bunches, each with approximately 50 pC anda bunch length of approximately 1 ps.
The CDR experimental setup is shown in Fig. 1. A
diffraction radiator is mounted at an angle of 45◦ to theelectron beam. The gap of the radiator is adjustable, whenclosed it operates as a transition radiator. DR or TR is emitted as the electron beam passes through the radiator. This
radiation passes through a quartz window and is reflectedby a parabolic mirror and a couple of flat mirrors into an

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B.F. Feng et al. / Proceedings of the 2004 FEL Conference, 546-549

interferometer to measure the radiation spectrum. The experimental system was aligned using a HeNe laser injected
upstream into the beam line.

power peak at the frequency of 0.13 THz (wavelength of
2.3 mm). The low frequency part of the spectrum is suppressed by the detector and the interferometer.

Signal intensity [a.u.]

0.8experimental data
fitting curve

0.6
0.4
0.2
0
-0.2
-0.4
-40

-20

0

Time delay [ps]20

40

Figure 2: Typical CDR interferogram and time domain fit.

Figure 1: Schematic of the experimental setup.
The diffraction radiator consists of two separated screensand a stepping motor to adjust the width of slit. The resolution of the stepping motor is 5 µm per step. We select a polished silicon wafer as the screen because of its
flatness. The thickness of screen is about 500 µm and its
size is about 75 × 50mm2 . One of the silicon screens ismounted on an adjustable frame, so the reflection angle canbe changed in order to keep both screens coplanar.
The interferometer is a wire grid Martin-Puplett type asshown in Fig. 1. The incident light is split onto orthogonal polarization components by a 45◦ tilted polarizing grid
splitter. One component is reflected and focused onto a reference detector; the other is incident onto another verticalpolarizing grid where the light is split into two beams, reflected by the roof mirrors, and finally recombined and focused onto a pyroelectric detector(P4-45,Molectron Inc.).
Only one detector was used in this experiment becauseof another Golay cell detector malfunctioning. The frequency limitation of the interferometer is determined by
the diffraction losses, the finite aperture of the detector andthe grating constant of the wire grid. The frequency range
is estimated between 2 cm−1 and 50 cm−1 (wavelengthsof 5 mm to 200 µm).
A typical CDR interferogram is shown in Fig. 2. The
electron beam had an energy of 25 MeV and an average
macropulse current of 135 mA. It was focused and centered
between the edges of the two screens. The beam size wasabout 2.5 mm and the slit width was set to 5 mm. The CDR
spectrum is obtained by Fourier transformation of the interferogram as shown in Fig. 3. We observed relative strong

CDR Spectrum (a.u.)

6
5
4
3
2
1
0
0

0.1

0.2

Frequency (THz)

0.3

0.4

Figure 3: CDR spectrum corresponding to interferogram in
Fig. 2.
A calculation of the coherent emission is shown in Eq. 1,
giving the longitudinal bunch form factor F (ω) and hence
providing information about the longitudinal bunch distribution function S(z). Therefore, the electron distribution
in a bunch can be obtained from the inverse Fourier transform of the form factor through the Kramers-Kronig relation [8].
A simpler technique to extract the electron beam bunch
length from the CDR interference spectrum was introduced
in reference [9]. Assuming a Gaussian longitudinal electron distribution of pulse length σ and the low frequency
suppressed by the interferometer at cut-off frequency 1/ξ,the time domain interferogram of the coherent radiation is
described as

2

− t2

S(t) = e

4σ

−

2σe
− 

t2
4(σ 2 +ξ2 )σ2 + ξ2−t2

σe 4(σ2 +2ξ2 )+ .
σ 2 + 2ξ 2

(2)

The bunch length σ can be obtained by fitting this two
parameter formula to the time-domain interferogram. For
example, a fit is shown in Fig. 2,which gives the electron
bunch length σ  0.87 ps.

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1

30

Bunch length [ps]Radiation Intensity (a.u)

B.F. Feng et al. / Proceedings of the 2004 FEL Conference, 546-549

20

10

5

80

60

100

120 140 160

0.8

0.7

0.6
1

Electron beam current (mA)

Figure 4: Dependence of CDR intensity on the electron
beam current. Two measurement sets as symbols; solid line
is 0.016I 2 , a fit to aI 2 .

experimental datalinear fit

0.9

1.1

1.2

1.3

Cathode heating set point

Figure 6: Bunch length vs. RF gun heating.
1

Bunch length [ps]

40
30
20
10
0
0

0.8

0.7

11.6

11.8

12

12.2

12.4

Alpha magnet current [A]48

Slit width (mm)1216Figure 5: Dependence of CDR intensity on the slit width.
The experiment confirms that the CDR intensity is proportional to the square of the beam current (Fig.4). CDR
is emitted from the slit with width of 5 mm, and using anelectron beam size of 2.5 mm and energy of 39 MeV. As
shown in the figure, the intensity is approximately proportional to the square of the beam current and therefore to thesquare of the electron number N in a bunch.
The dependence of the intensity on the slit width isshown in Fig.5. The electron beam has an energy of 29
MeV and a current of 154 mA. It has a diameter of 2.5 mm
and it passes through the center of the slit. The CDR intensity decreases exponentially with increasing slit width.
The electron bunch length is affected by many parameters in the injection section and in the accelerator, including
cathode heat, alpha magnet current, and accelerator phase.
We observed the bunch length change while tuning theseparameters. The accelerator was operating at 30 MeV, andthe electron beam current was about 130 mA. The cathodeneeds to run within a certain temperature range to provide
high current emission density and to keep the final electron
beam current constant. Cathode heating in a RF gun affects
the FEL efficiency. Fig. 6 shows the electron bunch lengthchange while changing the cathode heat.
Alpha magnet strength is another important parameterfor controlling the electron bunch length and optimizing afree electron laser. The alpha magnet acts both as both a

TUPOS58

experimental datalinear fit

0.9

0.6
11.4

Figure 7: Dependence of electron bunch length on alphamagnet current.

momentum filter and a bunch compressor for the electron
beam. Changing magnet strength selects a different energy
partition of the electron beam. Fig.7 shows the dependenceof electron bunch length on alpha magnet current. Electron
beam bunch length decreases with respect to increasing alpha magnet current.
Changing the RF phase between the gun and the accelerator, we also observed the bunch length change. By increasing RF phase, the bunch length becomes longer asshown in Fig. 8.

1Bunch length [ps]Radiation Intensity (a.u)

50experimental datalinear fit

0.9

0.8

0.7

0.6
13

14

15

16

17

18

19

Phase

Figure 8: Dependence of electron bunch length on RFphase.

B.F. Feng et al. / Proceedings of the 2004 FEL Conference, 546-549

549

CONCLUSION
As a first stage of electron beam diagnostics using
diffraction radiation, we have measured coherent DR spectrum from a slit of silicon wafer screens, and extracted thebunch length from the interferogram. We applied this diagnostic technique to the parameter study at Vanderbilt FEL
linac.
We are planning to measure the electron beam transverse
dimensions through the analysis of the angular distributionof incoherent DR. The total intensity of angular distribution
in the normal plane has a minimum value when the beam
passes through the center of slit. In practice, this property
can be used to center the electron beam in the slit, and it
may be a useful tool with which a cavity BPM can be centered on the beam. In order to get more accurate angular
information, we plan to place two parallel slits to generate
DR. The forward radiation from the first slit interferes coherently with the backward radiation from the second. Analyzing the whole angular distribution in the normal planeand fitting it to the theoretical prediction will allow us todetermine the transverse dimension, the energy and emittance of the electron beam.

REFERENCES[1] A.H. Lumpkin, N.S. Sereno, D.W. Rule,”First measurementsof subpicosecond electron beam structure by autocorrelationof coherent diffraction radiation”, Nucl. Inst. and Meth. A
475 (2001) 470-475;[2] B. Feng, M. Oyamada, F. Hinode, S. Sato, Y. Kondo, Y. Shibata and M. Ikezawa,”Electron bunch shape measurement using coherent diffraction radiation”, Nucl. Inst. and Meth.A
475(2001),492-497;[3] R.B. Fiorito, D.W. Rule, ”Diffraction radiation diagnostics
for moderate to high energy charged particle beams”, Nucl.
Inst. and Meth. B 173 (2001) 67-82;[4] M. Castellano, ”A new non-intercepting beam size diagnostics using diffraction radiation from a slit”, Nucl. Inst andMeth. A 394(1997)275-280;[5] M. Castellano, V.A. Verzilov, L. Catani, A. Cianchi, G. Orlandi and M. Geitz, ”Measurements of coherent diffraction
radiation and its application for bunch length diagnostics inparticle accelerators”, Phys. Rev. E, 63 (2001) 056501-8;[6] P. Karataev, S.Araki, R. Hamatsu, H. Hayano, T. Hirose, T.
Muto, G. Naumenko, A. Potylitsyn, J. Urakawa, ”Status of
optical diffraction radiation experiment at KEK-ATF extraction line”, Nucl. Inst and Meth. B 201 (2003) 140-152.
[7] T. I. Smith,”Instrumentation and diagnostics for free electron
lasers”, AIP Conference Proceeding No.252, p124, 1992.
[8] R. Lai and A. J. Sievers, Phys. Rev. E 50(1994) R3342.
[9] A. Murokh, J.B. Rosenzweig,M. Hogan, H. Suk, G. Travish,
U. Happek, ”Bunch length measurement of picosecond electron beams from a photoinjector using coherent transition radiation”, Nucl. Inst and Meth. A 410(1998) 452-460.

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SIMULATIONS OF THE NEWARK FIR FEL OPERATION
Jianjun Zheng, Ken K. Chin, NJIT, Newark, NJ 07032, USA
Eric B. Szarmes, John M. J. Madey, UH, Honolulu, HI 96816 USA
Abstract
The operation of the Newark FIR FEL is simulated forthe first time using a simulation code based on the
coupled Maxwell-Lorentz equations of motion. The lasing
behavior is explored for a wide range of parameters.
Particularly, we studied the effects of the e-beam pulse
phase stability on the operation of the microtron based
FIR FEL. The study shows that for even very small
systematic phase slews the lasing is suppressed. However,for a random phase slew up to 7 ps/pulse centered at thenominal micropulse frequency, the laser is still capable ofturning on. We estimate the tolerance for different typesof phase slew and discuss the possible proper operation
condition of the device.

INTRODUCTION
The Newark FEL has been under re-commissioning
recently. The device was initially developed in the 1980's
at AT&T Bell Laboratory under the direction of Kumar
Patel and Earl Shaw[1]. The system was integrated in thelate 1980's, and in 1991 it achieved first lasing at AT&T.
Soon after, the device was transferred to the campus ofRutgers University (Newark)[2]. During the last decade,considerable effort was devoted to commission thesystem. However, the slow progress of re-commissioning
suggests that there could be design and component
problems. The basic design specification includes:
Electron beam parameter:
16 µs macropulse
30 Hz macropulse repetition rate
19 Mev (γ=38) nominal energy
70 mA nominal macropulse electron current
30 ps micropulse width
3 GHz micropulse repetition rate
Undulator and cavity parameters:
Helical polarization
20 cm period
50 periods
10 meter length
10 cm bore
15 meter cavity length
Laser output parameters:
Optical wavelength tunable between 100-250 µm
Micropulse length ~50 periods
Micropulse peak power ~200 kW
Macropulse length 16µs
Macropulse average power ~10 kW
If operated at its nominal specifications, the Newark
FEL would closely match the performance of the Felix1[3]. However, the Newark system had never met thedesign expectations. We are hereby trying to find out the

TUPOS59

reason. Investigations of the fully integrated system showthat all the required components are complete. The device
has no obvious design problems, although engineering
errors are often hard to exclude. If the system has any
prospects for further development, we must have a clear
understanding of the source of the problems encounteredin the commissioning of the system. To this purpose, wehave initiated a diagnosis of the system based oncomputer simulations. Many simulation codes aimed atentire FEL systems or particular subsystems weredeveloped in the 1980's and 1990's, each code having
been designed for a specific system. Although thesesystems are similar to the Newark FEL in certain aspects[4, 5, 6], the simulations reported in this paper are the firstto be done specifically on the Newark FEL system. The
simulation code used in the present study was originallydeveloped at Stanford University to study pulse
propagation effects and system performance in the MarkIII FEL[7,8], and was modified here to incorporate thehelical undulator and system parameters of the Newark
FEL. The lasing behavior can be explored for a wide
range of parameters using this modified simulation code.

POSSIBLE SOURCES OF PROBLEMS
There are two primary problems which could possibly
affect the performance of the Newark FEL:a)Study of the first lasering behavior[2] suggests thatthe resonator losses are anomalous, with anobserved “ring-down time” for the optical resonatorindicating 6% total losses versus 1% absorption
losses per round trip. This number is also consistent
with the net gain observed in the earlyexperiments[2]. A possible source of these
unanticipated losses may be the hole bored throughthe resonator mirror, which may outcouple more
loss than anticipated.

b) Traditionally, the phase of the electron pulses has
not been considered an experimental variable
relevant to the operation of microtrons, and hence
has not been treated as a source of problems. The
mechanism that makes the energy stability intrinsic
to microtrons also makes the phase of the electron
pulses a function of accelerating cavity voltage.
Interestingly, the cathode temperature change willlead to a significant change of the accelerated
electron current[9], which in turn changes theaccelerating voltage and hence the phase of theelectron pulses. The change in phase of the electron
pulses could suppress the lasing operation of the
FEL

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J. Zheng et al. / Proceedings of the 2004 FEL Conference, 550-553

The simulation presented in this work employs theparameters used in the first lasing experiment on the
Newark FEL with more efforts concentrating on the
problems mentioned above.

ASSUMPTIONS OF THE SIMULATIONS
AND ANALYSISThe simulations are restricted to the performance ofthe resonant cavity, disregarding physical process used
to prepare the electron pulses which are fed into theundulator; we study only what happens in the opticalcavity if certain operating parameters are changed. The
code assumes that the undulator is ideal without
fluctuation of magnetic field, and incorporates only thelowest order Gaussian mode. The e-beam pulse isassumed to have a top-hat density profile whose
amplitude and profile do not change during themacropulse. In other words, all of the e-beam pulses
injected into the cavity during the macropulse arestatistically identical in the simulation.
The electron pulse slew imposed on the micropulse,on the time scale of the µs macropulses, is modulated infour categories:a)Linear phase slew (first order of Taylor expansion)dφ
φ (t ) = φ 0 +⋅ t = φ 0 + 2πft
dt
dφ
where
is the angular frequency 2πf evaluateddt
at t=0, and f is the RF frequency. In practicaloperation of the FEL, the gun repetition rate f canassume any value as an operational parameter.
However, as long as it does not change during themacropulse and remains constant over many
macropulses, we can simply tune the cavity length
to synchronize the electron pulses with the opticalpulses, thereby maintaining good overlap between
them. In other words, a linear phase slew is not a
problem for the operation of the FEL.

φ (t ) = φ0 + 2πft + Random _ noise
Both uniform (i.e. square) and Gaussian
distributions of the random noise are considered.
Here we assume that operation frequency f does notchange, and the phase fluctuates evenly around thecentral value within a specified range. The
simulation studies are designed to reveal the noise
tolerance for this type of phase slew. Previous workon the phase stability issue has been published in
the last two decades, and the estimated micropulse
jitter tolerance is also discussed in the literature[10],but none of these studies provides systematic
experimental or simulation data that can be applied
to the Newark FEL.
d) Characteristic phase slew due to cathode heating byback bombardment of the electrons (assuming botha) and b) are presented).

SIMULATION RESULTS
Parameters employed (in addition to design parameters):
Cavity length detuning = 76µm
∆γ
Energy spread= 0.25%γ

Emittance εx = 8π mm mrad, εy = 3π mm mrad
Micropulse length 20 ps
Normalized wiggler parameter K = 1
Rayleigh range R = 288 cm (instead of 433 cm in ref. [2])Target operation wavelength 140 µm
In simulations of the effects of cavity loss, the 6% total
loss (propagation and output coupling) of the Newark
FEL was sufficient to suppress lasing. The output
micropulse peak power versus total loss is shown in
Figure 1.

b) Higher order systematic phase slew (i.e. themicropulse repetition rate changes during lasering)dφ
1 d 2φ 2 1 d 3φ 3
φ(t) = φ0 + ⋅ t +⋅t +⋅t +⋅⋅⋅
dt
2 dt2
6 dt3

= φ0 + 2πft + c1t 2 + c2t 3 + ⋅ ⋅ ⋅1 d 2φ1 d 3φ, c2 =, and the22 dt
6 dt 3derivatives are evaluated at t=0. The effect of theelectron pulse on the lasing due to the c1 and c2
terms in the above equation can not be eliminatedby tuning the cavity length. One purpose of thesimulations is to determine the extent to whichthese systematic higher order terms will suppress
the lasing of the FEL.

where

c)

c1 =

First order random phase slew

Figure 1: Loss performance
Simulations show that with an e-beam micropulse
current of 2 A, lasing operation is optimized by reducing
the total losses to 2%. However, if the micropulse peakcurrent is increased from 2 A to 7 A, saturated lasing canbe easily achieved even with losses up to 25%.

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J. Zheng et al. / Proceedings of the 2004 FEL Conference, 550-553

Simulations of higher order phase slew (i.e. systematic
microwave "chirping", Figure 2) reveal that, even with avery small second order coefficient c1 on the order ofseveral rad/µs2, e.g. 6 rad/µs2, the laser could not giveappreciable output, indicating that the FEL has almost
zero tolerance to this kind of systematic phase slew. It is
likely that third order or higher order terms give similar
results.

This result is consistent with expectations, since thesynchronization between the e-beam pulse and the opticalpulse cannot be maintained for this situation and lasing iskilled. To simulate the phase slew caused by random
noise, two kinds of distribution are studied, uniform andGaussian. The random noise sequence with uniform
distribution is generated using the pseudo random
process, which is good enough to mimic the natural
random process.
The effect of the noise sequences with different
standard deviations are simulated, and results show thatthe lasing could be achieved with relatively large electron
pulse time jitters (standard deviation). Surprisingly, jittersof less than 2 ps/pulse show no effect on the laser
performance, a result which is quite out of our
expectations. Jitters of 7 ps/pulse are, however, sufficient
to suppress the lasing. A summary of these simulations isshown in Figure 4. For the Gaussian distribution of jitter,
the results appear to be indistinguishable from the results
for the uniform distribution. Our simulations also
demonstrate that the lasing behavior strongly depends on
the noise sequence. When the averaged jitter is between 3
and 8 ps/pulse, the laser power could differ by as much as
an order of magnitude depending on the specific noise
sequence. The data in Figure 4 are indeed the average fordifferent sequences with the same standard deviation.

Figure 2: Effects of the second order phase slew
The real-time macropulse behavior of the FEL under
this kind of phase slew (c1>7 rad/µs2) is shown in Figure
3. Evidently, at the early stages of oscillation, where theaccumulated desynchronism between the pulses is still
small, the lasing starts to build up, but it cannot continue
as the phase desynchronism increases on subsequentpasses in the cavity: eventually the lasing is suppressed.
Simulations also show that, even with higher peakcurrent, no lasing trend is observed, further indicating that
this kind of phase slew is not permitted.

Figure 4: Effects of random electron pulse jitters on theoperation of the Newark FEL

Figure 3: Lasing performances under the condition whenc1>7 rad/µs2

TUPOS59

This simulation indicates that, if the e-beam pulse
frequency is stable, jitters are not critical to lasing. This
result can be understood in the following manner: thejitter changes the overlap between the electron and opticalpulses at the beginning of the macropulse, but it does not
destroy the synchronization between these pulses.
Eventually, the jitter broadens the optical pulse, which inturn enhances the overlap between the electron and opticalpulses. Thus, in actual operation, if the e-beam pulse iscentered at one frequency, but with small fluctuations inarrival time as opposed to systematic frequency
migrations, the FEL probably will produce laser output.
This tolerance of 7 ps/pulse on the jitter differs

J. Zheng et al. / Proceedings of the 2004 FEL Conference, 550-553

substantially from the tolerance of 0.5 ps/pulse previously
estimated in the literature[10].

DISCUSSION
Simulations show that a cavity loss of 6%,
corresponding to the 6cm hole used for outcoupling in the
Newark FIR FEL, is sufficient to suppress lasing. For apeak micropulse current of 2 A, the optimum total loss
(cavity and coupling loss) is approximately 2% per roundtrip. The simulation results suggest that an analysis of thehole-coupling and re-fabrication of the resonator mirrors
may be beneficial.
The actual phase slew of the e-beam pulses could be
more complex than we have assumed in our simulations
and analysis, due to nonlinear e-beam properties
originating in the injector. These non-linearities arise in
the microwave cavity and gun because the real andreactive components of their shunt impedance depend on
the current drawn from the cathode, and this current
depends in a non-linear and non-local way on the applied
RF voltage due to Schottky non-linearities in the fieldemission process and the induced heating of the cathodeby electron back bombardment. Consequently, the emitted
current increases substantially during each macropulse
and yields a non-linear and systematic variation with timein both the amplitude and phase of the accelerating
voltage in the cavity during each macropulse.
In addition to the systematic variations in the RF
amplitude and phase described above, the non-linear andstochastic nature of electron back-heating may also
introduce a degree of pulse jitter, although the relative
importance with respect to the systematic variations is
unknown. Thus, a combination of the systematic andrandom types of phase slew may be appropriate todescribe the microtron pulse generator. From the record of
the first lasing experiment, the e-beam current did
increase with time during the macropulse, suggesting thatlarge phase variations could possibly have suppressed thelasing operation in later efforts to commission the facility.
Possible solutions to the cathode heating issue include theinstallation of a phase-pick off electrode, replacing the dc
gun with a microwave gun[9], and designing the feed-

553

forward compensation or feedback control system to lockthe phase to the RF system master oscillator. Furthermore,since the Newark FEL shows almost zero tolerance to thesystematic frequency migration, an ultra-stable RFgenerator is also in high demand.

CONCLUSION
The first computer simulation of the Newark FIR FEL
was performed. It was found that the anomalous loss perround trip could suppress the lasing of the FEL. It also
showed that the FEL has a greater tolerance for random
electron pulse jitter than conventionally estimated.
However, the FEL has almost zero tolerance forsystematic electron pulse frequency migration. As aresult, we are examining techniques to suppress orcompensate these systematic variations, including
installation of a phase pick-off electrode, use of a
microwave gun[9], and design of feed-forward or
feedback compensation to control the RF phase.

REFERENCES[1] E.D. Shaw and C.K.N. Patel, Proc. Int. Conf. on
Lasers 1980, p.53-57[2] E.D. Shaw and R.J. Chichester, Nucl. Instr. andMeth. A318 (1992) 47[3] P.W. van Amersfoort et al., Nucl. Instr. and Meth.
A318 (1992) 42[4] J. Blau and W.B. Colson, Nucl. Instr. and Meth.
A318 (1992) 717[5] S. Krishnagopal, M. Xie, K.J.Kim and A. Sessler,
Nucl. Instr. and Meth. A318 (1992) 661[6] G.M. Kazakevitch et al., Nucl. Instr. and Meth. A475
(2001) 599[7] S.V. Benson et al., Nucl. Instr. and Meth., A272
(1987) 22[8] S.V. Benson et al., Nucl. Instr. and Meth., A296
(1990) 110[9] C.B. Mckee and J.M.J. Madey, Nucl. Instr. andMeth. A296 (1990) 716[10] W.E. Stein, W.J.D. Johnson and J.F.Power, Nucl.
Instr. and Meth. A296 (1990) 697.

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G. H. Biallas et al. / Proceedings of the 2004 FEL Conference, 554-557

MAKING AN INEXPENSIVE ELECTROMAGNETIC WIGGLER USING SHEETMATERIALS FOR THE COILS*
George H. Biallas#, Stephen V. Benson, Tommy Hiatt, George Neil, Michael Snyder, Thomas
Jefferson National Accelerator Facility, 12000 Jefferson Blvd. Newport News VA 23606, USA
Abstract
An inexpensive electromagnetic wiggler, made withtwenty-eight, 8 cm periods with a K of 1 and gap of 2.6
cm was made within 11 weeks after receipt of order by anindustrial machine shop. The coil design used sheet andplate materials cut to shapes using water jet cutting andwas assembled in a simple stack design. The coil design
extends the serpentine conductor design of the Duke OK4
to more and smaller conductors. The coils are conduction
cooled with imbedded cooling plates. The wiggler
features graded end pole fields, trim coil compensation forend field errors, and mirror plates on the ends to avoid
three dimensional end field effects. Details of the methods
used in construction and the wiggler performance arepresented.

INTRODUCTION
An electromagnetic (EM) wiggler with 28, 8 cm
periods and a K of 1 was manufactured for us in a very
short time, 11 weeks, for a purchase cost of $176,000.
Even more unusual, the magnet was made entirely using
machine shop technology without the use of traditionalcoils. We needed the wiggler as part of multi trackprogram to reach the goal of 10 kW from our FEL. Halfof the wiggler is shown in Figure 1

Figure 1, One Half of the EM Wiggler
We needed a back-up EM Wiggler for the low energy
track of our expanded effort to obtain 10 kW at the FEL
Upgrade Program at Jefferson Lab1,2. The characteristicsof the wiggler, 8 cm period, and 0.134 T rms field are in
the range of a normal conducting, electromagnetic
wiggler, but design and production of coils in the required
three month time frame was thought to be improbable.
A lunchtime conversation led to the possibility of using
a new, inexpensive approach. Make the wiggler coils outof sheet copper cut in a serpentine pattern like theundulators used in the Duke OK-4 FEL3 that use fourlarge, internally water-cooled, alternating orientation,
serpentine conductors in each wiggler half. Since our

TUPOS60

existing power supplies are limited to 220 A, we needed
many more layers of a smaller conductor. Sheet copper,
1.5 mm thick that fits in the 2 cm space between poles is aworkable cross section and has acceptable power loss.
The real breakthrough came when we realized thecopper sheet could be cut to high precision using newly
available, water jet cutting technology. Design began in
mid February, aiming at having a wiggler in 10 weeks.

DESIGN
Four Main Coil Elements
We were ready to design after setting the wiggler gap,
(2.6 cm) and the number of poles, (60). The first question
is: How many ampere-turns are required to excite thepoles of a wiggler with serpentine conductors? Does themissing portion of the coil turn result in not creating thefull field of a full turn? We didn’t have time to do a 3D
magnetic model of this complexity. We checked on thecurrent used for the OK4 and there seemed to be a small
effect. (Our measurements show that before any
saturation effects are seen, a factor of 10% more Ampereturns are required). We chose 24 turns per pole per halfof the wiggler, about 19 % more than theoreticallyrequired by our 2D magnetic model when operating at
200 A. The power supply had 20 A additional margin.
The second most important consideration in design wascoil cooling. At our selected parameters, with a current
density of 6.4 A/mm2, effective cooling is still possible.
Our sheet conductor design needed cooling plates thatwould cool by conduction through a layer of insulation.
The cooling plate has to have enough surface area totransfer the heat and enough cross section to conduct theheat to a tube of flowing cooling fluid. Early in thedesign process we realized that the water jet cut process
gives design freedom. Our conductor didn’t look like aserpent. It followed the pole tip’s square corners and had
three times the electrical conduction width as well as heattransfer area outside the slots. See a typical conductor
shape in Figure 2. We chose cooling plates made of thesame 1.5 mm sheet copper as the conductor. We used a
conservative philosophy of one cooling plate for every
two conductors, leading to every conductor having one
surface in contact with a cooling plate through insulation.
The cooling plates are cooled by tubing brazed to theiroutside edges beyond the outer conductor edge. See thecooling plates in Figure 3.
We chose 76 µm Kapton as the insulation between
conductors and between conductors and cooling plates.
*Work supported by the US DOE Contract #DE-AC05-84ER40150, theOffice of Naval Research, The Air Force Research Laboratory, the US
Army Night Vision Laboratory and the Commonwealth of Virginia,# Email: biallas@jlab.org

Available online at http://www.JACoW.org

G. H. Biallas et al. / Proceedings of the 2004 FEL Conference, 554-557

Figure 2, Conductors

555

accurately using a computer controlled water jet, themodern rendition of the jigsaw.
Simple calculations of the potential power dissipation
came to 8 kW, well within the limits of the available
power supply. One dimensional thermal calculations of
the heat flow through the insulation, the thermal contact
resistances and the heat flow through the copper
conductor and cooling plate showed that temperature
differences between the copper conduction strip at thecenter of the slot (highest temperature point) and thecooling water were limited to several degrees K.

End Complexities

Figure 3, Cooling PlatesThis is a robust insulation, with high dielectric strength,
no cold flow under pressure and capable of withstanding
several hundred °C in case of marginal cooling
performance. An insulation sheet is shown in Figure 4.

Figure 4, Insulation Sheet
We used 6.3 mm aluminum clamp plates on theoutsides of the conductor stacks to package and press the
conductors, insulation and cooling plates into a unit where
thermal conduction could take place reliably. A set of
sixty-four 6.3 mm brass and bronze bolts and studs, run
through the stacks provide uniformly distributed clamping
force.
We extended our water jet cutting philosophy. We
made all four of the major coil components of thiscomplex electromagnetic wiggler very rapidly andWe have to thank Stepan Mikhailov of the Duke
University FEL Center for very constructive discussion on
wiggler design at this point in the design. We copied theOK4 design’s grading of end pole field’s strengths,
aiming for 25% field integral at the end poles and 75% at
the second poles. One fourth of the conductors that
serpent through the poles of the body of the wiggler end
in a connection-loop around the end poles, exciting themto 25% of full field. Half of the remaining serpentine
conductors end in a connection-loop around the second
poles. They are excited to 75% by these turns combinedwith the second undulation of the quarter of the
conductors looping around the end poles. The remaining
one quarter of the conductors end in connection-loops
around the third poles, exciting them and all subsequentpoles to full field. With our chosen 24 conductors (turns)
per pole in the main body of the wiggler, the ratios for end
pole grading led us to stacks of 6-12-6 of the threeprogressively shorter serpentine conductor styles.
A simple method of connecting the 24 alternating
serpentine conductors was the next design hurdle. We
copied a design used on the coils of the SpreaderRecombiner Dipoles of CEBAF. At the head and tail ofeach serpentine conductor, we added tabs to extend the
conductor termination outside the bounds ofconductor/cooling plate stack. The silver plated tabs havea hole in their center and are designed to stack over one
another. A series coil is formed when an insulator film isslipped between every other tab-to-tab interface and thestack of tabs is compressed to make electrical contact
between the non-insulated tabs. A single bolt passing
through the hole in the tabs provides the compression
force. The bolt is insulated from the edges of the tab holesby an epoxy fiberglass sleeve and isolated from the end
tabs by thick epoxy fiberglass washers.
The cable lug connections to the wiggler coil are madedirectly to the tab of a top or bottom serpentine conductorof a stack. The same bolt used to compress the tabs
provides the compression force to make good electricalcontact with the lug.
The grading of field in the end poles added complexity
to the above connections. The stacks of tabs at each end
come out of the conductor stack in three positions. The
first is from the six conductors ending around the first
pole. The second stack of 12 tabs is comes out at thesecond pole. The third stack of 6 tabs comes out at the

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G. H. Biallas et al. / Proceedings of the 2004 FEL Conference, 554-557

third pole. We added jumper strips between tab stacks toform the 24-turn coil. These stacks and connections areshown in Figure 5.

Figure 5, Lead Tabs & Bolts with Manifold
This system of tab and lug contacts and the jumpers
enabled a very complex connection problem to be solved
within a very small volume.
We are again indebted to Stepan Mikhailov for two
additional suggestions that we adopted in our wiggler.
We added trim coil sets, one set to the four end poles anda second set to the second poles. They allow us to zeroout the first field integral. The second suggestion was to
add mirror plates to the end of the wiggler to cancel out
the 3 dimensional end field distortions.
We will run the power lead cables from or back to thepower supply and to or from the opposite half of the
wiggler via drops from an over-head cable tray. The pairsof opposing current cables are tied next to one anotheralong these paths to minimize the flux lines of the 0.7 mT
field created between the leads at operating current.

Cores
We planned to substitute our new wiggler for the
upstream wiggler of the installed Optical Klystron (OK).
We would reuse the mounting features of the common
strong-back that supports both OK wigglers. This
substitution requirement determined the new wiggler
core’s vertical dimension (10 cm thickness), the same as
the core of the OK wiggler with the 20 cm periods. We
reasoned that transverse field uniformity would be as
good or better. We had a surplus slab of 1006 magnet
steel from CEBAF’s 3 m dipole program that we split inhalf to form the two multi poled core halves. Thisguaranteed identical magnetic properties in the two
halves. We annealed the cores just before final machining
using our standard vacuum oven, slow cool method foriron cores.

Insulation Details
We decided to forego insulating our coil packs withconventional cast epoxy-fiberglass. The chosen Kapton
film is capable of holding off 30,000 V as a 2 dimensional
insulation. Our challenge with this 2 dimensional

TUPOS60

insulation was to prevent arc-over to the grounded coolingplates and clamp plates from the conductor edges. Theseedges are found around all sixty poles, at all 64 bolt
penetrations and the outer edges running the length andwidth of the conductor. As a design philosophy, we
decided that a nominal insulation overhang of 1 mm
would be applied to all such edges. Thus, at the poles, theconductors were withdrawn from the surface of the poleedge by 1 mm plus a 0.25 mm manufacturing tolerance.
The Kapton film’s holes to fit over the poles included
only a 0.25 mm assembly tolerance. For this philosophy
to succeed we would have to keep the voltage low, say
below 100 V, to minimize the possibility of flash overalong a surface path between conductor and ground.
Fortunately, the water jet process achieved tolerances of ±130 !m in cutting the film insulation to make the concept
a reality.
The second part of the philosophy of extending 2
dimensional Kapton insulation to a 3 dimensional wiggler
was to directly insulate the surfaces of the two classes ofobjects penetrating the conductor stacks. The pole tips
are insulated with pre-formed, 76 !m Mylar sleeves andthe bolts through the stacks are insulated with 50 !m
Mylar tape.
To build redundancy into the insulation system, we also
specified that the cores and cooling plates be coated with
Sherman Williams “Clear Coat”, an organic coating.

Cooling Details
We developed a compact manifold system that
distributes the cooling water to the twelve parallel cooling
circuits on each side of the conductor stacks and still fits
within the confines of the installed strong back. The 3.2mm outside diameter copper water tubes were bent
outward in unison at the ends of the cooling plates. The
manifolds are made of two parts, a pan-like vessel and asealable cover. The pan-vessels were made with 12 holes
in their bottom. The design calls for impaling the panbottoms over the 12 tube ends and soldering the tubes into
the holes from the inside of the pan while it is concave
outward. Applying the sealed covers to the pan completes
the manifold vessel. See figure four. This method ofsoldering from the front assures the small tubes are notplugged and the joints are leak free.

MANUFACTURING
We were fortunate to have a relationship with anexcellent manufacturing company to make our wiggler.
Process Equipment Co. (PECo) of the Dayton Ohio areamachined the cores of 400 CEBAF dipoles and had
performed their assembly. They were also familiar withwigglers, having machined the four core halves of theoriginal OK Wigglers and built their strong-back. They
had the additional advantage of routinely using a very
good Dayton water jet company (Kerf Water Jet Co.) anda noted furnace brazing company (Wall Colmonoy).
After supplying PECo with preliminary sketches inearly February followed by actual details, a contract was

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G. H. Biallas et al. / Proceedings of the 2004 FEL Conference, 554-557

placed for the Electromagnetic Wiggler on March 8 per a
fixed price bid and promised 10 to 12 week delivery.
This period was not our original 10 weeks from lunchtime
conversation, but close to it.
We also contracted with PECo for prototype efforts ofwater jet cutting of both insulation and copper sheets.
During this phase we transmitted CAD generated outlinesof the parts directly to the water jet vendor. That vendor’s
software transferred the outlines into cutting code withouttranslation error. We also funded prototype brazing oftubes to cooling plates. The prototyping gave PECo andtheir vendors the confidence to rapidly proceed withproduction once the production run materials arrived.
The production water jet cutting took about three
weeks. Prototyping showed that water jet cutting forms aburr on the edges of the sheets that had to be removed.
The radius left by the water jet turned out to be large
enough to minimize the tear-from-an-inside-cornerproperty of the Kapton film. This was very important;
there are 240 inside corners per sheet and we only had to
use tape to fix a hand full of tears. Brazing the tubes tothe cooling plates took about two weeks.
As part of our contractual agreement with PECo, we
designed a simple assembly tool to ease the draping of the
conductors, insulation sheets and cooling plates over the
60 poles. The tool has comb like teeth. It supports thecoil pieces while lowering them between the poles andcan then be withdrawn. The tool was made of a sheet ofpolycarbonate and also cut by water jet.
Assembly took about three weeks by several skilledassembly workers and their project manager. Each coilpack was assembled twice because the first assemblies
had low resistance to ground. Small chips were foundembedded in the Kapton film in at least four interfaces,
even though the assembly took place with extensive
wiping-down in a relatively clean assembly area. They
performed the second assembly in the plant’s clean-roomlike metrology lab.
The wiggler was received at Jefferson Lab 11 weeks
after receipt of order.

RESULTSThe Jefferson Lab semi-automatic hall probe scanningtable is used to measure the wiggler We removed theupper gap spacer blocks and brought the poles back toparallel using clamps. We are still qualifying the wiggler
and calibrating the trim coil values vs. K. as this paper iswrittenVertical scans at lower fields show excellent uniformityof the fields in the body of the wiggler. We also foundthat the field has a 2.5% third harmonic component that
reduces the peak field for a given rms field. The new peakfield for an rms K of one is 0.1850 T.
A marginally acceptable trajectory (30 !m peak topeak) for an rms K of .85 is shown in figure 6, indicating
the wiggler is capable of qualification. The first trial at a
trajectory for the design rms K of 1.0 is shown in Figure
7. The offset and entry angle are already quite small andthe trajectory is straight to 50 microns peak to peak. In
both scans, a superposed saw-tooth field along the
wiggler’s length, increasing at higher fields leads to the Sshaped electron trajectory. The trim coils on the first andsecond poles do not cancel it. We are exploring several
approaches, some involving trim coils. Fortunately, weleft a 3 mm space between the coil pack and the bottom of
the coil slot to add the coils.

Figure 6, Trajectory for a K = 0.85

Figure 7, Trajectory for a K = 1

CONCLUSIONS•
An inexpensive wiggler may be made very
rapidly using water jet cutting technology.
•
Transverse field quality is not compromised by
the use of serpentine conductor in this configuration.
•
Field quality for this wiggler is limited by asmall saturation effect - this is correctable by trim coils.
•
This manufacturing method may be extended tomore complicated wigglers with higher fields and shorter
periods using of 3D magnetic and thermal modeling.

REFERENCES[1] D. Douglas et.al. "A 10 kW IRFEL Design For
Jefferson Lab", Proc. PAC2001, Chicago, June 2001.
[2] S. Benson et.al., High Power Lasing in the IR Upgrade
FEL at Jefferson Lab, these Proceedings.
[3] G.N. Kulipanov et al, “Thee VEPP-3 Storage-Ring
Optical Klystron: Lasing in the visible and ultraviolet
Regions”, Proc. Of the 11th FEL Conf. Naples, Fl,
USA, Aug-Sept 1989.

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C.H.G. Hernandez-Garcia et al. / Proceedings of the 2004 FEL Conference, 558-561

PERFORMANCE AND MODELING OF THE JLAB IR FEL UPGRADEINJECTOR
C. Hernandez-Garcia*, K. Beard, S. Benson, G. Biallas, D. Bullard, D. Douglas, H. F. Dylla, R.
Evans, A. Grippo, J. Gubeli, K. Jordan, G. Neil, M. Shinn, T. Siggins, R. Walker, B. Yunn, S.
Zhang, TJNAF, Newport News, VA 23606, USA
Abstract
The JLab IR Upgrade Injector has delivered up to 9.1
mA of CW electron beam current at 9 MeV. The injector
is driven by a 350 kV DC Photocathode Gun. Injector
behavior and beam-based measurements are in good
agreement with PARMELA simulations. The injectedbeam envelopes were established by measuring beam spot
sizes and comparing them with those predicted by atransport matrix based model. The emittances were
measured by fitting an initial trial beam matrix to themeasured data. The injected bunch length was establishedby measuring the energy spread downstream of the Linac
while operating at either side of crest.

INTRODUCTION
The injector for the Jefferson Lab 10kW Upgrade IR
FEL is very similar to the 1kW IR Demo FEL [1]. The IR
Demo injector has been described elsewhere [2,3]. A
block diagram of the injector is shown in Figure 1. It
consists of a high-DC-voltage GaAs Photocathode Gundriven by a frequency-doubled, mode-locked Nd:YLF
laser, two solenoidal lenses, a room temperature buncher
cavity, a 10 MeV cryounit with two CEBAF-type 5-cellsuperconducting cavities, a matching section composedby four quadrupoles and a bunch compressor composedby three, 20°-bending-angle dipoles. Beam diagnostics in
the injector include a ceramic viewer at the entrance of thecryounit, and three optical transition radiation (OTR)
profile monitors.
Ceramic
viewer
SRF2

SRF1

S2 BC S1 Gun

OTR3
OTR2

Injection
point

OTR1
Q4 Q3

B3

B2

Q2 Q1

B1

Figure 1: Block diagram of the Injector. S1 and S2 aresolenoidal lenses. BC is the RF Buncher Cavity. SRF1
and SRF2 the superconducting RF cavities, Q1, Q2, Q3,
and Q4 are quadrupoles, B1, B2, and B3 are dipoles.
__________________________________________* Corresponding author: Tel: 1-757-269-6862;
fax:1-757-269-5519; E-mail address: chgarcia@jlab.org

TUPOS61

The 10kW Upgrade IR FEL DC Photocathode Gun is
an upgrade version of the 1 kW IR Demo DC
Photocathode Gun, which was operated at 320 kV andachieved 5 mA of CW beam at 37.425 MHz (fortieth subharmonic of the accelerator rf fundamental frequency,
1.497 GHz) with 135 pC per bunch [4]. With a new 600
kV DC HVPS the current capability in the Upgrade Gun
has been increased from 5 mA to 10 mA at 74.85 MHz
and 135 pC/bunch, as required by the 10kW Upgrade IR
FEL [5]. The 10kW Upgrade IR FEL Injector hasdelivered up to 9.1 mA of recirculated CW beam at 9.1
MeV with the gun operating at 350 kV and 122 pC/bunch.
Pulsed operation has also been demonstrated. 8 mA/pulse
in 2-16 ms-long pulses have been achieved with the drive
laser operating at 75 MHz (micro-pulse frequency) and 2
Hz repetition rate. The gun routinely delivers 350 kV, 5
mA pulsed and CW beam for FEL operations. The charge
extracted from the photocathode between re-cesiations ison the order of 200 C. A typical day of operations draws
between 30 and 40 Coulombs from the photocathode.

MODELING
The IR FEL Demo Injector has been modeled andstudied previously as a function of gun voltage [6], bunchcharge [7], and number of particles [8], using a modified
version of the particle-pushing code PARMELA [9]implementing the CEBAF-type SRF cavities [10].
Further modifications to the code have been recently
made to incorporate overlapping of the electric field of the
gun with the magnetic field of the solenoid [11]. For theUpgrade Gun, the first solenoid (S1 in Figure 1) has beenshifted upstream so that now the solenoid is right against
the gun’s anode plate and the fields overlap. In the IR
Demo Gun, the solenoid was positioned so that themagnetic field started where the electric field ended.
The design beam parameters at injection for the 10kW
Upgrade IR FEL are listed in Table 1 [12,13,14].
Table 1: Beam parameters specification at injection
Transverse
εN_x,y = 10 π mm-mrad
βx,y = 10 m
αx,y = 0

Longitudinal
εN_z ≤ 28 π ps-keV
σE ≤ 15 keV
1.5 ≤ σz ≤2.5 ps

The design operating voltage of the IR Demo
Photocathode Gun was 500 kV (10 MV/m at the cathode),but field emission from the electrode structuresencountered during its commissioning led to a decrease in
the gradient at the cathode achieved by lowering theoperating voltage to 320kV and by increasing the

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C.H.G. Hernandez-Garcia et al. / Proceedings of the 2004 FEL Conference, 558-561

Injector setup
The Injector modeling starts at the photocathode.
Transversely, the distribution is a Gaussian truncated at
2σr, with σr=2 mm. Longitudinally the distribution is
Gaussian as well with σt =23 ps and truncated at 3σt. The
first solenoidal lens (S1 in Figure 1) strength is adjusted
to focus the highly divergent electron beam following the
3σx,y=beampipe-radius criterion. The buncher (BC) is a
1.497 GHz copper cavity operated at zero-crossing phase.
Its gradient is set to minimize the longitudinal emittanceat injection by finding the minimum energy spread at
OTR2 (see Figure 1). A second solenoidal lens (S2)matches the beam transversely into the cryounit.
The cryounit accelerates the 350 keV beam to 9.1 MeV.
Ideally, the solenoid (S2) strength is adjusted to position
the beam waist at the middle of the first cell of the
upstream (SRF1) cavity. However, this is not possible forthis particular geometry due to transverse space charge
effects, so the solenoid strength is set to position the beam
waist as close as possible to the entrance of the SRF1
cavity. The upstream cavity (SRF1) is operated on crest,
while the downstream (SRF2) cavity is operated at 20°
ahead of crest for proper longitudinal beam match to theachromatic compression chicane (B1, B2, and B3).
Downstream of the cryounit, four quadrupoles (Q1, Q2,
Q3, and Q4) transversely match the beam to the injection
point, located 1.0 m upstream of the first accelerator
cryomodule (see Figure 1).
There are only two parameters that can be set in theinjector and be stated as accurate, the gun voltage and thedrive laser pulse length. All the rest have to be set andverified using beam-based measurements in concert withmodeling results.

Code calibration
Dependencies of downstream beam parameters on agiven parameter can be used to calibrate just about all theparameters. Beam-based measurements have been used tocalibrate almost all of the injector parameters.
To calibrate S1, the field that produced a waist at theceramic viewer (see Figure 1) was found by running
PARMELA with the space charge option turned off. Thenthe same procedure was followed in the actual injector
and the two field setpoints compared. It was found thatthe actual solenoid field is 2.24% larger than thatpredicted by the model.
It is difficult to calibrate the gradient value for the SRF
cavities in the model against the actual setpoints, sinceeven in EPICS there is an uncertainty of about 10%.
However, the gradient ratio SRF1/SRF2 was measured byoperating both cavities on crest [16]. The model was thenadjusted to match the measured ratio.
There is a big discrepancy in the buncher gradient
between model and the actual value reported in EPICS.

The buncher setting for smallest energy spread at OTR2
corresponds in PARMELA to 0.41 MV/m, while for theactual injector is 2.5 MV/m. Therefore, the buncher
gradient is set in both, model and machine, to produce thesmallest energy spread at OTR2. Variations from this
setpoint in the machine are translated to the model bytaking the percentile increase or decrease. A carefulmeasurement of the actual buncher gradient will be
conducted later.

INJECTOR PERFORMANCE AND
MODEL PREDICTIONSContinuous feedback between PARMELA modelingand machine behavior observations proved to be an
important tool during the FEL commissioning.

Longitudinal dynamics
The longitudinal match is achieved with the buncher
cavity (BC), the downstream cryounit cavity (SRF2), andthe downstream solenoid (S2). The buncher gradient isadjusted to minimize the energy spread at injection. The
injected bunch length is adjusted with the off-crest phaseon the downstream cryounit cavity (the injected bunch
length is also controlled with the buncher gradient, but theenergy spread grows if the buncher is not at the optimum
for smallest energy spread). The downstream solenoid
controls the longitudinal space charge force at theentrance of the cryounit by adjusting the beam spot size.
Figure 2 shows the normalized longitudinal emittancefrom the cathode to the injection point.
35.00
30.00
εNz (π-ps-keV)

cathode-anode gap (6 MV/m at 500 kV [15]). Simulations
showed that operating the gun at lower gradient would
still keep the transverse emittance within specifications[6], as measurements later proved [4].

Buncher

25.00
20.00

Compression
chicane15.00
Cryounit

10.00

Injection

5.00
0.00
0

200

400

600

800

1000

1200

z (cm)

Figure 2: Normalized longitudinal emittance as a functionof distance from the cathode to the injection point.
The IR Upgrade design requires an injector setup withthe smallest injector energy spread. The energy spread is
set using the buncher gradient, which in turn determines
the injected bunch length. According to PARMELA, sucha setup provides the smallest longitudinal emittance at
injection (buncher gradient at 2.5 MV/m). Although the
FEL lased with those settings (with the linac operating at
15° off crest), it lased better with a lower buncher gradient(2.0 MV/m) that minimized the injected bunch length.

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C.H.G. Hernandez-Garcia et al. / Proceedings of the 2004 FEL Conference, 558-561

Furthermore, the maximum Happek signal was notproduced for the design buncher gradient. The optimum
was a compromise between producing a small injectedenergy spread and a long injected bunch.
PARMELA predicts that this configuration occurs for abuncher setting 20% lower than the one that minimized
the energy spread at injection. In fact this is what wasobserved. Measurements of the full-energy momentum
spread after acceleration can be back propagated toevaluate the bunch length at injection [17]. A comparisonof longitudinal phase space parameters predicted by
PARMELA and those inferred via back-propagation isshown in Table 2.
Table 2: Model predictions at injection for two buncher
settings compared to measurements inferred via backpropagation of energy spread measured at 80 MeV toinjected energy of 9.2 MeV.

PARMELA

Inferred via
back-propagation

Buncher at 2.5
MV/m
σz =1.85 ps
σE =13.2 keV
εz =22.4 ps-keV
σz =1.65 ps

Buncher at 2.0
MV/m
σz =0.74 ps
σE =50 keV
εz=36.5 ps-keV
σz =0.55 ps

Note that the longitudinal emittance is much larger forthe lower buncher gradient setup. The predictedlongitudinal distributions at injection for the buncher
gradient settings listed in Table 2 are shown in Figure 2.
The energy distribution becomes the temporal distribution
at the FEL and the phase distribution becomes the energy
distribution. Note the large energy spread seen on the
PARMELA distribution for the lower buncher gradient.
This may be one of the causes for the lower FEL gain at
the lower buncher setting [18].

(a)

(b)

Figure 2: PARMELA longitudinal phase space at
injection for: a) Buncher gradient (2.5 MV/m) optimized
for smallest energy spread, and b) buncher gradient (2.0MV/m) optimized for shortest bunch length.
For the lower buncher setting, the injected energy
spread is too large and the bunch is too short. Although
the injector setting with the buncher gradient thatminimized the energy spread provided the design phasespace at injection -a long bunch with small energy spread,it was not the best setup for lasing.

TUPOS61

While modeling in search for an alternative injector
setting, an asymmetry in the energy spread vs. linac phaseand its apparent relation to bunch length were observed
during the FEL commissioning. To confirm thoseobservations, the PARMELA model was extended
through the first accelerator module. The simulations
confirmed the observations, indicating that thelongitudinal space charge will induce what appears to be aphase-dependent asymmetry in the beam momentum
spread during and after acceleration [19].
To alleviate the longitudinal space charge problem, a
new injector setup was modeled to produce a longer
bunch while maintaining a small energy spread. This isachieved by running the cryounit downstream cavity(SRF2) closer to crest, at 10° ahead of crest instead of thedesign value (20° ahead of crest). PARMELA predicts forthis configuration (with the buncher gradient optimized
for minimum injected energy spread) σz=2.4 ps, σE=10
keV, and εz =19.5 ps-keV. When the new injector
configuration was implemented the injected rms bunch
length inferred via back-propagation was 2.3 ps, in
excellent agreement with PARMELA. Laser gain withthis configuration was about as strong as the previous
configuration but the peak efficiency in the detuning
curve was much higher (1.25%).

Transverse Dynamics
To meet the design transverse beam envelopes atinjection (see Table 1), the quadrupoles (see Figure 1) areadjusted in the model. Once a solution is found, thequadrupoles in the injector are set to the value specified
by PARMELA. Then the beam transverse spot size ismeasured at each OTR monitor and compared to values
predicted by PARMELA. The quadrupoles have not beencalibrated yet against the model, but it was found thatbeam spots in all three OTR monitors agree with thosepredicted by PARMELA within 10% if the field for eachquadrupole is shifted by –10 Gauss with respect to the
PARMELA setpoint.
However, there is a discrepancy between the injectedbeam envelopes predicted by PARMELA and thoseestablished in the injector. The injected beam envelopes
were established by measuring beam spot sizes after
acceleration and comparing them with those predicted bya transport matrix based model. The transverse beamemittance, however agrees well with the model and it iswithin design specifications. The transverse emittanceswere measured by fitting an initial trial beam matrix to themeasured data. Table 3 shows PARMELA and measured
transverse beam parameters at injection with the buncher
gradient set for minimum injected energy spread.

C.H.G. Hernandez-Garcia et al. / Proceedings of the 2004 FEL Conference, 558-561

Table 3: Transverse beam parameters at injection with
SRF2 cavity operating at –10 degrees off crest, buncher
gradient at 2.6 MV/m, Q1=-30.5, Q2=-5, Q3=240,Q4=248 Gauss.
PARMELA
εN_x/εN_x π mm-mrad
βx/βy mαx/αy11.2 / 7.6
14.1 / 8.4-3.7 / 0.3

Established at
injection
10.0 / 10.0
10.7 / 6.1-0.3 / 0.4

CONCLUSIONS
The 10 kW Upgrade IR FEL Injector has demonstrated
operation at 9.1 mA CW, 9.2 MeV and 122 pC/bunch.
Routinely the injector delivers 5 mA pulsed and CW at
135 pC/bunch for FEL operations. In general there isgood agreement between PARMELA predictions andmachine behavior. The measured performance matches demodel in detail.
The operational experience gained during the injector
commissioning process and the constant feedback
between model and machine will be very valuable formodeling and operation of future 100 mA class injectors.

ACKNOWLEDGMENTS
This work supported by The Office of Naval Research,
the Joint Technology Office, NAVSEA PMS-405, the Air
Force Research Laboratory, U.S. Army Night Vision Lab,
the Commonwealth of Virginia, and by DOE Contract
DE- AC05-84ER40150.

561

11 K. B. Beard, B. C. Yunn, and C. Hernandez-Garcia,“FEL Injector Simulation”, JLAB-TN-03-28, October
2003.
12 D. Douglas, “IR Upgrade Driver Design, Rev 1.1.2”,
JLAB-TN-01-051, October 26, 2001.
13 D. Douglas, “Longitudinal Phase Space Managementin the IR Upgrade FEL Driver”, JLAB-TN-00-020,
September 2000.
14 B. C. Yunn, private communication.
15 D. Engwall et al., “A high-dc-voltage GaAs
photoemission gun: transverse emittance andmomentum spread measurements” PAC’99, pp.
2693-5, Vancouver, May 1997.
16 S. Benson, FEL electronic logbook, entry#1193708,
Feb 2, 2004.
17 D. X. Wang, et al., “Measurement of femtosecond
electron buncher using rf zero-phasing method”, PR
E, 57, 2, 1998.
18 C. Hernandez-Garcia, S. Benson, and D. Douglas,“Qualitative behavior of the 10 kW IR Upgrade FEL
Injector vs. PARMELA modeling”, JLAB-TN-03040, October 2003.
19 C. Hernandez-Garcia, et al., “Longitudinal Space
Charge effects in the JLAB IR FEL SRF Linac”,
these proceedings.

REFERENCES
1 S. Benson, et al., “First lasing of the Jefferson Lab IR
Demo FEL”, Nucl. Inst. Meth. A 429 (1999) 27-32.
2 P. Piot, et al., “Experimental results from an injector for
an IR FEL”, EPAC’98, pp. 1447-49, Stockholm,
Sweden, June 1998.
3 B. C. Yunn, “Physics of the JLab FEL injector”,
PAC’99, pp. 2453-5, New York, April 1999.
4 T. Siggins et al., “Performance of a GaAs DC
photocathode gun for the Jefferson Lab FEL”, Nucl.
Inst. Meth. A 475 (2001) 549-553.
5 D. Douglas et al., “A 10kW IR FEL Design for
Jefferson Lab”, PAC2001, pp. 249-52,Chicago, June
2001.
6 B. C. Yunn, “Alternative FEL Injector Setup”, JLABTN-99-010, April 21, 1999.
7 B. C. Yunn, “High Brightness Injectors Based on
Photocathode DC Gun”, PAC2001, pp. 2254-6,
Chicago, June 2001.
8 H. Liu, and B. C. Yunn, “A new nominal setting for the
FEL injector”, TJNAF TN#96-071, December 9,1996.
9 K. Crandall and L. Young, Los Alamos National
Laboratory.
10 H. Liu, et al., Nucl. Instr. And Meth., A358 475 (1995)

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SHORT ELECTRON BEAM BUNCH CHARACTERIZATION THROUGHMEASUREMENT OF TERAHERTZ RADIATION
S. Zhang, S. Benson, D. Douglas, M. Shinn, G. P. Williams, TJNAF, Newport News, VA23606,
USA
Abstract
This paper presents measurements of sub-picosecond
relativistic electron beam bunch lengths derived from ananalysis of the spectra of the coherent terahertz pulses
using Kramers-Kronig transformation. The results arecompared with autocorrelation from a scanningpolarization autocorrelator that measures the coherent
optical transition radiation. The limitations of the different
methods to beam characterization are discussed.

INTRODUCTION
Very high-power THz radiation has been successfully
generated at Jefferson Lab[1]. The powerful short pulse
THz source provides unprecedented opportunities forapplications such as THz imaging and material studies.
These THz pulses also carry important characteristic
information about the electron bunch length which is very
important to FEL and accelerator physics studies.
A measurement of the radiation spectrum will give theform factor and the electron density distribution through a
Fourier Transform[2-4]. However, this always provides asymmetric distribution. By introducing a mini-phase
under certain conditions, the lost phase information can berecovered and the bunch distribution asymmetry may berevealed[6]. This method requires a Kramers-Kronigtransformation (KKT) analysis to calculate the mini-phasefollowed by an inverse Fourier transform, resulting in the
expected longitudinal electron density distribution.
Different from Coherent Transitional Radiation (CTR),
the Coherent Synchrotron Radiation (CSR) is generated
by the electrons through bending magnets and therefore
requires no foils. There is no interruption to the runningbeam while the measurement is going on. We will use the
CSR that is conveniently available form our FEL facility
for the beam bunch measurement. Discussions andcomparisons with other measurement methods will also
be addressed.

SETUP AND MEASUREMENT
Fig.1 is an overall sketch of the Jefferson Lab 10KW
upgrade FEL facility. Electrons coming from the gun are
accelerated by linac and then compressed into very shortbunches before traveling to the optical cavity.
Synchrotron radiation is generated in several locations
where the magnets bend the beam orbit. For theexperiments, the primary instrument used in is a Nicolet
FT-IR spectrometer. Fig.2 shows the optical layout of theexperimental setup with a simplified spectrometer
schematic. The THz pulses from relativistic electrons exita diamond window through a vacuum beam port near thebending magnet that directs the 89Mev electron beam into

TUPOS62

the optical cavity and wiggler. Several silver mirrors areused to bring the THz beam into the spectrometer bench.
To minimize the water absorption by THz pulses, thewhole optical beam path is purged with nitrogen.

Fig.1. Layout of FEL facility and THz beam port.
GUN is the photo-cathode electron source. HPVS,
high-voltage power supply. CM, Linac Cryo-Module.
HR, high-reflector. OC, output coupler.

THz pulses

Window port
MirrorMirrorBeam splliter

Detector

MirrorAnalyzer

Moving mirror

Fig.2. Schematic of the optical setup for THz spectral
measurement.

RESULTS AND DISCUSSIONS
Typical spectra taken from the spectrometer are shownin Fig. 3. We used a DTGS detector with a polyethylene
window. The efficiency of the detector has a spectral rolloff on the low frequency side. This can clearly be seen in
the spectrum. Another major factor contributing to thelow frequency cut-off is the limited diamond window
aperture that restricts the diffracted beam from reaching
the optical bench. Appropriate spectral fitting in the low
and high frequency region is used to help reconstruct thewhole spectrum and has turned out to be very effective.
Before extraction of the form factor, the spectrum wascorrected by the ω
frequency dependence of the single
electron emittance. We assume that the form factor shouldbe parabolic at low frequencies, and use
2/3

f (ω ) = 1 − aω 2

as

a

good

approximation.

At

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563

20

60

15.6

47.6
Intensity (a.u.)

Intensity (a.u.)

S. Zhang et al. / Proceedings of the 2004 FEL Conference, 562-565

11.2
6.8
2.4
2

35.2
22.8
10.4

0

20

40
60
80
Frequency (1/cm)

2

100

0

20

(a1) Spectrum

0.8

0.6

Fm (a.u.)

Fm (a.u.)

Form factor

1

0.8

0.4
0.2
0

0.6
0.4
0.2

0

20
40
60
80
Frequency (1/cm)

0100(b1) Form factor

0

20
40
60
80
Frequency (1/cm)

100(b2) Form factor

1

1

FWHM=0.244mm
FWHM=0.22mm
Density (a.u.)

FWHM=0.386mm
Density (a.u.)

100(a2) Spectrum

Form factor

1

40
60
80
Frequency (1/cm)

0.5

0.5

0

0

0

0.25 0.5

0.75 1 1.25 1.5
Z (mm)

1.75

2(c1) electron density

00.25 0.5

0.75 1 1.25 1.5
Z (mm)

1.75

2(c2) electron density

Fig.3. Two sets of measurement and analysis with different beam settings. (a) Typical THz radiation spectrum,(b) Form factor extracted from the THz spectrum, (c) Retrieved longitudinal electron density distribution. The
FWHM width is 0.386mm (about 1.29ps in time duration) for in (c1) and 0.244mm (about 0.81ps) for (c2). The
bunch is much shorter for the latter. The dashed curves in (b2) and (c2) are explained in text.
high frequency we use f (ω ) = bω(a and b are
constants, depending on and decided by each specificspectral distribution). With these asymptotic attachments−4

to each respective side, a reconstructed form factor can beobtained. Applying the KKT to the new form factor, wewere able to retrieve the longitudinal electron density
distribution or the beam bunch shape. Fig.3 presents the

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calculated results based on two groups of measured THz
spectra. The electron beam energy is 89MeV. Bothprofiles show clear asymmetry. The asymptotic
attachment on both ends has only limited influence on theoverall shape of the distribution, especially within small
distances from the point where z=0[6]. Fortunately this is
the region where the bunch shape and length is decided.
More precise measurements at lower frequencies will lead
to better determinations of the shapes of longer bunches.
The negative values in the density distribution are nonphysical and were partly due to the low frequency
attachment. With the low frequency attachment pushed
farther to the left, as shown in the dashed curves in Fig.3,
the negative values in calculated density distribution areapparently reduced. The overall shape of the density
distribution basically remains unchanged while a small
reduction on the width can be seen.
The data in the right column of Fig.3 shows anapparently shorter bunch than that in the left. The
observed higher FEL output power can also be anindication of this shorter bunch. So it is possible to get afairly good idea about how the beam setting is by justlooking at the THz spectrum while tuning the electron
beams. We also did calculations on the CSR based on theexperimental electron beam parameters and assuming a
Gaussian beam. The spectra at different bunch lengths areshown in Fig.4. The low frequency fall-off is due todiffraction. The two sets of spectra are the same as thosein Fig.3. Each of them falls into the expected bunch
length range. When compared with the purely theoretical
calculations, the lack of the low frequency experimental
data is once again clearly evident. It can be imagined that
better estimates on the bunch could be made bycomparing predicted with measured data that included
more low frequencies. One aspect worth mentioning isthat the shorter bunch tends to push the spectrum tohigher frequencies.

N o r m a liz e d P o w e r (a .u .)

1.0

fs500
fs1000fs1500fs2000
exp1
exp2

0.8
0.6

0.4

0.2

0.0
0.1

2

3

4 5 6 78

1

2

3

4 5 678102

3

4 5 678100

Frequency (1/cm)
Fig.4. Comparison between the measured THz spectra
and calculations with different bunch lengths. Exp1
and Exp2 correspond to the spectra shown in the left
and the right column in Fig.3, respectively. The
estimated bunch lengths agree with the KKT results.

TUPOS62

Since we are dealing with THz pulses with time durationon the order of a few picoseconds or shorter, the electricfield of each individual pulse only has a few cycles orless. This has been referred to as single-cycle electric fieldthat has drawn much research interests for basic research.
Compared with other ultrashort optical pulses in thevisible and near IR, this type of pulse imposes certain
difficulties in the determination of its temporal pulse
width because of the limited number of fringes in the time
window. The clear temporal intensity profile does notexist anymore and the electric field may give a better ideaof the temporal characteristics. This is especially true forthe measurement using polarization autocorrelation
method.

E-beamCTR
Al foil

MirrorPolarizer

Detector
Polarizer

Polarizer

Roof
MirrorMoving mirror

Fig.5. Simplified optical layout of a polarization
autocorrelator (Martin-Pupllet interferometer). The
optical pulses come from the optical transitionalradiation generated by the short electron bunchesinteracting with a thin aluminum foil.
To have a further look at the issue, we took data from an
autocorrelator,ortheso-called
Martin-Puplettinterferometer (MPI)[7]. Fig.5 is an optical schematic of
the MPI. It was set to measure the coherent opticaltransitional radiation (CTR) when a thin aluminum foil
was inserted into the electron beam path. The MPI is a
modified Michelson interferometer with thin wire gridpolarizors and beam splitters. A Golay cell was used as adetector. The MPI is actually a polarization autocorrelator
and the detected signal is the electric field correlation of
two input replica pulses. The width of the autocorrelation
traces is an indication of the input pulse width, but is notexactly the same as the width of the temporal intensity
profile which is normally used for the determination of an
ultrashort pulse length. In fact for a Gaussian distribution,a factor of 0.7 applies. The measured autocorrelation tracefrom our experiment is given in Fig.6 along with aGaussian fitted center peak and the envelope. The FWHM
values obtained from KKT method and MPI are in generalagreement with each other, as can be seen from (c1) in
Fig.3 and the fitted curve in Fig.6 (where data comes from

S. Zhang et al. / Proceedings of the 2004 FEL Conference, 562-565

beams under same condition) . However, there are someerrors which come from many factors and can be above
10%. The precision of the fitting data is primarily limitedby the number of available fringes in the pulse. In thepresent case, there are only a few fringes and fitting isimpractical. However, to obtain the fitting (blue curve) we
generated the dotted curve by inverting value of the solid
curve which lay below a baseline from the asymptotic
limits. We note in passing, however, that in practice thecentral peak is frequently used as an indication of thebunch length because this peak has a clear envelope of its
own which is easy to fit.

565

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G. Williams, Nature, 420 153-156 (2002).
[2] K.Ishi et al., Phys. Rev. A43, 5597 (1991).
[3] J. S. Nodvick, D. S. Saxon, Phys. Rev., 96, 180(1954).
[4] E. B. Blum, U. Happek,A. J. Sievers, Nucl. Instr.
Meth. A307, 568 (1991).
[5] R. Lai, A. J. Sievers, Nucl. Instr. Meth. A397, 221 –
231 (1997).
[6] R. Lai, A. J. Sievers, Phys. Rev. E52, 4576-4579(1995).
[7] D.Martin, Polarizing Interferometric Spectrometers for
the Near and Sub-millimeter Spectra, Chpt.2, New
York, Academic Press, (1982).

Field Amplitude (a.u.)

1

0.75

0.5

0.25

0

6

4

2

0
Delay (ps)

2

4

6

Fig.6. The red solid line is an CTR autocorrelation
trace from MPI. Blue dotted curve is the fittedenvelope with 1.34ps FWHM. Fitted central peak
0.71ps FWHM(green dashed line).

SUMMARY
The temporal characterization of sub-picosecond
relativistic electron bunches has been performed throughthe measurements of THz radiation and subsequent KKT
analysis. Comparisons between the CSR calculation andthe result from an MPI that measures the CTR were
presented. The issues with the determination of short THz
pulse length are also discussed. The KKT analysis of the
CSR may become a useful tool for bunch shapemeasurement but the precision primarily depends on the
spectral measurement, especially at the lower frequency
end in our case. Further studies along with a comparison
with other methods such as electro-optical sampling will
be helpful to clarify the above mentioned issues.
Acknowledgement
The authors would like to thank the FEL team for theirassistance during the experiment and for beam operations.
This work is supported by the Office of Naval Research,
Research, the Joint Technology Office, NAVSEA PMS405, the Air Force Research Laboratory, the US Army
Night Vision Lab, the Commonwealth of Virginia and
DOE Contract DE-AC05-84ER40150.

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S. J. Lenci et al. / Proceedings of the 2004 FEL Conference, 566-569

RF SOURCES FOR 3RD & 4TH GENERATION LIGHT SOURCES
S. Lenci, H. Bohlen, E. Wright, A. Balkcum, A. Mizuhara, CPI MPP, Palo Alto, California, USA
R. Tornoe, Y. Li, CPI Eimac, San Carlos, California, USA
Abstract
The growing number of third and fourth generation
light sources has resulted in an increase of the available rf
sources to power them. Single beam klystrons are thetraditional power source, but the development of IOT’sand multiple-beam klystrons (MBK’s) in L-Band haveincreased the options for these machines. The Eimac
division of CPI has recently built and tested a prototype
L-Band IOT, which delivered 30 kW CW at 1.3 GHz.
Future work includes the building of an IOT at 1.5 GHz.
Meanwhile the MPP division of CPI is currently testing
the prototype 10 MW peak, 1.3 GHz MBK for the TESLA
x-ray free-electron laser (XFEL). Test results for thesenew products as well as information on all CPI products
at 500 MHz, 1.3 GHz, and 1.5 GHz will be presented.

years of proven service. The VKP-7953A is a slightly
modified version of our UHF-TV klystron and rated for
70 kW CW and the VKP-7953B is rated for 100 kW CW.
The “A” version has been in service at Taiwan’s
Synchrotron Radiation Research Center (SRRC) for the
past 10 years. The first of higher power “B” version ispresently being built. These tubes have a 5-cavity rf
circuit, mod anode gun, and a single output window.
At 800 kW CW CPI has built the VKP-7957A for theCornell Electron Storage Ring (CESR) at Cornell
University and the VKP-7958A for the HERA ring at
DESY. These tubes share the same rf circuit, have asingle output window, and an electron gun with amodulating anode. The VKP-7957A operates horizontallywith the gun in oil; the VKP-7958A operated verticallywith the gun up and in air, see Figure 1.

INTRODUCTION
CPI, formerly the Electron Device Group of Varian
Associates, has a long history of building high-power
pulsed and CW klystrons for many applications. For many
years, klystrons have been the preferred RF power
amplifiers for both pulsed and CW linacs at UHF andhigher frequencies. Their high power capability,
reasonable efficiency, stability, robustness and long life
expectancy have earned them that position. Recent
developments are encroaching into the klystrons dominantposition. Advancements in Inductive Output Tubes (IOT)
and Multiple-Beam Klystrons (MBK) make these devices
very attractive in a growing number of applications.
Operation at 500 MHz provides many options at power
levels below 60 kW CW. This frequency is in the UHFTV broadcast band and can often utilize existing devices
with little or no modification. Devices for L-band tend tobe specifically designed for a given application, but thenbecome available to others interested in using thedeveloped hardware.

KLYSTRONS
Klystrons have been the traditional device foraccelerators for many years. They come in a variety of
power levels and frequencies. Modern design tools andthe plethora of existing designs make this device easily
adaptable to the needs of the accelerator community.
Klystrons at 500 MHz, 1.3 GHz, and 1.5 GHz are
available in many power levels, both pulsed and CW.
Beam conversion to rf efficiency can exceed 65% and rf
gain ranges from 40 to 55 dB.

UHF Klystrons
At 500 MHz, CPI has klystrons up to 800 kW CW. The
lower power tubes are the VKP-7953 series klystron. The
device is based on our UHF-TV klystron that has many

TUPOS63

Figure 1: VKP-7958A Klystron for DESY
Additionally there are a number of klystrons at otherUHF frequencies. The VKP-7952A was developed for the
APT Project and produces 1 MW CW at 700 MHz. At
805 MHz, the VKP-8291A is in production for the
Spallation Neutron Source project at Oak Ridge National
Lab. CPI is building 81 of these 550 kW peak pulsed
devices with a beam conversion to rf efficiency in excess
of 65% [1]. Additionally there is the VKP-7955 which
operates at 200 kW pulsed at 1 msec at 805 MHz.

L-Band Klystrons
In this frequency band CPI has a series of low power
klystrons that have been in service for a number of years.
The VKL-7811 series have been reliable klystrons for anumber of facilities around the world. These compact
devices use diode guns, liquid cooling, and permanent
magnets for focusing. The VKL-7811W was developed in
the early 1990’s for the Continuous Electron Beam
Accelerator Facility (CEBAF) at the Thomas Jefferson

Available online at http://www.JACoW.org

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S. J. Lenci et al. / Proceedings of the 2004 FEL Conference, 566-569

National Accelerator Facility. These tubes are rated for 5
kW CW at 1.497 GHz. Approximately 380 units weremade in the original production run to populate theaccelerator. Next came the VKL-7811M (5 kW CW at 1.3
GHz) for an application in Japan. Finally the VKL7811ST (10 kW CW at 1.3 GHz) was developed for
Stanford University and Forschungszentrum Rossendorf(FZR).
The VKL-7966A is a 100 kW CW klystron at 1.497
GHz that was recently built to drive the cryogenic cavities
in the injector stage of the FEL Driver Accelerator at
TJNAF [2]. These units were used in their experiment that
achieved 10 kilowatts of infrared laser light, making it themost powerful tunable laser in the world.
In addition to these klystrons that were specificallydesigned for accelerator applications, CPI has tubes
designed for radar that are available as well. The VA963A is rated for 6.5 MW peak power and 10 kW of
average power. It’s a pulsed device that can provide 5µseconds pulses at 1.3 GHz. The VKL-7796 is rated for 4
MW peak and 300 kW average with pulse lengths up to
130 µseconds.
Table 1: Various UHF and L-Band Klystrons
Model
Frequency
OutputDuty
Power,kW
VKP-7953A
500 MHz70
CW
VKP-7953B
500 MHz
100
CW
VKP-7957A
500 MHz
800
CW
VKP-7958A
500 MHz
800
CW
VKP-7952A
700 MHz
1000
CW
VKP-8291A
805 MHz
550.09
VKP-7955
805 MHz
200.002
VKL-7811M
1.3 GHz5CW
VKL-7811ST
1.3 GHz
10
CW
VA-963A
1.3 GHz
6500.001
VKL-7796
1.3 GHz
4000.075
VKL-7811W
1.497 GHz
5CW
VKL-7966A
1.497 GHz100
CW

MULTIPLE BEAM KLYSTRONS (MBK)MBK technology can be separated into two categories:
Fundamental Mode (FM) and Higher-Order Mode (HM)
MBKs [3]. The differences between the two are theproximity of neighboring beams and the proximity ofneighboring cavity modes. The primary drawback to the
FM-MBK is that the clustered electron beams areconstrained to fall within a circle of approximately λ0/4
for optimum cavity interaction. The FM-MBK are
generally used for applications requiring large
instantaneous bandwidth. The HM-MBK electron beams
can be widely separated from each other operating intohigher-order-mode cavities. The HM-MBK is selected
when relatively narrow bandwidths are acceptable, aswith conventional single-beam klystrons, at high average
power. However, for this geometry, the cathode loading is

not constrained by the circuit and is instead limited by theskill of the beam-optics designer.
An equally important factor is that as a result of beaminterception with and without rf, the cavity thermalloading is distributed along a relatively large surface area,
increasing the average power handling capability of the
HM-MBK versus the FM-MBK. A comparison of MBKs
to single-beam klystrons can be seen below.
Advantages• Lower operating voltage for a given rf power level• Lower x-ray level due to lower operating voltage• High efficiency vs. microperveance• Large instantaneous bandwidths (FM-MBK)• Compact, lightweight• Low Noise
Disadvantages• Difficult to focus the electron beams• Lower average power (FM-MBK only)• High cathode loading (FM-MBK only)

1.3 GHz MBK for TESLAThe first opportunity for CPI to build an MBK was for
the TESLA project at DESY. The CPI-DESY engineering
team agreed to use the HM-MBK approach. The primaryreason for doing so is discussed above and worth
repeating: low cathode loading combined with distributed
thermal loading of the rf circuit. This HM-MBK uses six
off-axis electron beams emitted from six individual
cathodes. Table 2 lists the essential design parameters forthis device.
Table 2: TESLA MBK Typical Operating Parameters
Parameter
Value
Units
Peak Output Power
10MW
Average Output Power
150
kW
Beam Voltage
114
kV
Beam Current
131
A
Efficiency
65-67%
Frequency
1300
MHz
Pulse Duration
1.5
ms
Saturated Gain
47
dB
Number of Electron Beams
6--Number of Cavities
6--Cathode Loading
~2.1
A/cm2
Solenoid Power4000
W, max.
Cathode Loading
~2.0
A/cm2

TESLA MBK Prototype Test Results
Initial testing of the device has validated the basic
design approach [4]. Six 120 kV electron beams of
measurably identical currents of 22.9 A each have beensuccessfully propagated through the klystron circuit with
99.5% DC beam transmission at full operating video duty
and with 98.5% saturated RF transmission. A peak powerof 10 MW at 1.3 GHz with 60% efficiency and 49 dB ofgain have been measured. The output power versus input

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S. J. Lenci et al. / Proceedings of the 2004 FEL Conference, 566-569

power curves for varying beam voltages is shown in
Figure 2. As can be seen, the curve characteristics for the
MBK are substantially the same as a conventional
klystron. A photo of the device is shown in Figure 3.

Output Power (MW)1210120 kV
118 kV
116 kV114 kV112 kV8
6

F = 1300 MHz
Po = 10 MW4

η = 60%Gain = 49 dB
Eb = 120 kV

range of IOTs to the VHF and UHF bands; 1 GHz was
considered a threshold beyond which the performance of
IOTs as fundamental frequency amplifiers would fall off
rapidly.
Several key advantages of the IOT make them desirable
for accelerator use. The salient parameters in this case are:1.

2.

Ib = 139 A

2
0
0

50

100

150

Drive Power (W)Figure 2: Measured output power versus drive power for
five beam voltages

3.

Most particle accelerator applications do not require
high linearity. The IOT can be operated in class C andthus provide efficiency levels far beyond the reach of
klystrons, see Figure 4.
The IOT does not saturate at the point of its highest
efficiency like the klystron. The device does not
require power back-off from optimum efficiency toallow fast feedback.
Since the beam current in an IOT is grid-controlled, a
HV modulator is not required for pulse operation. It
is sufficient to pulse the drive power.
90%
80%

IOT (Class C Operation)

70%

Klystron

Efficiency

60%
50%
40%
30%
20%
10%
0%
0

10

20

30
40
50
60
Output Power, kW

70

80

90

Figure 4: IOT Efficiency vs. Typical KlystronFigure 3: Prototype MBK for TESLA
Unfortunately testing was stopped due to a problem
with one of the two output windows. During long pulse,
high-average power testing several gas bursts wereexperienced, along with severe rf pulse shortening. The
average power capability of the MBK degraded after these
events. The problem with the window was verified. The
klystron is in the process of being repaired with the targetof shipping it to DESY by the end of the year.

INDUCTIVE OUTPUT TUBES (IOT)
Since the late 1980s the Inductive Output Tube (IOT)
has established itself as a useful device for broadcast,applied science and industrial applications in the UHF
range. Compared to a klystron, the IOT compensates for
its lower gain with both superior efficiency and linearity,and it outperforms the tetrode, its next of kin, with regard
to power capability and gain. However, it has long beenthought that transit time effects limit the useful frequency

TUPOS63

The existing UHF-TV IOT, EIMAC K2 series, is well
suited for use at 500 MHz, or anywhere within the UHFTV operating band (470-810 MHz) and has a very
positive track record in TV broadcast service (up to 130
kW peak in digital or up to 75 kW peak sync in analogue
operation, respectively), as well as a CW amplifier for
scientific purposes (up to 80 kW CW) with the addition ofsome cooling.
UHF IOTs are in CW operation in the 5 MeV CW
Microtron at MELCO in Kobe, Japan. Two IOTs are
combined to generate 100 kW of RF power at 500 MHz.
At the FEL at the Japan Atomic Energy ResearchInstitute, Tokai, Japan, two IOTs are used independently
as RF sources for the pre-acceleration super conducting
cavities (499.8 MHz). See Table 3.
Table 3: Eimac K2 IOT Operation at 500 MHz
Power Level (kW)Beam Voltage (kV)Beam Current (A)Grid Current (A)RF Drive Power (W)Power Gain (dB)
Efficiency (%)

50
30
2.14
0.14
190
24.2
77.9

60
30
2.67
0.24
267
23.5
74.9

67
35
2.6
0.14
275
23.9
73.6

80
35
2.98
0.22
380
23.2
76.7

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S. J. Lenci et al. / Proceedings of the 2004 FEL Conference, 566-569

Eimac has delivered 15 IOTs for pulsed operation in a
US government project. Each IOT delivers 80 kW peak
power and operates at a different frequency in the UHF
range.

The First L-band IOT design
The fundamental-frequency IOT seemed to be thesingle solution to maintain the well-appreciated IOT
properties for an L-band version [5]. It was decided tomodify EIMAC K2 as little as needed only to arrive at a
1.3 GHz version. To replace the external-cavity UHF
output section with an internal 1.3 GHz resonator was astraight-forward development step. The output section
consists of a standard 1-5/8 inch coaxial line, whichcontains an alumina window of the same type that is in
use in numerous L-band klystrons. The cavity is watercooled which serves to remove the loss energy from thecavity and provide stability against de-tuning.
Much more concern was spent on the input circuit. The
input impedance of an IOT is of the order of 10 Ω only;
thus the input circuit has to transform the impedance
downward from that of the input line, instead of upward
like in the case of a klystron. Beyond that, the input signal
has to be transferred safely and reliably from ground levelto the high-voltage DC potential of the electron gun.
High-voltage-safe dimensions and low impedance are noteasily married, but it was possible to find an elegant
solution to the problem.
Apart from these two segments, almost all otherelements are identical with those of the UHF version. The
1.3 GHz prototype is shown in Fig. 5.

Table 4: Prototype 3 Test Results at 1.3 GHz
Beam
Voltage
(kV)
24
25
26
32
34

Beam
Current
(A)
0.79
1.10
1.46
1.35
1.39

Drive
Power
(W)
208
203
183
192
253

Output
Power
(kW)
10.0
15.1
20.6
25.7
30.2

Gain
(dB)
17
19
21
21
21

Efficiency
(%)
52.7
54.9
54.3
59.5
63.8

Even at almost 30 kW CW the body of the IOT and its
output section did not show signs of meeting any
limitations. The thermal output power measurements are
believed to be pessimistic because the power-absorbing
bricks of the load were operating at very hightemperatures and reflected a considerable part of thepower back into the waveguide in the form of infrared
radiation.
It is believed that these tests, performed in December of2003 and January of 2004, mark the first time that an IOT
has been operated at a frequency beyond the UHF band.
The encouraging results have driven the development of a
1.5 GHz, 15 kW CW version, which is scheduled fortesting in early 2005, and a 300 kW long pulse IOT at 1.3
GHz.

SUMMARY
CPI has expanded its catalogue of vacuum electron
devices with the addition of the MBK and IOT. The
particle accelerator community has more options in typesof devices to power their machines in UHF and L-band.
The klystron will remain the workhorse with the ability tocover virtually any power need. The MBK provides highefficiency at lower operating voltage while the IOT
provides high efficiency over a wide range of power level.
These newcomers will provide system designers lowering
procurement and operating costs.

REFERENCES

Figure 5: 1.3 GHz IOT

L-Band Prototype Test Results
The first prototype was slightly off frequency; thesecond unit was slightly overcoupled. Prototype 3 was on
frequency and measured data shown in Table 4.

[1] S. Lenci, et al., “Large Scale Production of 805-MHz
Pulsed Klystrons for SNS”, Proceedings of EPAC
2004, paper TUPKF076.
[2] A. Mizuhara, “A 100 kW, 1497 MHz, CW Klystronfor FEL Driver Accelerator”, Proceedings from FEL
2002 Conference, p II-27 – II-28.
[3] E. Wright, et al., “Development of a 10 MW, L-Band
Multiple Beam Klystron for TESLA”, Proceedings of
PAC 2003, paper TPAE029, p. 1144-1146.
[4] E. Wright, et al., “Test Results for a 10 MW, L-Band
Multiple Beam Klystron for TESLA”, Proceedings of
EPAC 2004, paper TUPKF077.
[5] H. Bohlen, et al., “Development of a 1.3 GHz
Inductive Output Tube for Particle Accelerators”,
Proceedings of Displays and Vacuum Electronics
2004 Conference, Garmisch-Partenkirchen, Germany

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V.N. Litvinenko et al. / Proceedings of the 2004 FEL Conference, 570-573

HIGH CURRENT ENERGY RECOVERY LINAC AT BNL*
V.N. Litvinenko#, I. Ben-Zvi, D.S. Barton, D. Beavis, M. Blaskiewicz, J.M. Brennan A. Burrill, R. Calaga, P. Cameron,
X. Chang, R. Connolly, D.M. Gassner, H. Hahn, A. Hershcovitch, H.-C.Hseuh, P. Johnson, D. Kayran, J. Kewisch, R.
Lambiase, W. Meng, G. McIntyre, T.C. Nehring, A. Nicoletti, D. Pate, J. Rank, T. Roser, T. Russo, J. Scaduto, K.S.
Smith, T. Srinivasan-Rao, N.W. Williams, K.-C. Wu, V. Yakimenko, K. Yip, A. Zaltsman, Y. Zhao,
Brookhaven National Laboratory, Upton, NY, USA
H.P. Bluem, A. Burger, M. Cole, A. Favale, D. Holmes, J. Rathke, T. Schultheiss, A. Todd,
Advanced Energy Systems, Medford, NY, USA
J. Delayen, W. Funk, L. Phillips, J. Preble,Thomas Jefferson National Accelerator Facility, Newport News, VA, USA

Abstract
We present the design and the parameters of a small
Energy Recovery Linac (ERL) facility, which is underconstruction at Collider-Accelerator Department, BNL.
This R&D facility has goals to demonstrate CW operationof ERL with average beam current in the range of 0.1 - 1
ampere, combined with very high efficiency of energy
recovery. The possibility for future up-grade to a two-pass
ERL is being considered. The heart of the facility is a 5cell 703.75 MHz super-conducting RF linac with HOM
damping. Flexible lattice of ERL provides a test-bed fortesting issues of transverse and longitudinal instabilities
and diagnostics of intense CW e-beam. ERL is also
perfectly suited for a far-IR FEL. We present the status
and plans for construction and commissioning of thisfacility.

vacuum beyond the discovery phase towards their fullcharacterization [1]. The ERL-based eRHIC withluminosity of 1034 cm-2sec-1 per nucleon will extend thecapability of RHIC even further using polarized electrons
to probe Colour Glass Condensate and spin structure of
nuclear, to mention a few. These projects are the driving
force behind the development of ampere-class ERL
technology [4], which will find many applications
including light sources and FELs, These programs also
define the goals for the R&D ERL development:

GOALS OF ERL R&D PROGRAM AT BNL
The ERL R&D program is pursued by the Collider
Accelerator Department (C-AD) at BNL as an important
stepping-stone for 10-fold increase of the luminosity of
the Relativistic Heavy Ion Collider (RHIC) [1] using
relativistic electron cooling [2] of gold ion beams withenergy of 100 GeV per nucleon. The system withincreased luminosity and electron cooling, called RHIC
II, is sketched below.

Figure 1. Electron cooling of RHIC, pictorial diagram.
Electron cooling is used to reduce the emittance of an ion
beam circulating in a storage ring by transferring thetransverse motion (the heat) from a high emittance (hot)ion beam to a low emittance (cold) electron beam.
Furthermore, the ERL R&D program extends toward a
possibility of using 10-20 GeV ERL for future electronhadron/heavy ion collider, eRHIC [3].
The 10-fold increase of luminosity in RHIC II will
extend the studies of quark-gluon plasma and QCD

TUPOS64



Test the key components of the RHIC II electron
coolerTest the key components of the High Current Energy
Recovery Linac based solely on SRF technology
o 703.75 MHz SRF gun test with 500 mA
o High current 5-cell SRF linac test with HOM
absorbers (one turn - 500 mA, two turns - 1 A)o Test the beam current stability criteria for CW
beam currents ~ 1 A
Test the key components and scalability for future
linac-ring collider eRHIC witho 10-25 GeV SRF ERL for eRHIC
o SRF ERL based an FEL-driver for high current
polarized electron gun
o Test the attainable ranges of electron beam
parameters in SRF ERL

Figure 2. Layout of eRHIC with 10-20 GeV ERL in the
RHIC tunnel and with circularly polarized FEL-driver forpolarized electron photo-injector [3].
The plans call for construction and commissioning of the
prototype ERL within 3 years. The ERL will be located in
one of the spacious bays in Bldg. 912 of the RHIC/AGS
complex.

Available online at http://www.JACoW.org

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V.N. Litvinenko et al. / Proceedings of the 2004 FEL Conference, 570-573

construction at Advanced Energy Systems and is planned
to be installed and tested in Bldg. 912 in the middle of2005. The 50 KW 703.75 MHz RF transmitter for the
linac has been installed at the site and is undergoingcommissioning.
The lattice of the ERL is designed and needs some final
refinements to fit with the SRF injector. The main featureof the lattice is that it provides a wide range of transport
matrix parameters to study both longitudinal andtransverse beam break-up instability (BBU), whileremaining achromatic.
In this paper we describe the current design, the main
component and the expected performance of the R&D
ERL.

LAYOUT AND MAIN COMPONENTS OF
THE ERL

Fig.3 The layout of the facility (top) and the photographof the shielded vault for R&D ERL under construction in
the bay of Bldg. 912. The bay is equipped with an
overhead crane. The control room is located outside of thebay in a separate building.
Technical details of R&D ERL constitute a significant
part of the 260-page ZDR (Zero’s-order Design Report),
for the RHIC II electron cooler, which is undergoing final
polishing. The intensive R&D program geared towards
the construction of the prototype ERL is under way: fromdevelopment of high efficiency photo-cathodes [4] to thedevelopment of new merging system compatible withemittance compensation.

30-35 MeVe- 15-20 MeV

Table I. Parameters of the R&D ERL in Bldg. 912
High
High
charge current
Injection energy, MeV
2.5
2.5
Maximum beam energy, MeV
20
20
Average beam current, A, up to
0.2
0.5
Bunch rep-rate, MHz
9.4
703.75Charge per bunch, nC~20
1.3
Normalized emittance, mm*mrad ~ 30
~1-3Efficiency of current recovery, > 99.95% 99.95%
A description of the SRF gun and its photocathode system
can be found elsewhere [4]. The maximum current fromthis gun will be limited to a maximum value of about 0.5
A by the RF power of 1 MW 703.75 MHz CW klystron.

Laser

Cryo-module

SC RF Gun

The base-line design has one turn: electrons are
generated in the superconducting half-cell gun to about
2.5 MeV and injected through the merging system withemittance compensation (see below) into the main linac.
Linac accelerates electrons 15-20 MeV, which passthrough a one turn re-circulating loop with achromatic
flexible optics (see below). The path-length of the loop
provides for 180 degrees change of the RF phase, causing
electron deceleration (hence energy recovery) down to 2.5
MeV. The decelerated beam separates from the higher
energy beam and goes to the beam-dump. The main
expected parameters of this system are listed in Table I.

Beam dump

e- 2.5MeVSRF cavity

1 MW
703.75 MHz
Klystrone2.5 MeV

50 kW 703.75 MHz
systemControl room

Fig. 4 Layout of the R&D linac in the shielded vault
The SRF gun is currently under design at Advanced
Energy Systems with the participation of BNL. The
703.75 MHz, 1 MW CW RF system for the SRF gun is
under procurement. The 5-cell SRF linac is under

Zigzag merging system
One of the novel systems we plan to use for the R&D
ERL is a merging system providing achromatic conditions
for the space charge dominated beam and compatible withthe emittance compensation scheme [6].
The idea of the Z-system is to provide achromaticconditions for electron whose energy is changing while itpropagates through the merging system. A detailed
description of this mechanism will be publishedelsewhere [6]. Fig. 6 shows results of Parmela simulations
for the R&D ERL injection system. In contrast withtraditional chicane, where horizontal emittance suffers a

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V.N. Litvinenko et al. / Proceedings of the 2004 FEL Conference, 570-573

significant growth as result of the bending trajectory, with
the Z-system the emittances are equal to each other andare very close to attainable for the straight pass.

4” RF shieldedgate valve

HOM ferrite
assembly

Tuner location

2K main line

Space frame
support structure
Cavity assembly
Vacuum vessel

2K fill line
Outer magnetic shield
Thermal shieldHe vessel

Inner magnetic shield

Fundamental Power
Coupler assembly

Fig. 7. The 5-cell SRF linac with HOM absorbers
 Advanced Energy System

Fig. 5. Schematics of traditional chicane and Zigzagsystem (Z-system) for merging system of low and highenergy beams in an ERL. In contrast with chicane, which
provides achromatic conditions and emittancepreservation only for low-charge beams, the Z-systemprovide for emittance preservation and emittancecompensation of e-beams with a high charge.
14
12

Emittances, mm mrad

Emittance X
Emittance Y
Emittance X

10

Emittance Y
Emittances X, Y

8
6
4
2
0
0

1

2

3
4
Length, m

5

6

7

Fig. 6. Results of Parmela simulation for 1 nC e-bunchfrom the cathode to the end of the linac in R&D ERL:
black dashed curve is for a round beam passing without
bends (the baseline); blue curves are for that with acompensated chicane, red curves are for that with the
Zigzag merging system.

5-cell SRF linac
The heart of the ERL facility is 5-cell SRF linac, which isdesigned for operating with ampere-class CW e-beams[4,5]. The main feature of this design is very large
apertures of the structure which effectively couples all
Higher Order Modes (HOMs) to two ferrite absorbers,
which is located on both sides of the cryo-module (seeFig.7). This design provides for very low Q’s for HOMs
and hence very high ERL stability. Thresholds of thetransverse beam break-up instability (TBBU) for ERL
with one 5-cell linacs is measured in amperes (seeexample in Fig. 8). We plan to intentionally tune thelattice of the ERL to a special mode (see below) to test
the TDBBU predictions for our SRF linac with current
limited only to few hundreds of milliamps.

TUPOS64

Fig. 8. Results of TBBU simulations for ERL with four 5cell linacs [5].

Lattice of the loop
The lattice of the ERL loop controls the parameters of a
symplectic transport matrix:
 x 
 m11 m12 ...
....
...
Dx   x 

 



′
m21
m22
...
...
...
D
x
x' 



 x′ 
 y 
 ...
... m33 m34...
Dy   y 
 =
⋅ 


′
′
...
...
m43
m44
...
D
y
y' 



 y 

 −cδt  ...
−cδt 
...
...
... m55 m56

 



δ
E
/
E
...
...
...
...
...
m66
δ
s2 
  E / E s1which affect the stability and operation conditions of the
ERL. The lattice of the loop is intentionally chosen to bevery flexible for the R&D ERL to be a test-bed of newampere-range of beam currents in ERL technology. The
adjustable part of the lattice has two arcs and a straightsection. Each arc is a three-bend achromat with adjustable
longitudinal dispersion. Twelve quadrupoles in thedispersion-free straight section provides for matching ofthe β-function and for choosing the desirable phaseadvances independently in horizontal and vertical planes.

573

V.N. Litvinenko et al. / Proceedings of the 2004 FEL Conference, 570-573

Potential up-grade of the R&D
We consider the potential extension of this facility into
two turn configuration and installation of IR FEL, if funds
are available. The shielded vault is designed for ERL withmaximum energy of 54 MeV to accommodate thesefuture up-grades. The loop of the ERL is designed toaccommodate large energy spread of electron beam in thecase of operating a high power FEL.
Table 2. Parameters of a test FEL for R&D ERL
Energy [MeV]Wavelength [µm]with micro-wiggler
Beam Power (MW)FEL ext. efficiency
FEL power (kW)Charge/bunch (nC)

20
10
5
10
1%
100
1.3

40
2.5
1
20
1%
200
1.3

CONCLUSIONS

Fig. 9. Lattice β- and D- functions of the R&D ERL for
the case of zero, positive (+2m) and negative (-2m)
longitudinal dispersion Ds = m56. The m12 and m34
elements are controlled independently using twelve
quadrupoles in the dispersion-free straight section.

We are designing, constructing, and commissioning asmall (about 20 meters in circumference) R&D ERL to
test the key issues of an amp-class CW electron
accelerator with high brightness beams, required for
future nuclear physics experiments at RHIC-II andeRHIC. An extensive R&D program on many novelcomponents to be used in the ERL is under way. Thisfacility, planned to be commissioned in 2007, will serveas the test-bet for new ranges of beam parameters whose
application will extend well beyond the goals set forward
by the Collider Accelerator Department at BNL.

REFERENCES

Fig. 10 A sketch of TBBU interaction in R&D ERL:
injected electron beam kicked transversely by HOM
passes the loop and comes to the cavity with adisplacement proportional to m12 (for vertical - m34)
element of the loop matrix. The displaced beam excites
the HOM, which closes the excitation loop of TBBU
process.
As shown in a simple sketch below, the threshold of
TBBU instability will depend on the values of m12 andm34. Hence, we plan to increase these elements to thelevel of few hundreds of mA, required to observe or toreliably measure TBBU instability threshold and tocompare it with the prediction based on the cavity model.

[1] http://www.bnl.gov/henp/docs/NSAC_RHICIIeRHIC_2-15-03.pdf, T. Hallman, T. Kirk, T. Roserand R.G. Milner, RHIC II/eRHIC White Paper,
Submitted to the NSAC Sub-Committee on Future
Facilities, February 15, 2003,[2] Electron Cooling for RHIC, I. Ben-Zvi, et al.,Proceedings of the 2001 Particle Accelerator
Conference, Chicago, IL, USA, June 18-22, 2001,
p.48[3] http://www.agsrhichome.bnl.gov/eRHIC/,
Appendix A, Linac-Ring Option“eRHIC, Future Electron-ion Collider at BNL”, V.
Ptitsyn at al., MOPLT170, Proceedings of EPAC2004, Geneva, Switzerland, July 5-9, 2004
[4] I. Ben-Zvi at al., Ampere Average Current PhotoInjector and Energy Recovery Linac, these
Proceedings.
[5] R. Calaga et al., High Current Superconducting
Cavities at RHIC, TUPKF078, Proceedings of
EPAC-2004, Geneva, Switzerland, July 5-9, 2004
[6] D. Kayran, V. Litvinenko, Novel merging systempreserving the emittance of high brightness highcharge beams in energy recovery linacs, in
preparation

FEL Technology

574

K. L. Jensen et al. / Proceedings of the 2004 FEL Conference, 574-577

THERMAL AND FIELD ENHANCED PHOTOEMISSION: COMPARISON
OF THEORY TO EXPERIMENT
K. L. Jensen, Naval Research Laboratory, Washington DC, USA
D. W. Feldman, N. Moody, D. Demske, P. G. O’Shea, U. of Maryland, College Park, MD, USA
Abstract
Photocathodes are a critical component of high-gain
FEL’s and the analysis of their emission is complex. We
have developed a time-dependent model accounting forthe effects of laser heating and thermal propagation on
photoemission.
It accounts for surface conditions(coating, field enhancement, reflectivity), laser parameters(duration, intensity, wavelength), and material
characteristics (reflectivity, laser penetration depth,
scattering rates) to predict current distribution andquantum efficiency. The photoemission and quantum
efficiency from metals and, in particular, dispenser
photocathodes, is evaluated: the later introducescomplications such as coverage non-uniformity and fieldenhancement.

INTRODUCTION
Photoinjectors are important electron sources for Free
Electron Lasers (FEL’s) due to the high quality electron
beams that can be achieved, and may impact synchrotron
light sources, high energy linear colliders, X-ray sources,and other applications [1-4] and in particular, Naval
shipboard defense systems [5]. Photo injector concepts
share a drive laser (which produces short bunches ofphotons) and photocathode (which converts the photon
bunch into short bunches of electrons). The Quantum
Efficiency, emittance generated at the cathode, cathodelifetime, survivability, emission promptness anduniformity are all issues. Metallic photocathodes arerugged and have fast response times (which allows forpulse shaping), but they have low QE and require incident
UV light [6]. Direct band-gap p-type semiconductors(alkali antimonides and alkali tellurides [7-8], and bulk
III-V with Cesium and oxidant [9]) are the highest QE
photocathodes available and operate at longer
wavelengths, but they are chemically reactive and easily
poisoned by, e.g., H20 and CO2, damaged by back ion
bombardment [10], and (for NEA III-V photocathodes)
insufficiently responsive for pulse shaping in an rf injector
due to their long emission time (> 40 ps for GaAs).
The ideal photocathode will have a high QE at thelongest possible wavelength, be capable of in situ repair
or rehabilitation, and demonstrate good lifetime. To meetthe particular needs of a megawatt (MW) class FEL, it
must produce 1 nC of charge in a 10-50 ps pulse every
nanosecond (ns) (100 A peak and 1 A average current) inapplied fields of 10-50 MV/m and background pressuresof 0.01 mTorr – and to do so for several seconds. Such acathode is presently unavailable, and even if it were, theability to predict its performance and the beam it
generates lacks adequate emission models. Dispenser
cathodes have shown to have promise as photoemitters

TUPOS65[11,12]. They consist of a work function coating diffusing
out from a porous metal base and their operation has been
extensively investigated. While dispenser cathodes are
the focus of our program to develop rugged
photocathodes, the theory and modeling developed todescribe them have wider application
In this work, we characterize various dispenser
cathodes and implement models of time-dependent andspatially varying laser interactions with various materials,
in which an incident laser heats the electron gas within themetal and which subsequently equilibrates with thebackground lattice, and use those models to examine
tungsten-based dispenser photocathodes and simple
metals. The present work is an integral component in theexecution of the agenda to qualify dispenser
photocathodes and develop a suite of simulation tools thatcan characterize and predicatively estimate theirperformance.

CURRENT AND QUANTUM EFFICIENCY
Photoemitted current is the product of several factors:(i) the charge of the electron q; (ii) the amount of incident
light absorbed (1-R), where R is the reflectivity; (iii) the
number of incident photons; (iv) the probability that anelectron has an energy greater than the barrier height
following its absorption of a photon of frequency f; and(v) the probability that the electron migrates to the surface
without suffering a scattering event.
Using theRichardson approximation, the probability of (iv) can be
expressed as a ratio of Fowler functions U(x) defined by

U ( x ) = ∫ ln (1 + e y ) dy
x

−∞

[1]

The probability of emission is then U[β(φ–hf)]/U[βµ],where β = 1/kBTe, kB is Boltzmann’s constant, Te istemperature, and φ is the barrier height above thechemical potential µ. The current density is thenU  β ( !ω − φ ) qJ λ (Te , F , Φ ) = f λ[2](1 − R ) I λ (t ) !ωU [ βµ ]to which must be added the thermal current given by
Richardson’s Equation, JRLD = A T2 exp(–βφ). From thedefinition of quantum efficiency (QE) as the ratio of thetotal emitted electrons with total incident (not absorbed)
photons, it follows that∞∞!ω ∫−∞ ∫0 J  F ( ρ ) , T ( ρ , t )  2πρ d ρ dt
QE =
∞
∞
q
I ( ρ , t )2πρ d ρ dt

∫ ∫

[3]

−∞ 0

where F is the spatially varying applied field, T is thetime-dependentandspatiallyvarying
electrontemperature, ρ is a cylindrical coordinate, and t is time.

Available online at http://www.JACoW.org

575

K. L. Jensen et al. / Proceedings of the 2004 FEL Conference, 574-577

We shall neglect the contribution of tunneling current(though we have treated it elsewhere [13]), even though
for machined dispenser cathodes, sporadic fieldenhancement factors can be large and contribute to darkcurrent due to field emission [14]. Dispenser cathodes
have non-uniform low work-function (Φ) coatings.
Consequently, Φ is spatially varying, making theevaluation of Eq. [3], if not impossible, then very
difficult. We use instead a patch modelJ ( x, y ) dAi , j

[4]

th

Eq. (5)
Longo
Haas

4

3
2.5
2
0

0.2

0.4

0.6

Coverage

0.8

25
W

Reflectivity [%]

3.5

80
70
60
50

1

Figure 1: Work function dependence on coveragecompared to experimental data [17,18] for BaO on W.

TIME DEPENDENT ELECTRON AND
LATTICE TEMPERATURE EVALUATIONThe Heat Diffusion Equations
Laser illumination and temperature variation for various
metals have been considered extensively in the literature[19-23]. Here, we discuss the time dependent extensionof procedures introduced in Ref. [5] insofar is it diverges
from the steady state models therein. For those electrons
not directly photoemitted, laser energy is transferred into
electronic excitations. The hot electrons then come into
equilibrium with other electrons via electron-electron
scattering. The hot thermal Fermi-Dirac distribution
comes into thermal equilibrium with the lattice via
electron-phonon scattering. For laser pulse durations
longer than the relaxation times associated with theseprocesses, photons will encounter a heated electron
distribution that, depending on intensity, can have

40

20

1

2

3
4
Energy [eV]15266 nm4.5

where R is the reflectivity, θi the incidence angle, I thelaser intensity, and δ is the penetration depth. R and δ arefunctions of wavelength and evaluated from tabulated
data of the index of refraction n(E) and damping constantk(E), as a function of photon energy E, from which R andδ follow [24], as in Figure 2. For normal incidence (θi =0), R reduces to R = [(n-–1)2+k2]/ [(n+1)2+k2].

105Penetration Depth [nm]Work Function [eV]

where Aij is the area of the i,j patch on a grid, andassume that all patches are equivalent. The patch
encompasses one pore from which Barium (or othercoatings) dispense, and the coverage θ is assumed to varyradially from the pore like θ(ρ) = {1 + exp[(ρ-ρo)/∆ρ]}-1.
Φ(θ) is evaluated from our version of Gyftopolous-Levine
theoryΦ (θ ) = Φ f + ( ΦW − Φ f ) 1 − G (θ )  H (θ )[5]2
H (θ ) = (1 − θ ) (1 + 2θ )where G is a function of atomic and covalent radii of thebulk (tungsten) and coverage (barium) atoms, and Φf is
the work function of a monolayer of coverage [15, 16].
the performance of Eq. [5] is shown in Figure 1.

355 nmpatch

532 nmi, j1064 nm∫ J ( x, y ) dA = ∑ ∫temperatures significantly in excess of the bulk
temperature, leading to complicating effects. In metals, a
hot electron gas requires a fraction of a nanosecond torelax to its equilibrium state. The differential equations todetermine electron and lattice temperatures are∂∂  ∂ Ce Te =  κ Te  − g (Te − Ti ) + G ( z , t )∂t∂z  ∂z [6]∂
Ci Ti = g (Te − Ti )∂twhere: Ce, Ci, and κ are the temperature-dependent
specific heats and thermal conductivity; G(z,t) governs
the incident laser; and g governs the transfer of electronenergy to the lattice (the notation follows Papadogiannis,
et al.). Each term in Eq. [6] is replete with complications.
The laser term is given by e− z / δ   U  β ( !ω − φ )  
G ( z , t ) = (1 − R (θ i ) ) I (t )  [7] 1 −
U [ βµ ] δ  5

Figure 2: Reflectivity and penetration depth as a functionof photon energy for normal incidence on tungsten.
The derivation of the specific heat terms for electronsand phonons follows standard solid state formulae,
approximated from their exact forms in order to provide a
reasonable fit over the temperature ranges we desire fornumerical expedience. In these calculations, the electron
number density, Debye temperature, atoms per unit cell,and sound velocity determine Ce and Ci and are calculated
via a library of data for various bulk and coating materials(e.g., the number of atoms per unit cell, the soundvelocity, and the Debye temperature for tungsten is0.2697, 5220 m/s, and 400 K, respectively). At high(er)temperatures, Ce and Ci are linear and constant in electron
and lattice temperature, respectively.
The coefficient g and the thermal conductivity κ dependon electron-electron and electron-lattice relaxation time τ(see [5] and references therein), though now the joint
relaxation time can depend on differeing Te and Ti, as in

FEL Technology

576

K. L. Jensen et al. / Proceedings of the 2004 FEL Conference, 574-577

τ (Te , Ti ) = τ ee (Te ) + τ ph (Ti )
−1

−1

−1

2
[8]
!  1 !µ  1  ;τ ph (Ti ) =Ao  k BTe 
2πλo  k BTi 
Thermal conductivity is an experimentally tabulated
property as a function of temperature. Consequently, thedimensionless constants Ao and λo can be extrapolated
from it and Eq. [8] – which is adequate for a many metals
from room temperature to high temperatures – thoughtungsten contains behavior which departs from thatapproximation around room temprature. For dispenser
cathodes, λo is allowed to vary slightly, reflecting that thebase is an odd compilation of tungsten pellets andimpregnants, and therefore not bulk material.
After an electron absorbs a photon, it is assumed totravel in a random direction and possibly suffer one ormore collisions on its journey to the surface. Let any
collision terminate the probability of emission (anoverzealous assumption).
The factor fλ is thenapproximated by f λ ( mδ / !koτ ) [13] where ! is Planck’sτ ee (Te ) =EXPERIMENTAL RESULTS AND
COMPARISONS TO THEORY

0.3
Experiment
Theory0.2∆Q vs Field
To = 386 C

0.1∆E =20.9 mJ
B-TypeB-Type*Scandate
M-TypeB Theory
B* Theory
M Theory
M* Theory
Scan Theory

0

0

0.5

1

1.5
2
Field [MV/m]

2.5

3

Figure 4: Emitted charge vs. field for scandate cathode.

10-4

0

10

Theory fit: y(x) = y x poy o = 1.173 pC

10-5
250

300

350

400

450

500

550

WAVELENGTH [nm]Figure 3: QE of Dispenser photocathodes. Lines aretheory, points are exp. data. See text for details.
We have extensively described the experimental
apparatus and conditions under which measurements weretaken in previous works [5, 12]. Here, we report on
intensity and field variation of emitted charge, thewavelength dependence of the quantum efficiency of bothdispenser cathodes and simple metals, and theircomparisons with predictions of the time dependent laser
heating and photoemission modeling described above.
Theory and experimental data points for dispenser
photocathodes are shown in Figure 3.
Thecorrespondence is as follows: white circle = B-type (Ref.

TUPOS65

Charge [nC]

QUANTUM EFFICIENCY

Dispenser Cathode Quantum Efficiency
10-3

Dispenser Cathode performance

Charge [nC]

constant over 2π, ko is the wave vector equivalent of theenergy height of the barrier above the conduction band
minimum, and the fλ(x) is defined by
1 π / 2 cos ( s )fλ ( x ) = ∫ds[9]
π 0 cos ( s ) + x[11]). Black circle = B-type (Ref. [25]. ) Black diamond:scandate. Thick solid & short dashed line: theory using
Ref. [11] and Ref. [25] parameters, respectively. Thinsolid and short dashed line: M-type using actual andextrapolated fields of 1.7 MV/m and 50 MV/m (a fieldtypical of the operational environment of a MW-class FEL
injector), respectively for 4.5 ns pulses and bulk
temperature of 723 K. Thick long-dashed line: Scandate
theory. The M-type cathodes have a coating of Osmiumon the surface. It is seen that with the rather genericparameters used, theory underestimates the experimental
performance of the M-type cathode by less than a factorof 2 at shorter wavelengths; at longer wavelengths, where
the photon energy is comparable to the barrier height, thedifferences are more pronounced: a possibility is thattunneling effects may contribute more for such work
functions and conditions.
Both B and M-type
performance vary depending on conditioning andprocessing of the cathode. For the scandate theory line, asmaller value of ρo was used in the patch model than for
the field and intensity analysis (below), resulting in asmaller coverage factor of θ = 12%.

10-1

x = 0.1 x I
p = 6.5534∆Q vs. Intensity
T = 386 Co

F = 1.7 MV/mExperiment
TheoryPower fit

-2

10

-3

10

12

16
20
24
2
Intensity [MW/cm ]28

Figure 5: Same as Fig. 4, but for variation in intensity.
The modeling of Scandate dispenser cathodes using
standard dispenser models is complicated by the barrier
lowering mechanism, which may be more semiconductorlike band bending than patchy surface [26]. The
simulations of QE for the scandate cathodes used the
input data used to model the field and intensity variation:
while these measurements occurred on separate occasions

K. L. Jensen et al. / Proceedings of the 2004 FEL Conference, 574-577

and illuminating different regions of the cathode, andrequired θ =45%, and a field enhancement of 4.46, we
did not separately adjust parameters when modelingintensity, using the same parameters as used for field.
The field variation is shown in Figure 4 using a 4.5 ns
FWHM pulse and the first harmonic (1064 nm)
wavelength. Using the input data of Figure 4, theintensity dependence was calculated and compared toexperiment, as shown in Figure 5.

Quantum Efficiency of Metals

QUANTUM EFFICIENCY

Dispenser cathodes, owing to their odd constitution,induce complications that bulk metals do not. We
therefore sought to compare the simulation code withquantum efficiencies for various metals determined by
Srinivasan-Rao, et al. [27], for which gold, magnesium,and copper were selected.
10

-3

10

-4

10

-5

250

Mg ExpCu ExpAu ExpMg Theory
Cu Theory
Au Theory
260

270
280
290
WAVELENGTH [nm]300

Figure 6: QE for Au, Cu, and Mg using theoretical modelcompared to 266 nm data from Ref. [26].
In Figure 6, all parameters were based on bulk values
obtained from CRC and AIP Handbook tables, andoperating conditions and parameters cited in Ref. [26].
The only adjustable parameter was field enhancement,
which was set to 1.0, 2.5, and 7.0 for Au, Cu, and Mg,
respectively, a range no different than that found for thedispenser cathode simulations. The performance of themodel for Mg and Cu was good. The modeling performs
less satisfactorily for Au, but nevertheless reasonable.

SUMMARY
We have reported on the characterization of several
dispenser cathodes, and have confirmed their potentiallyattractive features as photoemitters, e.g., low work
function and high quantum efficiency, rejuvenation
capabilities, and wavelength characteristics. Models weredeveloped to simulate and predict their performance andperformed well for our data as well as results fordispenser and metal photocathodes reported in theliterature.
Acknowledgements
We gratefully acknowledge funding provided by the
Joint Technology Office and the Office of Naval Research.

577

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P. Parvin et al. / Proceedings of the 2004 FEL Conference, 578-581

A MODE LOCKED UV-FEL
P. Parvin* (AUT, IR-Tehran; AEOI-RCLA, IR-Tehran), G. R. Davoud-Abadi (AUT, IR-Tehran), A.
Basam (IHU, IR-Tehran), B. Jaleh (BASU, IR-Hamadan), Z. Zamanipour (AEOI-RCLA, IRTehran), B. Sajad (AU, IR-Tehran), F. Ebadpour (AUT, IR-Tehran)
Abstract
An appropriate resonator has been designed to generate
femtosecond mode locked pulses in a UV FEL with themodulator performance based on the gain switching. The
gain broadening due to electron energy spread affects on
the gain parameters, small signal gain γ0 and saturation
intensity Is, to determine the optimum output coupling as
well.
INTRODUCTION
Today, there is an increasing interest in the generationof intense, tunable, coherent light in short wavelength
region. Laser pulses of very short duration in UV/VUVspectrum, find applications in large number of areas, suchas analysis of transit-response of atoms and molecules,
non-linear optics in generation of harmonics, plasma
remote sensing and range finding, induced plasma
spectroscopy, time resolved UV photochemistry,
diagnostic
process,
highspeed
photography,
microlithography, space astronomy and the advanced
research on laser induced fusion.
Short pulse phenomena in atomic and molecular lasers
have been studied extensively in the last decades. These
include the nonlinear phenomena of self spiking, as well
as a wide range of mode-locking mechanisms and soliton
formation. Mode-locked oscillation is known to be a very
useful technique to get ultra short pulses in conventionallaser oscillators [1-3].
The pulse duration obtained by this technique isroughly the inverse of the gain spectrum width. Using thistechnique, femtosecond pulses have been generated from
Dye or Ti:Sa lasers, which possess the broad gain
bandwidth among conventional lasers. Excimer lasers aretaken into account as the most powerful commercial UV
sources, whereas the UV mode-locking of those lasers do
not generate a train of short pulses smaller thanpicosecond. Therefore, they do not resemble to be very
attractive short pulse generators, mainly because of theirnarrow bandwidth. Among other UV lasers with modelocking ability to generate tuneable ultra short pulses in
VUV region, presently SHG Nd:YAG laser pumped
THG/ FHG Ti:Al2O3 laser is considered as an attractive
alternative.
Free-electron lasers (FELs) potentially have the ability
to produce ultra short mode-locked pulses, because thegain spectrum width is inherently very wide compared tothat of most conventional lasers [4]. In FEL oscillators,
radiation burst and spikes have been observed in the
nonlinear regime by several groups [5-10]. Althoughmode-locked FEL oscillators in microwave region havebeen formerly investigated both in theory and practice[11-12], however, a few papers are available to explain*

FEL mode-locking phenomena for shorter wavelengths in
far-infrared and infrared range of spectrum [13, 14].
In free-electron laser operating at the FIR and IR
spectral regions, using a radio-frequency accelerator forthe electron beam, when the electron pulse length can beof the same order as the slippage length or even shorter,
the laser emits short pulses of multimode broad-bandradiation [14].
On the other hand, Storage ring FEL represents a very
competitive technical approach to produce photons withthese characteristics. After the first lasing of a storage
ring FEL (SRFEL) in visible [15], the operation
wavelength has been pushed to shorter values in various
laboratories. It is based on progressive performance ofparticle accelerators and multilayer UV mirrors
technology as to withstand the intense synchrotron
radiation which damages the output coupler. An
ultraviolet FEL oscillator has also been achieved using
the VEPP ring at Novosobirsk [16].
Radio-frequency linacs employ a series of cavities that
contain radio-frequency (r.f.) electromagnetic fields toaccelerate streams of electrons. Typically time structure
for a laser pulse from a FEL is based on a pulse radiofrequency linear accelerator. The laser macropulse of
microsecond duration consist of a train of shortmicropulses which are picosecond in length. The
macropulses repeat at a repetition ratio limited by theaccelerator in several tens of Hz. The micropulse
repetition rate can be from several MHz to several GHz.
A remarkable improvement has been obtained in recent
years at various laboratories [17-21] to produce laser
lights as short as 190 nm, whose wavelength is similar to
ArF excimer laser as an alternative powerful VUVcoherent source. In this work, we investigate a modelocked UV-FEL at 190 nm to compare it to existing ultra
short pulse lasers with gaseous and solid-state gain media.
THEORY
Depending on the current density and beam energy,
FELs operate in one of three different regimes: Raman,
low-gain Compton and high-gain collective regime. The
Raman regime occurs at low energy and high current
density. It is typical for devices that produce microwaves,
whereas FELs aiming at the extreme ultraviolet, where
the high reflectivity mirrors are non-existent, will
necessary have to operate in the high-gain collective
regime. The existing Compton FELs cover the UV
wavelength range to 200 nm.
In order to design the resonator with the gain medium, thegain parameters, small signal gain γ0 and saturation
intensity Is, are taken into account.

Parvin@aut.ac.ir

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The normalized gain function, g( υ ), is a function of theparameter υ = 2πN u (ω s − ω ) ω s , where Nu is the

[ (

)]

The electron beam itself is a source of inhomogeneous
broadening, which is related

number of undulator periods, ω s = 4πcγ 2 λ u 1 + K 2 2
is the resonant frequency and λu is the undulator period,
and reads [22]:g (υ ) =2 − 2 cos(υ ) − υ sin(υ )

(1)

υ3

which is antisymmetric in υ .
The main positive gain region is located at υ >0 andcorresponds to electrons traveling at velocities exceeding
the synchronous value ( υ =0). The condition υ =0 is
equivalent
tothesynchronism
condition:
λs = λ Vz (c − Vz ) = λβ z /(1 − β z ) where β z = Vz / c and(Figure 1: The spontaneous emission profile interms of detuning parameter.

)

FSR

Figure 2: Gain versus detuning parameter.

Gain

λs is the resonant wavelength λ s = λ u 1 + K 2 2 2γ 2
being K the undulator strength. Vz is the electron velocity
in the undulator direction. It should be noted that since υdepends on the optical frequency, the function g( υ )describes the frequency dependence of the gain.
The small-signal gain is directly proportional to thederivative of the spontaneous emission spectral profile.
Fig. (1) depicts the spontaneous emission profile which isa sinc function in terms of detuning parameters (λ- λs)/ λs,
where λs is the emission wavelength at resonanceλ s = 2πc / ω s .
Fig. (2) represents the derivative of the
profile as shown in Fig (1) to express the gain versus
detuning parameter. As this profile becomes rather
narrow, especially for a large number of undulator periods
Nu, and the constant of proportionality is small, a highquality electron beam with small energy spread and acorresponding high current density is required. In theextreme UV, however, the demands on the transverse
emittance of the beam are also very challenging.
Fig. (2) illustrates thegain of FEL with theassumption of a negligible energy spread as shown incurve 1 Fig.(3), as well, though, the electron beam is notmonoenergetic in practice. Therefore, curves 2, 3, 4
represent the broadened optical gain profile due to several
electron energy spreads, as to that of curve 4 is four timesof curve 2 and two times of curve 3 respectively.
The sources of energy spread cause further gain
broadening homogeneously and inhomogeneously. The
effect of energy spread in broadening can be corrected by
the terms according to Fig. (3) which illustrates the smallsignal gain variation versus detuning parameter forseveral electron energy spread. It obviously denotes thatthe gain peak becomes to decrease when thecorresponding gain profiles is broadened.
Small-signal gain and saturation intensity strongly
depend on the broadening effects. The gain spectrum ischaracterized by an homogeneous width of the same orderof the spontaneous spectrum. There are additional
inhomogeneous broadening mechanisms related to the
spread of individual electron parameters.

1/Nu

2/Nu
(λ- λs)/ λs

Figure 3: The effect of electron energy spread on thegain broadening of FEL. The curves 2, 3, 4 denote
the relative electron energy spread [22].
to momentum spread of electrons, to the finite transverse
size of the electron distribution. When the electrons enter
the undulator, electrons located at different radii will
experience different undulator fields and this will cause
an additional inhomogeneous broadening. The undulator
inhomogeneity and the energy spread of electron from theaccelerator, as noted above, act to be the important
inhomogeneous broadening sources accordingly. Due tothe long cavity and the broad gain bandwidth, an FEL canoscillate in a very large number of cavity modes.

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The homogeneous bandwidth usually exceeds theinhomogeneous one, and mode competition can cause anarrowing of the spectrum as in other lasers. The final
width is determined by the quality factor of the cavity, theextending source of noise and by the duration of thepulse. For short pulses, the other effect dominates and theresulting spectrum width is to be transform limited in a
FEL operating in the IR and FIR spectral regions, using aradio-frequency accelerator for the electron beam. A
radio-frequency accelerator produces electrons in
micropulses with a duration in the ps range. In a IR-FEL,
based on such an accelerator, many modes are coupled
due to the short pulse length.
The simulation of the coupling of pulses by an
intracavity interferometric device, have shown that it ispossible to induce coherence between independent pulses
in an RF-linac based FEL. Apart from an ideal delay inthe growth of the power and a gain reduction, due toabsorption losses, the basic operation of the FEL is
unaffected. The effect of an intracavity etalon on the
spectral structure has shown that a low finess etalon
suffices to suppress most of the cavity modes and toconcentrate the power in modes with a much larger
frequency separation. Intracavity etalons or equivalentintraferometric elements are commonly used inconvetional lasers to reduce the spectral bandwidth.
The application discussed here differs in that the free
spectral range of etalon is much narrower than the fullgain bandwidth and a sufficient number of active modes
must remain present to compose the short pulses [14].
A MODEL OF MODE-LOCKED UV FEL
Let us assume, FEL oscillating on a homogeneous orinhomogeneous transition with many modes above
threshold and lasing. A general equation describing theclassical electromagnetic field at a particular point inspace is eT(t)=∑Enexpj[(ωo +nωc)t +φn] , En indicates theamplitude of nth mode, which is oscillating at thefrequency (ωo +nωc ) ,where ωc =2π * FSR. It is tempting
to lock each mode to a common time origin and assign
each phase to be zero. It leads to short pulse occurring at arepetitive rate.
We assume a Fabry-Perot cavity for the operation of
FEL as a mode-locked laser. A characteristic parameter
for a FEL is the slippage length Nuλs where Nu is thenumber of undulator period and λs is the optical
wavelength. It gives the difference between the distancetraveled by an electron and by an optical wavefront,
especially, in transit time for an electron through theundulator. The homogeneous gain bandwidth of a FEL isdetermined by the slippage length:( ∆ υ ) gain =c
2 N u λs(2)

The Fourier transform limit for the bandwidth is givenby ∆υ=1/τ where τ is duration of light micropulse. For
electron pulse long compared to the slippage length, theoptical pulse length is almost equal to that of electron

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pulse. For short electron pulse, the optical pulse length ison the order of the slippage length. In that case, thetransform limit is as wide as the gain bandwidth so that nofurther narrowing is possible. Instead of mode
competition, there is mode coupling and the FEL operates
as synchronously pumped mode-locked laser.
For a resonator of length L, assuming the back mirror tobe high reflective with R1 ~1, then the output coupler
reflectance R2 is directly determined. Similarly, thecorresponding equations are given as below:
τRT=2L/c(3)

FSR=c/2L=1/ τRT(4)

where τRT, FSR and L denote the round trip time, free
spectral range and length of the resonator respectively.
The number of modes n is proportional to gain bandwidth
which is written as below:n=(δυ)gain /FSR.

(5)

The duration of mode locked pulses τp is related to τRT
and n according to eq (6). For simplicity, assuming theconstant mode amplitudes
τp ~ 1/(δυ)gain = τRT /n(6)however, for Gaussian distribution τp~ 0.44/(δυ)gain
accordingly.
A typical plane Fabry-Perot cavity scheme with length
L for undulator parameters Lu and Nu, is shown in Fig 4.
The gain parameters are related to undulator
characteristics as well. The output temporal response of
the resonator includes a train of ultrashort pulses withduration τp and period τRT between repetitive pulses.
Lu

R1~1

L

R2

(a)
I (t)

τRT
τp

(b)

time

Figure 4: (a) A schematics Fabry-perot cavity(b) Typical mode-locked output pulses,, R2 is output coupler.
According to laser amplification theory, for pulses
whose shapes are sufficiently near the eigenfunction for

P. Parvin et al. / Proceedings of the 2004 FEL Conference, 578-581

propagation in the homogeneous broadening, the change
in the average temporal width τ of the pulse can bereasonably expected to be negligible, in such case, theeffective saturation intensity is given by Is =hυ/2σstτ,where τ is the full width at half maximum (FWHM) of theprobe pulse into gain medium, if I << Is, then for low
input intensities the gain increases and become equal tosmall-signal gain and for high intensities, the gain reduces
to a saturated value with an intensity increment equivalent
to Is γo L.
For a mode-locked laser, the small signal gain is also
proportional to the population and stimulated crosssection which in turn depends on gain profile and the
bandwidth. It indicates the frequency dependent γo and Is
as well.
Fig.4 shows a typical Fabry-Perot with gain parameters
γo and Is as to the axial mode width becomes relatively
sharper. Topt of the output coupler is given as below:
Topt/A=(1-A- Topt)[γ0L +ln(1-A - Topt )]/(A+ Topt)(7)

where Topt and A denote the optimum transmittance andthe absorbance respectively for an optimum output
coupler such that Topt=1-Ropt- A.
The optimum design of mirrors in UV region ofspectrum is achieved by the fabrication of pure multilayer
coating of Aluminum oxide (or Halfnium oxide) on SiO2
substrate. The gain switching for mode-locked laser
requires to match the frequency of modulator to FSR (i.e.
the spectral separation between the adjacent axial modes)of the resonator. In other words, the microbunchingfrequency should be tuned to FSR of Fabry-Perot
resonator so as the repetition time of both electron
micropulse and laser mode locked pulse become equal to
the round trip time of the resonators τRT .
CONCLUSION
It is well understood, if the repetition time of theelectron pulses is short compared to the round trip time ofan optical pulse in the resonator cavity, then phaselocking between successive optical pulses can be induced
by an intracavity interferometer device. Moreover, forshort electron pulse, the optical pulse length is in theorder of the slippage length such that instead of mode
competition, there is mode coupling and FEL operates assynchronously pumped mode-locked laser.
In UV region of spectrum, the slippage becomes
smaller compared to that of IR region, therefore it isrequired to achieve shorter electron pulse length andbroader gain bandwidth .
Moreover, for longer resonator cavity in UV-FEL, theresonator parameter FSR becomes relatively smaller for agiven bandwidth to allow multimode operation with agreat number of the active modes. In order to fulfill gain
switching to generate a train of fs mode–locked pulses,
the time repetition between successive pulses should beapproximately equal to the round trip time of each pulse

581

in the resonator and the gain bandwidth broadens
adequately.
We have proposed a preliminary design for the
resonator based on the Fabry-Perot cavity to implement a
UV self mode-locked FEL according to gain switching
phenomena. It is shown that effects of gain broadening
on the gain parameters strongly affects on the number of
the axial modes within the bandwidth of the gain profileand the output coupling of the resonator consequently.
The simulation have shown that the optimum mode
locking occurs when the repetition time of the electron
pulses is approximately equal to the round trip time of an
optical pulse in the resonator cavity with the optimum
output coupling, given by eq (7) for the definite gain
parameters of a UV FEL.
REFERENCES[1] L. F. Mollenauer and R. H. Stoller, Opt. Lett., 9(1984) 13[2] P. G. Kryukov, and V. S. Letokhov, IEEE J. Quantum
Electron. 8 (1972) 766.
[3] H. W. Mocker and R. J. Collins, Appl. Phys. Lett., 7(1985) 270.
[4] Y. Kawamura,et al., Appl. Phys. Lett., 51 (1987) 795.
[5] R. W. Warren, B. E. Newman, and J. C. Goldestein,IEEE J. Quantum Electron.,21 (1984) 13.
[6] J. C. Goldestein, et al., Nucl. Instrum. Methods
Phys. Rev.,250 (1986) 4.
[7] J. Masud, et al.,Phys. Rev. Lett., 56 (1986) 1567.
[8] J. W. Dood and T. C. Marshal, Nucl. Instrum.
Methods Phys. Rev., A296 (1990) 4.
[9] B. A. R. Chman, J. M. Madey, and E. Szames, Phys.
Rev. Lett., 63 (1989) 1682.
[10] E. Jerby, G. Bekefi, and S. Wurtel, IEEE J. Quantum
Electron. 27 (1991) 2512.
[11] E. Jerby, G. Bekefi, and T. Hana, Nucl. Instrum.
Methods Phys. Rev., A 318, (1992) 114.
[12] E. Jerby and G. Bekefi, IEEE J. Quntum Electron.
29 (1993) 2845.
[13] D. Oepts, et al., Nucl. Instr. and Meth. A,285(1989) 204.
[14] D.Oepts and W.B Colson, IEEE J. Quantum.
Electron.26(1990) 723.
[15] M. Billardon, et al., Phys. Rev. Lett.,51 (1983) 1652.
[16] G. N. Kuliapanov, et al., Nucl. Instrum and Methods
Phys. Rev., A 296, (1990) 1.
[17] V. Litvinenko, et al., Nucl. Instrum. and Methods
Phys. Rev., A 429 (1999) 151.
[18] K. Yamada, et al., Nucl. Instrum. And Methods
Phys. Rev., A 445 (2000) 173.
[19] M.Marsi, at al. Synchrotron Radiat. News, 14 (2001)19.
[20] A. Gatto, et al. , Nucl. Instrum. and Methods Phys.
Rev., A 483 (2002) 357.
[21] M. Trovò, et. al., Nucl. Instrum. Methods Phys. Rev.
A 483 (2002) 157.
[22] See e.g. G. Dattoli, A. Renieri, A. Torre, Lectureson the free electron laser theory and related topics, World
Scientific, Singapore (1993)

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CURRENT-ENHANCED SASE USING AN OPTICAL LASER AND ITSAPPLICATION TO THE LCLS∗
A.A. Zholents, W.M. Fawley† , LBNL, Berkeley, CA 94720-8211, USA
P. Emma, Z. Huang, G. Stupakov, SLAC, Stanford, CA 94309, USA
S. Reiche, UCLA, Los Angeles, CA 90095-1547, USA
Abstract
We propose a significant enhancement of the electron
peak current entering a SASE undulator by inducing an energy modulation in an upstream wiggler magnet via resonant interaction with an optical laser, followed by microbunching of the energy-modulated electrons at the accelerator exit. This current enhancement allows a reduction of the FEL gain length. The x-ray output consists ofa series of uniformly spaced spikes, each spike being temporally coherent. The duration of this series is controlled
by the laser pulse and in principle can be narrowed down
to just a single, ∼ 200-attosecond spike. Given potentiallyabsolute temporal synchronization of the x-ray spikes tothe energy-modulating laser pulse, this scheme naturally
makes pump-probe experiments available to SASE FEL’s.
We also study various detrimental effects related to the highelectron peak current .

INTRODUCTION
SASE-based x-ray FEL projects continue to gather momentum at SLAC[1] and DESY[2]. Recently, Ref. [3]has proposed a technique (which we call current-Enhanced
SASE or ESASE for short) to shorten the exponential gain
length and provide temporal synchronization of the x-ray
pulse to a master laser. Figure 1 shows a schematic of
this technique as applied to the LCLS. An external, shortpulse (∼30-100 fs) from a high power (∼1-10 GW) laser
at wavelength λL ∼2.2 µm (e.g.TOPAS laser [4]) overlaps
a short e-beam section at moderate energy (∼4.5 GeV)
in a short, appropriately-tuned wiggler (e.g.λu ≈30 cm,
Bu ≈1.7 T). This induces a periodic energy modulation
with relative amplitude B ≡ ∆γ/σγ0 ∼ 5-10, where
σγ0 is the uncorrelated energy spread, but with minimal
microbunching. Following final acceleration the electron
beam passes through a dog-leg bend whose chromatic dispersion produces a periodic enhancement of the peak current to ≈20 kA. Finally, the electrons enter a long undulator and emit x-rays via the standard SASE process butwith first saturation occurring by z ≈45-60 m. The radiation output from the current-enhanced portions will bea train of spikes at uniform spacing λL whose total duration is directly related to that of the upstream, energymodulating laser. This emission will dominate SASE emis∗ Work supported in part by the Office of Science, U.S. Dept. of Energy
under Contracts DE-AC03-76SF0098 and DE-AC03-76SF00515.
† WMFawley@lbl.gov

WEBOS01

sion from the remainder of the e-beam if the exponential
gain lengths in the current spikes have been reduced by≈25% or greater.
The ESASE technique shares with other recent proposals [5, 6, 7] the common feature of employing an opticallaser to induce energy modulation to produce short duration (τP ≤500 as) output pulses from an FEL together
with absolute synchronization of the x-ray probe pulse to
the laser pump pulse, thus permitting pump-probe experiments. In principle, it is also related to harmonic cascadeconfigurations [8]. However, via the use of a dispersion
section to strongly enhance the current, ESASE has the
additional advantage of significantly reduced gain lengths.
This may allow possible relaxation of the required electron
beam emittance for saturation in the ”standard” LCLS undulator or (for the same base emittance) saturation at x-ray
wavelengths shorter than 0.15 nm.
We now present initial “start-to-end” numerical simulation results, investigate some potential detrimental effects
due to the high peak currents, and then conclude with some
remarks concerning possible experimental applications.

ACCELERATOR SIMULATIONS
We initiated “start-to-end” ESASE simulations with 2 ×
105 macro-particles in the Parmela[9] code for the RF
photo-cathode gun and low-energy injector systems, up to
an energy of 135 MeV. After this point, the macroparticle number is increased 10×, retaining all second moments
and coordinate correlations, and then transported with the
Elegant[10] code through the main linac, up to the entranceof the FEL undulator. These simulations included 2ndorder optics, accelerating structure wakefields, a model forthe laser/wiggler energy modulator (EM) at 4.54 GeV, anda line-charge (1D) model of coherent synchrotron radiation(CSR) in and after the bends.

Figure 1: A schematic of ESASE as applied to the LCLS.

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A.A. Zholents et al. / Proceedings of the 2004 FEL Conference, 582-585

1

−2

0
z (µm)02

γεx (solid)
γεy (dash)−20z (µm)

02−20
z (µm)

1
0.5

y

0

2

γε (solid)xγε (dash)−20
z (µm)2−2

0
z (µm)

2

σE/E0 (%)

0.1
0.05

0

∆E/E (%)

0.06

0.01

E

0

σ /E (%)

0.02

0

10

0

−0.05
−2

0
z (µm)2−2

0
z (µm)

2

Figure 2: ELEGANT tracking results for a short sectionof 0.8-µm energy-modulated e− bunch at 14 GeV, with instantaneous current, transverse emittances, rms relative energy spread, and relative energy centroid modulation plotted versus bunch coordinate z.
The EM consists of a resonant laser-electron interaction
in an 2.5-m long planar wiggler located immediately after
the second bunch compressor chicane where the FWHM
bunch length is 65µm. The EM can easily be installed inplace of one existing 3-m long accelerating structure. Table 1 gives the EM and the final buncher parameters.
Figure 2 displays the resulting current profile, transverse
slice emittance, rms energy spread, and centroid energy
modulation induced by an 0.8-µm wavelength EM for ashort core-section of the beam at 14.1 GeV. The current
profile shows weak density modulation due to the wiggler’s
small momentum compaction (opposite in sign to the final
buncher). Similar weak modulation of σE is also apparent.
Following final acceleration, the beam passes through a‘dog-leg’ transport line (DL2) which is used to produce
a 1.25-m jog in the beamline to the south, in order to allow energy measurement and collimation. The DL2 beamline nominally has a very small momentum compaction of
R56 ≈0.1 mm, but it can be easily increased, or even reversed in sign, by small adjustments in the gradients ofthree nearby quadrupole magnets. For the energy modulation shown in Fig. 2, R56 = 0.30 mm is optimum. Fig. 3
shows the beam characteristics immediately following thisbend system, including CSR effects.
CSR calculations require both a large number of macroTable 1: Energy modulator (EM) at 4.54 GeV for B=5 andtwo laser wavelengths (λL =0.8 µm and 2.2 µm).
Parameter
N wiggler periods
period of wiggler
peak laser power
laser rms waist
modulation amp.
buncher R56

sym
Nw
λw
Ppk
σr
∆γ
R56

0.8 µm
8
25
9.7
0.25
±14
0.30

2.2 µm
8
30
10.7
0.25
±14
0.78

unit
—
cm
GW
mm
—
mm

∆E/E0 (%)

00.5

γεx,y (µm)

220
Ipk (kA)

I

pk

(kA)

γεx,y (µm)

4

0.04
0.02
0

0.1
0

−0.1

−2

0
z (µm)

2

Figure 3: Same plots as in Fig. 2, but at a z-position immediately following the DL2 beamline. Strong current modulation and CSR effects are now apparent.
particles and narrow bin width (∼6 nm) due to the short
ESASE bunching length (≈30 nm rms). This spike
length still greatly exceeds the CSR point-charge wakelimit of R/γ 3 ≈ 0.01 nm at 14 GeV for bends with radiusR ≈300 m [11]. It is worth noting that the CSR in the DL2
dipoles will be partially suppressed by a combination of anon-zero R51 component and a relatively large transverse
beam size. The projected spike length in the bends along
the axis of propagation will broaden to σx |θ| ≈ 400 nm,
where σx ≈ 45µm is the rms horizontal beam size at thebend entrance and θ ≈ 0.5◦ is the bend angle. This longer
effective length, the low charge in each spike, and the weak
bend angles all minimize CSR effects, although a 20% horizontal emittance growth and some phase space distortionis still evident in Fig. 3. Nonetheless, a fully 3D CSR calculation is needed to verify these 1D results.

FEL SIMULATION RESULTS
The 6D macroparticle distributions resulting from the
ELEGANT tracking studies were directly imported as
input to the FEL simulation codes GINGER[12] andGENESIS[13]. We performed a number of fully timedependent (∆tslice ∼10 as) SASE runs at two different
energy modulation wavelengths (0.8 and 2.2 µm) and two
undulator focusing lattices (β =26 and 12 m) with thestandard LCLS λu =30 mm undulator period. For thesecalculations wakefield effects were neglected. Table 2 sumTable 2: Simulation results from GINGER and GENESIS.
Param.
β = 26 mβ = 12 m unit
λL
STD
0.8 2.2 0.8
2.2
µm
Lsat
70
58
57
44
45
m
P 
13
2.0 3.0 2.9
7.6
GW
Pspike2401765
40
160 GWω/∆ω
1500 550 660 660 790–

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uniformly-spaced spikes with effective widths ≤0.5 fs up
to and about one-to-two gain lengths beyond Lsat . Between the individual spikes, the instantaneous SASE poweris smaller by three orders of magnitude or greater. As predicted by Ref. [14] for SASE in the short pulse limit, the individual spikes support a single coherent longitudinal modeand their bandwidth is approximately transform-limited forz ≤ Lsat (presuming one has matched λL /B to approximately one coherence length). Fig. 5 shows P (t) snapshots at various z-locations for a 2.2-µm laser-modulated
pulse with β=12 m. At z=57 m, approximately three gain
lengths beyond saturation, some spikes begin to display
multi-peak structure and pulse widths approaching 1-fs orgreater due to slippage effects.
Figure 4: P  plotted versus z for ESASE and standard
LCLS configurations. The solid lines and boxes represent
GINGER and GENESIS results, respectively.

COLLECTIVE EFFECTS
The high peak current in the ESASE spikes raises concerns that impedance effects may induce sufficient energy
spread to seriously degrade FEL performance. We now estimate the effects from three different sources.

Wakefield Effects

Figure 5: P (t) snapshots at 5 different z-locations for a
2.2 µm-energy-modulated ESASE pulse with β =12 m,
plotted with staggered offsets of 1.5 fs in time and 15 GW
in power. For legibility, the z =37 m data has been multiplied by a factor of 2.0.
marizes various output parameters from the simulations.
For simplicity, we have defined the saturation point as that
where the normalized inverse spectral bandwidth ω/∆ω
reaches a maximum and Pspike as the average peak powerof the spikes measured at z = Lsat . The ESASE results
show significantly reduced saturation lengths, albeit withsomewhat smaller average powers and inverse bandwidths
than the “standard” LCLS configuration. In particular, if itwere possible to achieve an β=12 m or less, Lsat is reduced to less than 50 m. We believe the enhanced gain fromsuch an ESASE configuration would allow the LCLS to operate at a somewhat larger normalized emittance than thenominal 1.2 mm-mrad or at somewhat shorter wavelengths
than the nominal 0.15 nm. The time-averaged powers forboth the ESASE cases and standard LCLS parameter cases(“STD”) are shown in Fig. 4. Because GENESIS unlike
GINGER includes non-axisymmetric modes, in the early
regions of exponential gain it will tend to show a significantly higher power.
One important feature of the ESASE runs is that the
instantaneous power is essentially composed of simple,

WEBOS01

The longitudinal resistive wall wake of high-current
spikes will be partially suppressed by the large catch up
distance zc associated with the short spike length. Indeed,for σspike =30 nm and undulator pipe radius a=2.5 mm,
we find zc = a2 /2σspike ≈ 100 m, which exceeds the expected FEL saturation length. Due to the finite beam γ, theextension of the image charge induced on the wall by a single spike, a/γ ≈100 nm, is larger than σspike . This somewhat reduces zc . However, even without this reduction, thewake induced by a single spike inside itself is expected tobe small due to the small charge of the spike (∼ O(10) pC).
If we take for the wake the value w = Z0 c/πa2 (thelimit of the steady state wake for very short bunches; see,e.g.Ref. [15]) where Z0 =377Ω is the vacuum impedance,
we estimate the induced energy spread in the spike due tothis wake will be δE/E ≈ 4 × 10−4 at z=100 m. This issmaller than the intrinsic energy spread σE of the ESASE
spike and should only slightly affect FEL performance.
The total charge in the spikes is a relatively small fraction of the total charge of the bunch. This means that the
average wake of multiple spikes will be dominated by theaveraged smooth current distribution in the bunch. This
wake is not supposed to generate excessive energy spreadin the beam.

Coherent Undulator Radiation
Coherent undulator radiation (CUR) at wavelengths
comparable to the spike length (∼30 nm) but much
longer than the resonant FEL wavelength λr = 2π/kr(=0.15 nm) can be an important impedance source. The
CUR impedance per unit length at wavenumber k for a long

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A.A. Zholents et al. / Proceedings of the 2004 FEL Conference, 582-585

pencil beam is [16, 17]
1D
ZCU
R (k) =

2

Z0 K k4π γ 2 8
2π + 4i lnkrk

CONCLUDING REMARKS


,

(1)

where K is the undulator parameter. However, longwavelength undulator radiation is emitted primarily offaxis at an angle θ ≈ 2λ/λu ∼ 1 mrad. Consequently,
the effective radiation impedance taking into account thetransverse size of the bunch is modified to
2 2

2

2

3D
1D
−k θ σx
1D−2kku σx
ZCU
= ZCU
.
R ≈ ZCU R e
Re(2)

with ku ≡ 2π/λu . For an infinite train of ESASE bunches
spaced by laser wavelength λL , the modulated electron current is (see e.g., Ref. [8])∞I(z) = I0 1 + 2
Jn (nkL R56 Bσδ )
n=1




2 2 2
× exp −n2 kL
R56 σδ /2 cos(nkL z) , (3)where I0 =3.4 kA is the unmodulated beam current, Jn isthe Bessel function of order n, kL = 2π/λL , z is the longitudinal position along the bunch, and σδ ≡ σγ0 /γ is thenormalized rms energy spread. At the optimal compression
kL R56 Bσδ ≈ 1, the energy loss per unit length is∞
2I0 K 2 
n2
d(∆γ)
2
≈−
Jn (n) exp − 2 − 2kn ku σx
ds
IA γ 2 n=1
2B
 


kr
πkn
kn
cos (2πnz̄) −ln×sin (2πnz̄) ,(4)42kn

The ESASE technique allows obtaining electron beam
micro-bunches with a peak current unthinkable from a standard electron bunch compressor. Our preliminary investigations suggest that the high peak currents induce only
limited beam quality degradation due to collective effects
such as CSR, wakefields, and space charge; nonethelessmore detailed studies are needed for greater certainty. Although the exponential ESASE gain length is only somewhat shortened relative to an unmodulated beam for the
standard LCLS undulator with β=26 m, there is a much
shorter gain length and more rapid saturation in z for
β=12 m. For this latter case, detailed “start-to-end” simulations show that the output SASE x-ray pulse will bedominated by periodic spikes of a few hundred attosecondor less duration. Consequently, the duration of the overall
output envelope can be controlled by adjusting the modulating laser pulse. One can also obtain absolute synchronization between these two pulses which can be used in thepump-probe experiments for ultra-fast dynamics studies at
the femtosecond time scale and beyond. We plan further
studies to explore more fully the potential of ESASE techniques at the LCLS.

REFERENCES[1] LCLS Conceptual Design Report, SLAC-R-593 (2002).
[2] TESLA Technical Design Report, DESY TESLA-FEL
2001-05 (2001).

where IA ≈ 17 kA is the Alfvén current, kn ≡ nkL
and z̄ ≡ z/λL . For B=5, λL =0.8µm, and γ = 2.8 ×
104 and σx =33 µm in the undulator, Eq. (4) yields maximum d(∆γ)/ds ≈ 0.003 m−1 , more than two orders ofmagnitude smaller than that obtained using the 1-D CUR
impedance (i.e., Eq. (1)).

[3] Zholents, A.A., submitted to Phys. Rev. Lett. (2004)

Longitudinal Space Charge Effects[7] Saldin, E.L, Schneidmiller, E.A., and Yurkov, M.V., Opt.
Comm., in press, (2004)

Another high-frequency impedance is the longitudinal
space charge (LSC). Since kn σx /γ  1 (pencil beam in
1 for all n except n = 1 at
the rest frame) and kn a/γ
λL =0.8 µm, we use the free-space LSC impedance per unit
length (see, e.g., Ref. [18]):


Z0 k
γ
ZLSC (k) ≈ i
1
+
2
ln
. (5)
4π γ 2k (σx + σy )For B=5, λL =0.8 µm, and σx =33 µm, we find thatthe maximum d(∆γ)/ds ∼ 0.1 m−1 . For λL =2.2 µm,d(∆γ)/ds ∼0.05 m−1 . For the ≈200-m long diagnostic
section between DL2 and the undulator, the space-chargeinduced growth in ∆γ to O(20) is large enough for concern.
If necessary, the current bunching could be delayed bymaking the DL2 dogleg isochronous together with installation of a weak chicane just before the undulator. Over the
100-m length of the undulator, the space-charge-induced
energy spread increase is less than that of the spikes’s initial value σE .

[4] http://www.lightcon.com/lc/scientific/topas.htm[5] Zholents, A.A. and Fawley, W.M., Phys. Rev. Lett. 92,
224801 (2004).
[6] Saldin, E.L, Schneidmiller, E.A., and Yurkov, M.V., Opt.
Comm, 237, 153 (2004)[8] L.H. Yu, Phys. Rev. A, 44, 5178 (1991).
[9] J. Billen, LANL Report LA-UR-96-1835 (1996).
[10] M. Borland, ANL report APS LS-287 (2000).
[11] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Nucl.
Inst. Meth. A, 398, 373 (1997).
[12] W.M. Fawley, LBNL-49625 (2002).
[13] S. Reiche, Nucl. Inst. Meth. A, 429, 243 (1999).
[14] R. Bonifacio et al., Phys. Rev. Lett. 73, 70 (1994).
[15] K.L.F. Bane and M. Sands, SLAC-PUB-95-7074 (1995).
[16] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. Meth. A, 417, 158 (1998).
[17] J. Wu, T. Raubenheimer, G. Stupakov, Phys. Rev. ST Accel.
Beams, 6, 040701 (2003).
[18] A. Chao, Physics of Collective Beam Instabilities in HighEnergy Accelerators (Wiley, New York, 1993).

New Concepts

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J.G. Neumann et al. / Proceedings of the 2004 FEL Conference, 586-589

GENERATION OF TERAHERTZ RADIATION BY MODULATING THE
ELECTRON BEAM AT THE CATHODE
J. Neumann*, R. Fiorito, H. Freund, P. O'Shea,
IREAP, Univ of MD, College Park, MD 20742, USA
G. L. Carr, H. Loos, T. Shaftan, B. Sheehy, Y. Shen, Z. Wu,
Brookhaven National Lab, Upton, NY 11973, USA
A bunched electron beam can be used to generate
coherent radiation in a particle accelerator. This
experiment, a collaboration between the University of
Maryland and the Source Development Laboratory at
Brookhaven National Laboratory, uses a drive laser
modulated at terahertz frequencies in an RFphotoinjecting electron accelerator to produce a bunchedbeam at the cathode. The experiment is designed todetermine if such a scheme could be used to develop a
compact, high power terahertz emitter. After acceleration
to approximately 73 MeV, a mirror intercepts the beam.
The backwards transition radiation from the mirror ismeasured with a bolometer. The experiment was
conducted at various modulation frequencies and levels of
charge.

INTRODUCTION
Shaping the profile of a laser pulse incident on a
photocathode is important for many types of radiative
devices.
In some free electron laser applications,smoothing the profile may be necessary to prevent
unwanted emission of radiation. In other cases, laser
modulation can be used as a radiation source. This work
explores using a modulated drive laser to produce asimilarly modulated electron beam in order to generate
terahertz radiation. There are many potential applications
for terahertz light including exploration of vibrationalmodes in DNA and proteins, weapons and explosives
detection, and communications. A review of some
applications and available sources of terahertz radiation is
given by Siegel [1].
In general, the radiation emitted by a bunch of electrons
can be expressed as

d 2W
d 2W1
[N e + N e (N e − 1)F (ω ,θ , φ )] (1)=dω dΩ dω dΩwhere Ne is the number of electrons, and F(ω,θ,φ) is theform factor. The form factor is a number between zeroand one that depends on the geometry of the electron
beam. A tightly bunched beam (the bunches are much___________________________________________*neumann@glue.umd.edu

WEBOS02

smaller than the wavelength separating the bunches) will
yield a form factor of 1, while an unbunched beam will
yield a form factor of zero.
The single particle term, d2W1/(dωdΩ) applies to any
radiative mechanism, such as a wiggler, a bend magnet, ora transition radiator. While this experiment focuses on atransition radiator, injecting a prebunched beam into awiggler causes it to reach saturation faster than an
unbunched beam (Fig. 1)

Power (W)

Abstract

10

6

10

4

10

2

Uniform
Beam

PrebunchedBeam

E = 3.5 MeV

f = 0.8 THzb

I = 100 Ab

10

B = 3.46 kG0w

λ = 3.0 cm

ε = 5.0 mm-mradn∆E /E = 0.01
b

w

b

-2

10

0

1

2

3

z (m)

4

5

6

Fig. 1: Comparison of the growth of 0.8 THz radiation in
WIGGLIN simulation using both prebunched and uniform
beams.
This experiment, conducted at the Source Development
Laboratory (SDL), at Brookhaven National Laboratory,
used a modulated Ti:sapphire drive laser to produce a
modulated electron beam. The electrons are accelerated
to approximately 73 MeV, and transition radiation is
produced by interaction of the beam with a 2cm diameter
mirror placed at 45 degrees with respect to the beam
direction. The terahertz light passes through a transportsystem to a bolometric detector. Information about the
spectrum of the radiation is obtained by using various
terahertz filters.
In an ideal case, a periodic train of short electron
bunches would be accelerated to the radiator. One
example of this type of profile is shown in Fig. 2. The
expected spectrum of the terahertz radiation that could beemitted by such a beam is shown in Fig. 3, depicting cases
for 1, 2, 4, and 8 bunches. Note that a single short bunch
produces a broadband coherent signal, whereas thebunched cases result in a more narrow band source.

Available online at http://www.JACoW.org

J.G. Neumann et al. / Proceedings of the 2004 FEL Conference, 586-589

587

succeeded in generating several different pulse train
configurations, varying in modulation frequency andnumber of bunches. Two representative cross correlationsof obtained UV laser pulses follow in Fig. 4.

Fig. 2: "Ideal" train of short electron bunches

Fig. 3: Calculated spectrum for bunch train of 1,2,3 and 4
equally spaced bunches.
Assuming 1 nC of charge and a the finite metal disc in
the SDL as a transition radiator, the total backwards
transition radiation is calculated to be 112.2 µJ, 54.8 µJ,
25.9 µJ, and 12.1 µJ for N=1, 2, 4, and 8 respectively.
This experiment focuses on generating a narrow bandsource, in contrast to other electron beam-based
broadband coherent terahertz sources including one
demonstrated at the Source Development Laboratory [2]and the Thomas Jefferson National Laboratory [3].

DRIVE LASER MODULATION
The drive laser at the Source Development Lab is basedon a commerical 800 nm Ti:sapphire laser. The systemproduces a 100 fs pulse. A chirped pulse amplification
system increases the pulse energy, and it is frequency
tripled to 266 nm. In normal operation, a multipicosecond
UV laser pulse is directed to the cathode. A scanningcross correlator is used to measure the time profile of theincident laser pulse [4].
In this experiment, an interferometer was used in order
to induce drive laser modulations. This techniqueFig. 4: Examples of UV drive laser cross correlations.

ELECTRON BEAM MEASUREMENTS
After acceleration, the electron beam longitudinal
profile is measured. The measurement is made by
applying an energy chirp, passing the beam through amagnetic dipole, and examining the beam on a screen.
Measurements are made using the RF zero phasing
technique, but it has been shown that energy modulation
may appear as density modulation using thistechnique [5]. Varying the energy chirp allowed atomographic reconstruction technique [6] to be applied toa series of projections in order to recover a time profile ofthe electron bunch.
Fig. 5 shows two examples of electron beam profiles
for different charge levels. Notice that as the charge
increases, the entire bunch spreads in time and eachindividual peak also expands. This has a corresponding
effect on the spectrum of the terahertz radiation.

New Concepts

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J.G. Neumann et al. / Proceedings of the 2004 FEL Conference, 586-589

measurements at the detector.
comparison is shown in Fig. 7.

a)One result of such ab)Fig. 6: Characterization of the terahertz filters

Fig. 5: Two electron beam profiles from tomographic
reconstruction corresponding to the second laser pulse
shown above. The total charge in (a) is 20 pC and thetotal charge in (b) is 65 pC.

TERAHERTZ MEASUREMENTS
As a first step for characterizing this source, it was
important to determine the energy and spectrum of theterahertz light. Although the spectrum could not bemeasured directly, four filters were used to sample the thespectrum. The filters are a metal mesh design, and theirtransmission characteristics were measured on the U12 IR
beamline at the National Synchrotron Light Source. The
measured filter transmission curve is shown in Fig. 6.
Each of the filters is referred to by a color for
convenience. For each charge and modulation setting, thetransition radiation produced by the electron beam wasmeasured with a helium cooled bolometer, and with eachfilter. The expected amount of energy was calculatedusing equation (1) to determine the expected spectral
density per solid angle, taking into account losses due toabsorption in air and the geometry of the transport system;
the appropriate filter transmission curves were applied,
and the total integrated energy was compared to the

WEBOS02

Fig. 7:detector

Terahertz energy measured/calculated at theAgreement between the experimental measurements
and theoretical calculations are an indicator that thecalculated spectrum is representative of the actual
terahertz radiation spectrum produced by the electron
beam.
Fig. 8 shows the spectral density calculated from thetwo electron beam profiles shown above. Note how
increasing charge affects the electron beam density
profile, and therefore the spectrum.
The total energy arriving at the detector for the 20 pC
case was 1.5 pJ (measured) compared to 2.5 pJ(calculated). Estimation of losses in the transport systemsuggest that the terahertz light exiting the accelerator
window is approximately 0.4 nJ. In the 65 pC case, thetotal energy arriving at the detector was 5.4 pC, whichcorresponds to 2.4 nJ at the accelerator window.

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J.G. Neumann et al. / Proceedings of the 2004 FEL Conference, 586-589

One of the problems with pre-modulation of theelectron beam is washout of the density modulation. It is
important to note, however, that there is still evidence of
the initial density modulation in the energy-time phasespace even if the density modulation is washed out. Thismeans that it may be possible to recover this density
modulation through an appropriate dispersive mechanism.

ACKNOWLEDGEMENTS

Fig. 8: Achieved Spectral Density

This work was carried out with the support of the U.S.
Department of Energy, Division of Materials Sciences
and Division of Chemical Sciences, under Contract No.
DE-AC02-98CH10886 and with support from NAVSEA
and the JTO.

REFERENCES
CONCLUSION
This experiment indicates that information from drive
laser fluctuations are passed on to the electron beam andcan be detected after acceleration. Although the totalenergy measured at the detector was small, one mightachieve higher single shot terahertz pulse energy, as well
as a narrower bandwidth, by implementing a better laser
control system or a customized electron beam transportsystem in order to generate a pulse train closer to the ideal
case.

[1] P.H. Siegel, IEEE Trans. Microwave Theory &Techniques 50, 910 (2002).
[2] H. Loos. Personal communication.
[3] G.L. Carr et al., Nature, 420, 153 (2002).
[4] H. Loos, et al. Proc. 2002 Adv. Accel. Concepts[5] T. Shaftan et al, Proc. 2003 Particle Accel. Conf.
329 (2003).
[6] H. Loos, et al. Nucl. Intr. and Meth. A 528, 189(2004).

New Concepts

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C. Tennant et al. / Proceedings of the 2004 FEL Conference, 590-593

SUPPRESSION OF MULTIPASS, MULTIBUNCH BEAM BREAKUPIN TWO PASS RECIRCULATING ACCELERATORS*
C. Tennant#, D. Douglas, K. Jordan, L. Merminga, E. Pozdeyev, TJNAF, Newport News, VA 23606
T. Smith, W.W. Hansen Experimental Physics Laboratory, Stanford, CA 94305
Abstract
Beam Breakup (BBU) occurs in all accelerators at
sufficiently high currents. In recirculating accelerators,
such as the energy recovery linacs used for high power
FELs, the maximum current has historically been limited
by multipass, multibunch BBU, a form that occurs whenthe electron beam interacts with the higher-order modes(HOMs) of an accelerating cavity on one pass and thenagain on the second pass. This effect is of particularconcern in the designs of modern high average current
energy recovery accelerators utilizing superconducting
technology. In such two pass machines rotation of thebetatron planes by 90°, first proposed by Smith and Rand
in 1980 [1], should significantly increase the thresholdcurrent of the multibunch BBU. Using a newly developed
two-dimensional tracking code, we study the effect of
optical suppression techniques on the threshold current of
the JLAB FEL Upgrade. We examine several opticalrotator schemes and evaluate their performance in termsof the instability threshold current increase.

INTRODUCTION
In May of 2004 the multipass, multibunch beam
breakup instability was observed at 3 mA of average
beam current for the first time in the Jefferson Lab FEL
Upgrade Driver. At the onset of the instability weobserved HOM power levels in one particular cavity growexponentially until the beam losses tripped off themachine (see Figure 1). With the knowledge that beam
breakup is a real limitation to machine operation, thefocus turns to finding a means of suppressing the
instability.

Figure 1: An oscilloscope trace from a BBU induced
machine trip. The green trace is the cavity HOM voltage
and the red trace is the total HOM power as measured
from a Schottky diode. The time scale is 5 msec/div.
____________________________________________________________________________________________________*

Supported by the Office of Naval Research, the Joint Technology
Office, the Commonwealth of Virginia, the Air Force ResearchLaboratory, and by DOE Contract DE-AC05-84ER40150#
tennant@jlab.org

WEBOS03

The intent of this paper is to describe how BBU can besuppressed, or eliminated altogether, by modifying therecirculation transfer matrix from an unstable cavity backto itself in such a way that BBU cannot develop (or it
does so at a sufficiently high average current). Applying
conventional means of suppressing beam instabilities such as beam-based feedback and HOM damping
techniques - to BBU are discussed elsewhere [2]. The
techniques described in this paper are applicable to any
two-pass ERL machine; however, for simplicity we study
the effect of applying this method to Jefferson Lab’s FEL
Upgrade Driver.
The Driver is an energy-recovery based linear
accelerator used to condition an electron beam for highpower lasing [3]. Electrons are injected at 10 MeV and areaccelerated to 145 MeV through three cryomodules (eachcontaining 8 superconducting niobium cavities). The
beam is transported to a wiggler where up to 10 kW oflaser power is generated. The spent electron beam isrecirculated and phased in such a way that the beam isdecelerated through the linac region on the second pass.
Upon exiting the linac, the 10 MeV recirculated beam isextracted to a dump (see Figure 2 for a layout of the FEL).

EFFECTS OF ARBITRARY MODE
POLARIZATION AND GENERALIZEDTRANSPORT ON BBU
A beam bunch will excite dipole HOMs in a cavity if it
passes through the cavity off-axis. The magnetic field of
the excited mode then acts to deflect the following
bunches. The kick produced by the mode is translated intoa transverse displacement at the cavity after recirculation.
Thus, the recirculated beam constitutes a feedback which
can cause the voltage of the HOMs to grow. An approachbased on the consideration of energy deposited by thebeam into a cavity HOM was used to derive the thresholdcurrent. We consider only a single cavity and a single
beam recirculation. However, instead of limiting the
HOM orientations to either 0° or 90°, we allow for an
arbitrary orientation angle, α, with respect to thehorizontal axis. We also allow for a full 4x4 recirculation
matrix (i.e. the off-diagonal 2x2 matrices need not bezero). The threshold current is then given by the following
expression [4]:I th = −2 pb c*(1)ek ( R Q ) Q M 12sin(ωTr )*2
2
M 12 ≡ M 12 cos α + ( M 14 + M 32 ) sin α cos α + M 34 sin α

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C. Tennant et al. / Proceedings of the 2004 FEL Conference, 590-593

Injector
Superconducting RF Linac
3F Region
IR Wiggler
UV Wiggler
Figure 2: Layout of the JLab FEL Upgrade Driver (the UV transport line is currently being installed).
where pb is the beam momentum at the cavity, c is the
speed of light, e is the electron charge, k is thewavenumber ( ω /c) of the HOM, (R/Q)Q is the shunt
impedance of the HOM, Tr is the recirculation time andthe Mij are the elements of the recirculation transport
matrix from the cavity back to itself (which can describe
coupled transverse motion).

OPTICAL SUPPRESSION SCHEMES
We consider two methods for beam optical control of
BBU. The first method is a reflection which is mosteffective at suppressing BBU when the HOMs areoriented at 0° or 90°, while the second method utilizes a
90° rotation of the betatron planes in which BBU iseliminated regardless of HOM orientation.

Reflection
The transport matrix describing a reflection about aplane at 45° to the horizontal or vertical axis takes thefollowing form, where each element represents a 2x2
matrix;
 0 M
 .
(2)
M 0 

The 2x2 sub-block transport matrix M is the same for bothexchanges (x to y, y to x). Thus, such a reflector cleanly
exchanges the horizontal and vertical phase spaces.
To see how a reflection can be effective in suppressing
BBU, consider equations (1) and (2). Since M12 = M34 = 0,
for a mode oriented at 0° or 90° the threshold current
becomes infinity. However, if an HOM is rotated at anangleα, not equal to 0° or 90°, then the recirculated beam
will not come back to the cavity with the angle (α + 90°)
and its projection on the HOM will be non-zero. To get an
infinite threshold for all HOM polarizations requires that
M32 = -M14.
A practical implementation of a reflector using skewquadrupoles has been non-invasively embedded in the 3F“backleg” region of the FEL Upgrade Driver (see Figure2) [5]. Operationally, normal quadrupoles upstream anddownstream of the module are used as betatron matchingtelescopes. These allow transverse matching of the phasespaces across the reflector, so that the 3F region, in its
entirety, remains transparent to the rest of the machine save for the exchange of horizontal and vertical emittance,
the interchange of incident steering, and possible

differences in phase advance, nothing is changed. While
the skew-quadruples produce a reflection across the 3F
region, the transport matrix of interest for suppressing
BBU is from the unstable cavity back to itself. Thus, withnominal operating conditions, the effect of the embedded
skew-quadrupole reflector is to produce a pseudoreflection; a matrix similar in form to equation (2) but
with the off-diagonal matrices not exactly equal to eachother.

Rotation
A more robust optical scheme which suppresses BBU
regardless of HOM orientation is a 90° rotation. The
transport matrix describing a 90° rotation takes thefollowing form, where as before, each element represents
a 2x2 matrix;
M
 0

.
(3)
−
M
0 

Consider now equations (1) and (3). Since M12 = M34 = 0
and M32 = -M14, the threshold current is infinity and BBU
is eliminated - independent of the mode orientation. A
rotation implemented in a two-pass system effectively
breaks the feedback loop formed between the beam andcavity HOM so there can be no exchange of energy. The
idea is conceptually simple and is illustrated in Figure 3.
If on the first pass an offending mode imparts an angulardeflection α, to a bunch, then on the second pass (andafter a 90° rotation), the resultant displacement will beorthogonal to the deflection. Thus the bunch will be
unable to couple energy to the mode that caused thedeflection.
y’

y

v
r'
α

x’

x

α

v
r

Figure 3: The effect of a 90° rotation. A deflection on thefirst pass (left) is transformed to a displacement which isorthogonal to the deflection which caused it (right).

New Concepts

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C. Tennant et al. / Proceedings of the 2004 FEL Conference, 590-593

One way of implementing a rotation is by the use of asolenoid. However, in high energy machines a solenoid
becomes impractical because of the large magnetic field
integral required. In addition, a solenoid introduces
undesirable strong transverse focusing. Another way of
implementing a rotation is via a reflection. An embedded
reflection in the recirculator can, in principle, be made to
produce a pure rotation from the unstable cryomodule
back to itself [6].

(2) pseudo-reflector optics (3) rotated optics. The results
are summarized in Table 1.

DESCRIPTION OF THE TWODIMENSIONAL BBU SIMULATION CODE

With no suppression techniques applied, the thresholdcurrent for the case of “aligned modes” is just under
3 mA. The threshold current remains virtually unchanged
for the “skewed modes” case.

Simulations to study the effectiveness of the opticalsuppression schemes described above were performed
using a newly developed BBU code (yet to be named) [7].
The code was written in the Standard ANSI C++ language
and the first version of the code has been tested andbenchmarked. The primary motivation for developing a
new code was the necessity for a correct treatment of twodimensional transverse beam dynamics and the capability
to handle HOMs with arbitrary orientations. The codeworks by tracking particles through a machine
characterized by transfer matrices and follows the HOM
energy buildups in accelerating cavities. In the present
configuration, the code simulates beam dynamics in a
two-pass recirculating accelerator.
The code has been used to simulate beam breakup inseveral one-dimensional cases including the FEL Upgrade
Driver. The results are in 3% agreement with results
simulated by the previous BBU simulation codes used at
Jefferson Laboratory, TDBBU [8, 9] and MATBBU [10].
Because the results for two-dimensional simulations havenot been compared with existing BBU codes, the results
were compared to the formula given in equation (1). The
simulation results for two-dimensional cases show
excellent agreement with the theory [11]. In addition to
the capability of handling two-dimensional transverse
motion and arbitrarily oriented HOMs, the new code isfaster than TDBBU and MATBBU by an order ofmagnitude or more depending on the particular problem.

SIMULATION RESULTS
To see the effectiveness of the two aforementioned
methods for beam optical control of BBU, twodimensional simulations were performed. The simulation
model uses the FEL design optics including the RF
focusing effects and uses measured data to describe the
HOMs (frequencies and loaded Qs). The only unknown isthe polarization of each HOM. Thus two sets ofsimulations were performed. The first set simulates
HOMs with orientations of either 0° or 90° (“aligned
modes”). A second simulation was performed with theorientations “skewed” slightly. Each mode from the firstset was changed (randomly) by an amount between 1°
and 15° to see the effects of different HOM orientations(“skewed modes”). For each set, three different machine
optics were simulated: (1) nominal, uncoupled optics

WEBOS03“Aligned”“Skewed”

Nominal2.83 mA
2.87 mA

Pseudo-Reflection
288 mA
18.3 mA

Rotation
613 mA208 mA

Table 1: Simulation results of the BBU threshold currents.

Nominal Optics

Pseudo-Reflector Optics
With the modes “aligned” the threshold current isincreased substantially from the nominal optics case (by afactor of ~100). The threshold is not infinite - as one
might expect – since coupling between HOMs is possible
due to the finite Q’s and frequency separation, thus
facilitating BBU at lower currents. The point of interest,
however, is that due to mode orientations being “skewed”,
a pseudo-reflection alone does not effectively suppress
BBU. The factor of 6 increase in the threshold current is
consistent with a misaligned mode as given in equation(1), but is significantly less effective than with the modes“aligned” (e.g. 18.3 mA versus 288 mA). Thus, unless it
is known that dangerous HOMs are oriented very nearly
to 0° or 90°, a reflection scheme may not adequately
suppress BBU. Figure 4 illustrates the effects of thepseudo-reflected optics as given by the BBU simulation
code. Each plot shows the transverse displacement(horizontal and vertical) versus time. The average beam
current for the simulations was 100 mA. In the case of“aligned modes” initial beam offsets damp down and thebeam is stable. In the case of the “skewed modes” thethreshold current is much lower than the current simulated
and hence BBU develops and the beam offset grows
exponentially.

Rotated Optics
For the case of “aligned modes” the threshold current isincreased by a factor of ~200. In theory, BBU should be
eliminated altogether with a pure 90° rotation of betatronplanes (see equation (1)). However, the recirculation
matrix used for the unstable region back to itself is not a
perfect rotation (i.e. the 2x2 off-diagonal matrices are of
opposite sign, but are not exactly equal). Hence BBU
occurs at a finite current. With the modes “skewed”, arotation is still very effective in raising the thresholdcurrent. This is expected since, as discussed previously, arotation suppresses BBU regardless of the modeorientations.

C. Tennant et al. / Proceedings of the 2004 FEL Conference, 590-593

593This has prompted investigations of methods for beam
optical control of BBU. From a simple, analytical modeland from two-dimensional BBU simulations, it was
shown that a 90° rotation of the betatron planes is themost effective means to suppress the instability in a twopass recirculator. Experimentally, the skew-quadrupolereflector has been successfully commissioned in the FEL
Upgrade Driver. A systematic and quantitative study of its
effect on the threshold current has yet to be performed.
However, operational experience has shown that thethreshold is increased from 5 mA to over 8 mA using thereflector without any evidence of BBU induced machine
trips.

REFERENCES

Figure 4: Transverse displacement versus time for“aligned modes” (top) and “skewed modes” (bottom) withpseudo-reflection optics. The average beam current foreach simulation is 100 mA.

FIRST OPERATIONAL EXPERIENCE
Operational experience with the FEL Upgrade isconsistent with this discussion of instability control. Bytuning the betatron phase advances and match, it waspossible to vary the BBU-driven current limit from as low
as 1 mA to over 5 mA (the usual operational current).
Such configurations did not always reproduce over thecourse of days due to irreproducibility in the transportsystem quadrupoles. When problematic, thresholds could
be moved to acceptable levels – often without invoking
adjustments in betatron phase advance – by improving
betatron matching and current transmission.
We have, further, succeeded at operating at over 8 mA
by use of the aforementioned skew-quadrupole reflection.
When activated, we have verified this system completely
cross-couples the two transverse planes. Modeling further
suggests that certain choices of phase advance render the
installed system a true reflection [12]. We note howeverthat this configuration awaits operational evaluation.
Though it is possible to manipulate the transfer matrix inthis manner, it is not certain that the machine will perform
properly, as internal mismatch can generate beam loss that
limits machine performance just as surely as BBU.
Conversely, it was found during FEL operation that
simply matching the machine well (so as to clean up thetransport, but ignoring BBU altogether) could result in afactor of 4 or 5 improvement in the threshold current.

CONCLUSIONS[1] Rand R., Smith T., Beam Optical Control of Beam
Breakup in a Recirculating Electron Accelerator,
Particle Accelerators, Vol. II, pp. 1-13 (1980).
[2] Tennant C., et al., “Methods for Measuring andControlling Beam Breakup in High Current ERLs,”
Proceedings of the LINAC 2004 Conference (2004).
[3] Benson S., et al., “High Power Lasing in the IR
Upgrade FEL at Jefferson Lab,” these proceedings(2004).
[4] Pozdeyev E., Tennant C., “Equation for the Multipass
Beam Breakup Threshold Current for a Single Modeand a 4x4 Recirculation Matrix,” JLAB-TN-04-019(2004).
[5] Douglas D., “A Skew-Quad Eigenmode Exchange
Module (SQEEM) for the FEL Upgrade Driver
Backleg Transport,” JLAB-TN-04-016 (2004).
[6] Douglas D., “Reflections on Rotators,” JLAB-TN-04023 (2004).
[7] The BBU code was developed by E. Pozdeyev(pozdeyev@jlab.org)[8] Krafft G., Bisognano J., “Two Dimensional
Simulations of Multipass Beam Breakup,”
Proceedings of the 1987 Particle Accelerator
Conference, p. 1356 (1987).
[9] Beard K., “TDBBU 1.6: Another Tool for Estimating
Beam Breakup Due to Higher-Order Modes,” JLABTN-02-045 (2002).
[10] Beard K., “MATBBU 2.4: A Tool to Estimate Beam
Breakup Due to Higher-Order Modes,” JLAB-TN02-044 (2002).
[11] Tennant C., Pozdeyev E., “Simulation Results of
Two-Dimensional Multipass Beam Breakup,” JLABTN-04-020 (2004).
[12] Douglas D., “Operation of the FEL Upgrade with
Skew Quad Reflection and Rotation,” JLAB-TN in
preparation (2004).
.

The multipass, multibunch beam breakup instability has
been observed at the Jefferson Lab FEL Upgrade Driver.

New Concepts

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V.N. Litvinenko et al. / Proceedings of the 2004 FEL Conference, 594-597

POTENTIAL USE OF eRHIC’s ERL FOR FELS AND LIGHT SOURCES
Vladimir N. Litvinenko and Ilan Ben-Zvi
Brookhaven National Laboratory, Upton, NY, USA
Abstract
One of the designs of a future electron-hadroncollider, eRHIC, is based on a 5-10 GeV high current
energy-recovery linac (ERL) with possible extension of
its energy to 20 GeV. This ERL will operate with highbrightness electron beams, which naturally match
requirements for X-ray FELs and other next generation
light sources. In this paper we discuss possible
scenarios of using the eRHIC ERL in parasitic anddedicated mode for SASE, HGHG and oscillator X-ray
FELs.

INTRODUCTION
A Twenty-Year Outlook DoE document on“Facilities for the Future Science” [1] includes a newelectron-hadron collider at BNL, based on the
Relativistic Heavy Ion Collider (RHIC) and a newelectron accelerator.
Table 1. Main parameters of eRHIC
RHIC
Ring circumference [m]Protons: number of bunches
Beam energy [GeV]
Protons per bunch (max)Normalized 96% emittance [µm]Gold ions: number of bunches
Beam energy [GeV/u]
Ions per bunch (max)Normalized 96% emittance [µm]Electrons: Beam rep-rate [MHz]Beam energy [GeV]γ, Relativistic factor
RMS normalized emittance [µm]Beam emittance @ 20 GeV [Å]RMS Bunch length [psec]
Charge per bunch [nC]
Average e-beam current [A]

3834
360
26 - 250
2.0 · 1011
14.5
360
50 - 100
2.0 · 1096
28.15
5 – 201 - 4 1045- 50
1.25-12.530
1.6 -16
0.45

The main goal of the eRHIC is to explore thephysics at so-called “low-x”, and the physics of colorglass condensate in electron-hadron collisions [2]. In
response, the Collider-Accelerator Department at BNL
in collaboration with Bates Laboratory at MIT issues
the eRHIC ZDR (0th–order design report), which
includes a linac-ring eRHIC design based on 10 GeV
ERL [3]. The design is based on CW linac with highcurrent super-conducting RF (SRF) 5-cell cavities,
which are under construction at BNL [4,5] and apolarized photo-injector using a dedicated 2 kW
circularly polarized FEL [3]. The main parameters of
the eRHIC are summarized in Table 1. The parametersof the electron beam are very impressive and it can

WEBOS04

easily be used as a next generation light source inparasitic mode.
In addition, RHIC rings operate only for about 30
weeks per year, which leaves about 4 and a halfmonths for dedicated mode of ERL operation as a lightsource. In this case we suggest using a lower charge
per bunch and a higher rep-rate, while keeping thesame level of average e-beam current (~ 500 mA). The
e-beam parameters for this mode of operation are listed
in Table 2.
Table 2. Main parameters in dedicated mode
Electrons
Beam rep-rate[MHz]703.75
Beam energy [GeV]
5 – 20γ, Relativistic factor
1 - 4 104
RMS normalized emittance [µm]0.9Beam emittance @ 20 GeV [Å]0.18
Full transverse coherence λ[Å]1.13
photon energy [keV]11
RMS Bunch length [psec]
0.03 - 3
Charge per bunch [nC]
0.7
Average e-beam current [A]0.5
Parameters of the electron beam in eRHIC’s ERL
naturally match the requirements for a next generation
light source. First, let us note that the eRHIC ERL lightsource would have transverse coherence in the X-ray
range up to 11 keV. Second, 20 GeV operation of the
ERL will extend the range of spontaneous radiationfrom undulators and bending magnets into γ-ray range
and open new possibilities for low energy nuclear
physics. Third, the ERL is a perfect driver for highpower (i.e. kilowatts of CW power) FELs ranging fromhard X-rays to VUV. Fourth, it is also a perfect matchfor generating beam of very intense circularly
polarized γ-rays with energies up to 12 GeV.
In this paper, we take a first look at the potentialof the ERL at eRHIC as a light source. We describe
two possible layouts, discuss the effects of synchrotron
radiation in the ERL’s arcs on the e-beam parameters
and, finally, present a straw-man design of X-ray FELs
based on SASE, distributed optical klystron (DOK) andoptics-free oscillator schemes.

LAYOUTS OF THE ERL-based eRHIC
Fig.1 shows a possible layout for a stand-along ERL.
The electron beam, generated in SRF photo-injector isaccelerated to an energy of 0.5 GeV by low energy
ERL, followed by two passes through high energy
linacs. This layout provides for a natural use of thebeam-lines installed on the 2.5, 5, 7.5 and 10 GeV arcs
for a variety of sources of spontaneous radiation. After
passing through the collision point, the beam is going

Available online at http://www.JACoW.org

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V.N. Litvinenko et al. / Proceedings of the 2004 FEL Conference, 594-597

through the energy recovery process, which doubles
the beam current in each arc (except that at 10 GeV).
FEL can be installed in a straight section connecting
the end of the 10-GeV arc with the linac. This scheme
is limited to maximum energy of ~ 10 GeV by the sizeof the accelerator and the acceptable power of thesynchrotron radiation.

linac, which it passes twice to reach maximum energy
of 20 GeV. Then the beam is decelerated to recover its
energy back into RF field and is finally dumped.
On the way to the final energy the electron beam
passes through the arcs, where synchrotron radiation
may significantly affect the e-beam parameters. Ourpresent design is based on 150 25-meter longachromatic cells (see sketch in Fig. 3) with a bending
radius of 400 m in the dipoles. The energy loss forsynchrotron radiation is 35 MeV for 20 GeV electrons.

Fig. 3 A sketch of 25 meter-long achromatic cell for 10
and 20 GeV arcs in the eRHIC’s ERL.
Table 3. Parameters of the 10 GeV e-beam
Energy10

GeV

Radius, average

610.20m

B, magnets

0.83

kGs

9.50E-07m rad

ε normFig. 1 Layout of eRHIC with a stand-along 10 GeV
ERL.
Fig.2 shows a more attractive layout of ERL sharing
a 3.8 km tunnel with two hadron storage rings (called
the blue and the yellow).

εBunchlength

0.485

Å

from 0.1 to 2

psec

∆ε

0.001

Å

ε , final

0.486

Å

RMS energy spread

0.10%

4.49E-06

Table 4. Parameters of the 10 GeV e-beam
Energy20

GeV

Radius, average

610.20m

B, magnets

1.67

kGs

9.50E-07m rad

ε normεBunch length∆εε , final
RMS energy spread
Fig. 2 Layout of the eRHIC ERL in the RHIC tunnel.
This layout provides for multiple collision points for
eRHIC and also allows an increase in the energy ofelectron beam to 20 GeV or above while keeping
power of synchrotron radiation under control (andespecially keeping linear power density well below 1
kW/m). Obviously, this layout has many advantages
for the light source applications. It has best emittanceand hundreds of meters of free space for hard X-ray
FELs.
Similarly to other ERLs, the electron beam isgenerated in the gun, pre-accelerated in the low energy
SRF linac, then injected into the main high energy SRF

0.243

Å rad

from 0.1 to 2

psec

0.016

Å rad 6.70%

0.259

Å rad

2.54E-05

The beam parameters at the end of the arc for 10
GeV and 20 GeV beams and some basic parameters of
the arcs are given in Table 3 and Table 4,
correspondently. In this design, synchrotron radiation
determines the energy spread of both 10 GeV and 20
GeV, while contribution of the initial energy spread is
negligible. In contrast, this low emittance lattice of thearc provides for essential preservation of the initialnormalized transverse emittance: the horizontal
emittance grows by 0.1% for 10 GeV beam and by
6.7% for 20 GeV beam. Extremely high quality of theelectron beam in eRHIC’s ERL provides for a naturaluse of its strong spontaneous radiation from its regularor specialized magnets (see Table below).

New Concepts

596

V.N. Litvinenko et al. / Proceedings of the 2004 FEL Conference, 594-597

attractive driver for high gain X-ray FELs, which canoperate in SASE [6], and HGHG [7] modes. The very
low energy spread of this source makes it attractive to
use a scheme of distributed optical klystron (DOK) [8],schematically shown in Fig. 4. DOK driven by a low
energy spread beam has shorter gain length (L G DOK)
compared with that of a SASE FEL (LG):

Table 5. Synchrotron radiation at 20 GeV.
Loss per turn

35.40

MeV

Power
λc (regular bend)

17.70

MW

0.28

Å

Εc (regular bend)

44.35

KeV

λc (10 T bend)Εc (10 T bend)

0.0047

Å

2661

KeV

 1
4 πLG σ γ 3 / 2 L
LG DOK ≅ LG ⋅ e 4 ⋅ 2/κ ; κ = w .


λw γ
Lc

Energy of 20 GeV makes building hard X-ray sources
an easy task: a wiggler with period of 2 cm will
generate fundamental wavelength of ~ 0.1 Å. The
range of expected spectral brightness for these sourcesof spontaneous radiation is shown n Fig. 5.

where σ γ / γ is RMS energy spread of electron beamand λw is the wiggler period. DOK reduces the gain
length X-ray FELs at eRHIC 2.2 and 5 fold at energies
of 20 GeV and 10 GeV, correspondingly. Table 6
summarizes the parameters of ERL based FELs at
eRHIC.

ERL-based FELs
Low emittance, high peak current of the 20 GeV
ERL operating in dedicated mode (Table 2) make it an
Buncher

Buncher

Buncher
Wiggler

Wiggler

Lw
Lc

Fig. 4 A sketch of distributed optical klystron, which consists of repeating cells comprising a wiggler and a buncher.
Similar to the traditional optical klystron [1], the slippage in the buncher is significantly larger that in the wiggler. Thisadditional bunching combined with low energy spread beam enhances the FEL gain.

Table 6. Main parameters of X-ray FEL driven by ERL at eRHIC
Energy, GeV

20

20

15

15

10

10

Wavelength, Å

0.5

1

0.87

1.8

2

4

Bunch length, psec

0.2

0.2

0.27

0.27

0.4

0.4

Peak Current, kA

5

5

3.75

3.75

2.5

2.5

Wiggler period, cm

2.5

3

2.5

3

2.5

3

SASE gain length, m

7.5

4.3

5.5

3.3

3.7

2.4

SASE Saturation length, m

100

60

76

47

51

34

Saturation power, GW

7.7

19

6.4

14

4.5

9

DOK, gain length, m

3.5

1.4

1.5

0.65

0.51

0.25

DOK, saturation length, m

47

19

21

9

7

3.5

A simple use of SASE FEL combined with a very highrepetition rate of ERL at eRHIC leads to extremely
high average lasing power from 0.6 MW to 1.3 MW at
wavelength of 1Å (photon energy 12 keV). The
solution for this potential problem is either to use
Fourier limited source. i.e. either HGHG FEL or
optics-free FEL oscillator (OFFO) [10], the schematicof which is sketched in Fig. 6 The main ERL drives anhigh gain FEL amplifier with gain of ~ 105. Amplified
light passes through a micro-wiggler with low energy,
low current, low emittance e-beam used for feed-back.

WEBOS04

The feed-back-beam carries-on the modulation to theentrance of the FEL, where it radiates coherently inanother micro-wiggler. This radiation is then amplified
by the new electron bunch in the high energy FEL.
This process closes the loop and makes this FEL an
oscillator [12].
The advantage of this scheme is that this FEL is fully
tunable, optics independent and has a line-width of an
oscillator. This scheme would allow reducing the linewidth of X-ray FEL to a few parts per million
compared with a few parts per thousands, typical forV.N. Litvinenko et al. / Proceedings of the 2004 FEL Conference, 594-597

SASE FELs [11]. In this case, the average power of Xray FEL at eRHIC with average spectral brightness in

597

1030 range (see Fig.5) will reduce to manageable levelsof tens of hundreds of watts.

Fig.5 Average and peak spectral brightness of eRHIC light source (blue – FELs, green – spontaneous radiation)compared with other sources. While being similar to SASE FEL sources in peak spectral brightness, the average
spectral brightness of eRHIC FELs would exceed the rest of the light sources (existing and proposed) by about 5 ordersof magnitude.
Feed-backSourceBeam Dump
Modulator

Radiator

High Gain FEL
Photons

FEL
beam

Fig. 6 Schematic of OFFO using two ERLs.

CONCLUSION
Future high current 10-20 GeV ERL for eRHIC
electron-hadron collider has outstanding potential
to become a next generation light source with
unprecedented levels of average spectral
brightness.
This work is supported by the US Departmentof Energy and Office of Naval Research.

REFERENCES[1] http://www.er.doe.gov/Sub/Facilities_
for_future/facilities_future.htm[2] http://www.bnl.gov/henp/docs/NSAC_RHICIIeRHIC_2-15-03.
[3] http://www.agsrhichome.bnl.gov/eRHIC/,
Appendix A, Linac-Ring Option[4] I. Ben-Zvi at al., Ampere Average Current PhotoInjector and Energy Recovery Linac, these
Proceedings.
[5] R. Calaga et al., High Current Superconducting
Cavities at RHIC, Proceedings of EPAC-2004,
Geneva, Switzerland, July 5-9, 2004
[6] A.M. Kondratenko, and E.L. Saldin, Particle
Accelerators 10, 207 (1980); J.B. Murphy and C.
Pellegrini, Nuclear Instruments, and Methods
A237, 159 (1985);[7] L.H. Yu et al, Physics Review Letters 91, No. 7,
074801-1 (2003)[8] V.N. Litvinenko, Nuclear Instruments and Methods
A 304, (1991) 463[9] N.A. Vinokurov and A.N . Preprint INP 77-59,
Novosibirsk, 1977
[10] V.N. Litvinenko, Proceedings of FEL conference,
August 2002, APS, Argonne, IL, Eds. K.-J.Kim,
S.V.Milton, E.Gluskin, p. II-1
[11] V. Ayvazyan et al., Physics Review Letters 88,
104802 (2002)

New Concepts

598

B.W.J. McNeil et al. / Proceedings of the 2004 FEL Conference, 598-601

THE HARMONICALLY COUPLED 2-BEAM FEL
B. W. J. Mc Neil∗ and G. R. M. Robb, University of Strathclyde, Glasgow G4 0NG, UK
M. W. Poole, ASTeC, Daresbury Laboratory, Warrington WA4 4AD, UK
Abstract
A model of a Free Electron Laser amplifier operating simultaneously with two electron beams of different energy
is presented. The electron beam energies are chosen sothat the fundamental resonance of the higher energy beam
is at an harmonic of the lower energy beam. By seeding
the lower energy FEL interaction at its fundamental radiation wavelength, an improved coherence of the un-seededhigher energy FEL emission is predicted and may offer analternative to current proposals for seeding XUV and x-ray
FELs. An initial study of the effects of beam energy spreadon the intearction is presented.

INTRODUCTION
It is now well established that high gain FELs operatingin the SASE mode [1] are characterised by a noisy FEL
output at saturation with relatively poor temporal coherence and large fluctuations [2]. The simplest conceptual
method to resolve this problem is to inject a well-formed
resonant coherent seed field at the beginning of the FEL interaction that dominates the intrinsic noise. The FEL output is then significantly improved over that of SASE at saturation. However, there are, as yet, no suitable seed sources
available in the XUV and x-ray. Seeding at longer wavelengths can generate shorter wavelengths by using the twowiggler harmonic method of [3]. Variations on this theme
have been suggested and implemented experimantally [4].
Another self-seeding method proposes using a monochromator either at the early stages of the FEL interaction [5] orwith some feedback [6] to improve temporal coherence. In
this paper an alternative method of seeding, based on a twoelectron beam FEL interaction [7], is described and investigated in the 1-D limit. Preliminary results of the effects ofelectron beam quality on the two-beam FEL are also presented.

THE MODEL
A simple FEL wiggler system, of constant period λw ,and field strength Bw , was proposed, through which twoelectron beams of different energy co-propogate [7]. The
lower energy electron beam has a Lorentz factor of γ1 andthe higher energy γn . The higher energy electron beam ischosen so that its fundamental resonant wavelength is anharmonic resonant wavelength of the lower energy beam.
From the FEL resonance relation, λ√= λw (1 + a2w )/2γ 2 ,it may easily be shown that γn = nγ1 . It should thenbe possible to seed the co-propagating electron beams with∗ b.w.j.mcneil@strath.ac.uk

WEBOS05

an externally injected seed radiation field at the fundamental of the lower energy electron beam. If such a seed field
is significantly above the noise level then the lower energy
electrons will begin to bunch at their fundamental resonant
wavelength and retain the coherence properties of the seed.
Such bunching at the fundamental also generates significant components of bunching at its harmonics which canalso be expected to retain the coherence properties of theseed. In a planar FEL this also results in on-axis radiation
emission at these harmonics. This process should couple
strongly with the the co-propagating higher energy beam
whose fundamental FEL interaction is at one of the lower
energy beam’s harmonics. This coupling between lowerand higher energy FEL interactions may allow the transferal of the coherence properties of the longer wavelength
seed field to the un-seeded shorter harmonic wavelengthinteraction.
Another coupling between the lower and higher energy
electron beams, which has the potential to degrade beam
quality, is the two-stream instability [8]. Using the resultsof [8], however, it can be shown that the instability is either
below threshold or has an insignificant effect for electron>
beam currents ( >∼ 1 kA) and energies ( ∼ 500 MeV) typicalto those used in the FEL interactions presented here.
The physics of the planar wiggler FEL in the 1D Compton limit may be described by the coupled
Maxwell/Lorentz equations which, under the simplifying
assumptions, universal scaling and notation of [1, 9], arewritten:
dϑj
dz̄
dpj
dz̄
dAh
dz̄

= pj
= −

(1)




Fh Ah eihϑj + c.c.

(2)

h,odd



= Fh e−ihϑ ,(3)where j = 1..N are the total number of electrons, h =1, 3, 5... are the odd harmonic components of the field andFh are the usual difference of Bessel function factor associated with planar wiggler FELs. This set of equations (1..3)
is used to describe the FEL interaction of the lower energy(γ1 ) electron beam.
Strongest coupling between the lower and higher energy
electron beams would be expected for the lowest harmonicinteraction h = n = 3 so
√ that the higher energy electron
beam has energy γ3 = 3γ1 . Higher harmonic interactions h = n > 3 may also be of interest, as those harmonics
h < n of the lower energy beam are not resonant with thehigher energy beam and would not be expected to unduly
disrupt the coupling to the higher harmonic.

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599

B.W.J. McNeil et al. / Proceedings of the 2004 FEL Conference, 598-601

The equations describing the FEL interaction of thehigher energy electron beam, with its fundamental resonant
field only, may be written in the similar form:
dϕj
dz 
d℘j
dz 
dA1
dz 

= ℘j

(4)



= −F1 A1 eiϕj + c.c.

(5)



= F1 e−iϕ .

(6)

We shall neglect harmonics of the higher energy electron
beam as these will have a weaker coupling to the lower
energy beam , e.g. if n = 3 then the third harmonic of thehigher energy beam will be the ninth harmonic of the lower
energy beam.
In their universally scaled forms the two sets of equations (1..3) and (4..6) have different Pierce parameters [1],ρ, due to the different energy and current density of theelectron beams. In [7], by using the usual relations between scaled and unscaled fields and lengths [1], equations (4..6) were written with the same scaling of equations (1..3) to give the final set of working equations describing the coupled FEL system. Here, we use the scalingof equations (4..6) to rescale equations (1..3). For purely
notational convenience we rewrite z  → z̄ and Ah → Ah
in equations (1..6) after rescaling to give the final set ofworking equations:
dϑj
dz̄
dϕj
dz̄
dpj
dz̄
d℘j
dz̄
dAh
dz̄
dAn
dz̄

= pj

(7)

= ℘j

(8)

n


1 
= −
Fh Ah eihϑj + c.c.
c1

(9)

h,odd




= − F1 An eiϕj + c.c.

(10)

= Shϑ

(11)

= Sϕ + Snϑ ,

(12)

where
Skϑ
c1
c2





1
(13)
Fk e−ikϑ , Sϕ ≡ F1 e−iϕc2√ 3/2
ρn
Rn
1
1 In
(14)
=
=
≡
n I1
n
n1/4 ρ1√ 3/2ρnInRn
1= n1/4=√≡ √ , (15)
ρ1
n I1
n
≡

and in (11) h refers to all odd harmonics h < n, I is thebeam current and subscripts 1 (n) refers to the parametersof the lower (higher) energy beam. Note that all harmonicinteractions have been assumed negligable for h > n inequation (9). By assuming both beams have the same transverse cross section (or equivalently the same normalised

transverse emittance in a common, matched focusing chan1/3
nel through the wiggler) then ρ1,n ∝ I1,n /γ1,n and thesecond equalities of (14) and (15) are obtained in terms of
the beam currents. This assumption is applied to the work
presented hereafter. Note that the equations (3) and (6),describing evolution of the fields An and A1 , refer to thesame field, which, once (3) has been re-scaled, allows thetwo source terms to be combined into the single differential
equation (12) for the harmonic field An → An .
The coupling of the low energy electrons to both fundamental and harmonic field is seen in equation (9). Fromequation (10), the higher energy electrons only couple tothe harmonic field An (their fundamental) - the fields Ah
are sub-harmonic to the higher energy electrons and are
therefore not resonant. The fields Ah , are seen from equation (11), to be driven only by the lower energy electron
beam (the higher energy electrons are not resonant with
Ah .) Equation (12) demonstrates that the highest harmonic
field has two driving sources, both the lower and higher energy electron beams. From these couplings it is seen that,
whereas the shorter wavelength radiation field is directly
coupled to both lower and higher energy electron beams,
the longer wavelengths have no direct coupling with thehigher energy beam. In this sense, the short wavelengthharmonic interaction may be described as ‘parasitic’ as it
may resonantly extract energy directly from both lower andhigher energy electron beams, whereas the longer wavelengths may only directly extract energy from the lower
energy beam.
The working equations readily yield a constant of motion
corresponding to conservation of energy:
n

h,odd

p
|Ah |2 + √ + ℘ .
n(16)

It is seen from the definitions of the scaled electron energy
parameters pj ≡ (γj −γ1 )/ρn γ1 and ℘j ≡ (γj −γ√n )/ρn γnthat the electron beam√energy relation γn = nγ1 accounts for the factor of n in (16).
A linear analysis of the system (7..12) was carried out
using the method of collective variables [1]. Assuming resonant interactions for both electron beams, and that bothbeams are effectively ‘cold’ so that neither emittance norenergy spread have a deleterious effect upon the FEL interaction, this analysis yields a condition for the beam current
ratio, Rn ≡ In /I1 , above which gain at the harmonic isgreater than gain at the longer wavelength:2√
n |Fn |
Rn > n n 1 −
2
|F1 |

.

(17)

A NUMERICAL EXAMPLE
The evolution of the coupled two-beam FEL system isdemonstrated by numerically solving the working equations (7..12). Two (noiseless) electron beams were usedwith n = 3 and of current ratio R3 = 5, co-propagating in

New Concepts

600

B.W.J. McNeil et al. / Proceedings of the 2004 FEL Conference, 598-601

Figure 1: The scaled radiation intensities |A1 |2 and |A3 |2
as a function of scaled distance z̄ through the FEL interaction region for n = 3, R3 = 5, σp = 0.1 and σ℘ = 0.4.

Figure 2: The source terms Sϕ and S3ϑ as a function ofscaled distance through the FEL interaction region for n =3, R3 = 5, σp = 0.1 and σ℘ = 0.4.

a wiggler of parameter aw = 2. Both beams were given a
Gaussian energy spread of scaled width in p of σp = 0.1,
and in ℘ of σ℘ = 0.4. The seed field at the longer wavelength is modelled by defining its initial scaled intensity
at the beginning of the FEL interaction |A1 (z̄ = 0)|2 to
be two orders of magnitude greater than that of the harmonic. In figure (1) the scaled intensities |A1 |2 and |A3 |2
are plotted as a function of scaled distance, z̄, through the
FEL interaction region. The feature of interest from figure (1) is the rapid growth in the harmonic intensity |A3 |2
by approximately two orders of magnitude in the interval<
6.5 <∼ z̄ ∼ 8. This period of more rapid growth (approximately n = 3 times the fundamental growth rate) is driven
by the strong harmonic component of the bunching |b3 | ofthe lower energy beam [9, 10, 11]. This harmonic bunching is caused, not by electrons bunching at the harmonic
wavelength, but by the significant harmonic component of
the strong, non-linear, bunching at the fundamental |b1 | as
the lower energy FEL interaction approaches its saturation
at z̄ ≈ 8.5. The harmonic bunching and subsequent harmonic emission of A3 from the lower energy beam, canbe expected to retain the coherence properties of the initial radiation seed field at the fundamental. This process
should therefore act as a harmonic seed field with good coherence properties. Following this harmonic seeding by thelower energy electron beam it is seen that the harmonic intensity continues exponential growth by approximately another two orders of magnitude until saturation at z̄ ≈ 12.5.
Further insight is gained by plotting individually themoduli of the source terms Sϕ and S3ϑ of the harmonic
field evolution equation (12), as shown in figure (2). The
contribution Sϕ is due to the higher energy electron beam,
and S3ϑ , the lower energy beam. The figure clearly shows<
the strong seeding phase between 6.5 <∼ z̄ ∼ 8, as discussed above, where the harmonic field is strongly driven
by the lower energy beam (S3ϑ > Sϕ ). This is followed by
the amplification phase where the harmonic field is driven
by the higher energy beam (Sϕ > S3ϑ ).

The above results also suggest that a hybrid HGHG
scheme may be possible if the interaction is stopped atz̄ ≈ 8.0 and the mildly bunched higher energy electron
beam injected into another wiggler which would allow
strong emission at one of its higher harmonics.
The equations have also been numerically solved, in thecold beam limit (σp = σ℘ = 0) to demonstrate the sameseeding mechanism for a fifth harmonic interaction [7]. A
similar interaction to that for the above simulation was observed, except the intermediate third harmonic field had
no resonant coupling with the higher energy beam. This
results in the fifth harmonic having both a greater linear growth rate and saturation intensity than the third harmonic.

WEBOS05

ENERGY SPREAD EFFECTS
An initial study of the effects of energy spread in a higher
energy beam with n = 3, was conducted by solving theworking equations for a range of values of initial Gaussian spread σ℘ . The same lower energy beam as above(R3 = 5 and σp = 0.1), wiggler parameter (aw = 2)
and initial field intensities (|A1 (z̄ = 0)|2 = 10−4 and|A3 (z̄ = 0)|2 = 10−6 ) were assumed. For comparative
purposes, FEL evolution of the higher energy beam in theabsence of the lower energy beam was also modelled byconducting a set of simulations with a large electron beam
current ratio of R3 = 103 and a reduced initial longer
wavelength scaled intensity of |A1 (z̄ = 0)|2 = 10−16 .
With these parameters there is no effective FEL evolutionof the lower energy beam and the higher energy harmonicinteraction evolves as though the lower energy beam wereabsent.
Figure (3) plots the scaled harmonic saturation intensity,|A3 |2sat , for a range of Gaussian energy spread parameterσ℘ and figure (4) plots the corresponding scaled harmonic
field sataration lengths z̄sat .
From these figures one distinguishing difference be-

B.W.J. McNeil et al. / Proceedings of the 2004 FEL Conference, 598-601

Figure 3: Saturation intensity |A3 |2sat as a function of energy spread σ℘ (σ3 in plot) of the higher energy beam.

Figure 4: Scaled saturation length of harmonic intensityz̄sat as a function of energy spread σ℘ (σ3 in plot) of thehigher energy beam.
tween the coupled two-beam interaction (R3 = 5) and thehigher energy beam only interaction (R3 = 103 ) is apparent: for the coupled two-beam interaction case, boththe harmonic saturation intensity|A3 |2sat and its sataration
length are less sensative to the energy spread σ℘ of thehigher energy beam. This encouraging preliminary result
will be extended to a wider range of energy spread parameter space of the two beams in future work.

CONCLUSIONS
A simple 1-D model of a two-beam FEL has been presented. This concept introduces potentially interesting coupled FEL interactions some of which may have beneficial
properties over single beam interactions. Indeed, one neednot be limited to only two beams and can envisage more
complex systems with more than two harmonically coupled beams - a multi-beam FEL equivalent of the cascaded
HGHG scheme [4]. Such multi-beam FELs may offer the601prospect of a reduction in overall length when comparedwith an equivalent HGHG scheme. One can also envisage
possible hybrid schemes involving combinations of multibeam FELs with HGHG. Clearly, these suggestions are
speculative at this stage and will require further research.
As an illustration of the type of interactions possible, numerical simulations of the coupled two-beam FEL interaction demonstrated that a seeded lower energy beam interaction may evolve to effectively seed that of the higher
energy. The conjecture was made that the improved coherence properties of the seeded interaction at the longer
wavelength would be inherited by the higher beam energy,
shorter wavelength, interaction. Such seeding may be ofinterest to proposals for FELs operating at sub-VUV wavelengths where no ‘conventional’ seed sources are yet available. Further analysis is required to verify any predicted
improvement in the coherence properties. Any analysis
will need to model a minimum of two independent variables (e.g. (z, t) or (z, ω)) and include the effects of therelative slippage between the lower and higher energy electron pulses. This relative slippage must be less than thatbetween the lower energy beam and the radiation field.
An initial study of the effects of an electron beam energy spread on the two-beam FEL system has shown nodebilitating effects. Indeed, the results encourage a more
complete investigation of parameter space.
No assessment has yet been made of the importance ofother factors that will effect such two-beam interactions,e.g. accelerator physics issues such as electron pulse synchronism, beam focussing and emittance, the relative energy detuning between the electron beams and transverse
modes. Some of these issues will undoubtedly require thedevelopment of new simulation models.

REFERENCES[1] R. Bonifacio, C. Pelligrini and L.M. Narducci, Opt. Commun. 50, 373 (1984)[2] E.L. Saldin, E. A. Schneidmiller, and M.V. Yurkov, TESLAFEL Report No. 97-02, 1997, DESY, Hamburg, Germany.
[3] R. Bonifacio, L. De Salvo Souza, P. Pierini and E.T. Scharlemann, Nucl. Instrum. and Meth. A 296, 787 (1990)[4] L.-H. Yu et al, Science 289, 932 (2000)[5] J. Feldhaus, E.L. Saldin, J.R. Schneider, E.A. Schneidmiller
and M.V. Yurkov, Opt. Commun. 140, 341 (1997)[6] B. Faatz, J. Feldhaus, J. Krzywinski, E.L. Saldin, E.A.
Schneidmiller, and M.V. Yurkov, Nucl. Instrum. and Meth.
A 429, 424 (1999)[7] B.W.J. McNeil, M.W. Poole and G.R.M. Robb, Phys. Rev.
E, (in press)[8] J.D. Lawson, The Physics of Charged-Particle Beams, (Oxford Science Publications, New York, 1988.)[9] R. Bonifacio, L. De Salvo Souza and P. Pierini Nucl. Instrum. and Meth. A 296, 627 (1990)[10] H.P. Freund, S.G. Biedron, and S.V. Milton, IEEE J. Quantum Electron. QE-36, 275 (2000)[11] Z. Huang and K.-J. Kim, Phys. Rev. E 62, 7295 (2000)

New Concepts

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R.G. Ganter et al. / Proceedings of the 2004 FEL Conference, 602-605

LOW EMITTANCE GUN PROJECT BASED ON FIELD EMISSION
R. Ganter, J.-Y. Raguin, A. Candel, M. Dehler, J. Gobrecht, C. Gough, G. Ingold, S.C. Leemann,
K.Li, M. Paraliev, M. Pedrozzi, L. Rivkin, H. Sehr, V. Schlott, A. Streun, A. Wrulich, S. Zelenika
Paul Scherrer Institut – Villigen CH 5232 - Switzerland

MOTIVATION
A Free Electron Laser (FEL), driven by a single passlinear accelerator (linac), is today the most promisingmechanism able to produce 0.1 nm wavelength, withpulses shorter than 100 fs. In FELs, the electron beamemittance plays a major role in the laser saturation
process. For an ideal electron-photon matching, theelectron beam normalized emittance must satisfy thediffraction limit [1]:

ε<

β λγ
LG 4π

(1)

Where λ is the radiated wave length, γ the relativistic
factor, β the beta function, LG the gain length and ε thenormalized emittance. This relation shows that the energyof the electron beam can be decreased, together with thelinac length, provided that the emittance is sufficiently
small. The electron source, with its initial emittance andcurrent, becomes thus the first master piece of the driving
accelerator.
Emittances on the order of 10-6m.rad, and sufficientcharge to drive an FEL, are presently achieved using RF
photo-cathode guns. The linac energy for such a beam isin the 15-20 GeV range, for a peak current at theundulator between 2 and 5 kA. A substantial

THPOS01

improvement (small linac, short gain length and relaxedpeak current) would be achieved with emittances below
10-7m.rad. Fig. 1 presents the FEL gain length versus theundulator period for different peak magnetic fields andnormalized emittances of 1.2 mm.mrad and 0.1 mm.mrad.
In these computations, it was assumed that the relative
energy spread was 1.10-4. Fig. 2 shows the required linac
energy vs. the undulator period for three different
undulator peak magnetic fields, the linac energy being
determined by the resonance condition:

λ=λu  K 2 
1 +

2 
2γ 2 

(2)where λu is the undulator period, K=0.934 B[T] λu [cm] isthe undulator deflecting parameter and B the peakundulator magnetic field.
10

ε =1.2 m m m radn9

Ib=5000 A
β =15.9 m

0.6 T

8
7
6

g

Gain length L [m]The design of an electron gun capable of producing
beam emittance one order of magnitude lower thancurrent technology would reduce considerably the costand size of a free electron laser radiating at 0.1nm. Field
emitter arrays (FEAs) including a gate and a focusing
layer are an attractive technology for such high brightness
sources. Electrons are extracted from micrometric tips
thanks to voltage pulses applied between the gate and thetips. The focusing layer should then reduce the initial
divergence of each emitted beamlet. This FEA will beinserted in a high-gradient diode configuration coupledwith a radiofrequency (RF) structure. In the diode part thehigh electric field (several hundreds of MV/m) will limit
the degradation of emittance due to space-charge effects.
This first acceleration will be obtained with high voltage
pulses (about one megavolt in a few hundreds ofnanoseconds) synchronized with the low voltage pulses
applied to the FEA (~ 200 – 300V in less than one
nanosecond at a frequency lower than a kilohertz). This
diode part will then be followed by an RF accelerating
structure in order to bring the electrons to relativisticenergies.

0.95 T

5
4

2T

3
0.6 T

2
1

0.95 T

ε =0.1 m m m radn

2T

Ib=500 A
β =4.77 m

0
0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Undulator period λ u [m ]Figure 1: FEL gain length vs. undulator period forseveral undulator peak magnetic fields and two
different electron beam emittances.
40
2T

35
30
energy [GeV]

Abstract25
20

0.95 T

15

0.6 T

10
5
0
0

0.005

0.01

0.015

0.02

0.025

0.03

0.035

0.04

Undulator pe riod λ u [m ]Figure 2: Beam energy vs. undulator period for several
undulator peak magnetic fields.

Available online at http://www.JACoW.org

R.G. Ganter et al. / Proceedings of the 2004 FEL Conference, 602-605

The FEL parameters considered for these comparisons
have been fixed accordingly.
As shown in Fig. 1 the required beam current and the
FEL gain length can be considerably reduced by
improving the electron beam properties (see also [2]). The
size of the linac (Fig. 2) can be decreased as well,allowing an appreciable cost reduction of the accelerator
facility.
Ultimately, the normalized transverse emittance islimited by its initial value at the cathode which can be
expressed as follows:r2

ε =γ cE r ,kin(3)

m0 c 2where rc is the cathode radius and Er,kin the meantransverse kinetic energy just after emission. To lower theemittance one can reduce the size of the electron source(rc) and/or the mean transverse energy of emitted
electrons (roughly the initial divergence). In this project
we are aiming at reducing both parameters thanks to fieldemission based cathodes.

CONCEPT
Most of the accelerators use either photocathodes orthermionic cathodes. An alternative technology for
generating electrons is field emitters based cathode.
Applications of field emitters for X-ray tubes andmicrowave tubes have already been explored in the past[3,4]. More recent studies report on the use of photoassisted field emission from needles for table top freeelectron laser applications [5]. At Paul Scherrer Institut
we are studying the possibility of using field emitter tips
(field emitter arrays or individual tips) for high quality
beams in accelerator applications. Although the idea has
already been proposed [6-8], recent progress in vacuum
microelectronics and nanotechnology makes field emitters
an attractive solution for new electron sources. The best
advantages of field emitters on other types of cathode areprobably the high achievable current density of theemission (up to 108 A/cm2) and the low temperature of theemitted electrons. Field emission is a tunneling effect
Tip Array (ø < 1 mm)
50A peak / 1ns / 50Hz

Air Core
Technology Pulser

where electrons are emitted with energies close to the
Fermi level. They follow then mainly the electric fieldlines [7].
In field emitter arrays, emission arises from tips thanks
to a close spaced gate layer (see Fig. 2 and 3). In order toshape electron trajectories, FEAs can integrate a second
grid layer which focus the individual beamlets producedby each tip (see Fig. 2). The tips height is about one
micrometer as well as the distance apex - focusing layer.
Typical emission area is about a few nanometers square
per tip [10]. In such field emitter cathodes the emission
bunching is achieved by pulsing the tip to gate voltage.
After extracting and focusing the electrons, a highgradient acceleration is required to limit space charge
effects. The FEA will be inserted in the cathode side of adiode configuration. The anode would then be the iris of
an RF cavity (see Fig. 2). This combination of diode andRF acceleration is inspired from the DC photogun built at
TU Eindhoven [11]. In the diode gap, we hope to reachvery high values of electric field gradient. Arc probability
will be considerably reduced by applying short voltage
pulses (< 500 ns) between the cathode and the anode at
low repetition rate. The unwanted field emitted current or
dark current will be minimized thanks to various
conditioning methods, electrodes geometry optimizationand careful assembling. Emittance compensation schemes
will also be considered.
Many problems which could affect the achievable beamemittance are not solved yet. It is the aim of this project toevaluate the beam quality that could be obtained fromfield emitters.

PROJECT STATUS
In order to investigate the possibility of using fieldemitter tips to make an improved electron gun, several
activities are progressing in parallel.

Cathode Evaluation
Preliminary studies of field emitter arrays (or single tip)properties have been performed (see companion paper[12]) on commercially available field emitters. First tests
concerned the maximum emitted peak current. It has been

RF cavities
3GHz

300V / 1ns

500kV
500ns
50Hz

603

Diode Gap ~ 1mm
500 MV/m+ Solenoids …

Figure 2: Schematic of the gun concept which
combines diode acceleration with RF acceleration.
Electrons are extracted by modulation of the gate layer
and first acceleration is given by high voltage pulses(SEM picture of tip from [9])Figure 3: Scanning electron microscope picture ofgated diamond tips from XDI Inc. [13].

New Concepts

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R.G. Ganter et al. / Proceedings of the 2004 FEL Conference, 602-605

found that emission during short pulses ( ~ 100 ns) at low
repetition rate (few Hz) prevent tips from overheating andthus enable larger emission intensities and better stability
than in DC regime. In this pulsed regime we finallyreached the saturation of the FEAs at about 50 mA due tothe highly resistive silicon wafer. This high silicon
resistivity is required in DC operation but not for ourapplication which use short emission pulses at low
frequency. Another way to reach higher current is toincrease the emission uniformity. During the fabricationof FEAs, geometric differences at the nanometric scale
between tips lead to bad emission uniformity at initial
turn on. Fig. 3 illustrates such differences between two
neighbouring tips. A specific test stand, called SAFEM(scanning anode field emission microscope [14]) is underconstruction for studying non uniformities of theemission.
We also investigated characteristics from single tip in
ZrC. We showed that such single tip in ZrC is capable ofemitting several milliamperes during microsecond longpulses. This corresponds already to a quite highbrightness between 1012 and 1013 A.(m.rad)-2 if we take
into account an emitting area of 200 nm in diameter andan initial divergence angle of 20 degrees [8]. We hope toreach even higher peak current with shorter pulses.
These preliminary tests on commercially available fieldemitters enable us to better understand our needs in termsof cathode development for our particular application. In
parallel to collaborations with companies specialized infield emitter fabrication, we also initiated thedevelopment of field emitter arrays at the micro andnanotechnology laboratory of PSI.

High Gradient Acceleration in the Diode Gap
As described above, the electrons are extracted from thetips by a grid layer and focalized by a second grid layer
one micrometer above the tip apexes. After this focusing
layer, electrons enter a drift region until the iris of theradiofrequency cavity. In this gap the electric gradientmust be as high as possible in order to limit space charge
effects. Space charge forces have a non linear effect on
beam spreading which leads to emittance growth.

However, when a high electric field is applied between
two massive metallic pieces, unwanted field emission is
generated from all the surface defects of the cathodesupport [15]. This dark current must be as small as
possible in order to limit his influence on the useful beamand the risks of arcs. Since dark current is also fieldemitted current, it depends on local field enhancement
factor (roughness, dust, …) and surface work function(e.g. adsorbed contaminants). As for tips in FEAs (seecompanion paper [12]) it is the overheating of the darkcurrent emitter which eventually leads to the generationof an arc. In order to prevent local dark current emittersfrom generating arcs we plan to apply short voltage pulses(a few hundred of nanoseconds) at low repetition rate. For
this purpose, a first pulser prototype delivering pulses of
500 kV amplitude and 500ns length is currently underconstruction.
To limit dark current intensity (even if it does not
generate arcs) very good polishing and cleaning methods
for the electrodes as well as clean room conditions duringassembling are required. In addition, we are also looking
for some in-situ conditioning method once electrodes aresealed under vacuum. For this reason, a specific test standhas been developed in order to test the field strength
between two electrodes of similar size to what is foreseen
for the final gun (see Fig 4). Different in situ conditioning
techniques have been investigated in order to improve thefield strength. Fig. 5 represents the dark current measured
between two massive copper electrodes of several squarecentimetres. After glow discharge treatment of theelectrodes, the required electric field for 1 nA of darkcurrent went from about 50 MV/m to 75 MV/m. Then weapplied a series of 100 ns voltage pulses between
electrodes with a small gap in order to draw large darkcurrent pulses. These large current pulses tend to smoothand blunt the dark current emitters. This is a similar
method to the one used for the conditioning of tips in fieldemitter arrays [16]. Other materials, as well as polishingand cleaning processes are under investigation in this test
1.0 (a)
0.5

600µm

0.0

I (nA)

1.0

(b)

0.5
0.0

1.0 (c)

50µm

0.5
0.0

Figure 4: Picture of the high gradient test standduring helium glow discharge treatment used forcleaning / polishing the electrodes.

THPOS01

0

5

100µm
10

200µm
15
20
V (kV)

300µm
25

400µm

30

35

Figure 5: Dark current versus applied DC voltage. The
numbers 50 to 600 indicate the electrode gaps in µm.
(a) Initial situation at 10-9 mbar, (b) after glow
discharge treatment of electrodes for several hours and(c) after pulse conditioning (100ns at 50 Hz).

R.G. Ganter et al. / Proceedings of the 2004 FEL Conference, 602-605

Figure 6: 100kV test stand for evaluation of beamemittance produced by field emitters.
stand in order to reduce dark current in the diode gap of
the gun.

developed [18]. Comparisons of this 3D PIC solver with
Mafia simulation gave good agreement [17].
For example, this 3D PIC code enables simulation of
non uniformity of the emission from a field emitter array,
when only a fraction of the total number of tips does
contribute to the emission. Fig 7 illustrates the evolutionof field emitted particles when only 20 % of the FEA tips
are emitting (see [18] for details). This preliminary
simulation shows a 20 % increases in the normalized
transverse emittance when going from a uniform
distribution of beamlets to this much worse case where 80% of the tips are not emitting.

CONCLUSIONSpace Charge Compensation
In addition to high-gradient acceleration, magnetic
compensation schemes are also considered for emittancepreservation. A 100 kV DC gun test stand (see Fig. 6)
integrating several beam diagnostic tools is currently
under development. This should provide preliminary
measurements of beam emittance at 100 keV. This gun
prototype will also be used to test various magnetic
compensation schemes with solenoids. Fig 6 shows thetest stand (not yet completed). This test stand will alsoenable comparisons with simulation results on beam
dynamics.

Simulations
MAFIA simulations have been performed in order toimprove the anode – cathode geometry in the 100 kV gun
test stand [17]. The purpose of these simulations was tominimize emittance increase at gun exit. Further
simulations including solenoid effects have been done andwill be compared to measurements done in the gun test
stand.
In order to simulate the granularity of the beam emitted
by a matrix of thousands of tips, a full 3 dimensional
Maxwell solver using particle in cell method has been

In order to achieve high quality electron beam for a
free electron laser application, a research project on afield emission based gun has been initiated. This gun
would combine diode and RF acceleration and theelectrons would be produced by field emission cathodes.
Test stands development, beam dynamic simulations aswell as preliminary studies of cathode properties are
currently in progress. In parallel to field emission cathodeevaluation, tests of integrating such cathodes in highelectric gradients are under way.

References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]

(a)

(b)

[11]
[12]
[13]
[14]
[15]

(c)

605

(d)

Figure 7: Time evolution of particles emitted by amatrix of individual emitters with 80 % failures.
Position in the A – K gap (a), (b) and after the anodeiris (c), (d).

[16]
[17]
[18]

L. H. Yu et al., NIM A 272, 436-441 (1988).
M. Pedrozzi et al., Proc. LINAC, Luebeck Germany, 2004.
F. Charbonnier, Appl. Surf. Sci. 94/95, 26-43(1996).
D. R. Whaley et al., IEEE Trans. Plasma Sci. 30,
998-1008 (2002).
C. H. Garcia et al., NIM A 483, 273-276 (2002).
G. Bekefi et al., J. Appl. Phys. 62, 1564-1567(1987).
Y. Liu et al., J. Vac. Sci. Technol. B 14 (1996).
K. L. Jensen et al., Appl. Surf. Sci. 111, 204-212(1997).
L. Dvorson et al., J. Vac. Sci. Technol. B 20, 5359 (2002).
W. Zhu, Vacuum Microelectronics (John Wiley& Sons, 2001).
F. Kiewiet, Thesis, TU Eindhoven, 2003.
K. Li et al., these proceedings.
K. D. Jamison et al., J. Vac. Sci. Technol. B 21
(2003).
L. Nilsson et al., Applied Physics Letters 76,
2071-2073 (2000).
M. E. Cuneo, IEEE Trans. Diel. Electr. Insul. 6(1999).
P. R. Schwoebel et al., J. Vac. Sci. Technol. B
19, 582-584 (2001).
A. Candel et al., Proc. EPAC, Luzern Switzerland, 2004
A. Candel et al., Proc. ICAP, St-Petersburg,
Russia, 2004

New Concepts

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K.L. Li et al. / Proceedings of the 2004 FEL Conference, 606-609

FIELD EMITTER ARRAYS FOR A FREE ELECTRON LASERAPPLICATION
K. Li, R. Ganter, J.-Y. Raguin, M. Dehler, J. Gobrecht, L. Rivkin, A. Wrulich
Paul Scherrer Institut – Villigen CH 5232 - Switzerland
Abstract
The development of a new electron gun with the lowest
possible emittance would help reduce the total length andcost of a free electron laser. Recent progress in vacuum
microelectronics makes field emitter arrays (FEAs) an
attractive technology to explore for high brightness
electron sources. Indeed, several thousands ofmicroscopic tips can be deposited on a one millimeter
diameter area. Electrons are then extracted by a first gridlayer close to the tip apex and focused by a second gridlayer one micrometer above the tip apex. In order to be agood candidate for a low emittance gun, field emission
cathodes must provide at least the peak current, stability
and homogeneity of current state of the art electron
sources. Smaller initial divergence should then beachieved by the focusing grid and the intrinsic propertiesof the field emission process.

MOTIVATIONS
In a free electron laser undulator, the required
normalized transverse electron beam emittance εn mustsatisfy the following condition:
4πε n < λγ
(1)where λ is the radiated wavelength and γ the relativistic
factor. Small normalized beam emittance would
considerably reduce the required beam energy and thus
the cost and size of the accelerator facility. On the other
hand a smaller emittance would also reduce the required
minimum peak current to efficiently drive a free electron
laser. Ultimately the emittance is limited by its initialvalue at the cathode which can be expressed as follows:r2

εn = γ c

E r , kinm0 c 2(2)where rc is the cathode radius and Er,kin the meantransverse kinetic energy just after emission. To lower theemittance one can reduce the size of the electron source(rc) and/or the mean transverse energy of emitted
electrons (roughly the initial divergence).

temperature. This already limits the minimum achievable
initial transverse kinetic energy of the produced electron
beam. In addition, the diameter of these cathodes isusually larger than a few millimeters. One alternative
process is field emission where electrons are emitted withenergies around the Fermi level and the mean transverse
energy is mainly determined by the geometry of theelectric field lines [2]. The achievable current density by
field emission is also much higher than with other type ofcathodes so that the emitting area could be smaller. Field
emission cathodes are usually made with tips, either
single tip or array of tips with an integrated gate layer (ie.
field emitter arrays FEAs). These FEAs consist of
thousands of conductive tips in the micrometer size range
separated from a conductive gate layer by a one
micrometer thick dielectric layer (see Fig. 3 and 4). By
applying a voltage between the tips and the gate layer(Vge) electrons are emitted from the tip’s apexes. In orderto shape electron trajectories, FEAs can integrate two gridlayers. The first grid is used for extracting the electrons
while the second grid provides focusing of the electrons.

Field Emitters Characteristics
To be a good candidate for free electron laser
application, field emitters must achieve higher peakcurrents than in usual applications like flat panel displays
or scanning electron microscopes. In addition we must beable to focus the field emitted beam thanks to a focusing
layer deposited a few micrometers above the tips. Finallythe emission must have a good uniformity and stability intime.
In a first approach we focused our work on the
maximum achievable emitted current. Typically a

1 µm

SiO2

Mo

FIELD EMISSION CATHODES
Current accelerator guns use photocathodes orthermionic cathodes [1]. In both cases, the meantransverse energy of the extracted electrons is several
hundred meV either due to the difference between photon
energy and cathode work function or due to the cathodeTHPOS02

Figure 1: Top view (Atomic force microscope) of two
pyramidal diamond tips (height 1 µm) from XDI Inc.
Tips are separated by SiO2 dielectric material (1 µm
thick). SiO2 is covered by a conductive Mo layer: thegate layer

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K.L. Li et al. / Proceedings of the 2004 FEL Conference, 606-609

2∆Ι (µA)

1
0
-1
-5

0

5

Time (ms)10

Figure 2: Fluctuations of the field emitted current versus
time due to thermally induced surface changes. The DC
component (200 µA) of the field emitted current has
been removed.

standard gated molybdenum tip is capable of emitting a
few microamperes in DC operation [3]. Above this level,
the risk of overheating the tip and generate a destructive
arc increases. One way to obtain higher current is to use amatrix with thousands of tips (FEAs).
For these preliminary tests, we used cathodes
available on the market. The SEM pictures in Fig. 3 and 4
represent diamond tips from the company XDI Inc [4] andmolybdenum tips from SRI Inc [5] respectively. XDI’s
cathode has around 3,000 tips distributed on a 170 µm
diameter disc area. These diamond tips have a pyramidal
shape due to the molding technique used for theirelaboration (Fig. 1). The tip material is a mixing of
diamond and graphite which is electrically conductive.
Tips are surrounded by a dielectric material (SiO2) whichisolated them from the molybdenum gate layer. The
typical height and base size of each tip as well as the gate
aperture diameter is about one micrometer.

The FEAs from SRI support around 50,000
molybdenum tips on a 1 mm diameter disc area. The
dimensions of these conical tips are close to XDI’s
pyramidal tips but the growing method is different. SRI
Inc. has developed the so called Spindt method [3] togrow molybdenum tips in a gated structure withnanometer tolerances. In order to test the emission ofthese gated structures we used a triode configuration.
Field emitted current is measured on a collector positively
biased in respect to the gate and tip voltages. If too muchelectrons are directly collected on the gate, the risk ofoverheating the gate is too high.
In addition to gated structure, we also investigated theemission from single tips in Zr covered by a ZrC layerfrom the company APTech Inc. [6]. These tips areinserted in a Vogel mounting without any extracting gatelayer (Fig. 6). We tested these single tips in a simple
diode configuration.

Field Emission Current Instabilities
As already mentioned, the limiting factor for highcurrent emission in DC operation is the excessive heatingof the tip and the surrounding materials (gate, anode,etc.). This leads to a series of thermally induced surfacechanges like desorption of contaminants or surface
migration. When ionized, these desorbed contaminants
can also back bombard the tips. Eventually, local pressure
rise can initiate destructive arcs.
These well known environmental problems are also
responsible for current emission fluctuations by changing
either the surface work function or the tip geometry [5].
Fig. 2 represents such typical current fluctuations
observed on the emission of one XDI field emitter array.
Only the variations of the current are represented, the DC
component (~ 200 µA) of the signal has been removed.
The amplitude of these fluctuations corresponds to a few
2

1

10

10

0

-1

10

-2

10

DC
Pulsed

-2

10

-4

10

-3

10

-6

-4

10

0

10

DC
PulsedI [mA]I (mA)

10

100

V200
(V)
ge

300

Figure 3: Current voltage characteristic in DC andpulsed regime for a FEA from the company XDI Inc(~3,000 diamond tips, ø = 170 µm). Insert: SEM
picture of diamond tips.

10

50

100
Vge [V]

150

Figure 4: Current voltage characteristic in DC andpulsed regime for a FEA from the company SRI Inc(50,000 Mo Tips, ø = 1000 µm). Insert: SEM pictureof conical Mo tips from SRI website [5].

New Concepts

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K.L. Li et al. / Proceedings of the 2004 FEL Conference, 606-609

percents of the total emitted current. The “steplike”
behaviour of the fluctuations corresponds to instantaneouschanges in the surface state due to successive adsorption,
desorption and migration processes [8].
Because of the strong dependence of field emitted
current on the geometry of the tip (field enhancement
factor β) and his surface composition (work function Φ),even small surface changes lead to strong variations in thecurrent intensity. This can be illustrated by FowlerNordheim’s equation which describes the dependence ofthe field emitted current density on these parameters:

emission and promising results have been achieved byscientist from SRI Inc. [7]. In fact, they found that selfheating of tips by drawing large current during shortpulses, tends to smoothen and clean tips without
destruction. The uniformity of electron emission could be
improved by this method. This is in favour of a freeelectron laser application which does not require DC but
only pulsed emission.

 − B.Φ 3 / 2 A.( β .V ) 2 . expΦ β .V 
where A, B are constant values, V represents the applied
voltage between electrodes, Φ is the work function in eV
and β is the enhancement factor of the electric field due togeometrical effect.

By operating the FEA with short voltage pulses at low
frequency it is possible to considerably reduce the heatbrought to the tips and therefore to eliminate most of thethermally induced problems. Consequently the emitted
current can be increased with less risk of deterioration.
Fig. 3 represents the emitted current versus the applied
tip to gate voltage for an array of about 3,000 diamondtips distributed on a 200 micrometers diameter disc area.
The maximum current measured in continuous mode wasabout 800 µA but emission was subject to fluctuations
and monotonic decay with time was observed as in [7].
However in the 50 Hz pulsed regime, with 100 ns voltage
pulses it was possible to reach up to 6 mA peak current.
In this mode of operation, emission was very stable andno decrease of the emitted current was observed after one
day of operation. The maximum current performance waslimited by the internal resistance of the field emitter array(~ 25 kΩ). This internal resistance originates from thesilicon wafer on which tips are deposited. In DC
applications it is preferable to have a highly resistive
silicon wafer in order to protect tips from brutal current
rises. In a pulsed mode, a smaller resistivity could be
tolerated. This internal resistance also limits the minimum
pulse length that can be applied between gate and tips byintroducing a large charging time constant. Fig. 4
represents a similar current voltage characteristic but for aJ=

One way to increase the total emitted current without
overheating is to use a large number of tips. However thestrong dependence of the field emitted current on tip
geometry and surface composition makes the uniformity
between tips very important. After fabrication, it is usual
to observe that only a few percent of the total number oftips contributes significantly to the total emission [9].
Field emission will occur preferably from the sharpest
tips. Variation of the geometry of the tip apexes at a
nanometric scale can lead to non uniformity of emission
between tips. Fig. 1 represents atomic force microscopemeasurements of two neighbouring tips from an XDI
array. The nanometric roughness of the tip surface can beseen on Fig. 1. These nanoprotrusions contribute to theoverall field enhancement factor and can introduce non
uniformity that are not easily controlled during
fabrication. Several conditioning processes have beendeveloped in order to improve the uniformity of the
142 V

40

118 V

0.8

I (mA)I (mA)

4897 V

1.0

126 V

30

Pulse Mode of Operation

20

4835 V

0.6

700 µm

0.4

10

0.2

4800 V

0
0.0

100

200

Time (ns)300

Figure 5: Current pulses emitted by a FEA with
50,000 Mo tips from the company SRI Inc. when
applying square voltage pulses with amplitude of118, 126 and 142V.

THPOS02

0

100

200

Time (µs)
Figure 6: Current pulses emitted by a single ZrC tipfrom the company APTech Inc. for different squarevoltage amplitudes of 100 microseconds.

K.L. Li et al. / Proceedings of the 2004 FEL Conference, 606-609

609

standard FEA from the company SRI Inc. This FEA
consists of 50,000 Mo tips grown by the so called Spindt
method [3] on a one millimeter diameter disc area. Again,
the sensitivity to environmental conditions was much lessimportant in the pulsed regime than in DC. The maximum
current performance was limited by the silicon wafer
resistance to values around 50 mA. Fig. 5 shows typical
100 ns current pulses collected from a 50,000 Mo tips
FEA.
We have also tested the maximum peak current thatcan be emitted by a single tip in zirconium carbide (ZrC)(see Fig. 6). Since this tip does not have any gate layer acopper anode has been placed five millimeter away fromthe tip and large voltage pulses (kilovolts) were applied.
To protect the tip from too high current values, a 10 kΩ
resistor was placed in series with the tip. The effect of theresistor is the slow charging ramp on the current pulses
seen in Fig. 6. More than 3 mA peak current have beenmeasured out of such a single tip. Only the apex of theZrC tip emits and the tip apex radius is less than one
micrometer (specifications give values between 20 and
100 nm). If we assumed an emission area of one squaremicrometer, the corresponding current densities is as highas 105 A/cm2.

CONCLUSION
Preliminary tests on commercial field emitter samples
showed that higher peak current and more stable emission
can be achieved when using short square voltage pulses at
low frequency. For a free electron laser application suchpeak current values are still too small [10], but with thehelp of even shorter pulses and smaller internal FEA
resistance we hope to reach the required current.

References[1] Fred Kiewiet, Thesis, TU Eindhoven, 2003
[2] Y. Liu, Y. Y. Lau, J. Vac. Sci. Technol. B 14(3),1996[3] W. Zhu, Vacuum Micro-electronics, John Wiley &Sons, New York (2001)[4] K. D. Jamison, B. G. Zollars, D.E. Patterson, R.
Schueller, H. Windischmann, G. A. Mulhollan and
A. Kloba, J. Vac. Sci. Technol. B 21(4), 2003
[5] http://www.sri.com/psd/microsys/[6] http://www.a-p-tech.com/[7] P.R. Schwoebel, C.A. Spindt, C.E. Holland and J.A.
Panitz, J. Vac. Sci. Technol. B 19(3), 2001
[8] R.T. Olson,
G.R. Condon,
J.A. Panitz,
P.R.
Schwoebel, J. Appl. Phys., Vol. 87 ,4 pp. 2031
(2000).
[9] P.R. Schwoebel, C.A. Spindt, C.E. Holland and J.A.
Panitz, J. Vac. Sci. Technol. B 19(2), 2001[10] R. Ganter et al., THPOS01, in these proceedings.

New Concepts

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j.b. Bahrdt et al. / Proceedings of the 2004 FEL Conference, 610-613

UNDULATORS FOR THE BESSY SOFT-X-RAY FELJ. Bahrdt # , W. Frentrup, A. Gaupp, B. Kuske, A. Meseck, M. Scheer, BESSY, Berlin, Germany
Abstract
BESSY plans to build a linac based Soft-X-ray FEL
facility. Three FEL lines will cover the energy range
between 24eV and 1000 eV. The FELs are operated in ahigh gain harmonic generation scheme providing shortpulses and stable operation. This paper describes theundulator systems for the FELs.

INTRODUCTION
The time structure of a high gain harmonic generation
FEL is determined by the time structure of the Laser
system. The FWHM of the FEL radiation is expected tobe below 30 fs. Furthermore, the shot to shot intensity

variations are small compared to a SASE FEL scheme.
The three FELs will be operated at electron energies of
1GeV (LE-FEL) and 2.3GeV (ME-FEL and HE-FEL),
respectively. They consist of 2, 3, and 4 stages with amodulator, a dispersive section and a radiator eachfollowed by a final amplifier (table 1).
The photon energy tuning will be done via gap motion.
For the HE-FEL the electron beam energy has to bemodified additionally to provide the full tuning range.
The last radiators and the final amplifiers will be devices
with full polarization control. The other modules which
are responsible for the electron beam bunching are planar
undulators.

Table 1: Parameters of the BESSY Soft-X-Ray FEL. Period lengths (1 st number) and section lengths (2nd number) are
given in mm and m, respectively [1].
DeviceEnergy range
Stage 1
Stage 2
Stage 3
Stage 4
Final amplifier
Total length / m

LE-FEL24-120 eV
Modulator
80 / 1.60
62 / 1.61

Radiator
62 / 3.47
50 / 3.45

50 / 3x3.85
21.68

ME-FEL
100-600 eV
Modulator
122 / 2.56
92 / 2.21
70 / 2.31
50 / 3x3.85
37.55

LAYOUT OF THE UNDULATORS
Since all gaps are variable a separated function
focussing scheme has been adopted. The quadrupoles of
the FODO structure are located between the undulator
segments. Permanent magnet phase shifters withadjustable magnetic gaps provide the correct phase
adaption between the undulator segments. Correction
coils, and diagnostic systems are located in theintersections as well.
A dogleg collimator with a spatial and an energy
collimation stage protects the magnets from being hit bydark current electrons.

Radiator
92 / 3.86
70 / 2x3.78
50 2x3.75

HE-FEL500-1000 eV
Modulator
122 / 2.20
92 / 2.01
70 / 2.1
50 / 2x2.65
28.5 / 5x3.65
60.98

Radiator
92 / 3.86
70 / 3x3.80
50 / 3x 3.1
28.5 / 2x 3.28

beam pipe can be used and more magnetic material can belocated close to the electron beam. Side access to themagnetic structure is needed only for Hall probe
measurements and for the chamber support. A minimum
magnetic gap at the side of only 5.4mm can be realized
still providing the space for a 10.4mm diameter tube. The
magnetic field can be further enhanced by tilting themagnetization direction to 45 degrees. The reverse fields
in an APPLE III structure require a more stable material
compared to an APPLE II undulator and as a consequence
the remanence of the material is about 6% lower.
Nevertheless, the effective magnetic field is a factor of
1.4 higher than for an APPLE II with a gap of 10.4mm.

MAGNETIC DESIGN
The modulators and the first radiators will be purepermanent magnet structures. The last radiator and thefinal amplifier are of the APPLE III type (see figure 1)[2]. An APPLE III provides the same flexibility
concerning the polarization control as an APPLE II but
the maximum field is larger at the expense of a reduced
access from the side. In a linac driven FEL a circular____________________________________________#

bahrdt@bessy.de

THPOS03

Figure 1: Magnetic structure of an APPLE III (left)
compared to an APPLE II design (right).

Available online at http://www.JACoW.org

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The magnetic field of an APPLE III undulator can beparametrized with:

B(T ) = a ⋅ exp(b ⋅ ( gap / λ0 ) + c ⋅ ( gap / λ0 ) 2 )useing the parameters of table 2.
The parameters of table 2 have been evaluated with the
3D-code RADIA [3] for remanence = 1.13T and 1.19T(longitudinally and 45° magnetized blocks), block
dimensions = 40x40mm2, minimum vertical distance =5.4mm, free aperture = 10.4mm. The parameters are valid
for period lengths of 20mm ≤ λ0 ≤ 50mm.
Table 2: Field parameters of the APPLE III design
hor. lin.
vert. lin.
circular lin. 45°
A
2.481
2.035
2.209
1.569
B
-6.258-6.576-6.400-6.392
C
0.112
0.602
0.285
0.231

r r r

∞ ∞ r
r
1
e ik ( r −r ')E ( x' , y ' ) = ∫ ∫ E ( x, y ) r r cos( β ) ⋅ dx ⋅ dy
λ − ∞− ∞| r − r '|2: Application of Fourier optic methods.
A FFT yields the angle distribution of the FEL output∞ ∞ rr− 2πi (ν x x +ν y y )E0 (ν x ,ν y ) = ∫ ∫ E ( x, y ) ⋅ edx ⋅ dy− ∞ −∞

This distribution is multiplied by a factor which
represents a longitudinal drift of ∆z.

rr
2πi⋅∆z⋅ 1 / λ2 −ν x2 −ν 2y
E (ν x ,ν y ) = E0 (ν x ,ν y ) ⋅ e

An inverse FFT provides the spatial distribution at
z=z0+∆z.
∞ ∞ rr
2πi⋅(ν x x +ν y y )E ( x ' , y ' ) = ∫ ∫ E (ν x ,ν y ) ⋅ e⋅ dν x ⋅ dν y
− ∞− ∞

0.8
vertical field

0.6
0.4
horizontal field

0.2
0

APPLE III
APPLE II

-0.2
-20

-15

-10

-5

0

5

10

15

20

x / mmFigure 2: Comparison of the transverse field profiles of
the APPLE II and the APPLE III design evaluated for the
HE-FEL.

10
9

LE-FEL8

124 eV
L=L0-20λ0

7
6

L=L0-40λ0

5
L=L0-60λ04

L=L0-81λ0

3Three dimensional FEL codes provide information
about the electric field distribution at the end of the final
amplifier, z=z0. This point is not the location of thephoton beam waist. The beamline designer needs to know
the exact location and the size of the photon beam waist
in order to maximize the brightness at the sample. This
information can be derived from the results of alongitudinal propagation of the electric field distribution.
There are two ways to proceed:
1: Integration of the diffraction equation of Fresnel andKirchhoff:.

2
1slice 1

SOURCE CHARACTERIZATION

L=L0

0
0.04

0.05

0.06

slice 5

HE-FEL1

slice 3

1.2

The second method is much faster in cases where thetransverse dimension of the photon beam size does notchange too much within ∆z. The following results arederived with this method.
To study the development of the radiation properties
within the final amplifier time dependent GENESIS
simulations [4] have been performed for various lengths Lof the LE-FEL final amplifier of L=L0-81λ0, L0-60λ0, L040λ0, L0-20λ0 and L0, where L0 is the length of the final
amplifier given in table 1.The power distributions areplotted in figure 3. The corresponding electric fields havebeen propagated by amounts of ∆z with -30m ≤ ∆z ≤+20m and the intensities have been projected onto thehorizontal and the vertical plane. The first and second
moments of these projections have been evaluated and theresults for slice 4 are plotted in figure 4. Similar numbers
have been obtained for slices 2,3 and 5.
power / GWatt

field / Tesla

The horizontal roll off of the vertical field component islarger for an APPLE III than for an APPLE II whereas theroll off of the horizontal field component is smaller(figure 2). For the HE-FEL a relative alignment accuracyof the undulator modules of ±20µm is required. The
undulator segments will be mounted onto remotecontrolled transversely movable stages in order to meetthis tight tolerance. The indication for a correct alignment
will be the FEL output.

0.07

0.08

0.09

time / ps

Figure 3: GENESIS simulations for different lengths Lof the final amplifier. The electric fields of five slices(black circles) have been propagated.
The photon beam waist is located several meters
upstream from the FEL end and this distance increases
with L. As a consequence the brightness at the sample canbe increased by a factor of two if the waist is focussed
instead of the FEL end.

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0.15
0.14

σx

L=L0

σy

0.13

design. The question has to be answered whether thelocation of the waist moves with photon energy which
would imply the necessity of a variably focussing
beamline optic. Further studies for more photon energies
and also for the ME-FEL and the HE-FEL are in progress.
σx/y / mm

σx/y / mm

The photon beam size increases with the length of the
final amplifier (figure 4). This might be partly due to theincreasing electron beam size which varies between 115
and 127µm horizontally and between 105 to 130µm
vertically for L0-81λ0 ≤ L ≤ L0.

0.11

0.11

σy

0.1
0.09

L=L0-81λ0

0.08

0.08

0.07
-30

0.07
-30

-20

-10

0

10

20

∆z / mhor. projection
vert. projection
L=L0

L=L0-81λ0

-20

-10

0

10

20

∆z / mFigure 4: Photon beam size (top) and maxima of the
projected intensity (bottom) versus longitudinal distanceto the final amplifier end. The data of slice 4 are plotted.

σσp / 10 m

The photon beam divergence decreases with L and thephase space product σσ’ is nearly independent of L forslice 4 (figure 5) and also for slices 2, 3 and 5. For adiffraction limited beam we expect a product of σσ’ =λ/4π = 0.8nm (124eV). Based on the GENESIS
simulations we obtain for each of the slices 2, 3, 4 and 5 a
product of about 1.25nm which is close to the theoreticallimit.
2.25
2slice 11.75
1.5

slice 4

1.25
1
0.75

diffraction limit for 124eV

0.5
0.25
0
-90

-80

-70

-60

-50

-40

-30

-20

-10

0

10

∆L / λ0

Figure 5: Phase space volume of the LE_FEL radiationfor various lengths of the final amplifier.
For L= L0-81λ0 slice 1 is far below saturation. The
waist is located close to the FEL end and moves further
upstream for increasing L (figure 6). The phase space
product of slice 1 is a factor of 2.5 above the diffraction
limit for L= L0-81λ0 and approaches the value of the slices
2-5 for increasing L (figure 5).
The specific case of the LE-FEL at 124eV indicatesthat the location of the waist moves upstream relative to
the FEL end when the FEL goes into saturation. A
distance of 10m between the FEL end and the waist issignificant and has to be regarded in a monochromator

maximum intensity / a.u.

1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
-30

-9

σx

L=L0

0.13
0.12

0.09

maximum intensity / a.u.

0.14

0.12
0.1

THPOS030.15

L=L0-81λ0

-20

-10

0

10

0.3
0.25

20

∆z / mhor. projection
vert. projection
L=L0

0.2
0.15
0.1
0.05
0
-30

L=L0-81λ0

-20

-10

0

10

20

∆z / mFigure 6: Photon beam size (top) and maxima of the
projected intensity (bottom) versus longitudinal distanceto the final amplifier end. The data of slice 1 are plotted.

FIELD OPTIMIZATION
The field tuning for the planar modulators and theradiators of the first stages is straight forward [5].
Shimming of the last radiator and the final amplifier ismore complicated due to several reasons: i) Iron shims
can not be used as usual because the signature changes
with magnet row shift. ii) the shims do not stick bymagnetic forces. iii) The shims can not be applied directly
above or below the electron beam because the magnet
rows are separated by a slit of 1mm. iv) The field
integrals depend on the shift of the magnet rows which isdue to the non unity of the magnetic permeability.
Magnet sorting techniques based on detailed field dataof individual magnets are essential for these devices toreduce the work on shimming after assembly. At BESSY
a precise set-up for the characterization of magnet blockinhomogeneities has been developed [6]. Using theinhomogeneity data together with the Helmholtz coil data
in a simulated annealing code the best magnet
configuration is evaluated. It has been demonstrated at
BESSY that even for devices consisting of more than
1000 individual blocks the field integrals can be predictedwith an accuracy of ± 1.5Gm [6]. The prediction is based
only on single block data and no further fieldmeasurement and resorting has been performed during
magnet assembly. The remaining field errors can beremoved in three steps:
1: Trajectory and phase errors are minimized withtransverse block movements (virtual shimming).
2: The endpoles can be designed such that the field
integral variation with gap is small [1] [7]. The remaining

613

shift dependent terms are minimized with iron shims
which are glued onto the magnets.
3: Shift independent field integrals are removed withpermanent magnet arrays at both ends of the device.
These techniques have been applied to several APPLE
II undulators at BESSY and they are documented in detailin [6].

SUPPORT AND DRIVE SYSTEM
The support structure (cast iron) consists of a baseframe carrying two C-frames. The magnetic structures
will have a length of up to 4m. The magnet girders will bemade from aluminum. The deflection is minimized withfour supports (instead of two) using two cross bars. This
design has already been implemented successfully at
BESSY.
Four longitudinal drive systems give the flexibility tomove each row individually. This provides fullpolarization control for the user. Parallel motion of two
rows changes the polarization from horizontal linear tocircular and to vertical linear. Anti-parallel motion tilts thelinear polarization vector continuously from 0° to 90°.
Sometimes, the orientation of the sample is not wellknown. In these cases it is useful to rotate the polarization
vector by more than 90°. With 4 motors a rotation of 180°
is possible.

Figure 7: The new gap measurement system as
implemented at the BESSY UE49 undulator.
Two servo motors provide the gap tunability. The gapsof the individual undulator sections have to be adjustedwith a relative accuracy better than 3µm. This tighttolerance can not be achieved with measurement systems
used so far. Rotary encoders suffer from backlash of
gearboxes and linear encoders coupled to the upper andthe lower I-beam do not follow Abbe’s comparator
principle. We have developed a new measurement system
where the linear encoder is located directly above theelectron beam thus following Abbe’s comparator
principle. The system recently installed at the BESSY
APPLE II undulator UE49 (figure 7) demonstrated a gap
reproducibility of ±1µm independent of the gap history(figure 8).

reduced gap / µm

j.b. Bahrdt et al. / Proceedings of the 2004 FEL Conference, 610-613

54

53

52

51

50

0.62

0.64

0.66

0.68

0.7

0.72

0.74

field / Tesla

Figure 8: Measured gaps versus magnetic field forseveral cycles of gap opening and closing. A 4th orderpolynomial has been subtracted from the raw data to show
the residual error.

REFERENCES[1] The BESSY Soft-X-Ray Free Electron Laser,
Technical Design Report, Berlin, Germany, March,
2004.
[2] J. Bahrdt, W. Frentrup, A. Gaupp, B. Kuske, A.
Meseck, M. Scheer, “Undulators for the BESSY
SASE-FEL Project”, 8th International Conference on
Synchrotron
Radiation
Instrumentation,
San
Francisco, Cal., 2003, AIP 0-7354-0180-2/04, p215.
[3] P. Elleaume, O. Chubar, J. Chavanne, ''Computing
3D magnetic fields from insertion devices'', Proc. of
the 1997 PAC, Vancouver, Canada (1997) 35093511. O. Chubar, P. Elleaume, J. Chavanne, ''A threedimensional magnetostatics computer code for
insertion devices'', J. Synchr. Rad. 5 (1998) 481-484.
[4] A. Meseck, B. Kuske, these proceedings[5] D.C. Quimby, S.C. Gottschalk, F.E. James, K.E.
Robinson, J.M. Slater, A.S. Valla, ''Development of a
10-meter wedged-pole undulator'', Nucl. Instr. andMeth., A285 (1989) 281-289. S.C. Gottschalk, D.C.
Quimby, K.E. Robinson, J.M. Slater, ''Wiggler error
reduction through shim tuning'', Nucl. Instr. andMeth., A296 (1990) 579-587. B. Diviacco, R.P.
Walker, ''Recent advances in undulator performance
optimization'', Nucl. Instr. and Meth., A368 (1996)
522-532. J. Chavanne, P. Elleaume, ''Undulator andwiggler shimming'', Synchr. Rad. News, Vol.8 No.1
(1995) 18-22.
[6] J. Bahrdt, W. Frentrup, A. Gaupp, M. Scheer,“Magnetic field optimization of permanent magnet
undulators for arbitrary polarization”, Nucl. Instr. andMeth. A, 516 (2004) 575-585.
[7] J. Chavanne, P. Elleaume, P. Van Vaerenbergh, ''End
field structures for linear/helical insertion devices'',Proc. of the PAC, New York, NY, USA (1999) 26652667.

New Concepts

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D. Li et al. / Proceedings of the 2004 FEL Conference, 614-617

PROPOSAL OF LASER-DRIVEN ACCELERATION WITH BESSEL BEAM
D. Li*, K. Imasaki, Institute for Laser Technology, 2-6 yamada-oka, suita, Osaka 565-0871,Japan
Abstract
A novel approach of laser-driven acceleration with
Bessel beam is presented in this paper. Bessel beam, incontrast to the Gaussian beam, demonstrates “diffractionfree” characteristics in its propagation, which implies
potential in laser-driven acceleration. A configuration ofBessel beam truncated by a set of annular slits makes
several special regions in its travelling path, where thelaser field becomes very weak and the accelerated
particles are possible to receive slight deceleration as they
undergo decelerating phase. Thus, multistage accelerationis realizable. With the help of numerical computation, we
have shown the potential of multistage acceleration basedon a three-stage model.

INTRODUCTION
The intense laser field provides an ultrastrong field
gradient implying an attractive potential in particles
acceleration. Laser-driven accelerator, an active current
research area, has received considerable attention inrecent years [1-7]. Many proposals, such as inverse freeelectron laser [8], plasma-wave accelerator [9],ponderomotive schemes [10], inverse Cherenkov
acceleration [11], and vacuum acceleration directly by thelongitudinal component of electric field [12,13] were
presented and extensively studied.
In general, laser beam from a laser cavity travels in theform of Gaussian mode, exhibiting manifest transverse
spreading when it is focused down to small spot size. A
strongly focused Gaussian beam will show apparent
divergence after it passes a short certain distance, known
as Rayleigh length. Thus, even there exist schemes tokeep synchronization between accelerated particles andthe wave, the effective acceleration can only occur withina relative short range. In order to extend the interaction,“diffraction-free” Bessel beams are introduced to the laser
driven accelerator [12,13].
Since Durnin experimentally demonstrated thenondiffracting property of Bessel beam, it has been
widely studied in various applications [14-16]. Hafizi et.al
analysed the vacuum beat wave accelerator with using
laser Bessel beam [17], and other Bessel beam driven
acceleration schemes were also discussed recently.
This paper is aimed at an innovative approach invacuum laser-driven acceleration with using Bessel beam.
We truncate the Bessel beam by a set of annular slits(hereafter, we call it slits-truncated Bessel beam), so thatseveral special regions are formed in its propagation,
where the laser field becomes rather weak, and___________________________________________*

lidazhi@ile.osaka-u.ac.jp

THPOS13consequently, the accelerated particles, which slide
behind the wave, are possible to receive slightdeceleration as they undergo the decelerating phase of the
wave field by just travelling in these regions. Because of
the “diffraction-free” characteristic of Bessel beam,
multistage acceleration comes to be feasible.

BESSEL BEAM
General Theory
A solution of the Helmholtz wave equation for anazimuthally symmetric wave of frequency ω that
propagates in the positive z direction gives the Bessel
beam expressionv
ψ ( r , t ) = J 0 ( k sin( α ) ρ ) e i ( k cos( α ) z − ω t )(1)
An ideal Bessel beam maintains the same radial profile
over arbitrary propagation distance and has maximum
amplitude on-axis and hence is called “diffraction-free”.
The following integral representation of Bessel function is
helpful to comprehend the angle α,

J 0 ( k sin( α ) ρ ) e i ( k cos( α ) z − ω t )1 2π
d φ e i ( k sin α x cos φ + k sin α y sin φ + k cos α z − ω t )2 π ∫0(2)which exhibits that Bessel beam is superposition of an
infinite set of ordinary plane waves making angle α withrespect to the z axis [18]. And this is also the principle togenerate Bessel beam, i.e., superpose plane waves withequal amplitude and a common phase that make angle α
to the z axis.
A simple geometrical relation tells that, if the Bessel
beam is formed at z=0 plane and to propagate a distance z,
extent of R=z tanα at z=0. That means an ideal Bessel
beam needs arbitrarily large initial radial extent andarbitrarily large energy, to retain its “diffraction-free”
character over an arbitrarily large distance, which is
impossible to realize in practice. The physically meaning
beam is an aperture-truncated one, which possesses nearly
diffraction-free properties within some axial distance. The
generation of aperture-truncated Bessel beam was widely
studied elsewhere [14,15].
The phase velocity of a Bessel beam relies on the angle
α,i.e., vp= c/cos(α), which is larger than the light speedc. If such a beam is used for direct laser-driven
acceleration in vacuum, the particle will slide behind thewave and cannot gain net energy during a wave period.
Naturally, we conceive a scheme that after the particle isaccelerated in the first half circle of the wave period, thelaser field suddenly disappears to allow the particle avoid
the following deceleration; and when the particle slides=

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D. Li et al. / Proceedings of the 2004 FEL Conference, 614-617

into the next accelerating phase, the laser field takes on
again. In other words, we have to make “laser-on” and“laser-off” regions alternatively appearing during laser
propagation and well arrange the intervals among them torealize required phase matching.

Annular Slits-truncated Bessel Beamwhere R1=w1, R2=R1+d1, R3=R2+w2, R4=R3+d2, R5=R4+w3.
Together with the initial conditions, Eq. 3 can be
numerically calculated to understand the propagation
properties. As an example, here we consider the on-axis
case (r=0) and employ the following parameters: laser
wavelength λ =1 μ m, α =1o, and w1 =4 mm, w2 =4

A Bessel beam truncated by a set of annular slits can do
the work, as schematically shown in Fig. 1, where laser

Fig. 1 schematic configuration of annular slitstruncated Bessel beam
field disappears at those shadow regions. The lengths of“laser-on” and “laser-off” regions are related to the slits’
parameters, width wi (i=1,2,3) and the interval between
two slits di (i=1,2). Using the geometrical method we caneasily work out those lengths. Actually, the “laser-off”
areas are not entirely free of laser field because of thediffraction effect induced by annular slits. To precisely
analysis Bessel beam diffraction, we employ scalar
diffraction theory.
In the Fresnel approximation the amplitude A(r, z) at a
distance z can be obtained from diffraction integral. For acircularly symmetric incident amplitude A( ρ , 0), we
have [19]A ( r , z ) = exp( ikz +ikr 2 k
)( )
iz
2z

a

kρr

0

z

× ∫ ρ A ( ρ ,0 ) J 0 () exp(

ik ρ 2)dρ
2z(3)where a is the radius of a circular aperture. For the case ofBessel beam, we have A( ρ ,0)=J0 (ksin( α ) ρ ) as theinitial amplitude distribution. If the beam is truncated by aset of annular slits, e.g., for the case as shown in Fig. 1,
the incident amplitude should be modified as
A ( ρ , 0 ) = ζ ( ρ ) J 0 ( k sin αρ )(4)and ζ ( ρ ) is given by

1
0

1
ζ (ρ ) = 
0
1

0

(0 ≤ ρ < R1 )( R1 ≤ ρ < R2 )( R2 ≤ ρ < R3 )( R3 ≤ ρ < R4 )( R4 ≤ ρ < R5 )( R5 ≤ ρ < ∞)Fig. 2 Propagation of aperture-truncated (bluecurve) and slits-truncated (grey curve) Bessel beamshown from z=16 cm. Synthesized function χ(z)(red curve) gives out the approximation to the grey
curve
mm, w3 =6 mm, d1 =2 mm, d 2 =4 mm. The computation
results for slits-truncated Bessel beam are illustrated inFig. 2, and for the sake of comparison, aperture-truncatedBessel beam (with circular aperture radius of a=20 mm,
summation of wi and di ) is also presented. The blue andgrey curves represent aperture- and slits-truncated beams,
respectively. It is seen that, their amplitudes characterizeoscillation and decay at a finite distance ~a/tan( α ).
Contrast to the aperture-truncated beam, the slitstruncated one exhibits two special zones where theamplitude falls down by two orders in magnitude. With
properly setting the parameters of annular slits, theinjected electrons are possible to spend the deceleratingphase in those regions and receive slight deceleration. The
red curve is synthesized to approximate the grey curvewith showing an average effect, in ignorance of theoscillation. It takes the below form, with the use of
exponential functions to fit the falling and rising edges,χ ( z ) = [H ( z − 0 ) − H ( z − 21 .6 ) ]+ [H ( z − 21 .6 ) − H ( z − 28 .3) ]exp( − 0 .056 × ( z − 21 .6 ))+ [H ( z − 28 .3) − H ( z − 36 .5 ) ]exp( 0 .056 × ( z − 36 . 5 ))+ [H ( z − 36 .5 ) − H ( z − 54 . 8 ) ]+ [H ( z − 54 . 8 ) − Η ( z − 69 . 2 ) ]exp( − 0 . 032 × ( z − 54 . 8 ))+ [H ( z − 69 .2 ) − H ( z − 83 . 4 ) ]exp( 0 .032 × ( z − 83 . 4 ))+ [H ( z − 83 . 4 ) − H ( z − 111 .2 ) ]+ [H ( z − 111 . 2 ) ]exp( − 0 . 02 × ( z − 111 . 2 )) ,(5)

where H is the Heaviside function.

New Concepts

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D. Li et al. / Proceedings of the 2004 FEL Conference, 614-617

Laser Field
All field components satisfying Maxwell’s equation are
derived in reference [18] for ideal Bessel beam. For theconvenience, we made a summary as below,
Eρ = E0 cot(α ) J1 (k ρ ρ ) cos(η )acceleration scheme is shown in Fig. 3. From Fig. 3 (a)we know that the electron is accelerated from 150 MeV tomore than 1 GeV just over ~90 cm distance. The

E z = − E0 J 0 (k ρ ρ ) sin(η )E0
J1 (k ρ ρ ) cos(η )c sin(α )where E0 is the peak amplitude, andk ρ = k sin(α ) k z = k cos(α ) η = k z z − ωt . The otherBϕ =components are zero. In our proposal, we directly apply
the longitudinal electric field Ez to accelerating theparticles.

DYNAMICS
We first consider accelerating a single electron in theslits-truncated Bessel beam field. The motion of theelectron in an electromagnetic field is governed by
Lorentz equationv v vv
dp dt = −e E + v × B
(6)

(

)

v
v
v
where p = γm0 v represents the momentum, v is theelectron velocity, and γis the Lorentz factor. At first, let
us see the case of on-axis acceleration. According to theabove field expressions, only the longitudinal electricfield exists at ρ=0, while the others are cancelled out .
For a slits-truncated Bessel beam, the longitudinal field
could be rewritten as
E z = E0 A(0, z ) sin(η )(7)where A(0, z) is the combination of Eqs. (3) and (4).
However, the numerical calculation of A(0, z) was provento be terrible time-consuming, leading to inconveniencein processing phase-matching optimization. In order tosimplify computation, we take a function ε(z), which isin the form of χ(z), to substitute A(0, z), and we thereforehave
E z ≅ E0ε ( z ) sin(η )(8)This approximation will not damage the essential of thisacceleration approach, but only affects the details in
determining slits’ parameters. The concrete form ofε(z)concerning a given initial energy of an electron will be
optimized and figured out as one of simulation results.
Apparently, the present approach inclines toaccelerating the relativistic electrons. The static or slow
electrons cannot make effective interaction with theaccelerating field holding a phase velocity larger than thelight speed. As an example, we assume an electron withinitial energy of 150 MeV, only having axial velocity, is
injected together with the laser Bessel beam by anappropriate phase at z=0. The angle α is supposed to be
0.2 degree, in order to get lower phase velocity. We
choose the peak amplitude of field E0=1010 V/m, resulting
in that ~100 TW power should be contained in the central
lobe of Bessel beam. After carefully optimizing thelengths of “laser-on” and “laser-off” regions, a three-stage

THPOS13

Fig. 3 Three-stage acceleration mechanism. (a)total energy of the accelerated electron shown as afunction of distance, (b) corresponding ε (z)functioncorrespondingε(z) function is given by Fig.3 (b), fromwhich the slits parameters could be roughly deduced.
The radiation damping effect is not involved in above
computation. Making use of the Larmor’s formulav
P = (2re 3m0c )(dp dτ )2 − 1 c 2 (dε dτ )2the instantaneous radiated power from an accelerated
electron is calculable. Here re is the classical radius of
the electron, dτ=dt/γ, ε indicates the electron energy.
For the case of Fig. 3, the total radiated energy is ~0.042
eV, which means the radiation influence is unimportantby the parameters treated in this paper.
Actually, by such an approach, acceleration with morestages is possible to reach ． The maximum number ofacceleration stages relies on the laser pulse length, therealizable Bessel beam propagation distance, and thetechnology on manufacturing annular slits.

[

( )

]

OFF-AXIS INJECTION
Only a small fraction of the electrons in a bunch oftransverse dimensions of a few microns will be interact
with laser field with precisely zero initial transverse
coordinates. The rest will enter the interaction region with

D. Li et al. / Proceedings of the 2004 FEL Conference, 614-617

transverse distance from the axis. The field components
Eρ and Bφ lead to radial force, which probably inducestransverse spreading of electron bunch during
acceleration. To understand this effect, we conductedcomputation for off-axis injection.
We consider injecting 11 electrons with different initialradial positions: the first one is on-axis, while the others
are uniformly distributed along radial direction with aninterval of 1μm. These electrons are orderly numbered
0,1,2…10, and they have the same initial energy of 150
MeV, only with the longitudinal velocity, while the initialtransverse velocity components are set to zero. The ε(z)function shown in Fig. 3 (b) is adopted in this calculation,i.e., the on-axis electron is chosen for reference. The laserparameters are the same as used above.
After numerically solving the motion equation with full617

final 60 μ m. The outer electrons receive slighter
acceleration than the inner ones, which is due to thetransverse distribution of the longitudinal electric field,
described by the zero-order Bessel function.

CONCLUSION
We proposed a novel method for laser-driven
acceleration. Annular slits-truncated Bessel beam forms
some special regions, where the accelerated particles areallowed to “avoid” deceleration when they slide in the
decelerating phase of wave. We analysed the propagation
properties of annular slits-truncated Bessel laser beam anddemonstrated the acceleration mechanism by numericallysolving the motion equation. The results show thismethodconsiderable
potentialinlaser-driven
acceleration.

REFERENCES[1]

Fig. 4 Acceleration of off –axis injection electrons.
(a) energy evolution, and (b) electrons’
trajectories.
fields, we got the results as shown in Fig. 4. Note that the
final energies of off-axis injecting electrons are lower
than that of on-axis injecting one, and this therefore raises
energy spread. For the case of Fig. 4a, the maximum
energy deviation is ~92 MeV. Electron trajectories are
depicted in Fig. 4b, which illustrates that the radius ofelectron bunch spreads from the original 10 μm to the

A.Ting, C.I.Moore, K.Krushelnick, C.Manka, et.al,
Phys. Plasmas 4 (1997) 1889
[2] P.Sprangle, E.Esarey, J.Krall, Phys. Plasmas 3(1996) 2183
[3] Y.Liu, D.Cline, P.He, Nucl. Instrum. Methods Phys.
Res. A424 (1996) 296[4] J.A.Edighoffer, R.H.Pantell, J. Appl. Phys. 50(1979) 6120
[5] T.B.Zhang, T.C.Marshall, M.L.Lapointe, et.al,
Phys. Rev. E 54 (1996) 1918
[6] R.B.Palmer, J. Appl. Phys. 43 (1972) 3014
[7] R.H.Pantell, T.I.Smith, Appl. Phys. Lett. 40 (1982)
753[8] C.Pellegrini, P.Sprangle, W.Zacowicz, proceedingsof the 13th conference on particle acceleration,(1983) 473[9] T.Katsouleas, J.Dawson, Phys. Rev. Lett. 51 (1983)
392[10] L.Cicchitelli, H.Hora, R.postle, Phys. Rev. A 41
(1990) 3727
[11] G.Fontana, R.Pantell, J. Appl. Phys. 54 (1983) 4285
[12] Marlan O.Scully, M.S.Zubairy, Phys. Rev. A 44
(1991) 2656
[13] B.Hafizi, E.Esarey, P.Sprangle, Phys. Rev. E 55
(1997) 3539
[14] J.Durnin, J.J.Miceli, and J.H.Eberly, Phys. Rev. Lett.
58, (1987) 1499
[15] L.C. Laycock and S.C.Webster, GEC J. Res. 10(1992) 36[16] D.Li, K.Imasaki, M.Aoki, J. Nucl. Sci. Tech. 32(2003) 211[17] B.Hafizi, A.K.Ganguly, A.Ting, Phys. Rev. E 60
(1999) 4779
[18] http://arxiv.org/abs/physics/0006046[19] Zhiping Jiang, Qisheng Lu, and Zejin Liu, Appl.
Opt. 34 (1995) 7183

New Concepts

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M.R. Asakawa et al. / Proceedings of the 2004 FEL Conference, 618-621

AMPLIFICATION OF SHORT-PULSE RADIATION FROM THE
ELECTRON UNDERGOING HALF-CYCLOTRON ROTATION*
M. R. Asakawa, H. Marusaki, Y. Tsunawaki(a), N. Ohigashi(b) and K. Imasaki(c)Institute of Free Electron Laser Osaka university, Tsudayamte 2-9-5, Hirakata,
Osaka 573-0128, Japan(a) Osaka Sangyo University, Nakadaito, Daito, Osaka 574-8530, Japan(b) Department of Physics, Kansai University, Osaka 564-8680, Japan(c) Institute of Laser Technology, Yamadaoka, Suita, Osaka 565-0871, Japan

A novel light source which can generate an half-cycle
radiation pulse is being developing at Institute of Free
Electron Laser, Osaka university.

INTRODUCTION
The number of the optical cycles contained in aradiation pulse is simply determined by the number of theelectron wigglings or rotations during which the electron
emits the radiation pulse. Electrons passing through abending magnet emit a radiation pulse whose phasevariation is less than unity.
The bending magnet
radiation, thus, can be used as a broadband continuousspectrum light source. When such radiation is confined in
the optical cavity, the radiation should be amplified via
the interaction with the electrons periodically injected by
the accelerator. In the bending magnet, however, theinteraction length is usually short and the gain, then,should be small. Based on this idea, we are developing ahalf-cycle light source using the electrons which undergo
an half-cycle cyclotron motion in a solenoid field. As
described in the following, the pulse length isapproximately equal to that of the electron beam. Thus
this light source can produce broadband continuousspectrum radiation in the THz wave range, because theaccelerator produces the electron beam with a pulsewidthof a few picoseconds.

THEORETICAL CONSIDERATIONSThe electric field produced by the electron passing
through the solenoid field is calculated from the LiénardWiechert potential and given byq  R ( t ′)E ( x, t ) =( n ( t ′) -β ( t′) ) 1-β ( t′)24πε 0  s ( t ′ )3
(1),

(

+

R ( t ′))n ( t ′ ) × ( n ( t ′ ) -β ( t ′ ) ) ×β& ( t ′ ) 3
cs ( t ′ )

2

(

)

where q is the charge of the particle, c the light velocity,

ε0 the vacuum dielectric constant, β& is the normalized
acceleration vector, R (R) is the vector (distance) from the

THPOS16

particle to the observation point, n is a unit vector in the
direction of R, and s is defined as,
R ( t ′ ) ⋅υ ( t ′ )(2).
s (t′) = R (t ′) −c
Quantities on right-hand-side in equation (3) are to beevaluated at the retarded time,t′ = t −R ( t ′)c

(3).

The magnetic field is, then, given by1
B ( x, t ) = n ( t ′ ) × E ( x, t )c(4),

and then the magnitude of the Poynting vector is given by(5).
S ( x, t ) = ε 0 E 2
The calculations are made for a 150MeV electron beamwith pulse length of 3ps passing through the 3m-longsolenoid magnetic field of 0.7T and the radiation field isshown in figure 1. A uniform electron distribution in a
block, 4×4×0.9 mm3, is assumed. The bunch length of
0.9 mm corresponds to the pulsewidth of 3 ps. The
electrons are located at x0=[-2 mm, 2mm] and y0=[-2 mmrL, 2 mm-rL], so that the centres of the circular electron
motion lay in xc0=yc0=[-2 mm, 2mm] with the angle ofθ0x>0. Here rL is the Larmor radius. The initial angle andrL are 3 mrad and 2.6 mm in figure 1, respectively. The
coordinates of the observation points, (xob, yob, zob), is (0,0, 5 m), i.e., the centre of the resonator mirror whichreflects back the spontaneous emission. The resonant
wavelength is to be 65 µm, and corresponding optical
period is 217 fs. During passing through the 3 m-longsolenoid field, the electron with γ=300 executes a halfcirculation (166 degree in phase).
400

E (kV/m)

Abstract

Ey

200

0

-200

Ex

-400
0

1

3

2

4

5

t (ps)

Figure 1. The radiation field at the centre of the resonatormirror produced by a 150MeV electron beam which
undergoes a half cyclotron rotation in a 3m-long solenoid
field.

Available online at http://www.JACoW.org

M.R. Asakawa et al. / Proceedings of the 2004 FEL Conference, 618-621

619(0.15 cm, 0.2 cm) and falls to 10 % of the peak at a
distance of 1.6 cm from the origin, i.e., the axis of thecyclotron motion and the resonator. The radiation should
be confined in a radius of 2 cm on the mirror. The
contours tend to be displaced from the axis toward first
quadrant in the graph. This is because the electrons
undergo the half-circulation mainly in the region x>0, andrise from fourth quadrant to first quadrant as they are
passing through the solenoid field. This tendency
becomes more remarkable as larger the initial electron
angle is.
Note that the product of the electron velocity and theelectric field, υ ⊥ ⋅ E ⊥ , is positive in the most of the part,

Figure 2 The energy flux distribution and the polarizationof the radiation field.
The z-component of the field, Ez, is negligibly small
comparing to Ex, Ey. As expected, the phases of the fields,
Ex and Ey, do not vary by 2π: the field remains almost
constant during its pulsewidth. It depends on theobservation point that if the field starts from negative or
positive value.
The distribution of the energy flux of radiation,∫ dt ′ S ( x, t ′) , are shown in figure 2 for the same

condition used in figure 1. Typical electron trajectories,
for the centre and edge of the electron beam, are projectedon the figure as the arcs. The energy flux has a peak at

especially in the region where the radiation field is intense.
Thus it is possible to amplify the radiation via thesuccessive interaction with the electron beam if theradiation can be confined in the resonator.
Figure 3 shows the distribution of energy flux for the
initial angle of 1, 3, 5 and 10 mrad at zob=5 and 10 m.
The electron trajectories are set so that the guiding centreof the electron beam may be located at the centre of theresonator axis in all cases. All the distributions arenormalized by their peaks. The variation of the peakintensity is shown in figure 4.
It is clear that the increase in the initial angle enlarges
the cross-section of the radiation field. The position of
the peak flux also deviates remarkably with the large
initial angle. In detail, the position of the peak is almost
the same in the cases of 1mrad and 3 mrad injection,
while it deviates at larger initial angles. That is, theradiation propagates unparallel to the axis of the opticalcavity when initial angle is large.

Figure 3 Dependence of the field distribution on the initial angle. (a)-(d) and (e)-(h) show the distribution at
the zob=5 and 10m, respectively. The initial angle is 1mrad for (a) and (b), 3mrad for (b) and (f), 5mrad for(c) and (g), 10 mrad for (d) and (h). All distributions are normalized by their peak.

New Concepts

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M.R. Asakawa et al. / Proceedings of the 2004 FEL Conference, 618-621

Electron gun

7peak energy density (a.u.)

6

Accelerating tube 1

5

4

3

mid-infrared

2

FEL

Accelerating tube 3

1

0

0

2

4

6

8

10

angle (mrad)

Figure 4. Dependence of the peak flux on the initial
angle.
As shown in figure 4, the peak intensity rapidly increases
when the initial angle is increased and then slowly
decreases above 3mrad. Total energy of the radiation
increases monotonically with the angle, because the crosssection increases with the angle, though the angle should
be chosen around 3mrad to store the radiation in thecavity.
The divergence angle in the case of 3 mrad initial angle
is evaluated to be 4-5 mrad. The radiation field, therefore,
can be stored in the optical resonator. Because theradiation field has negative or positive value as shown infigure 1, it can be expected that the field can be added up
coherently at each round trips analogously to FEL fed by
the coherent synchrotron radiation emitted by electron
bunches.[1]Then this radiation source will produce
broadband far-infrared radiation. The additional growth
process via the interaction between the electron and theradiation, υ ⊥ ⋅ E ⊥ , is now being studied.

EXPERIMENTThe experiments are underway on the 150 MeV beamline, which was used for the demonstration of ultraviolet
free-electron laser. A S-band rf-linac produces theelectron bunch of 0.25 nC /3 ps at a repetition rate of 22.3
MHz (1/128 of S-band frequency) for 25 µs. Thus themacropulse contains 550 electron bunches. The UV
undulator was replaced with 3 m-long solenoid coilwound around a drift tube with an inner radius of 8.5 mm.
This solenoid is located between two pairs of bending
magnets used to detour the electron beam around thecavity mirrors. The coil is fed by a capacitor bank (0.1 F/
500 V) and generates a magnetic field of 1.0 T with acurrent of 1.5 kA. The discharge time constant is 30 ms
so that the change in the solenoid field is negligibly small(less than 0.2 %) during the macropulse duration of 25 µs.

THPOS16

Accelerating tube 2

far-infrared

Accelerating tube 4

FEL
Accelerating tube 5near-infrared
FEL

Accelerating tube 6
Accelerating tube 7

THz cyclotron
radiator

Figure 5. Accelerator system at iFEL andcyclotron radiator.
The incident angle of the bunch is controlled by a setof 'kicker coils' installed at the entrance of the solenoid.
The effect of the beam emittance (10 πmm⋅mrad innormalized emittance) on the beam trajectory is also
negligibly small, because the incident angle ranges from
1-5 mrad in the experiment. The optical resonatorconsists of a pair of the Au-coated concave mirrors
spaced 6.72 m apart. At the 22.3 MHz bunch repetition
rate, a single radiation pulse is stored in the resonator.
Thus the radiation pulse can interact with the electron
bunch 550 times during the macropulse.
The intensity of the spontaneous emission wasmeasured for various field strength of the solenoid byremoving the downstream cavity mirror. The cyclotron
resonance condition,ω = ω co (1 − β z )(6),signal (mV)signal (mV)signal (mV)

M.R. Asakawa et al. / Proceedings of the 2004 FEL Conference, 618-621

100

1 T. Under these conditions, the electron undergoes ahalf-cyclotron rotation while it passes through thesolenoid. Figure 6 shows the time traces of the responseof the microwave diode with a cutoff frequency of 100
GHz. The signal involves the pulses synchronized to theelectron bunches and thus appears as it is hatched in the
figure. The radiation signal when the solenoid field wasoff, in fig. 6 (a), generated at the bending magnets. And
the radiation power increased as increasing the magnetic
field up to 1T. The radiation power with the solenoid
field of 1 T exceeded that without the solenoid field by afactor 10.

(a)

0
-100
100

621

(b)

0
-100

CONCLUSION

100

(c)

0
-100
0

5

10

15

20

25

30

time (µs)

Figure 6. Time trace of the microwave dioderesponse. The solenoid field is 0 T, 0.7 T and 1.0T
for (a)-(c), respectively.
where ωco, γ and βz are the cyclotron frequency, theelectron relativistic factor and the normalized axial
velocity, gives a resonant frequency of 4.0 THz for
typical experimental condition, an electron energy of 150
MeV, an incident angle of 5 mrad and a solenoid field of

A novel radiation source, which can generate a halfcycle radiation, is being developed at iFEL Osaka
university. This source is based on the cyclotron
radiation from the electron that undergoes a halfcyclotron rotation in the solenoid field. The numerical
study revealed that the radiation can be stored with acertain initial pitch angle of electron. Furthermore thepolarization of the radiation directs the same direction
with electron cyclotron motion. Thus the radiation can beamplified by interacting with successive electron beam.
Substantial power of the spontaneous emission wasobserved experimentally on the 180 MeV electron beamling of iFEL accelerator. The lasing experiment is now
under way.

REFERENCES[1] M. Asakawa, et al., Appl. Phys. Lett. 64 (1994) 1601

New Concepts

622

w.h. Huang et al. / Proceedings of the 2004 FEL Conference, 622-624

RESEARCHES OF THOMSON SCATTERING X-RAY SOURCE AT
TSINGHUA UNIVERSITY*
CH.X. Tang, W.H. Huang*, H.B. Chen, C. Cheng, Y. Cheng, Q. Du, T.B. Du, Y.CH. Du, X.Z. He,
J.F. Hua, G. Huang, Y.CH. Ge, Y.ZH. Lin, B. Xia, M.J Xu, X.D. Yuan, SH.X. Zheng
Department of Engineering Physics, Tsinghua University, Beijing 100084, PR China
Abstract
The bright and tunable short pulse X-ray sources arebeing widely used in various research fields. Thomson
scattering is one of the most promising approaches toshort pulsed x-ray. Researches on Thomson scattering xray sources are being carried out in Tsinghua University.
Some theoretical results and the preliminary experimenton the Thomson scattering between electron beams andlaser pulses are described in this paper.

INTRODUCTION
Tunable, ultrashort pulsed x-ray source are useful invarious research fields, such as solid-state physics,
material, chemical, biological, medical sciences andindustrial applications. The x-ray can be produced withdifferent mechanisms, such as x-ray free-electron lasers[1], electron bunch slicing in synchrotrons [2], andrelativistic Thomson scattering[3,4]. The x-ray source
based Thomson scattering will possibly generate
ultrashort hard x-rays with comparatively low energies
electron beams.
The generation of x-ray by scattering between laser
light and relativistic electrons was originally proposed in
1960s. With the development of table-top-terawatt (T3)lasers, a number of experimental studies of Thomson
scattering have been performed recently. It is shown thatThomson scattering is one of the most promising
approaches to ultrashort pulsed x-ray. Researches on
Thomson scattering x-ray sources are being carried out inTsinghua University.
In this paper some theoretical results and thepreliminary experiment setup on the Thomson scattering
between electron beams and laser pulses are described.

X-RAY GENERATION VIA LINEAR
THOMSON SCATTERING AT
ARBITRARY INTERACTION ANGLES
To describe the kinematics of the linear Thomson
scattering at arbitrary interaction angle α, we consider theframes as given in figure 1. The two frames are bothlaboratory frame: the electron beam is along the + z axisof the electron frame and the laser beam is along the − z ′axis of the laser frame. We assume that the Rayleighrange of laser beam is much longer than laser pulse length,
the intensity profile of laser beam satisfy the Gaussian
distribution,

nl

ρl =

×

(1)

(2π )3 2 σ lx ′σ ly ′σ lz ′
 (x′ − xl′0 )2 ( y′ − yl′0 )2 (z ′ − zl′0 + ct )2 
−
−
exp −



2σ l2x ′2σ l2y ′2σ l2z ′where σ lx′ , σ ly′ , σ lz ′ and xl′0 , y l′0 , z l′0 are the laser beam’s
rms size and position offset in x ′, y ′, z ′ direction,
respectively. nl is the total number of laser photons in one
pulse. Similarly, we assume that the envelope function ofelectron beam is much greater than then electron beampulse length, the intensity of electron beam can be given
by
ne

ρe =

×

(2π )3 2 σ exσ eyσ ez
 ( x − xe 0 )2 ( y e − y e 0 )2 (z e − z e 0 )2 
exp − e−−

2σ ex2

2σ ey2(2)

2σ ez2where σ ex , σ ey , σ ez and xe 0 , ye 0 , ze 0 are the laser beam’s
rms size and position offset in x, y, z direction,
respectively. ne is the total number of electrons in one
pulse.

xx'
αElectron beamz'
Laser beam

θx
X-ray

z

y,y'
Figure 1: A schematic illustration of Thomson
scattering( xyz -electron frame; x′y ′z ′ -laser frame)
The differential cross section of the relativistic
Thomson scattering under the linear interaction isdΣ r02 (1 + β 2 )(1 + cos 2 θ x ) − 4 β cos θ x
(3)
=
dΩ

2

γ 2 (1 − β cos θ x )4

where θ x is emitting angle of x-ray, β is the velocity ofelectron, r0 is the classical radius of electron. Fromequation (1)-(3), we can get the number of photons in the
produced x-ray[5]___________________________________________*

huangwh@mail.tsinghua.edu.cn

THPOS35

Available online at http://www.JACoW.org

w.h. Huang et al. / Proceedings of the 2004 FEL Conference, 622-624

dn x
n n dΣ
= C off e l
×
dΩ
2π dΩ

(4)
1

(σ + σ )[(1 − cos α )(σ + σ ) + (1 + cos α )(σ + σ )]
2
ey

2
ly ′

2
ex

2
lx ′

2
ez

2
lz ′

where

 ( y − y ′ )2[(ze0 + zl′0 ) cos(α 2) − (xe0 − xl′0 ) sin (α 2)]2 
Coff = exp − e 02 l 0 2 − 2 σ + σ ′ (1 − cos α ) σ 2 + σ 2 ′ + (1 + cos α ) σ 2 + σ 2′ 
ey
ly
ex
lx
ez
lz 


(

)

(

)

(

)

(5)

is the decrease ratio of x-ray due to the mismatch of
position and time. The pulse length of the produced x-ray
isσT =σ ez (1 − cosα )(σ ex2 + σ l2x′ ) + (1 + cosα )σ l2z′

(

)

(

c (1 − cosα ) σ ex2 + σ l2x′ + (1 + cosα ) σ ez2 + σ l2z′)

(6)which is consistent with the result in Ref.[6] when
scattering angle α = 90° .

PRELIMINARY THOMSON SCATTERING
EXPERIMENT

623

Preliminary experiments of x-ray generation throughThomson scattering are made with the backward
travelling wave 16MeV electron linac[7] and the YAG
laser system. The electron beams are delivered from the
2856MHz RF linac with a 4µs macrobunch duration and
35ps total microbunch duration at a repetition rate of up
to 250 Hz. The YAG laser system produces ~10 ns output
pulses of λ=1064 nm with an energy ~2J at a repetition
rate of 10Hz. Head-on scattering geometry(177º) is adopt
to get the maximum x-ray yield. Due to long duration ofelectron macrobunch, the need of synchronization
between two beam is easily fulfilled.
The experimental layout of Thomson scattering isshown in figure 2. Laser pulses are finally focused by amirror with a focal length of 1.5m and reflected into
interaction chamber. The linac is separated with a 100µm
thick titanium widow from the interaction chamber tomaintain ultrahigh vacuum in the linac. The electron
beams are focused by quadrupole magnets before
interaction and swept off by a 45º bending magnet. The
x-ray photons are detected by a CsI(Tl) scintillator that iscoupled to the photomultiplier tube.

accelerator

Quadrupole &steer magnet
Interaction
chamber

CCD

Bending magnet
Faraday cup

He-Ne laser
YAG laser

Detector
He-Ne laser

Figure 2: The experimental layout for head-on
Thomson scattering

Figure 3: CCD image of electron and laser beam atinteraction point(left:electron, right:laser)
Table 1: Parameters of Preliminary Thomson scatteringexperiments
Laser beam
Wavelength 1064 nm
Pulse energy 2 J
Total pulse duration ~10 ns
Focal spot radius 0.5 mm
Electron beam
Energy 16 MeV
Microbunch peak current 1.2 A
Total microbunch duration 35 ps
Macrobunch duration 4μs
Charge/microbunch 0.042 nC
RMS beam radius 1.25 mm
x-ray pulse
Maximum photon energy 4.5 keV
Microbunch pulse duration 35 ps
Number of photons/microbunch ~1×103
Due to head-on geometry and long duration of electron
beam macrobunch, the laser beam will interact withseveral electron microbunchs, depending on the Rayleighrange of laser beam and beta function of electron beam.

New Concepts

624

w.h. Huang et al. / Proceedings of the 2004 FEL Conference, 622-624

This will help to increase the x-ray photon flux. Up tonow, the electron beam and the laser pulse focusing havebeen tested at the interaction point. The focal spot ofelectron and laser beam at interaction point are shown infigure 3. The parameters that both laser system and linac
now can provide and estimates of x-ray based onequation (4)-(5) are summarized in Table 1. Someupgrade with linac and laser system are going on. The
effects of emittance, energy spread, interaction position
and time mismatch of both beams are simulated by thecode CAIN[8].

PROPOSALOFATHOMSONSCATTERING X-RAY SOURCE FACILITY
IN TSINGHUA UNIVERSITYRF
Generator

1/36

79MHz

Feedback control
KLMOSC
Pulse shaper

2856MHz
Stretcher
Regen. Amp.

THG

SHG

Image
relay

Pre. Amp.

Compressor

Main Amp.

Phase
Plate

DF Mirror
modulatorand compressed by the bunch compression chicane, theninteracts with laser pulse via orthogonal and head-on
scattering geometry. Table 2 summarizes the design
parameters of Thomson scattering x-ray source.
Table 2: Design parameters of Proposal Thomson
scattering x-ray source
Laser beam
Wavelength 800 nm
Pulse energy 500 mJ
Pulse duration 25~50 fs
Focal spot radius ~0.1 mm
Electron beam
Energy 60~100 MeV
Bunch duration 1~10 ps
Charge/microbunch 1.0 nC
Beam radius 0.1 mm
x-ray pulse
Photon energy 36~200 keV
Pulse duration 50~1000 fs
Number of photons 9.5×105~1.5×108

Compressor
Klystron

ChicaneAccelerating
tube
Photo-CathodeRF-GunFaraday cup

Beam mearment area

Interaction
chamberdetector

Q-magnet
StreakCameraCCD Camera

Figure 4: The schematic layout of proposed Thomson
scattering x-ray source
As a next step we propose to build up a sub-picosecond
hard x-ray source based on Thomson scattering between
Ti:Sapphire T3 laser system and electron linac. The
simplified schematic layout is shown as Figure 4. The
laser pulses from oscillator are splitted into two beams
after the pre-amplification: one is tripled to 266 nm after
amplification to excite the photocathode RF gun; theother one is coupled into interaction chamber after
chirped-pulse-amplification. The electron beam generated
by the photoinjector is accelerated with four travelingwave accelerating tube up to 60~100 MeV. The electron
beam from the linac is focused by quadrupole magnets

THPOS35

REFERENCES[1] http:// http://www-ssrl.slac.stanford.edu/lcls/.
[2] R.W. Schoenlein, S. Chattopadhyay, H.H.W. Chong,
et al., Science 287,2237 (2000).
[3] R.W. Schoenlein, W.P. Leemans, A.H. Chin et al.,Science 274, 236(1996).
[4] D.J. Gibson, S.G. Anderson, P. J. Barty, et al., Phys.
Plasmas, Vol. 11, No. 5, 2857(2004)[5] W.H. Huang et al.,HEP&NP,Vol.28,No.4,446(2004)(in chinese)[6] K.J. Kim, S. Chattopadhyay, C.V. Shank, Nucl. Instr.
and Meth. A 341 (1994) 351.
[7] H.B. Chen et al, LINAC02, 623(2002).
[8] P.Chen, G. Horton-Smith, T. Ohgaki, A.W.
Weidemann, and K. Yokoya, Nucl. Instr. and Meth.
A 355, 107 (1995).

625

E.G. Bessonov et al. / Proceedings of the 2004 FEL Conference, 625-628

THE COHERENT SYNCHROTRON RADIATION INFLUENCE
ON THE STORAGE RING LONGITUDINAL BEAM DYNAMICS
E.G. Bessonov∗ , R.M. Feshchenko, Lebedev Physical Institute RAS, Moscow, Russia
V.I. Shvedunov, Moscow state University
Abstract
We investigate influence on the storage ring beam dynamics of the coherent Synchrotron Radiation (SR) self
fields produced by an electron bunch. We show that the
maximum energy gain in the RF cavity must far exceed theenergy loss of electrons due to the coherent SR.

INTRODUCTION
The energy ε of a particle in storage rings oscillates inthe vicinity of the equilibrium energyεs . The difference
between equilibrium and nonequilibrium energies is proportional to the derivative of the particle’s phase dϕ/dt =h(ωs − ωr ):∆ε = ε − εs =εs dϕ,hKωs dt(1)

where K = −∂ ln ωr /∂ ln ε = (αγs2 − 1)/(γs2 − 1) is self
phasing
R coefficient; α, the momentum compaction factor;
ϕ = ωr (t)dt, the particle’s phase; γ = ε/mc2 , the relative energy; ωr = 2πf ; f , the revolution frequency of aparticle in the storage ring. Equilibrium values have lower
index s [1-3]. The radio frequency (RF) voltage in the cavity’s gap is varying as V = Vrf cos ωrf t, where ωrf is theradio frequency; h, the subharmonic number of radio frequency.
Balance of energy gained by an electron during the period of a single revolution T = 1/f = C/c = 2πR(1 +µ)/c in the RF cavity and lost due to synchrotron radiation
and Thomson scattering defines an equation for electron
phase oscillations in the storage ring:dεeVrf cos ϕ=− < P rad >,
dt
T

(2)

where < P rad >= dεrad /dt is the power of radiation
losses averaged over the length of the orbit; C, the lengthof the orbit; R, the curvature
P radius of the particle orbit inbending magnets; µ = i li /2πR, the ratio of the sum ofstraight intervals li in the storage ring to the path length in
the bending magnets. The synchronous phase ϕs is definedas dεs /dt = 0 or eVrf cos ϕs = Psrad T .
The spontaneous coherent SR doesn’t depend on the particle energy but depends on the particle position in the longitudinal direction, the shape of the beam and on the number of particles. For the Gauss longitudinal distribution one
can obtain:∗ bessonov@x4u.lebedev.ru

Available online at http://www.JACoW.org

rad(ϕ) = −
Pcoh

31/6 Γ2 (2/3) N e2 c∗
(1 + µ)"2 #
1 R (ϕ − ϕs ) (1 + µ)
exp −
∗
2
hσs
√
21/6 π R (ϕ − ϕs ) (1 + µ)
[1 − √−hσs
3 3Γ (2/3)
2
1 R (ϕ − ϕs ) (1 + µ)
+ . . .].
6
hσs
4/3

21/3 πR2/3 σs(3)

It is supposed here that the phase in the center of thebunch is equal to synchronous phase ϕs , σs is the bunchmean square length and Γ(2/3) = 1.35 [4].
If the laser beam is homogeneous and its transversal dimensions far exceed ones of the electron beam, the powersof Thomson scattering radiation and spontaneous incoherent SR obey the simple power dependence as functions ofradradenergy< Pnoncoh>=< Ps,noncoh> (ε/εs )ki . The difference between radiated power of synchronous and nonsynchronous particles isradrad< Pnoncoh> − < Ps,noncoh>=radd < Ps,noncoh
>
∆ε =
dε

∆ε
,
(4)
εs
where ki = 2 for the Thompson backscattering, ki = 1 forthe Raleigh backscattering by ions and ki = 1÷ 1.5 for theSR.
Subtracting the power balance equation for synchronous
particles from the equation for nonsynchronous one (2) andtaking into account (1), (4) we obtain equation for phaseoscillations in the storage ring:radki < Ps,noncoh>radd2 ϕ ki < Pnoncoh> dϕ heωs2 K+−[V (ϕ)−V (ϕs )] = 0,
2
dt
εs
dt
2πεs
(5)
rad
where V (ϕ) = Vrf cos ϕ − 2πR (1 + µ)/c Pcoh(ϕ) .
The synchronous phase is determined by the equation
U (φs ) = 0.
Incoherent synchrotron radiation and Thompson scattering cause slow damping of phase oscillations (the damping
time far exceeds the period of oscillations) and can be neglected in the first approximation, so equation (5) can be
rewritten as:

New Concepts

626

E.G. Bessonov et al. / Proceedings of the 2004 FEL Conference, 625-628

1 d dϕ 2 heωs2 Kdϕ( ) −[V (ϕ) − V (ϕs )]= 0.
2 dt dt
2πεs
dt

(6)

The first integral, determining particle phase trajectories
behavior issZ
dϕheωs2 K=
[V (ϕ) − V (ϕs )]dϕ.
(7)
dt
πεs
The coherent synchrotron radiation force acts similar
to the radio frequency accelerating field. The autophasing force of the storage ring is defined by the derivative dV (ϕ)/dϕ. Thus, in accordance with (5), the reaction of the coherent SR makes this force weaker. This
weakening reaches maximum when the phase equals ϕ =ϕs + hσs /R (1 + µ). Therefore the stability of the electron
beam requires that the derivative dV (ϕ)/dϕ is negative in
the interval |ϕ − ϕs | < hσs /R(1 + µ). This phase range
corresponds to the stable oscillations of the majority of particles with amplitudes A ' σs . Using the formulas for the
power of the coherent SR (3) for a beam with Gauss longitudinal distribution of particles one can find:
Vrf > Vrf,c =2

rad
2πR2 (1 + µ) Pcoh
(ϕs )
,
√
en hσs(8)where en ≈ 2.72 is the natural logarithm foundation. In
reality the coherent SR can be neglected if the value Vrf is2 ÷ 3 times higher than Vrf,c and sin ϕs ≈ 1. The maximum energy gains in the RF cavity, according to (8), must
far exceed the energy loss of electrons due to the coherentSR.
rad
If the value Pcoh
is neglected, the equation (5) is transformed into the equation of small amplitude phase oscillations:radd2 ψ ki Pnoncohdψ++ Ω2 ψ = 0,
2
dt
εs
dt

εs

,
(10)
rad
Pnoncohp0
the damping time, Ω = Ω2 + τs−2 , the frequency ofsmall particle oscillations.

EXAMPLEAn electron storage ring has the radius R=50 cm, h=10,
σs = 1 cm, µ = 1, N = 1010 ,sin ϕs ≈ 1. In this casethe losses of a synchronous particle per a revolution isradVcoh(ϕs )= 9.25 kev, Vrf > 114 kV. Thus for the stable storage ring operation the RF cavity voltage should be

THPOS38APPENDIX
Suppose that a beam has small angular ∆θ ∼1/γ andenergy ∆ε/ε ∼1/γ spread (emittance). In such a case electromagnetic fields emitted by different particles are similar
to each other but have a temporal shift. The Fourier imagesof these fields are:Ei,ω = E1,ω exp(i∆ϕi ) i=1,2,3, ... N,
where the phase difference between waves emitted by the000
first and the i-th particles is ∆ϕ = ω(ti − t1 ) + k[r(ti ) −00r(t1 )]. The moments of emission t and detection t are connected as t = t0 − R0 /c − nr/c, R0 is the distance between
the points of emission and detection, k = ω · n/c, n isa unit vector pointing in the direction of emission, r – thevector lying in the plane perpendicular to the trajectory ofa particle. The time difference for ultrarelativistic particles
00ti − t1 is connected with the space distance by a simple
00
relation c(ti − t1 ) = zi − z1 . Therefore thePFourier imageof the sum of fields of N particles Eω = i Ei,ω can be
written as (for the electrical field):Z∞
Eω = Nρ(z, r)E1,ω exp[i∆ϕ(z, r)]dzdr,

(11)

−∞

where ρ(z, r) – the density distribution of particles normalized to unity.
If the transversal dimensions of the beam are small, theintegration in the equation (11) over transversal coordinate
r can be omitted:

(9)

where
=
ϕ − ϕs<<1 and Ω=
p Ψ
ωs qhKVrf sin ϕs /2πεs .
The equation (9) has solutions that can be expressed as0ψ = ψm (t) cos Ω t, where ψm = ψm,0 exp(−t/τph ) is thevarying amplitude andτph =much higher than the coherent radiation losses. The shielding by the vacuum chamber can weaken this requirement[5]. One should also note that the energy losses of a synchronous electron per a revolution are approximately 22/3
times greater than average losses of electrons in the beam(see Appendix).

Z∞Eω = N · E1,ωρ(z) exp[i
−∞

2πz
]dz.
λ

(12)

In this case the spectra-angular distribution of the emitted energy∂ 2 εcoh∂ 2 ε1= cR02 |E1,ω |2 = N 2
s(ω),
(13)
∂ω∂o
∂ω∂o
where ε1 is the energy of the radiation emitted by a single
2
R∞
particle, s (ω) = −∞ ρ (z) exp [i2πz/λ] dz , the spec-

tral radiation coherence factor, λ = 2πc/ω– the wavelength of SR. The spectral energy distribution and the fullemitted energy can be found by integration of (13) over angles
∂εcoh
∂ε1
= N2
s(ω)
∂ω
∂ω
and over frequency

(14)

627

E.G. Bessonov et al. / Proceedings of the 2004 FEL Conference, 625-628

εcoh = N 2Z∞0∂ε1 (ω)· s(ω) · dω.
∂ω

(15)

From (13) – (15) it follows that for a point-like
coh
beam
=
R ∞ρ(z) = δ(z) and therefore s(ω) = 1, ε
N 2 0 [∂ε1 (ω)/∂ω]dω = N 2 ε1 (ω), i.e. the energy emitted by the beam is N2 times larger than the energy emitted
by a single particle.
If the beam’s motion is periodical one can introduce
average radiation power:P coh = f · εcoh , ∂P coh /∂ω =f · ∂εcoh /∂ω, f = v/C – the revolution frequency, ν ≈ c–the particle’s velocity and C is the perimeter of the orbit.
The values ∂ε1 /∂ω and ∂P1 /∂ω = f · ∂ε1 /∂ω are
known. In particular, the spectral power of radiation is√∂P1
3 3e2 cγ 4=
F (ξ),(16)∂ξ
2RC
where β = v/c – the relative particle velocity, γ = ε/mc2 –R∞
the relative energy, F (ξ) = ξ K5/3 (ξ)dξ, ξ = ω/ωc ,ξωc = 3βγ 3 c/2R – the critical radiation frequency, R– theorbit radius in a bendingR magnet of the storage√ ring [6,7].
∞
One can also calculate 0 F (ξ)dξ = 8π/9 3[6]. Thus
the full radiation power for one particle can be expressedas:
4π e2 cγ 2
.
(17)
3 RC
In the case under consideration the radiation is coherent
if the wavelength is longer than the length of the bunch i.e.
ξ << 1, K5/3 (ξ) ≈ 24/3 Γ (2/3) ξ −5/3 ,
P1 =

Z∞

Z∞
K5/3 (ξ)dξ =Zξ
K5/3 (ξ)dξ −0

ξ

K5/3 (ξ)dξ0Z√= π 3 − K5/3 (ξ)dξ, F (ξ) = 22/3 Γ(2/3)ξ 1/3 .
ξ0

Now the formula (16) can be written as√∂P1
3 3e2 cγ 42
= 4/3 2
Γ( )ξ 1/3 .
∂ξ
3
2 πR (1 + µ)

(18)

The spectral coherence factor s(ω) is determined by theparticle density distribution law ρ(z) and for the Gaussian
distribution2−z1
ρ(z) = √e 2σx22πσx(19)can be derived from equations (13) and (19) as s(ω) =exp(−4π 2 σx2 /λ2 ) [8,9]. The value σx is the mean squarebunch length.
The full power of the spontaneous coherent SR, the average loss rate for a single particle and the losses overa revolution can be calculated numerically using the formula (15) and the expression P coh = f · εcoh . In thespecial case when the coherent SR is dominated by the
low frequency radiation ξ << 1, taking into account (18)R∞
4/3
and k 1/3 exp(−k 2 σx2 )dk = Γ(2/3)/2σx , one can de0

rive that
P coh = cdεcoh
31/6 Γ2 (2/3)re cN 2
=
mc2 ,
4/3
dt
2πR2/3 σx (1 + λ)(20)

The energy losses per a revolution are∆εcoh =dεcoh
31/6 Γ2 (2/3) re R1/3 N 2 2
T =
mc
4/3
dt
σx

≈ 3.1 · 10−7 R1/3 N 2 /σx4/3 [eV /revolution].

(21)

The formula (21) matches with the results of the firstwork on the coherent SR [10], is 21/6 ≈ 1.12 times lower
than one in the reference [4] , 27/3 ≈ 5.04 times lower thanthe value in the reference [11] and 28/3 ≈ 6.35 times lower
than one in the reference [12]. In the last reference the authors used formula from the work of Shiff [10] and erred inconverting it to their definition of the valueσx . They multiplied the Shiff’s formula by the 24/3 instead of dividing by
it. In the remaining references the source of errors is unclear but more probably connected with the same mistake.
The coherence factor is decreasing for the wavelengths
λ ≥ λd = 2πσx or if ω ≥ ωd = c/σx . The expression (21)is justified if the main part of the energy of the coherent SR
is emitted in the spectral range ω ≤ ωd ≈ ωc (ξ << 1)i.e. when σx > λc /2π, where λc = 2πc/ωc = 4πR/3γ 3 .
The expression also (21) doesn’t take into consideration theshielding of the beam by the vacuum chamber, which leads
to the weaker radiation for the wavelengths longer than thevacuum chamber gap.
The vast majority of the energy is emitted in the angular range ∆θ ∼1/γ relative to the direction of the particle’s motion when k · r (t0 ) << k · r/γ. So, the condition
when one can neglect the transversal beam dimensions is
kd · r << γ or r << (λd /2π)γ = σx γ.

REFERENCES[1] A.A. Kolomensky and A.N. Lebedev, Theory of Cyclic Accelerators. North Holland Publ., , 1966.
[2] H. Bruk, Accelerateurs Circulaires de Particules (Press Universitaires de France, 1966).
[3] C H. Wiedemann, Particle Accelerator Physics I \& II(Springer-Verlag, New York, 1993).
[4] L.V.Iogansen, M.S.Rabinovich, JETP, v.37, 118, 1959 (inRussian).
[5] J.B.Murphy, S.Krinsky, R.L.Gluckstern, Particle Accelerators, 1997, v.57, pp.9-64.

New Concepts

628

E.G. Bessonov et al. / Proceedings of the 2004 FEL Conference, 625-628[6] D.Ivanenko, A.Sokolov, Classical Theory of field, GITTL,
1951 (in Russian).
[7] L.D.Landau, E.M.Lifshits, The classical Theory of Fields,
Pergamon Press, Oxford, UK, 1975.
[8] H.Wiedemann, Particle Accelerator Physics, v.I, Springer –Verlag, NY, 1993, p.319.
[9] A.Andersson, M.Johnson, B.Nelander, Coherent synchrotron radiation in the far infrared from 1 mm electron
bunch, Opt. Eng. V.39, p. 3099-3115, 2000.
[10] L.Schiff, Rev. Sci. Instr., v.17, 7, 1946.
[11] E.L.Saldin, E.A.Schneidmiller, M.V.Yurkov, TESLA FEL
Report 96-14, November 1996 (corrected in Nucl. Instr.
Meth. v.A398 (1997), p.373).
[12] J.S.Nodvic, D.S.Saxon, Phys. Rev., v.96, No 1, p. 180-184,
1954.

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A.N. Matveenko et al. / Proceedings of the 2004 FEL Conference, 629-632

ISOCHRONOUS BEND FOR HIGH GAIN RING FEL
A.N. Matveenko, O.A. Shevchenko, N.A. Vinokurov
Budker Institute of Nuclear Physics, 11 Acad. Lavrentyev Prosp., 630090, Novosibirsk, Russia
Email:A.N.Matveenko@inp.nsk.su

Abstract
The recently proposed ring free electron laser (FEL)
consists of several undulators with isochronous bends
between them. Isochronous bends are necessary topreserve the beam bunching between undulators. Such
FEL configuration may be used as an independent soft Xray source or as a master oscillator for an X-ray FEL(high gain harmonic generator or other type). The latticeof the compact 500-MeV 60-degree bend for a soft X-ray(50 nm) FEL is proposed. Fundamental restrictions due toquantum fluctuations of synchrotron radiation andtechnically achievable fields to construct isochronous
bends of a shorter wavelength ring FEL are discussed.

INTRODUCTION
A mirror-free ring Free Electron Laser (FEL)
configuration consisting of several undulator sections
separated by isochronous bends is considered to be apossible solution for an X-ray FEL [1, 2]. In thisconfiguration the beam bunching grows from undulator toundulator and after a 360-degree turn radiation from thelast undulator illuminates the beam in the first undulator
and induces bunching in the incoming fresh beam. Such aconfiguration, driven by an energy recovery linac, isshown in Fig. 1.

Figure 1. Possible layout of ring FEL driven by anenergy recovery LINAC.
One of the critical parts of the scheme is theisochronous bend section between undulators. Their aim
is to preserve the beam bunching along the ring. If we
express the time delay of an electron from a reference
particle moving along the design orbit in terms of the firstorder transport matrix Rij we get (planar bend is assumed)c∆t = R51 x + R52 x ′ + R56

∆E
E

(1)

In an isochronous bend we must make all three matrix
elements in Eq. (1) equal to zero. Let d(s) is the(horizontal) dispersion function with zero initialconditions at the bend entrance s = 0, s is the coordinate
along the reference trajectory Then R52 and R51 areproportional to dispersion d(L) = R16 and it’s derivative

Available online at http://www.JACoW.org

d′(L) = R26 at the bend exit s = L, so the bend must be
achromatic in the first order. R56 can be expressed interms of dispersionL

R56 (0, L) ≈ ∫ h ( s )d ( s )ds(2)0Here h(s) is the orbit curvature. This matrix element
can be easily made zero in a symmetric three-bend
achromat.
It is worth noting, that bunching conservation in theachromatic bend for the visible wavelength range wasdemonstrated in [3].
In this paper we discuss two causes for bunchingdegradation and propose a compact 500-MeV 60-degree
bend for a soft X-ray (50 nm) ring FEL. Quantum
fluctuations of synchrotron radiation and second orderaberrations in the lattice are taken into account. Limiting
factors to construct an X-ray ring FEL are discussed
further.

EFFECT OF QUANTUM FLUCTUATIONSOF SYNCHROTRON RADIATION
An electron, moving in the bending magnet, emits
synchrotron radiation. In classical electrodynamics it
leads to the slow change of the beam energy. But reallythe quantum fluctuations of radiation increase the beamenergy spread. Due to the energy loss particles arrive thebend exit slightly later. If quantum nature of radiation istaken into account, the time delay spread appears*.
The delay caused by the emission of photon withenergy ε = ηω at the point s of the trajectory andmeasured at the point L (exit of achromat) isc∆t = − R56 ( s, L)

ε

(3)

E

The probability of this photon emission may be
expressed through the spectral power density ofsynchrotron radiation dI dω

dp =
Then

σ

2
c∆ t

the

square

dI
ds
dω
dω
εc

= (c∆t ) − c∆t
2

of
2

the

(4)
delay

dispersion

is the sum of contributions

from different parts of the trajectory ds and frequency
intervals dω
*The debunching due to quantum fluctuations waspointed out by V. N. Litvinenko.

New Concepts

630

A.N. Matveenko et al. / Proceedings of the 2004 FEL Conference, 629-632

∞L


0 0

σ c2∆t = ∫ ∫  R56 ( s, L)2

ε  dI dsdωE  dω εc(5)After the integration over frequencies it gives
2
σ c∆t
=

55 r0 2 5 L 2
γ ∫ R56 (s,L) ⋅ h 3 (s) ⋅ ds
24 3 α0(6)where r0 is the classical electron radius, α = 1/137 is thefine-structure constant, γ is the relativistic factor. For the
mirror symmetric isochronous systems R56(s,L)=-R56(0,s).
Thenσ c2∆t =2

L

55 r0 5 2γ ∫ R56 (0, s ) ⋅ h 3 ( s ) ⋅ ds
24 3 α0(7)

The reduction of the current Fourier harmonics at

e iω∆t . If

frequency ω = ck is given by the factor

kσ c∆t << 1 , the current spectral density reduction after the

pass through the bend may be estimated as

e

ikc∆t

1− k 22

k2(c∆t )2≈ 1 + ik c∆t −2( (c∆t ) − c∆t ) = 1 − k σ
2

2

2

2

≈

(8)

h2s3
6

(9)

and then, neglecting the contribution of the central
magnet,σ c2∆t =55 r0 5 α.
γ126
24 3 α
2

7
0

1

(10)

It is worth noting, that this limitation does not depend on
the orbit curvature h, therefore high-field superconducting
magnets may be used.
If we assume the beam emittance to be a limiting factor
for a short-wavelength FEL, the beam energy should belarge enough, γ > kεn , where εn is the normalized beamemittance. Therefore,

λ −5 7 − 2 7λε n r0 ≈
ο
2π
200 A

(εn=10-6 m·rad is taken for the estimation).

THPOS45

c∆t

c∆t

N

Taking N=1/α0 for the bend section of 1 radian andcomparing it to (λ/2π)2 we get an estimation of the
maximum permissible bend angle in the system for this
case
1

 6
 λ2
α 0 ~  2 2 5  or 4π r0 γ 

α0 < k−7 6

ε−5 6 −1 3
0
n

r

 λ 

≈
ο 

 200 A 

76

(13)

Making the bend angle small we can decrease thesynchrotron radiation effects to a desirable level.
However, the length of the bend section can become toolong. The bend section total length can be estimated in thefollowing manner. Let us denote the maximal achievable
gradient of the focusing lenses G. In order to make thedispersion zero in each bend its length must be

lmin ~ 2π

pc
eG

(14)
1

Comparing it to (λ/2π) , we get an estimation of the
maximum permissible bend angle in the system

α0 <For wavelength shorter then 100 Å the bend section canbe made up of a number of isochronous bends on asmaller angle. Such a system can be thought of as abended undulator. However, the focusing of an undulator
is too weak to make its period isochronous and additional
quadrupole focusing is necessary.
Total debunching in the section, consisting of N
isochronous bends, is(12)(σ 2 ) ~ σ 2 N

The total one-radian section length is given then by2

 λ2  7
α0 ~  2 2 5 
 4π r0 γ 

SHORT WAVELENGTH RING FELISOCHRONOUS BEND

2c∆t

As it is seen from Eq. (8), kσ c∆t < 1 is required to keep
significant bunching after the bend.
Consider, for simplicity, a three-bend isochronous
achromat. It may be shown, that the main (anduneliminable) contribution to the delay dispersion Eq. (7)is given by two side magnets. Let α0 is the bend angle foreach of these magnets, and α0<<1. At the first magnet wehave

R56 (0, s ) =Thus, the debunching, caused by quantum fluctuations ofsynchrotron radiation, can be neglected for the
wavelengths, larger then 200 Å. For shorter wavelengths
maximal bend angle scales as λ and going deep below
100 Å can be a problem.

(11)

pc  4π 2 r02γ 5  6
L ~ lminN ~ 2πeG  λ2 53ο 140A
 m

≈

λ




(15)
,

G = 10 kGs/cm was assumed. It is worth noting that for
short wavelengths this length is much longer then theorbit curvature radius in a bending magnet, i.e. the bend
section length of an X-ray ring FEL is limited by the
maximal achievable field gradient.

SECOND ORDER ABERRATIONS
The finite energy spread and transverse emittances will
also cause debunching. The delay longitudinal
dependence for a particle is given by

631

A.N. Matveenko et al. / Proceedings of the 2004 FEL Conference, 629-632

1 δ hxδ δ 2  β 2  x′2 y ′2 d hx − 2 − 2 + 2 1 + 0  +
+
c∆t =
2  2
2 
β 0 
γ0 γ0
γ0 
ds

(16)

Here p = p0 (1 + δ ) , and we retain only terms up to thesecond order in δ, x, y, and their derivatives. The first andsecond terms on the right are the first-order terms. Simple
estimations show that the third and the fourth term
contributions are negligible in comparison with the fifth
and the sixth ones. These last terms give the positive
contribution which can be estimated as
2

σ

2
c∆t

s

 ε 2y  s
ε x2 ≤  ∫ γ x ( τ )dτ  +  ∫ γ y ( τ )dτ 
2 0
2 0



2

(17)

where εx, εy are the rms beam emittances, γx, γy are theTwiss parameters. This debunching can be compensatedby the contribution of the first term in Eq.(16). For
example, one of the second order matrix elements is

T511( s ) =s
1  C x′2+ h( x | x02 ) ds′∫
β0 0  2


(18)

where Cx, Sx are the basic trajectories, and (x|x02)=T111.
Choosing the proper values of sextupoles one can adjust(x|x02) to make T511 zero.

ISOCHRONOUS BEND FOR 500 Å RING
FEL
According to [2], the 500 Å ring FEL shall be driven by
a 500MeV energy recovery LINAC. The parameters of
the LINAC and the laser are shown in table 1.
Table 1. Soft X-ray ring FEL parameters.
Energy, GeV
0.5
Relative energy spread, %0.05
Normalized rms emittance, micron
5
Peak current, kA
0.3
Undulator period, m
0.03
Undulator deflection parameter K
2
Radiation wavelength, Å
500
Undulator section length, m
12
Undulator first and last section length, m
5
Bend angle, degrees
60
Bend length, m
5
The proposed lattice of the 60û isochronous bendmodeled in MAD is shown in fig.2. It consists of two 30û
bending sections. Each section is essentially a symmetricisochronous three-bend achromat. Bends are proposed tobe made with the field gradient in order to shorten theoverall bend length. Bending sections are separated byquadruples. Sextupole correction is inserted into thenegative bends of each bending section.

Figure 2. Linear lattice functions βx, βy, and Dx of the isochronous bend of the 500 Å ring FEL.

New Concepts

632

A.N. Matveenko et al. / Proceedings of the 2004 FEL Conference, 629-632

Contribution of quantum fluctuations of synchrotron
radiation to the dispersion of the time of flight calculated
according to Eq.(7)οσ c∆t ~ 60 A

(19)
Second order aberrations are calculated using thesecond order transport matrix T5ij from MAD program in
the following way.
(20)c∆ t ( 2 ) = T x x

(

5ij i

j

σ c2∆t = (c∆t )2 − c∆t = T5ijT5kl xi x j xk xl − xi x j xk xl
2

)

(21)

If we consider plane system and upright phase plane
ellipses on the system entrance, the only nonzero
elements remain222
σ c2∆t = T511
⋅ 2 β x2 ε02x + T522
⋅ 2γ x2 ε02x + T512
⋅ 4ε02x +2
2
2+ T533⋅ 2 β y2 ε02 y + T544
⋅ 2γ 2y ε02 y + T534
⋅ 4ε02 y +

(22)
2
2
2
+ T566⋅ 2 β∆2 ε02∆ + T516
⋅ 4 β x ε0 x β∆ ε ∆ + T526
⋅ 4γ x ε 0 x β ∆ ε ∆where β, γ are the Twiss parameters at the entrance ofthe system, ε are the beam emittances. Indexes x, y, and ∆indicate transverse planes x and y, and longitudinalmotion respectively.
For the system shown in Fig. 2.
οσ c∆t ~ 60 A

(23)

Total dispersion thenοσ c∆t ~ 80 A ≈

λ
2π

(24)

CONCLUSION
The feasibility of the magnetic system for the ring FELat the soft X-ray band is shown. Quantum fluctuations ofsynchrotron radiation and second order aberrations in thelattice are taken into account. The collective effects
including CSR have to be considered yet.

REFERENCES[1] N. A. Vinokurov. Nucl. Instr. and Meth. A 375(1996), p. 264.
[2] N. A. Vinokurov and O. A. Shevchenko. Nucl. Instr.
and Meth. A 528 (2004), p. 491.
[3] N.G.Gavrilov, G.N.Kulipanov, V.N.Litvinenko,
I.V.Pinayev, V.M.Popik, I.G.Silvestrov, A.S.Sokolov,
P.D.Vobly, and N.A. Vinokurov. IEEE J. Quantum
Electron., v.27 (1991), p.2569.
[4] K.G.Steffen, High Energy Beam Optics, Intersciencepublishers, New York – London – Sydney, 1965.
[5] K.L.Brown, R.V.Servranckx, “First- and second-ordercharged particle optics”, SLAC-PUB-3381

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633

R. Thompson et al. / Proceedings of the 2004 FEL Conference, 633-636

THE TWO-BEAM FREE ELECTRON LASER OSCILLATOR
N. R. Thompson, ASTeC, Daresbury Laboratory, Warrington WA4 4AD, UK∗
B. W. J. Mc Neil, University of Strathclyde, Glasgow G4 0NG, UK

Abstract
A one-dimensional model of a free-electron laser operating simultaneously with two electron beams of different energies [1] is extended to an oscillator configuration.
The electron beam energies are chosen so that an harmonicof the lower energy beam is at the fundamental radiation
wavelength of the higher energy beam. Potential benefits
over a single-beam free-electron laser oscillator are discussed.

dA1
dz̄
dA3
dz̄

=

Sϑ

(5)

=

Sϕ + S3ϑ .

(6)

Here p and ϑ represent the energy detuning and phase of thelow energy electrons and ℘ and ϕ refer to the high energy
beam. For resonant beams p = ℘ = 0. The variable j =1 . . . N where N is the total number of sample electrons ineach beam and F 1 and F3 are the usual difference of Bessel
function factors for planar wigglers. Also

INTRODUCTION
A one-dimensional model of a single pass high-gain
free-electron laser operating with co-propagating electron
beams of different energies has been described elsewhere[1, 2]. The resonant beam energies are chosen such thatthe nth harmonic radiation wavelength of the lower energy beam is at the fundamental radiation wavelength of
the higher energy beam. It was suggested that this concept
may have certain advantages over a single beam FEL amplifier. For example, it may be possible to seed the lower
energy beam at the fundamental wavelength and use thecoupled interaction between the two beams to transfer thecoherence properties of the seed field to the harmonic radiation field. In this paper the model is extended to a onedimensional steady-state oscillator configuration. Numerical studies are done of the evolution of the system and theproperties of the model are explored, including the effectof different energy spreads in the higher energy beam.

THE MODELThe evolution of the two-beam system is given by a setof coupled equations whose derivation and underlying assumptions are outlined elsewhere [1]. For convenience theworking equations are repeated here in their final form, specialised to the case where n = 3:
dϑj
dz̄
dϕj
dz̄

=

pj

(1)

=

℘j

(2)

dpj
dz̄

=

−

d℘j
dz̄

=

3

1 
Fh (Ah eihϑj + c.c.)
c1

(3)

h,odd

−(F1 A3 eiϕj + c.c.)∗ n.r.thompson@dl.ac.uk

Available online at http://www.JACoW.org

(4)

Skϑ

≡

c1

=

1
Fk e−ikϑ , Sϕ ≡ F1 e−iϕ 
c2
√
√
R3
R3
, c2 = √
3
3

(7)
(8)

where R3 is the ratio of currents in the high energy and low
energy beams I3 /I1 .
In these equations the universal scaling is via the FEL
parameter ρ3 related to the higher energy beam. Hence theexplicit appearance of the additional scaling factors R 3 andn = 3 via c1 in equation (3), and via c 2 in equation (7).
By changing the value of R 3 we assume the current of thelower energy beam is altered whereas that of the higher
energy beam remains constant.
An important feature of the system is expressed in (6) the harmonic field has two source terms S ϕ and S3ϑ which
derive from the high and low energy beams respectively.
This feature is exploited in the work in this paper to allow
either beam to be ‘switched off’ by setting the appropriate
source term to zero. This is useful when comparing the behaviour of the two-beam system to the behaviour with one
or the other beam alone. An equivalent way of ‘switchingoff’ the lower energy beam is by setting R 3  1 making the low energy beam current negligibly small. From
(8) and (7) it can be seen that this reduces the source term
|S3ϑ |  1.
The oscillator model is very simple. At the end of eachpass the radiation intensities within the cavity are reduced
by appropriate factors depending on the mirror reflectivities then used as the input intensities for the next pass. We
assume mirror reflectivities r 1 and r3 which can be varied
independently for the two radiation wavelengths. We also
assume that any other cavity losses are zero so that the outcoupled intensities are given by|Ai |2out = (1 − ri )|Ai |2 ,i = 1, 3.

(9)

New Concepts

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R. Thompson et al. / Proceedings of the 2004 FEL Conference, 633-636

Figure 1: Both beams: third harmonic gain G 3 as a function of beam detunings in p and ℘. The current ratio R 3 =5,
so that the lower energy beam has one fifth the current of
the higher energy beam: G 3,peak ≈ 3.1.

Figure 2: Low energy beam ‘switched off’: third harmonic
gain G3 as a function of detunings in p and ℘. There is now
no p-dependence as expected. G 3,peak ≈ 1.7.

NUMERICAL METHODS
The system equations (2–6) were solved numerically using MATLAB and Fortran codes. The MATLAB code used
a variable step size intrinsic integration method and the Fortran code used the standard fixed step size 4th-order RungeKutta method. The codes were benchmarked against eachother and agreed well.

NUMERICAL INVESTIGATIONS
In a high-gain 2-beam amplifier, and assuming cold, resonant beams, linear analysis gives a threshold condition in
the beam currents for the harmonic gain to be greater thanthat of the fundamental [1]:√
3 |F3 |2.
(10)
R3 > 3 3 1 −2|F1 |Here this gives the condition R 3 > 2.13 for the chosen
wiggler parameter a w =2. Although an intermediate gain ofz̄ = 2 is assumed, and therefore the system is not highgain, a current ratio of R 3 = 5 was chosen and this is subsequently shown in the following section to similarly resultin a greater gain in the harmonic field than the fundamental.

Model Optimisation
The optimum beam detunings, p(z̄ = 0) and ℘(z̄ = 0),
were determined by a numerical scan of the single pass gainat the third harmonic G 3 . The result is shown in Fig. 1
where the peak gain is ≈ 3.1 (310%) at (p, ℘) ≈ (0.4, 1.2).
For comparison the scan was repeated for the high energy
beam only (Fig. 2), where the peak gain was found to be ≈1.7, and the low energy beam only (Fig. 3) where the peak
gain was found to be ≈ 0.9.

THPOS48

Figure 3: High energy beam ‘switched off’: third harmonic
gain G3 as a function of beam detunings in p and ℘. Thereis now no ℘-dependence. G 3,peak ≈ 0.89.

The gain for the two-beam system is greater than thesum of the gains due to the individual beams, even though
the current in the lower energy beam is only one fifth thecurrent in the higher energy beam. A similar scan was carried out for z̄ = 0.5 and it was found that in this linear small
signal gain regime the gain for the two-beam system was
the sum of the individual gains. The small enhancement in
the nonlinear (z̄ = 2) regime is due to the non-linear coupling between the two beams, there being no such couplingin the small signal/small gain regime.
It is clear from Fig. 1 that the gain is sensitive to therelative detuning between the two beams. Away from the
maximum at (p, ℘) ≈ (0.4, 1.2) the coupling decreases andthe surface evolves into a Madey gain curve as a functionof the low energy beam detuning p and a more asymmetrichigher gain curve as a function of the higher energy beam
detuning ℘. These curves are seen more clearly in Fig. 2

635

R. Thompson et al. / Proceedings of the 2004 FEL Conference, 633-636

Figure 4: Evolution of harmonic radiation field intensity|A3 |2 . Current ratio R3 = 5, z̄ = 2.
and Fig. 3 where the low and high energy beams respectively are ‘switched off’.
The mirror reflectivities r 1 and r3 were optimised via
numerical scans to maximise the saturation intensity of thethird harmonic, |A 3 |2sat .
The optimum reflectivity at the fundamental was foundto be r1 < 0.45, i.e. below threshold for the fundamental(G1 < cavity losses). Thus bunching of the lower energy
beam at the fundamental disrupts its coupling to the harmonic field.
The optimum reflectivity for the harmonic was determined to be r3 ≈ 0.7.
For all further simulations the following values were
therefore adopted: r 1 = 0.0, r3 = 0.7. Thus the fundamental resonant field of the lower energy beam A 1 is notstored in the cavity and so has little effect upon the coupledinteraction.

NUMERICAL EXAMPLES
A two-beam oscillator FEL with the above optimised parameters was simulated. A minimal gaussian energy spreadof σp = σ℘ = 0.1 was assumed. Fig. 4 shows the evolution of the harmonic output intensity over 50 passes. The
fundamental shows no growth due to the zero reflectivity atthat wavelength and so is not shown. The harmonic fieldsaturates after around 20 passes. The steepest growth in
the harmonic field (i.e. the maximum increase in intensity
over a single pass) occurs around pass 12. It can be seenfrom Fig. 5 and Fig. 6 that this coincides with peaks in theevolution of the source terms S ϕ and S3ϑ and peaks in thebunching terms |b 3 | and |bϕ |. These latter terms are measures of the bunching in the lower energy beam at its third
harmonic wavelength and in the higher energy beam at its
fundamental wavelength. The harmonic radiation field isclearly being driven here by both electron beams with thelower current, lower energy beam being the dominant contribution. The simulation was repeated twice more, eachtime with one of the beams ‘switched off’. For the low

Figure 5: Evolution of harmonic radiation field source
terms Sϕ and S3ϑ . Current ratio R3 = 5, z̄ = 2.

Figure 6: Evolution of electron beam bunching parameters|b1 |, |b3 | and |bϕ |. Current ratio R3 = 5, z̄ = 2.
energy beam only the source term is S 3ϑ , the other source
term Sϕ having been set to zero, and vice versa for the caseof the high energy beam only. The total source terms forthe three cases are shown in Fig. 7. It is seen that for the
coupled interaction the source term of the harmonic field issignificantly greater than for either of the two beams individually.

EFFECT OF ENERGY SPREAD
The equations (2–6) were solved numerically with thesame parameters as before, but now with a variation in thehigher energy beam energy spread σ ℘ . This was done bothfor the case of the higher energy beam alone (by setting
R3 = 1000) and for the coupled two-beam oscillator, with
R3 = 5 as before. The results are shown in Fig. 8 andFig. 9 respectively. The significance of the results is illustrated by considering first the performance due to thesingle electron beam, and then the change in performanceby adding a lower energy beam of one fifth the current. Fora minimal energy spread in the higher beam, σ ℘ = 0.1, thesaturation intensity |A3 |2sat is increased by 18% from 1.9 to

New Concepts

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R. Thompson et al. / Proceedings of the 2004 FEL Conference, 633-636|A3 |2sat

0.7

Nsat

0.5
0.4
0.3

3

0.2

Low beam only: S3θ
High beam only: Sφ

0.1

Both beams: S +S
3θ

0
0

10

20
30
Pass Number40σ℘ = 0.1
1.9
2.25
18%
50
30
40%

σ℘ = 1.4
0.8
1.5
87%
150
50
66%

Table 1: Changes in saturation intensity |A 3 |2sat and saturation time Nsat due to the introduction of a lower energy
beam of one fifth the current, for different energy spreadsσ℘ in the higher energy beam.

2|A | driving terms S

0.6

High beam only
Two beams
Increase
High beam only
Two beams
Decrease

φ50

Figure 7: Source terms for the two beam oscillator and forthe low energy and high energy beams individually.

2.25 and the number of passes to saturation, N sat , reduced
by 40% from 50 passes to 30 passes. However as the energy spread in the higher beam is increased the effect ofadding the lower energy beam becomes more significant—for σ℘ = 1.4 the saturation intensity |A 3 |2sat is increased
by 87% from 0.8 to 1.5 and N sat reduced by 66% from 150
passes to only 50 passes. These figures are summarised inTable 1.
These preliminary results examining the effect of energy spread in the higher energy beam deserve more study
but give an initial indication of the the potential benefit ofadding a smaller current, lower energy beam to the higher
energy beam.

CONCLUSION

Figure 8: Evolution of the harmonic intensity in the twobeam oscillator for varying gaussian energy spreads σ ℘ inthe higher energy beam.

A model of a one-dimensional two-beam oscillator freeelectron laser has been presented and investigated numerically in the steady-state regime for the case where thecurrent in the lower energy beam is one-fifth of the current
in the higher energy beam. It has been seen that in themildly nonlinear regime of z̄ = 2 considered here, the gainof the coupled two-beam system is enhanced slightly overthat obtained from a summation of the gains obtained fromthe individual beam interactions. It is seen that in the amplification phase before saturation the increase in intensityof the third harmonic is driven by both electron beams simultaneously. The effect of energy spread in the higher
energy beam has been investigated and there is evidence
that a two-beam oscillator may allow for a reduction in the
beam quality requirements.
Further analysis is required over a wider range of themulti-parameter space defining the system before any
definitive statements can be made as to whether the twobeam FEL oscillator offers real prospects of improvement
over that available from a single beam interaction only.

REFERENCES
Figure 9: Evolution of the harmonic intensity with thelower energy beam switched off, for varying gaussian energy spreads σ℘ in the higher energy beam.

THPOS48[1] B. W. J. McNeil, M.W. Poole and G.R.M. Robb, these proceedings.
[2] B. W. J. McNeil, G. R. M. Robb and M.W. Poole , Phys. Rev.
E (in press)

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J. John et al. / Proceedings of the 2004 FEL Conference, 637-639

HARMONIC CASCADE FEL DESIGNS FOR LUX, A FACILTY FORULTRAFAST X-RAY SCIENCE∗
J. Corlett, W. Fawley† , G. Penn, W. Wan, and A. Zholents, LBNL, Berkeley, CA 94720-8211, USA
M. Reinsch and J. Wurtele, Univ. Calif. Berkeley, Berkeley, CA 94720, USA
Abstract
LUX is a design study to develop concepts for future ultrafast x-ray facilities. Presently, LUX is based on an electron beam accelerated to ∼3-GeV energy in a superconducting, recirculating linac. Included in the design are multiple free-electron laser (FEL) beamlines which use the harmonic cascade approach to produce coherent XUV & soft
X-ray emission beginning with a strong input seed at ∼200nm wavelength obtained from a ”conventional” laser. Eachcascade module generally operates in the low-gain regime
and is composed of a radiator together with a modulator
section, separated by a magnetic chicane. The chicane
temporally delays the electron beam pulse in order that a”virgin” pulse region (with undegraded energy spread) bebrought into synchronism with the radiation pulse. For agiven cascade, the output photon energy can be selected
over a wide range by varying the seed laser wavelength andthe field strength in the undulators. We present numericalsimulation results, as well as those from analytical models, to examine certain aspects of the predicted FEL performance. We also discuss lattice considerations pertinent
to harmonic cascade FELs, somesensitivity studies and requirements on the undulator alignment, and temporal pulse
evolution initiated by short input radiation seeds.

INTRODUCTION
In the past decade, there has been an increasingly strong
interest in developing intense sources of tunable, coherent
radiation at extreme ultraviolet and soft x-ray wavelengths.
While much of this effort has been concentrated upon
SASE-based FEL’s, there is an alternative “harmonic cascade” FEL approach [1][2] which begins with a temporally
and transversely coherent input signal from a “conventional” laser in the ultraviolet region (e.g. λin ∼ 240 nm).
This input is then effectively frequency-upshifted via resonant electron-radiation interaction in a series of FEL undulators to produce a short wavelength (e.g. λf ∼1 nm) final
signal with excellent transverse and temporal coherence.
LUX is a design study underway at LBNL to develop
concepts for future ultrafast x-ray facilities with emphasis on parameters complementary to SASE-based projects.
Concepts have been developed for an integrated systemof ultrafast x-ray techniques and lasers, using laser-seeded
harmonic cascade FEL’s, rf- and laser-based electron∗ Work supported in part by the Office of Science, U.S. Dept. of Energy
under Contract DE-AC03-76SF0098† WMFawley@lbl.gov

Available online at http://www.JACoW.org

bunch manipulation, x-ray compression, high-brightness
high-repetition rate electron sources, and with timing andsynchronization systems as fundamental elements. This
paper follows on previous conference contributions [3][4]which have given details of possible cascade layouts together with expected performance and sensitivity to various e-beam and input laser parameters. Here we wantto present some additional work that has been performed
at LBNL on the LUX concept such as an analytic model
for cascade performance, a design for an isochronous bend
which would preserve microbunching exiting a modulator
at short wavelength scales, some results concerning sensitivity to undulator alignment and tilt, and the temporal
evolution of a short input pulse.

ANALYTICAL RESULTS FOR CASCADEPERFORMANCEAn analytic theory for seeded beams (please see [5] formuch greater detail) has been developed which allows forthe rapid numerical evaluation and optimization power output in low gain harmonic cascades. A key ansatz of thetheory holds that the “preferred” output mode from the radiator is that which maximizes the output power for a given
set of undulator and modulated electron beam parameters.
For the first stage, when seeded by a radially-large externallaser, the theory predicts that the optimal power output, P ,from the radiator scales at wavelength λ asP)
≈ 4.12 Z0 I 2 NU ζ [J0 (ζ) − J1 (ζ)]2 Jn2 (jn,1
 

−1
σ
j
β εN /γ
n,1 γ
× Fγ2
. (1)
1+4
∆γM
L λ/4πHere, Z0 = 377 Ω, I and εN are the beam current
and normalized emittance, respectively, NU is the numberof radiator undulator periods, n is the harmonic number,
is the first zero of the derivaζ ≡ a2U /2(1 + a2U ), jn,1
tive of Jn , ∆γM is the energy modulation produced by
the upstream modulator, and the function F depends onthe energy distribution and decreases with increasing argument. At this optimum, the Rayleigh length will be
ZR ≈ 0.15L + 2πσe2 /λ, where L is the radiator lengthand σe is the electron beam size. Quantitative comparisonof the analytic theory predictions (as evaluated via a Mathematica script) with numerical simulations with the GENESIS code show agreement of 20% or better for LUX cascade parameters. Consequently, we believe that the above

New Concepts

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60.

Win32 version 8.51/07

15/09/03 16.30.43

βx

βy

0.12

Dx
0.10

50.
0.08
40.
0.06

0.04

30.

0.02
20.
0.0
10.
-0.02

0.0

-0.04
0.0

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.
s (m)

δ E/ p 0 c = 0 .
Table name = TWISS

Figure 1: Plots of the bend lattice functions

mentioned ansatz has been confirmed, at least in the LUX
operational regime.

BEND SECTION DESIGN
The present design of LUX ([3, 6, 7, 8]) has included
the option of bending the electron beam immediately following the exit of each modulator. The purpose here wasto allow easy access to the radiation beam for experimentalists. However, various colleagues have raised the issue
as to whether it is possible to design a bend which would
retain the microbunching (and especially that at the higher
harmonic wanted for good radiator output) without unduedegradation. In the past year we have examined in detail abending section design to satisfy these concerns.
Type
Bend (B1)
Bend (B2)
Quad (QF)
Quad (QD)
Sextupole (S1)
Sextupole (S2)
Sextupole (S3)Length (cm)
30
30
60
60
60
60
30

Field at 1.5 cm (kG)
12.7375-6.6243-2.55132.54230.72971.5768-3.6514

Table 1: List of magnets (trims not included), along with
their lengths and strengths
First of all, the microbunching length scale of 1 nm is
at least an order of magnitude shorter than that examinedin any previous study ([9, 10]). There is no doubt that all
second order aberrations in time-of-flight will need to becorrected. It remains to be seen whether higher order aberrations are small enough to be effectively ignored. One efficient way of achieving this goal is to take full advantageof the four cell achromat first systematically studied andapplied in realistic design by K. Brown ([11]). The basic
result of that work was that a beamline is an achromat if

THPOS51Dx (m)β (m)J. John et al. / Proceedings of the 2004 FEL Conference, 637-639

it consists of 4 identical FODO cells with 90 degree phaseadvance in both planes. To the first order, time-of-flightdepends on momentum only (R56 = 0). If 2 families of
sextupoles are added to correct chromaticity, to the second
order, the time-of-flight depends on momentum only (T566
= 0). To maintain bunch structure at the 1 nm level, both
R56 and T566 have to be under control, which means that
one extra knob each on the first and second order optics.
It is certain that at 2.5 GeV, the knob to adjust T566 has tobe a sextupole. Yet there are at least two options to cancel
and adjust R56 . To cancel R56 , or to make R56 very small,which is the case here, either negative dispersion has to becreated or reverse bends must be used. Generally speaking,using reverse bends requires weaker quadrupoles. It was
found that third order aberrations are too large if negative
dispersion is used to cancel R56 . To adjust R56 , one option is to use an additional family of quads; this was not
adopted due to the concern of the cost and the length of thebeamline. Instead, the scheme used here is the redistribution of bending (keeping the total bending angle fixed). As
a result, the bending section consists of 4 identical cells.
Each cell contains 2 dipole, 2 quadrupole and 3 sextupole
magnets. The total bending angle of the beamline is 5 degrees. It turns out that, at sub-micron level, adjusting R56
does not affect focusing, making it an independent knob.
To shorten the length further, two families of sextupoles
are placed inside the quads. The spacing between magnets
is 10 cm, except that, after each quad, an extra 10 cm isreserved for BPM and correct/skew quad coils. The key
parameters of all main magnets are listed in Table 1 andthe lattice functions are shown in Fig. 1.
Preliminary tracking study for the last section (λ=1 nm)
has been done to evaluate the performance of the beamline.
The initial distribution of electrons was taken directly froma GINGER [12] FEL simulation of the LUX harmonic cascade through to the end of the 4-nm modulator. The energyof the electron beam was 2.5 GeV, the normalized transverse emittance (round beam) is 3π mm-mrad and the peak
to peak energy modulation is 5 MeV. First, the effect of
the remaining aberrations beyond the second order is examined, with fringe field included. The result is that there
is no net change in the bunch length.
The effect of errors is simulated through a computergenerated random Gaussian distribution. Up to now, only
static errors have been included, which are the setting errors of the dipoles, quadrupoles and sextupoles, the sextupole component in dipoles and quadrupoles, tilt and misalignment of quadrupoles and sextupoles. In order to ensure success in operation, dipole, quadrupole (normal andskew) and sextupole correctors are included in the design.
Trim coils are envisioned in each quad and two families of
sextupoles that are inside the quads. A 10-cm slot downstream of each quad is reserved for a BPM and a set of
dipole corrector/skew quad coils. The currents of the main
dipoles are used to restore R56 to the optimal value. Specifically, there are 8 horizontal dipole correctors and 8 verticalcorrectors, all of which are individually powered. The trim

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J. John et al. / Proceedings of the 2004 FEL Conference, 637-639

UNDULATOR MISALIGNMENTSENSITIVITY
We have conducted a survey study of the sensitivity ofradiator output to undulator misalignments and tilts using
the GENESIS [13] simulation code. For wavelengths asshort at 1 nm, offsets of up to 10 microns do not lower
the output power by more than 15%. For 20-micron offsets, at 2- and 1-nm wavelengths the power drops by 25%
and 40%, respectively. Offsets of 40 mcirons essentiallyeliminate the power at the shortest wavelengths and reduce
it by 40% at 10-nm. Simple angular tilts of up to 2 µrad
do not appreciably reduce the output whereas there is a
≈40% loss for a 4-µrad tilt; increasing the tilt to 8 µrad
essentially turns off the device at wavelengths 2.0-nm andshorter. These results suggest reasonably careful (but notabsurdly intricate) alignment will be necessary for operation below 10-nm wavelength.

SHORT PULSE EVOLUTION
Some user applications may require output radiation
pulse durations much shorter than the nominal ≈ 200 fs
adopted in our sample design for LUX. For a high gain FEL
cascade initiated with a Gaussian temporal profile, Saldin
et al.[14] have predicted that the rms√ radiation pulse duration will tend to shrink by a factor M from one stage tothe next where M is the harmonic ratio between the modulator resonant wavelength and that of the radiator immediately downstream. A high power, low gain design cascadeis less sensitive to input power variations and one therefore expects less shrinkage. Moreover, in the extreme limit
where the radiation pulse duration is quite short, one expects that slippage effects will place a lower limit on the
output pulse duration from each stage.
To study these phenomena, we initiated a LUX cascade with a Gaussian temporal profile seed pulse with σt=5 fs (11.2-fs FWHM) and examined the downstream P (t).
GINGER simulations were done in full time-dependent
mode and included shot noise effects. In order to obtainsufficient energy modulation in the first stage, the peak in-

1.2e+08240-nm * 0.04
48-nm * 0.25
12-nm
4-nm
1-nm * 10

1e+08

8e+07
Power (W)quads, skew quads and trim sextupole are grouped into 2
families. In one family, the elements are powered symmetrically about the midpoint of the beamline and, in theother family, they are powered anti-symmetrically. The twocurrents of the main dipoles are grouped into one family,
keeping the difference fixed, hence the total bending angle unchanged. The conclusion is that, with typical errors
in accelerators, bunch compression can be restored whentrim quads, skew quads, and trim sextupoles are turned on
and the dipole correctors are off. Without orbit correction,
both trim and skew quads must be energized to maintainthe short bunches. On the other hand, practical implementation remains an outstanding issue. A practical scheme is
yet to be developed to tune up the beamline and maintainstable operating conditions over time.

6e+07

4e+07

2e+07

0
-20

-10

0

10
20
Time (fs)

30

40

50

Figure 2: Predicted P (t) profiles at different stages for a
LUX cascade initiated with a Gaussian profile pulse witha 5-fs RMS duration. Each curve has been scaled by theindicated factor to fit on the plot.
put power was increased to 2.5 GW from the nominal timesteady value of 1.0 GW. Figure 2 shows the temporal output power profiles from each radiator stage. The FWHM
temporal duration first increases to ≈15 fs at λ=48 nm,
presumably because τslip =24 fs, but then shrinks back toa nearly constant ≈11 fs in the next 3 stages, in strong contrast to the scaling observed in [14]. Since the slippage isless than 3 fs in the 4- and 1-nm stages, the lack of additional pulse shrinkage must be due the design features of alow gain, high power configuration. Some noise modulation appears on the 1-nm output P (t) but the pulse remains
nearly completely temporally coherent.

REFERENCES[1] L.H. Yu, Phys. Rev. A, 44, 5178 (1991).
[2] R. Bonifacio et al., Nucl. Inst. Meth. A, 296, 787 (1990).
[3] W.M. Fawley et al., Proc. 2003 Particle Accel. Conf., IEEE
03CH37423, 923 (2003).
[4] G. Penn et al., EPAC2004, Paper MOPKF074 (2004).
[5] G. Penn, J. Wurtele and M. Reinsch, “Analytic Model of harmonic Generation in the Low-Gain FEL Regime”, Paper MOPOS57, these proceedings.
[6] J. Corlett et al., LBNL report LBNL-51766 (2002).
[7] J. Corlett et al., Proc. 2003 Particle Accel. Conf., IEEE
03CH37423, 186 (2003).
[8] A. A. Zholents et al., Beam Transport Lattice in a Cascaded
Harmonic FEL LBNL CBP Tech Note-281 (2003).
[9] S. Chattopadyay et al., LBNL report LBNL-39788 (1997).
[10] A. Zholents, M. Zolotorev and W. Wan, Proc. 2001 Particle
Accel. Conf., IEEE 01CH37268, 723 (2001).
[11] K. L. Brown, IEEE Trans. Nucl. Sci., NS-26, 3490 (1979).
[12] W.M. Fawley, LBNL report LBNL-49625 (2002).
[13] S. Reiche, Nucl. Inst. Meth. A, 429, 243 (1999).
[14] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Opt.
Comm., 202, 169 (2002).

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K. Chalut et al. / Proceedings of the 2004 FEL Conference, 640-643

NOVEL METHOD FOR PHASE-SPACE TOMOGRAPHY OF RAPIDLYEVOLVING E-BEAMS
K. Chalut, Duke University, Department of Physics, Durham, NC 27708, U.S.A,
V.N. Litvinenko, I.V. Pinayev, Brookhaven National Laboratory, Upton, NY 11973, U.S.A.
Abstract
In this paper, we describe a new method for phasespace tomography. This method allows one to restore
phase space density using a small number of projections
covering a limited angle of rotation or another linear
transformation in the phase space. Practical applicationsof this method for phase-space tomography are discussed.

INTRODUCTION
Traditional methods of phase-space tomography, such as
the Radon transform, require multiple, evenly spaced
projections of exactly a 180° rotation angle in the phasespace in order to reconstruct a frozen picture [1]. It meansthat reconstruction of the longitudinal phase space of thee-beam with Radon transforms require the evolution of
the e-beam to be slow (adiabatic) on the time scale ofsynchrotron oscillations. Radon transforms also apply
only to rotations, i.e. to a very small sub-group of linear
transformations and projections used in accelerator
physics and, generally, in imaging.

One
synchrotron
oscillation
Figure 1: Dual-sweep streak camera image of giant pulse.
The camera recorded the time structure of the intensity of
the light generated by the e-beam on multiple turns. The
vertical sweep, which is synchronized with the revolutionof the e-beam, is fast and has the full scale of 1.6 nsec.
The horizontal sweep is slow and has the full scale of 500µsec. The trace seen at top is the FEL light. The main
image is that of the spontaneous radiation of electron
beam, which is identical to the beam time profile.
In the giant pulse process in a storage ring FEL [2],the electron beam evolves dramatically and its energy
spread increases by up to a factor of three within one
synchrotron oscillation. For the giant pulse process, andother processes that evolve quickly, a new method ofreconstruction is needed. We investigate two new
methods of reconstruction that are not limited by

THPOS53

observation angle, and work for any linear process, notjust rotation. The only requirement is that we have someknown set of linear projections.

METHOD DESCRIPTION
Projection matrix
Supposearbitrary distribution of particles& & we have an
D
,
P
)
in
an
N
phase
space (D is its dimension),F(X
 n n&&
described by its spatial (X ) and momentum (P )coordinates, it follows that there is a projection operatorPˆ (α ) which, when acting upon the distribution, will&I( x m ,α )give us a set of linear projections (images) 

where

& &
&
I ( x m , α ) = Pˆ (α ) ⊗ F ( X n , Pn ) .

(1)&
x m is the sub-set of spatial coordinates in the projection(image) space. Typical projection space used for imaging
beam of charged particles has one or two dimensions. The
projection matrix depends only upon the parameter α ,which we use to identify projection.
In our specific example we used a dual sweep streak
camera (hence one dimensional images) for reconstructionof an evolution of electron beam density (F) in
longitudinal phase space (two dimensions). But themethod is applicable of any process with linear
transformations and projections [3].
The longitudinal phase space of electron beam in astorage ring can described by two dimensionlesscoordinates ε = (E − E 0 ) /σ E 0 and ζ = (t − t 0 ) /σ t 0 ,where E and t are the energy and arrival time of anelectron, Eo and to are, respectively, the energy and timeof the synchronous electron, σ E 0 and σ t 0 are
corresponding RMS spreads of a stationary beam.
Electron bunches under study are very short and theunperturbed motions of electrons in the longitudinal phasespace can be presented as a simple rotation in which theangle is the synchrotron phase advance ϕ:ε   cosϕ n  =
ζ n −sin ϕ n

sin ϕ n  ε  ⋅   ;ϕ = n ⋅ 2πQs (2)cosϕ n  ζ o n

where Qs << 1 is synchrotron tune [4] and n is the turnnumber. The rotation causes a transformation of the phasespace density governed by the Liouville theorem:

Fn (ζ,ε) = F0(ζ ⋅cosϕn −ε ⋅sinϕn,ε ⋅cosϕn + ζ ⋅sinϕn ) (3)Available online at http://www.JACoW.org

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K. Chalut et al. / Proceedings of the 2004 FEL Conference, 640-643

At each turn of the e-beam around the ring the dual
sweep streak camera records the time profile of the beam,i.e. the projection of the phase space density F(E,ζ) onto
the time coordinate:
∞

−∞

(4)

n

n

n

(pseudoinverse) as P+

= VD +U T , where the diagonalof D is made up of the inverse of each of the singularvalues of D, in descending order, so long as the singularvalue in question is not zero. If the singular value of D is+

∫ F (ζ ⋅ cosϕ − ε ⋅ sinϕ ,ε ⋅ cosϕ + ζ ⋅ sinϕ ) ⋅ dεoTeigenvalues) of PP . U and V are, by definition,orthogonal. This decomposition can be inverted+I(ζ ⋅ σ to)ϕ = P(ϕ) ⊗ Fo (ζ ,ε) = ∫ F(t /σ to,ε) ⋅ dε =∞matrix comprising the singular values (square root of thezero, then the corresponding element of D is also zero.
If we assume P is a u × v matrix, then as u increases,

n

−∞

+

Hence in our case the projection operator is completely
defined by the synchrotron phase ϕ. This is still a
description using continuous functions and coordinates.
To make the problem computer friendly we must translate
this problem into arrays and bits of information. Let’s
consider that we have a distribution function defined on
an N x N grid in the phase space, F=[Fij]. Our goal is now
to find a way to extract information about the array F
from the finite number of projections.
We get our full set of linear projections from a dualsweep streak camera [5], which captures the synchrotron
light from the electrons. A CCD camera digitizes theimages from the streak camera. Let’s select a sub-set of J
projections (along vertical lines in Fig. 1), which cover asmall portion of a synchrotron period, and use M pixels
from each image. The information contained in theseprojections has J x M bits. As long as J x M > N2 we havea chance to extract the information about the distributionfunction F=[fij].
The matrix form of equation (1) takes following form:[I]u = [P ]u,v ⋅ [F ]v ;u = N ;v = M ⋅ J
2D(5)where array I is a combination of ordered J projections, F
is the array of ordered Fij, and P is the projection matrix,
specific appearance of which we define later. In the caseof the giant pulse process in a storage ring FEL, therelevant parameter for the projection matrix is thesynchrotron phase, and knowing the synchrotron
frequency and the time of each projection provides us
with that knowledge.
The problem is now reduced to a robust way of solving
equation (1) and finding F with reasonable accuracy. The
projection matrices are typically very large, non-squareand singular, which makes singular value decomposition(SVD) method a natural choice for solving equation (1).

some diagonal elements of D can be very large, andundue emphasis can be put on the corresponding singularvalues. This may cause a very high sensitivity of themethod to errors and noise. Fortunately, SVD allows us totruncate the series at any desirable number of eigen values(which are all positive, or zero, and are numerated indescending order) with any K PLQ XY :K

P + = σ1 E1 + ...σ K E K = ∑σ k E k ; E k = U k Vk . (7)k=1

Truncation provides for robustness of this method andmakes it less sensitive to the errors in the knowledge of
projection matrix as well as to the noise in the images.
The projection matrix is defined both by the type of
projection (for example the angle of rotation), the size ofthe pixel in the image array and the type of discrete
representation of a continuous distribution. Here we
present two simple discrete models representation: pillbox
and Gaussian.

Pillbox representation
This is a simple representation of the distribution by
NxN pillboxes with Fij height located on an evenly spaced
2D-grid.

.

(4,5)

ϕ=6*π/25
m=34

Figure 2: Element of projection matrix P634 ,31 of grid-box
th

SVD
There is a wealth of information concerning SVD (seefor instance [6]), but it is, in brief, the decomposition
which, when inverted, satisfies the least-squares minimum
criteria for the function

Φ = I − P⋅F

2One decomposes a matrix P →(6)

UDV T , where theTcolumns of U are the eigenvectors of PP , the columns
Tof V are the eigenvectors of P P , and D is a diagonal(4,5) on the 34 pixel when the grid is rotated on the angleof ϕ =6*π/25 around the origin is equal to the area of theintersection shaded in light yellow.
The elements of the projection matrix are equal to thearea of intersection of a box located on (i,j)-grid nodewith the lines indicating the boundaries of the mth pixel.
The grid rotates around the origin according to the angle ϕof given projection. Figure 2 shows a specific example ofsuch a cross-section:
Pm, j,i,l = P634,35 = Areaovelap (8)New Concepts

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K. Chalut et al. / Proceedings of the 2004 FEL Conference, 640-643

The pillbox representation has the advantage of giving theexact projection matrix, but the sharp corners inherent in
the method do not provide for a smooth reconstruction.
Hence, these sharp corners can be exaggerated in thepresence of errors or/and noise.

Gaussian representation
It is a more elegant representation of a distributed
function by a set of NxN Gaussians centered at the evenly
spaced 2d-grid - see equation (9a). Each Gaussian has
individual height (Fij for (i,j)th node) and a common r.m.s.
width σ r , which plays the role of an adjustableparameter.

( xi , y l )Gaussian
representation

wm+1

wm

THEORETICAL COMPARISON
In order to study the theoretical aspects of the two
representations, we created a theoretical construction,
wherein we may compare a known function with ourreconstruction. Here we present few selected results withthe trial function a Gaussian with unit height, located offorigin and having r.m.s. width of 2 grid size. Bothrepresentations were using 13x13 2D-drid with using gridsize. Theoretical projections are 117 pixels for each image(an arbitrary number). We then use the SVD method
described above for both representations. We evaluatedthe accuracy of reconstruction by subtracting thetheoretical numbers from the reconstruction on the gridand comparing the norm of the difference with the normof original function:
norm(reconstruction − baseline)
Error[%] =*100norm(baseline)
Figure 4 shows results of preliminary studies of themethods accuracy as function of the number ofprojections (spaced 10° apart).

Figure 3: The projection of a pixel onto a Gaussian nodein the phase-space.

Pillboxrepresentation

The projection matrix is then found by projecting each
Gaussian mode onto each pixel using eq. (4) and the pixel
width (wm,wm+1):−(a) F(x, y) = ∑ Fi,l *e

1
2σ r2

(−(x−x i )2 −(y−y l )2 )

i.l

wm+1

−

(b) Pm,i, j,l = 2π σ rep ∫ e

1
2σ r2

(9)

(x i cosϕ j +y l sin ϕ j −u)

duwm

Figure 4: Error of reconstruction vs. # projections forpillbox and Gaussian representations.

Solution
When projection matrix is pseudo-inverted for a given
choice of K (i.e. cut-off number of eigen vectors used inreconstruction) using eq. (7), the P+(K) gives the resulting
elements of Fil as:[F ] = [P + (K)]⋅ [I].

(7’)

In pillbox case these are the heights of the boxes on thegrid with discontinuities on each grid edge. For Gaussian
representation, the result is a smooth function (9a), whose
scale of variations can be limited by increasing of σ r .
Increase of σ r to or above a size of a grid size will also
lead to the reduction of the accuracy of the representation.
Hence, there is an optimum σ r (depending of the errors
and the noise level), which provides a smooth but
reasonable accurate representation of the real distributionfunction.

THPOS53

We did not succeed so far in accurate reconstructing of
the trial functions using two projections and limited
number of pixels ~ 100 - the errors are too large. We
attribute it either to a need for a better image resolution(M >> 100) or to a possible “small bugs” in our programs.
It is clear from our preliminary studies that the Gaussian
representation provides a better reconstruction for smoothfunctions than the pillbox representation. We continue thestudies of the analytical features of the method, includingreconstruction of distributions with complex topology.

ANALYSIS OF GIANT PULSES
Figure 1 shows one of many measured dual sweep
streak camera images of electron beam evolution in theDuke OK-4 storage ring FEL during the giant pulse
process. During the above measurement the synchrotron
frequency was 24.3 kHz, and the image shows evolutionof the longitudinal distribution of the electron beam over

K. Chalut et al. / Proceedings of the 2004 FEL Conference, 640-643

approximately 12 synchrotron oscillations. One can seethat there is a transition region, where the length if the ebunch is evolving rapidly, and dramatically, in less than
one synchrotron oscillation.
The self-consistent theory of giant pulses [7] predicts
strongly asymmetric, snail-like distribution [8] generated
in the giant pulse process. Out new method allows us toreconstruct distributions from a limited number ofprojections, to observe the details of phase space
dynamics during the giant pulse and to compare themwith the theory. Preliminary results look promising, as
seen in the pictures below.

643

simulation using #vuvfel code [8] (with beam parameters
taken from experimental runs) and to compare thesimulated electron distributions with the reconstructions
we get from dual-sweep streak camera images. The
reconstruction passes the eye test, but the next step is to
do a quantitative comparison. We stress that only 8
projections, space 6.82° apart, were used to complete thisreconstruction, for a total observation angle of 47.8°.
There is reason to believe some improvements can bemade on the code so that we can get a betterreconstruction with an even smaller set of projections.

CONCLUSIONS

Figure 5: Reconstruction of e-beam distribution in
equilibrium (before lasing) using 8 projections, 6.82°
apart. Scale is arbitrary.

We developed a novel method of phase-space
tomography, which theoretically requires only a full set of
two or more linear projections. Currently, we are
improving the model to see how low the limit can be
pushed. Theoretical models indicate that, with limited
resolution, we can get a good reconstruction (<5%) with aset of five projections. Perhaps we could get betterreconstruction using greater resolution. We used
experimental data from giant-pulse measurements at theDuke storage ring FEL to test the model, and saw somepromising results.
It is important that this method works for any linear
projections, not only for rotations [3]. It has potential
applications of this method for accelerator physics,
medicine, military, and astronomy. Future work will be tofurther improve the model, compare it to giant-pulse
simulations, and apply the method to other problems.

REFERENCES

Figure 6: A reconstruction using 8 projections, 6.81°
apart, of the transition region. Noticeable double-hump isremarkably similar to the profile predicted by the theory[7,8].

[1] S.R. Deans, The Radon Transform and Some of Its
Applications, Wiley & Sons, 1983.
[2] I.V. Pinayev et al., Nucl. Instr. and Meth. A475
(2001), pp. 222-228[3] SVD-based tomography, K.Chalut, V.N. Litivinenko.
in preparation[4] see for example, “The Principles of circular
Accelerators and Storage Rings”, Philip J.Briant andKjell Johnsen, Cambridge University Press, 1993,
p.156[5] A.H. Lumpkin et al., Nucl. Instr. and Meth. A407
(1998), pp. 338-342.
[6] P.E.Gill et al, Numerical Linear Algebra and Its
Optimization, Addison-Wesley, 1989.
[7] V.N. Litvinenko, Proceedings of FEL conference,
August 2002, APS, Argonne, IL, Eds. K.-J.Kim,
S.V.Milton, E.Gluskin, p. II-1
[8] V.N. Litvinenko et al., Nucl. Instr. and Meth. A358
(1995), pp. 334

The pictures in Figures 5 and 6 were reconstructedusing the Gaussian representation. The reconstructions
using the pillbox representation had many jagged peaks.
The reconstructed distribution shown in Fig. 6
qualitatively agrees with the theoretical prediction [7,8].
Clearly, there is room for more studies and comparisons.
We plan to finish detailed comparison of a giant-pulse

New Concepts

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P. M. Musumeci et al. / Proceedings of the 2004 FEL Conference, 644-647

ACCELERATION OF ELECTRONS IN A DIFFRACTION DOMINATED
IFEL
P. Musumeci, S. Ya. Tochitsky, S. Boucher, A. Doyuran, R. J. England,
C. Joshi, C. Pellegrini, J. Ralph, J. B. Rosenzweig, C. Sung, G. Travish, R. Yoder
University of California at Los Angeles, CA 90095, USA
A. Varfolomeev, S. Tolmachev, A. Varfolomeev Jr., T. Yarovoi, RRCKI, Moscow, Russia
Abstract
is diffraction dominated.
We report on the observation of energy gain in excess of
20 MeV at the Inverse Free Electron Laser Accelerator experiment at the Neptune Laboratory at UCLA. A 14.5 MeV
electron beam is injected in a 50 cm long undulator strongly
tapered both in period and field amplitude. A CO2 10.6 µm
laser with power > 300 GW is used as the IFEL driver. The
Rayleigh range of the laser (∼ 1.8 cm) is shorter than theundulator length so that the interaction is diffraction dominated. Few per cent of the injected particles are trappedin stable accelerating buckets and electrons with energies
up to 35 MeV are detected on the magnetic spectrometer.
Three dimensional simulations are in good agreement withthe electron energy spectrums observed in the experimentand indicate that substantial energy exchange between laserand electron beam only occurs in the first 25-30 cm of theundulator. An energy gradient of > 70 MeV is inferred. In
the second section of the undulator higher harmonic IFEL
interaction is observed.

INTRODUCTION
Inverse Free Electron Laser (IFEL) schemes to accelerate particles have been proposed as advanced acceleratorsfor many years [1, 2]. Recent successful proof-of-principle
IFEL experiments have shown that along with acceleration [3, 4] this scheme offers the possibility to manipulate and control the longitudinal phase space of the output beam at the laser wavelength. First among other laser
accelerator schemes, the Inverse Free Electron Laser has
in fact experimentally demonstrated microbunching [5],phase-dependent acceleration of electrons [6], phase locking and multi-stage acceleration [7] and control of final energy spread [8]. Up to now, though, only modest energy
gains and gradients have been achieved in an IFEL accelerator mostly because of the relatively low peak laser power
employed in the experiments carried out so far.
The Inverse Free Electron Laser experiment at the Neptune laboratory at UCLA accelerated electrons from 14.5
MeV up to more than 35 MeV utilizing a CO2 laser beamwith a peak power ( ∼ 0.4 TW ), one order of magnitude
greater than any other previous IFEL experiment had used.
To maintain the resonant condition with the accelerating
electrons, the 50 cm long undulator is strongly tapered bothin period and magnetic field amplitude. An important pointof the Neptune IFEL configuration is that the Rayleighrange of the laser beam is much shorter than the undulator length and the Inverse Free Electron Laser interaction

THPOS57

EXPERIMENTAL SETUPIn Table 1 we report the design parameters of the Inverse
Free Electron Laser experiment at the Neptune Laboratory.
In Fig. 1 it is shown the experimental layout for the IFEL
experiment. An electron beam of 300 pC at 14.5 MeV isdelivered to the experimental region by the Neptune rf photoinjector [9]. Final focus quadrupoles with large aperture
to avoid clipping of the copropagating laser beam were installed on the beamline and focused the electron beam tothe nominal spot size of 120 µm rms in the middle of theundulator. A TW-class CO2 laser system [10] is used todrive the IFEL. The high power laser beam is brought invacuum through a NaCl lens that has both the function of
producing the correct focusing geometry and serves as avacuum window. The laser is made collinear to the e-beam
utilizing a plane copper mirror with a hole. The beams arealigned on the probe in the midplane of the undulator withan accuracy of < 100 µm and the angular misalignment is
kept below 1 mrad using the screens located before and after the undulator. After the interaction region, the e-beam isenergy analyzed by the magnetic spectrometer and the laser
beam is sent to the streak camera for timing measurements.
The undulator for the IFEL experiment at the Neptune
Laboratory was built at the Kurchatov Institute [11]. It is aunique magnet because of the very strong variation of theundulator parameters (wiggling period and magnetic field
amplitude) along the axis, carefully tailored to maintain theresonance condition of the IFEL interaction between theCO2 photons and the quickly accelerating electrons. The
undulator parameters are reported in Table 2.
Synchronization between electrons and photons is theElectron beamenergychargeemittance
pulse length (rms)
CO2 laser
Power
Wavelength
pulse length (rms)spot size

14.5 MeV
0.3 nC
5 mm-mrad
3 ps
400 GW
10.6 µ m
100 ps340 µ mTable 1: Electron beam and CO2 Laser parameters at the
Neptune Laboratory

Available online at http://www.JACoW.org

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P. M. Musumeci et al. / Proceedings of the 2004 FEL Conference, 644-647

To streak camera diagnostics
camerasFinal focus quadrupoles
Undulator vacuum box

CO2 beam
NaCl lensE-beam
CO2 beam dump

Magnetic
spectrometer

mirror with hole

Kurchatov undulator

Figure 1: Layout of Neptune IFEL experiment
resentative of the electron timing. On the upper right side
there is the streak of the CO2 pulse. The delay (1170 ps)
shown in Fig. 2 corresponds to the optimal timing and it
was found maximizing the output IFEL energy as a function of delay. Utilizing the streak camera diagnostics, wewere able to determine for each laser shot the pulse length(and so the peak power) of the CO2 beam and which part ofthe laser pulse intensity profile the electron beam sampledwith an accuracy of ± 10 ps.
The optical geometry used in the experiment to focus
and control transversely the laser beam size is of particularimportance. In the original design, a 2.56 m focal length
NaCl lens focused the laser in the middle of the undulator to a spot size of 340 µm with a Rayleigh range of 3.5
cm to increase as much as possible the extent of the region
where the beam is more intense. The resulting peak intensity is 2·1014 W/cm2 in the laser focus, about two orders ofmagnitude more than any previous IFEL experiment used
[7, 8]. Dealing with this very high laser intensities on theother hand had some disadvantages.
Experimentally, in fact, we were limited by damage
threshold on the last optical elements of the CO2 transportline and we could not increase the f-number of the opticalgeometry as we planned. For our typical pulse lengths of
200 ps, we observed damage on the copper mirrors for fluences above 3J/cm2 and on the single crystal NaCl optics
for fluences above 2J/cm2 . In the end, we measured a spot
size of 240 µm and Rayleigh range of 1.8 cm that, respect
to the original design geometry, implied a stronger varia-

20
15
10
5
0

Streak lineouta.u.

key for every laser accelerator with an externally injected
electron beam and it is even more delicate in an IFEL experiment. In this kind of interaction in fact, there is noresonant medium (or cavity) where the accelerating electromagnetic wave is resonating and can live independently
than the laser beam. The accelerator is virtually turned on
only at the time the laser pulse goes through the undulator
and the ponderomotive gradient that accelerates the electrons depends on the instantaneous power felt by the electrons.
At the Neptune laboratory, the electron pulse ( ∼ 15 ps
FWHM) and the longer CO2 laser pulse (∼ 240 ps FWHM)
have been synchronized in the past with a cross-correlation
method that was based on the e-beam controlled transmission of CO2 through a Germanium sample. This technique[12] constituted the first step of the synchronization procedure also in the IFEL experiment. On the other hand, thecross-correlation measurement is conducted with the unamplified laser pulse propagating through the final triple
passed, 2.5 m long multiatmosphere CO2 amplifier with noinversion of population and has an intrinsic systematic error due to the different group velocity of the laser pulse
within the inverted medium of the final amplifier in comparison with no-gain conditions. Moreover, fluctuations inlaser power (gain in the final amplifier) ± 50 % cause fluctuations in the time of arrival of ± 50 ps. This jitter isintrinsic in the laser amplification system and could not be
eliminated. In order to get very accurate information on
the relative timing between the electrons and the amplified
pulse on each shot, we set up a new streak camera basedtiming diagnostics.
In Fig. 2, it is shown a typical picture of the streak camera output. In the bottom left corner there is the reference
green pulse from the photocathode drive laser that is rep-1170 ps

0

Undulator period
Magnetic field amplitude
K
Resonant energy

initial
1.5 cm0.16 T
0.2
14.5 MeV

final
5 cm
0.65 T
2.8
52 MeV

Table 2: RRCKI IFEL undulator parameters500

250 ps1000

time (ps)

1500

2000

Figure 2: Streak camera picture of photocathode driver reference (lower-left corner) and CO2 pulse. The screen calibration gives a measurement of the laser pulse length andof the optimum delay between the reference and the CO2

New Concepts

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P. M. Musumeci et al. / Proceedings of the 2004 FEL Conference, 644-647

solved the Lorentz equation for the particle motion in the
combined fields of the undulator magnet and laser beam
(TREDI[13]). The same code was used to understand theexperimental results reproducing the experimental condition, and, once we put the correct laser intensity profile
along the undulator, agree quite well with the experiment.

2000

1600

a.u.

1200

800

400

0

20

25

30

35

Figure 3: Single shot spectrum of the Inverse Free Electron
Laser accelerator. More than 5 % of particles are accelerated to 35 MeV with 150 % energy gaintion of the beam size along the interaction region, and withthe same nominal focus position at the mid-point of the undulator, a larger and less intense beam at the entrance andexit of the undulator.
To trap and accelerate particles along the design resonant orbit, the ponderomotive IFEL gradient generated by
the laser electric field has to match the designed tapering
gradient. If this is not the case, no trapping or acceleration
are possible. Because of the differences between nominal
and measured Rayleigh range, it was found out necessary
to move the laser focus upstream from the nominal position
to increase the intensity at the undulator entrance above thetrapping threshold and start the acceleration process earlyin the undulator. Of course that would also cause the particles to fall out of resonance soon after the mid point of theundulator because of lack of enough ponderomotive force
to sustain the acceleration along the designed orbit. It was
found that the optimum position of the laser focus for the
power levels available, was 2 cm (one Rayleigh range) upstream of nominal focus position.

EXPERIMENTAL RESULTS ANDSIMULATIONSThe electrons were detected by a phosphorous screen observed by CCD cameras. The screen was attached to thethin mylar window at the exit slit of the spectrometer. Different neutral density filters were applied to each cameras
to get unsaturated images of the output slit. A postprocessing application that takes into account the different filtersand scales the horizontal axis of the images with energy,
reconstructed the single shot spectrum of the electron beamout of the IFEL accelerator for each laser shot. A typicalimage of a dispersed electron beam is presented in Fig. 3
along with a reconstructed spectrum.
The energy spectrum shows more than 5 % of particles
trapped and accelerated up to 35 MeV with a 150 % energy gain. The measured power in the CO2 pulse for thisIFEL shot was 400 GW of power and the laser was focused
upstream of the nominal position by 2 cm.
The code that was used to simulate the experiment at
the design phase is a 4th-order Runge-Kutta integrator thatTHPOS57

In Fig. 4 the simulated longitudinal phase-spaces at two
different distances along the undulator are shown. The histograms on the left of the graphs are the projection of thephase-spaces on the energy axis. The simulation results allowed us to draw several conclusions.
First of all (Fig. 4a) that the IFEL acceleration mostly
takes place in the first section of the undulator (first 25 cm).
Few cm after the mid-point the laser intensity has decreased
below the trapping threshold and the designed tapering is
too strong for the particles too follow. That allows us toinfer an accelerating gradient of > 70 MeV/m.
Secondly, Fig. 4b shows the structure of the high energy side of the spectrum observed in the experiment. This
structure is particularly interesting because experimentally
it was reproducible shot to shot, ruling out the possibility of micro-structures present in the e-beam or the laser
beam. Instead, the structure is due to a different kind of
IFEL interaction that takes place in the second section of
the undulator.
We know that efficient energy exchange between thetransverse EM wave and the particles wiggling in the undulator can only take place when the resonant condition issatisfied, and so the energy of the particles is such that in
the electron’s rest frame the wiggling induced by the undulator has the same frequency of the wiggling induced by
the laser. On the other hand, it is known that particles of a
fixed energy going through an undulator interact not onlywith the fundamental resonant frequency, but also with theradiation harmonics [14]. From another point of view, particles of different energy γr,n can interact with the samelaser frequency, because they see the EM wave as a higher
harmonic of the fundamental frequency that they are resonant with. In other words, for a given laser and undulator,

25 cm

45 cm

65

65

60

60

55

55

γ

15

Electron energy (MeV)

γ

10

50

50

a)

45

b)

45
40

40
0.240060.24008z0.240100.439700.43972

0.43974

0.43976

0.43978

0.43980z

Figure 4: Simulations of IFEL longitudinal phase spaceat different points along the z axis. a) Longitudinal phasespace at the undulator mid-point. The energy gain has already taken place in 25 cm. b) Energy modulation due tosecond harmonic interaction in the second section of theundulator. The structure in the simulated spectrum corresponds to the one in the measured spectrum

647

P. M. Musumeci et al. / Proceedings of the 2004 FEL Conference, 644-647(1)

In Fig. 5, we show the first three resonant energy curves
for the Neptune IFEL undulator. In the experiment the particles fall out of the accelerating bucket from the resonant
curve (red) because of the mismatched laser intensity distribution. At√some point later in the undulator the particles
energy is 1/ 2 times the resonant energy, at this point theelectrons can exchange energy with the 10.6 µm photons
mediated by the second harmonic IFEL interaction.
The equations for the Higher Harmonics IFEL interaction are the standard IFEL equation, with the coefficient JJ
for the first harmonic interaction replaced by the appropriate JJn coupling coefficient [15].
JJn =

+∞


Neptune IFEL undulator resonant energy

100

Jm (ξ) · (J2m+n+2 (σ) − J2m+n (σ)) (2)m=−∞with dependence on the undulator K factor hidden in ξ =K 2 /(4 + 2K 2 ), the usual Bessel function argument, and in
σ = K/(γkw w) where kw is the undulator wave number
and w is the laser spot size.
The parameter σ taking a closer look, is the ratio of
the particles wiggling amplitude to the laser spot size, andit can be viewed as a quantitative measure of how threedimensional the interaction is. We note that the even harmonics interaction should be suppressed as a consequenceof the known fact that the on-axis spectrum of a planar undulator has only the odd harmonics. This is reflected by the
behavior of the coupling coefficients for even harmonics(i.e. JJn → 0 when σ → 0. for even n). In other words
σ determines the strength of the IFEL coupling to the evenharmonics [16].
In the Neptune experiment, the trajectory wiggling amplitude increases along the undulator and it becomes comparable to the laser beam size around the focus region. The
σ parameter reaches relatively large values ( ∼ 0.5) and thesecond harmonic IFEL coupling is not negligible. Moreover, in this region of the undulator the CO2 laser is still
very intense, so that a significant amount of energy can betransferred to the e-beam. The longitudinal modulation induced by HHIFEL interaction that appears in the simulated
phase space is washed out after a short drift propagation,
because of the large energy spread. On the other hand, thedeep energy structure resulting from this kind of interaction remains imprinted on the experimental beam energy
spectrum. The energy exchange is not as efficient for thethird harmonic IFEL interaction that could take place at theend of the undulator. Here, regardless of the strength of thecoupling constant, the laser field is just not intense enoughto perturb significantly the electron energy spectrum.
The higher harmonic interaction is the origin of the energy modulation seen reproducibly in the output spectrumof the experiment.

Resonant energy

there are multiple resonant energies2
λw · 1 + K2
γr,n =
2λ · n

50

0

0.1

0.2
0.3
Distance along the undulator (m)

0.4

0.5

Fundamental
2nd harmonic
3rd harmonic

Figure 5: Neptune IFEL undulator different resonant energies.

CONCLUSION
We report on the observation of > 20 MeV energy gain
(150 %) at the Inverse Free Electron Laser experimentat the Neptune Laboratory. An energy gradient of > 70
MeV/m is inferred. The fraction of self-trapped particles
exceeded 5 % of the injected bunch. The acceleration gain
reported is to date the highest obtained with an IFEL accelerator. Self-trapping of particles in a stable accelerating bucket from a not-prebunched initial distribution wasdemonstrated. The effects of the laser diffraction were analyzed in the design phase and studied experimentally. Finally, for the first time higher harmonic IFEL (HH-IFEL)
interaction was observed in the second section of the undulator. The HH-IFEL adds a degree of freedom (the harmonic coupling number n) in the design of magnetic systems capable of coupling lasers and electron beams. This
work is supported by U.S. Dept. of Energy grant DE-FG0392ER40693

REFERENCES[1] R.B. Palmer. J. Applied Physics, 43:3014, 1972.
[2] E. D. Courant, C. Pellegrini, and W. Zakowicz. Phys. Rev.
A, 32:2813, 1985.
[3] I. Wernick and T. C. Marshall. Phys. Rev. A, 46:3566, 1992.
[4] A. Van Steenbergen et al. Phys. Rev. Lett., 77:2690, 1996.
[5] Y. Liu et al. Phys. Rev. Lett., 80:4418, 1998.
[6] R. B. Yoder, T. C. Marshall, and J. L. Hirshfield. Phys. Rev.
Lett., 86:1765, 2001.
[7] W. Kimura et al. Phys. Rev. Lett., 86:4041, 2001.
[8] W. Kimura et al. Phys. Rev. Lett., 92:054801, 2004.
[9] S. G. Anderson et al. AIP Conf. Proc., 569:487, 2000.
[10] S. Ya. Tochitsky et al. Opt. Lett., 24:1717, 1999.
[11] S. Tolmachev et al. these proceedings[12] S. Ya. Tochitsky et al. Phys. of Plasmas, 11:2875, 2004.
[13] L. Giannessi, P. Musumeci, M. Quattromini Nucl. Instr.
Meth. A, 436:443, 1999.
[14] Z. Huang and K. J. Kim. Phys. Rev. E, 62:7295, 2000.
[15] P. Musumeci et al. 2004. to be submitted for publication.
[16] M. J. Schmidt and C. J. Elliot Phys. Rev. A, 34:4843, 1986.

New Concepts

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M.S.H. Hutson et al. / Proceedings of the 2004 FEL Conference, 648-653

ADVANCES IN THE PHYSICAL UNDERSTANDING OF LASER SURGERY
AT 6.45 MICRONS
M. Shane Hutson*, Department of Physics & Astronomy, Vanderbilt University,
Nashville, TN 37235, USA
Glenn S. Edwards, Free Electron Laser Laboratory and Department of Physics, Duke University,
Durham, NC 27708, USA
Abstract
We previously presented a model that attributes the
wavelength-dependence of FEL tissue ablation topartitioning of absorbed energy between protein andsaline. This energy-partitioning subsequently influences
the competition between protein denaturation and saline
vaporization. The original model approximated cornea asa laminar material with a 50:50 saline-to-protein volume
ratio. We have now refined the microscopic geometry of
the model in two ways: (1) cornea is represented as asaline bath interpenetrated by a hexagonal array of protein
fibrils; (2) the volume ratio is matched to the measured
value, 85:15. With this volume fraction, the specificabsorption coefficient for protein is much larger thanpreviously reported. Thus, the fibril array model
magnifies the differences between wavelengths that target
saline versus protein. We will discuss: (1) the consistencyof this model with previous, seemingly conflicting,experimental data; (2) predictions of the model, with aparticular emphasis on the role of laser intensity; and (3)the experiments needed to test these predictions.

INTRODUCTION
Early on in the development of surgical applications forfree-electron lasers (FELs), the tunability of FELs was
exploited to investigate the wavelength-dependence oftissue removal [1]. In the mid-IR, wavelengths near 6.45
µm proved remarkably adept at removing definedvolumes of soft tissue with very little collateral damage.
In fact, tuned to this wavelength, the Vanderbilt Mark-III
FEL has been used successfully in both neurological andophthalmic surgeries on human patients [2-4]. However,
due to cost and size constraints, it seems unlikely thatsuch FELs will ever find widespread use in patient care.
We now face the challenge of translating the surgicalsuccesses of mid-IR FELs to cost-effective, compact, anddedicated medical laser systems.
Several 6.45-µm sources have already been evaluated,
including a Sr vapor laser and a picosecond OPA system[5-6]. Unfortunately, the surgical performance of both
sources was unacceptable. These failures highlight a key
point: the surgical performance of a laser system is notdetermined by wavelength alone, but by a combination of
wavelength, intensity and pulse structure. If a tabletop
system matched the Mark-III FEL in all thesecharacteristics, then one could be reasonably assured of its
success. Unfortunately, such an exact match is unlikely_*

shane.hutson@vanderbilt.edu

FRAIS01

given the complex pulse structure of a Mark-III FEL (i.e.
2-6 µs long superpulses, repeated at 1-30 Hz, with eachsuperpulse containing a 2.856 GHz train of picosecond
pulses) [7]. Guidance on how to relax these pulse
constraints has and will come from a better understandingof the dynamics governing mid-IR tissue ablation.
It should be noted that 6.45 µm is not an obvious choicefor FEL tissue ablation. Soft tissues absorb mid-infrared
light most strongly at the water absorption bands of 3.0
and 6.1 µm; however, wavelengths near 6.45 µm weresuperior for surgical applications [1-4]. This anomalous
wavelength-dependence was attributed to partitioning of
the absorbed energy between the aqueous components ofa tissue and its protein matrix. Thermodynamic argumentssuggested that wavelengths targeting the protein matrix(like 6.45 µm) could reduce collateral damage [1].
Subsequently, we reported a dynamic model that confirms
the plausibility of this argument [8]. The dynamic model
attributes the observed wavelength-dependence to the
influence of energy-partitioning and nanoscale thermal
diffusion on two competing thermal processes: protein
denaturation and explosive vaporization of saline.
This dynamic model has also been used to investigate
the role of FEL pulse structure. As a photothermal model,
it suggested that the characteristics of FEL tissue ablation
should not depend on high peak intensity in an FEL’s
picosecond pulses [8]. Pulse-broadening experiments
have recently confirmed that expanding the picosecond
pulses to widths in excess of 100 ps has little effect on theablation threshold and efficiency [9-10].
The model instead suggested a key role for highaverage intensity within a superpulse. By investigating awide range of incident intensities and pulsewidths, wedelineated regions of parameter space, or “sweet spots”,
within which the model predicts a reduced degree ofcollateral damage [11]. Importantly, each of the
wavelengths investigated (3.0, 6.1 and 6.45 µm) had sucha region, but the sweet spot for 6.45 µm was much larger
and encompassed much higher intensities. In
collaboration with industry (PASSAT Inc, Linthicum,
MD, USA), these predictions have guided the design
specifications of a new 6.45-µm laser source (several mJof energy in 12-15 ns pulses) [12]. This laser is currently
under development.
Our previous computational investigations of FEL
ablation were performed on a laminar model, in which
corneal stroma was approximated as alternating, 30-nm
layers of saline and protein [8,11]. Although the laminarmodel gets the characteristic distance for nanoscale heat

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diffusion correct, it underestimates the temperature rise in
the protein component. This underestimate arises because
the laminar model is equivalent to a tissue with a 50:50
volume ratio of saline:protein. However, the measured
ratio for corneal stroma is 85:15 [13]. Thus, the lightabsorbed by protein is actually confined to a much smaller
volume than in the laminar model, yielding higher energy
densities and larger temperature rises.
Here we expand our computational efforts to investigate
mid-infrared laser ablation in two important ways. First,
we use a geometry that more closely approximates theheterogeneous structure of corneal stroma. Results for6.45 and 3.0-µm irradiation are very similar to theprevious laminar model. However, results forwavelengths near 6.1 µm are qualitatively different. Most
interestingly, the sweet spot at this wavelength actually
splits in two. Second, we isolate the role of energypartitioning by investigating the five mid-infrared
wavelengths for which the tissue absorption coefficient ismatched to that at 6.45 µm. The computational resultsfrom this matched set help explain previous experimental
results and suggest new experiments to test thepredictions of our model.

METHODS
Corneal stroma consists of hundreds of lamellae, each
1-2 µm thick, where each lamella contains a quasihexagonal array of collagen fibrils [14]. The collagen
fibrils within a lamella are nearly parallel, whereas thosein adjacent lamellae are crossed. Based on thisultrastructure, we model corneal stroma with two layers.
The first layer is a single heterogeneous lamella (1-µm
thick) composed of a hexagonal array of collagen fibrils
in a saline bath. The interfibrillar spacing is 60 nm and thefibril diameter is 24 nm. These distances are consistent
with cross-sectional transmission electron micrographs ofstroma, [14] and yield a volume fraction ratio of 85:15.
We model the remainder of stroma as a 20-µm thickhomogeneous layer. A graphical representation of thisgeometry is shown in Figure 1.
The symmetries and length scales of the geometry
allow us to simplify the model. Since we are modeling
irradiation with spot diameters of 100 µm or more, heatdiffusion in the direction parallel to the tissue surface andparallel to the fibrils is negligible for times less than ~10
ms [15]. However, the onset of material removal in FEL
ablation occurs within 10’s to 100’s of nanoseconds.
Thus, we may reduce the geometry to a single plane. A
similar argument applies to long-range heat diffusion in
the direction parallel to the surface and perpendicular to
the fibrils. To maintain a proper consideration of shortrange heat diffusion in this direction, we (1) reduce thegeometry to the width of a unit cell in the hexagonallattice and (2) apply a zero heat flux boundary conditionon the lateral edges of this section (vertical solid lines).
Laser heating and heat diffusion within this thin strip ofstroma is described by Fourier’s equation, [16]ρc p

Figure 1. Geometry used to model laser heating in
corneal stroma. The microstructure of one lamella ismodeled as a hexagonal array of collagen fibrils (red)immersed in a saline bath (grey). Beyond the first lamella,
the stroma is treated as a homogeneous material (blue).

∂T= κ∇ 2T + Q∂t(1)

where ρ is the density, cp is the specific heat at constantpressure and κ is the thermal conductivity. Saline, protein
and homogeneous regions are assigned specific ρ, cp andκ [13]. The heat source term, Q, represents the absorptionof laser energy. A Neumann insulating boundary
condition is applied to the air-tissue interface and a
Dirichlet boundary condition (zero temperature rise) is
applied to the rear of the homogeneous stroma layer.
To compute the specific heat source terms for eachcomponent, we measured mid-infrared spectra of porcine
corneal stroma and saline. These spectra were measured
in attenuated total reflectance (ATR) with a Bruker IFS66 Fourier-Transform Infrared (FTIR) spectrometer and asingle-bounce ZnSe crystal. After correction for the 1/λdependence of the sampling depth, the saline absorbance
spectrum was interactively subtracted from the stroma
absorbance spectrum to minimize the water association
band centered at 4.7 µm. The resultant spectrum
represents the absorbance spectrum of the protein
component of stroma. The difference between this result
and the original stroma spectrum is the absorbance
spectrum of the saline component.

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Figure 2. Component-specific absorption of light by the two major components of corneal stroma. A. Absorption
coefficients for the protein (red solid) and saline (blue dashed) components based on stroma that is 85% saline byvolume. The ratio of these spectra represents the relative laser energy density deposited in each. B. Using the respective
heat capacities, one can calculate a ratio of the heating rates in the absence of heat diffusion.
A ratio of the component absorbance spectra reflects
how the total incident energy is partitioned. However, forthermal modeling, we need the magnitudes of the heatsources, i.e. the deposited energy density. To convert theabsorbance spectra, A, to the appropriate absorption
coefficients, α, we must consider the fraction of stromal
volume, fv, occupied by each component. Based on astroma that is 80% water by weight and the respective
densities of saline and protein, the volume fraction ratioof stroma is 85:15 (water-to-protein) [13]. Following asimple Beer-Lambert law, the absorbance of eachcomponent is related to its absorption coefficient by:f v lα = A ln 10 .
(2)
The unknown sampling depth, l, is found by forcing theabsorption coefficient of the 6.1-µm saline peak to 0.27µm-1 [17]. The resulting absorption coefficients are shownin Figure 2.
The local heat source term is then given by

Q = (1 − R) Iα i e − zα stroma(3)

where R is the reflection coefficient for the air-tissue
interface, I is the incident intensity of the laser, αi
represents the component-specific absorption coefficient,and z is depth into the tissue. Using this heat source term
and the geometry described above, Fourier’s equation was
solved numerically on a 2D triangular mesh using a finite
element model running under Matlab (The MathWorksFRAIS01

Inc., Natick, MA). Solutions were calculated for 181
logarithmically spaced times from 10-12 to 10-3 s.
From these thermal histories, the accumulated protein
denaturation was calculated by integrating an Arrhenius
formulation [8,13]. Explosive vaporization of saline wastreated as a threshold event at the superheat limit ofsaline, 575 K [18]. Note that the validity of this thermal
model only extends to the wavelength and intensitydependent onset of vaporization.

RESULTSThe component-specific absorption coefficients forcorneal stroma reveal that the energy density deposited
into protein exceeds that deposited into saline for a wide
range of wavelengths (3.4-4 and 6-10 µm). This region
includes the amide I, II and III, as well as the CH-stretch
absorption bands of protein. Since the heat capacity ofprotein is less than saline, the heating rate ratio is greaterthan one (i.e. protein is always hotter than saline) over aneven wider wavelength range. In Table 1, the penetration
depths (1/α) and heating rate ratios are reported for thethree strongest mid-infrared absorption bands of soft
tissues (3.0, 6.1 and 6.45 µm). Note that these penetration
depths reflect the measured volume fractions in cornea
and thus differ from those reported previously [11]. Also
included in Table 1 is a set of five wavelengths whose
overall absorption matches that at 6.45 µm. The heating
rate ratio varies more than a factor of 40 over this set.

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651

Table 1. Component-specific penetration depths ofcorneal stroma based on an 85:15 saline:protein volume
fraction. The last two columns give the relative rates atwhich the energy density and temperatures of eachcomponent would rise due to laser heating (in the absenceof heat diffusion).
λ (µm)

δstromaδproteinδsalinePower
Density
Ratio (p:s)

2.77
3.32
5.97
6.26
6.45
12.5
3.0
6.1

5.5
5.5
5.5
5.5
5.5
5.5
1.3
3.1

30.3
8.1
4.1
3.7
1.5
14.4
8.5
1.5

4.8
5.2
5.8
6.0
10.3
5.0
1.1
3.7

0.16
0.64
1.41
1.63
6.93
0.34
0.13
2.41

Penetration Depths (µm)

Heating
Rate Ratio
(p:s)
0.28
1.12
2.47
2.83
12.08
0.60
0.23
4.20

We first compared laser-heating calculations with the
hexagonal array and laminar models for 3.0 and 6.45 µm[8]. For an intensity of 7.3 x 107 W/cm2 (corresponding to
the superpulse intensity at the center of a Gaussian beam,with a 1/e2 spot radius of 50 µm, and a picosecond pulse
energy of 1 µJ), the temperature profiles at the superheat
limit differ as expected (not shown). At 3.0 µm, thehexagonal array model predicts a protein temperature risethat still trails that of saline, but the temperature
difference is smaller. At 6.45 µm, the protein temperatures
exceed those of saline by even more than in the laminarmodel. Both effects arise because the laminar model
underestimated the temperature rise in the protein regions.
The laminar model also predicted an exacerbatedtemperature difference between the surface layers. Thissurface effect is still present in the hexagonal array model,
but at a slightly reduced extent. In general, forwavelengths that strongly target either saline or protein,
the results of the hexagonal array and laminar models are
qualitatively similar.
As a next step, we constructed “sweet spot” plots foreach of the above wavelengths. These plots, shown in
Figure 3, consist of three curves in the parameter space ofintensity versus pulsewidth: (1 – green/dashed) the power
density necessary to superheat saline, i.e. to ensure thatenergy deposition outpaces energy consumption from thegrowth of pre-existing vapor bubbles; (2 – solid/red) for agiven intensity, the time required for the saline to reachthe superheat limit; and (3 – dotted/blue) for a given
intensity, the time required to accumulate 1% denaturationof protein. The sweet spot (yellow/shaded areas)
represents the area of parameter space for which thestructural integrity of protein is compromised (via 1%
denaturation) before the onset of explosive vaporization.
Graphically, this is any intensity for which curve 2 lies tothe right of curve 3. For intensities that meet this criterion,
the minimum pulsewidth lays on curve 2 and the
maximum on curve 1. We expect laser ablation in thisregion to be more efficient and to cause less collateral
damage.

Figure 3. Sweet spot plots for laser ablation of corneal
stroma at mid-IR wavelengths. The three curves in eachplot represent the following: (green/dashed) power
density necessary to superheat saline; (red/solid)
combination of time and intensity required to reach theonset of explosive vaporization; (blue/dotted)
combination of time and intensity required to accumulate
1% denaturation in the surface protein regions. The sweet
spot (shaded area) is the set of intensities andpulsewidths for which explosive vaporization occurs after
the protein matrix as been compromised by denaturation.
When compared to similar plots constructed with thelaminar model [11], those for 3.0 and 6.45 µm are similar,
but the plot for 6.1 µm is qualitatively different. Just as in
the previous report, the very small sweet spot for λ= 3.0µm stands in stark contrast to the enormous acceptableparameter range for 6.45 µm. In fact, the upper limit of
the 6.45-µm sweet spot now lies outside the range of ourmodel calculations. For 6.1 µm, the sweet spot actuallyencompasses two regions of parameter space. In ourprevious laminar model calculations, the uppermost
region was not included. For this wavelength, the model
predicts that intensities between 107 to 108 W/cm2 would
cause more collateral damage than either higher or lower
intensities.
When we expand the calculations to include a larger set
of wavelengths, we find that the sweet spot plots fall into

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three classes. For wavelengths that largely target saline
absorption (power density ratio less than one, e.g. 2.77,
3.0, 3.32, 12.5 µm), the sweet spot is very small. For
wavelengths that moderately target protein (power density
ratio of one to three, e.g. 5.97, 6.1, 6.26 µm), the sweet
spot splits into a large high-intensity region and small
low-intensity region that is only slightly larger than thesweet spots of saline-targeting wavelengths. Finally, if thepower density ratio is very large (6.45 µm), the tworegions merge into a single large sweet spot.
We have constructed these sweet spots on the somewhat
arbitrary choice of requiring 1% denaturation to occur
before the onset of vaporization. The 10% and 0.1%
denaturation curves are only slightly displaced(approximately a line width) from that of 1%. However,that small difference is enough to change the constructed
sweet spots. If we increased the requirement to 10%, theneven 6.45 µm would exhibit a split sweet spot. On theother hand, if we decreased the requirement to 0.1%, then
the two sweet spots for 5.97, 6.1 and 6.26 µm would
merge into one.
As a more robust way to look at the interplay of protein
and saline dynamics, we calculated the fractional
denaturation at vaporization (FDV), i.e. the amount ofdenaturation accumulated in the surface protein regions
when the saline reaches the superheat limit. In Figure 4A,
we compare FDV versus superpulse intensity for the setof six wavelengths with matched stromal absorption
coefficients. At very low intensities (<105 W/cm2), thelaser heating process is slow enough that vaporizationcommences after almost all of the protein has denatured.
At slightly higher intensities, FDV decreases for all six
wavelengths. In this regime, the time required to reach thesuperheat limit decreases to less than 1 µs, limiting theaccumulation of denatured protein. All six wavelengths
behave similarly because the intensity is not yet highenough to overcome nanoscale thermal diffusion. Thus,
the temperature differences between protein and saline
regions are negligible. This situation changes as theintensity increases further (>3 x 106 W/cm2). For
wavelengths that target saline, FDV continues to decline.
However, for wavelengths that target protein, the trend
reverses and FDV begins to increase with intensity. The
minimum FDV attained in this region depends on how
strongly the wavelength targets protein. The intensities
are now large enough to outpace thermal diffusion andlarge wavelength-dependent temperature differences may
arise between protein and saline regions. If the protein issubstantially hotter than saline, the exponential
dependence of the denaturation rate on temperature canovercome the shorter times. Finally, at very highintensities (>109 W/cm2), the protein-saline temperature
differences have been maximized and further increases inintensity serve only to decrease the time available fordenaturation. Thus, FDV again decreases with intensity.
Note that this is not yet apparent for 6.45 µm within therange of our calculations.

FRAIS01

Figure 4. Fractional denaturation accumulated prior tovaporization in the surface protein regions. A. Mid-IR
wavelengths with stromal absorption coefficients matchedto that at 6.45 µm. From top to bottom, the solid curves
are for wavelengths of 6.45, 6.26, 5.97, 3.32, 12.5 and2.77 µm. The dashed curve represents a hypothetical
wavelength for which there is no difference between
protein and saline absorption. B. Peaks in the mid-IR
spectra of soft tissues. From top to bottom, the curves arefor 6.45, 6.1 and 3.0 µm.
In Figure 4B, we compare FDVs for the three major
mid-IR absorption peaks of soft tissues. In this case, thestromal absorption coefficients are not matched and the
FDV versus intensity curves do not overlap at low
intensities. For a given intensity, a larger absorption
coefficient implies a faster heating rate and less time prior
to vaporization. Thus the FDV curve for 3.0 µm is always
below those of 6.1 and 6.45 µm. The curves are roughly
parallel until ~3 x 106 W/cm2. They begin to diverge as
the heating rate becomes sufficient to overcome nanoscale
thermal confusion. At this point, FDV begins to increase
with intensity for both 6.1 and 6.45 µm. Although thevery strong protein targeting of 6.45 µm ensures that its
FDV never drops below 1%, the slightly weaker targetingof 6.1 µm allows its FDV to drop slightly below this limit.

DISCUSSION
Can these computational results shed light on previous
experimental investigations of FEL tissue ablation?
Although the original study reported an anomalous

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wavelength-dependence [1], subsequent studies found thatthe ablation efficiency and threshold followed the mid-IR
spectra quite closely [19-20]. Interestingly, the superpulse
intensities used by Edwards et al ranged from of 4-8 x 107
W/cm2 [1]. In contrast, subsequent ablation efficiency
studies at FELIX and Vanderbilt were conducted between
1-3 x 106 W/cm2 [19-20]. For ablation threshold studies,
the intensities are even lower (order of 105 W/cm2) [20].
The model calculations presented here suggest that FEL
ablation metrics should follow a simple wavelengthdependence, i.e. one that does not depend on the degree ofprotein targeting, until the superpulse intensity exceeds ~3x 106 W/cm2. This is consistent with the available
experimental results on ablation efficiency and threshold.
However, there are reports of secondary ablation metrics(e.g. the size of ejected particulates in the plume) that doshow a low-intensity dependence on the dominant
chromophore [19]. Thus, the model presented here may
explain some of the previous experimental discrepancies,
but additional mechanisms must also contribute.
What sort of experiments should tell us whether the
degree of protein targeting, as modeled here, plays asignificant role in the wavelength-dependence of FEL
ablation? We suggest investigations of how the ablation
metrics vary with superpulse intensity. This isstraightforward for ablation efficiency and collateral
damage. Complementary information should be available
from measurements of how the ablation threshold fluencevaries with superpulse width. For such measurements on
cornea, at wavelengths with matched stromal absorption,
our model predicts that the thresholds should diverge
below 100 ns.
What about tissues besides cornea? For wavelengths
that strongly targeted saline or protein, the laminar andhexagonal array models agreed quite well. This agreement
implies that the form factor introduced by a specificgeometry is not as important as the characteristic length
for nanoscale diffusion. This length scale is the key
parameter for evaluating the role of energy-partitioning inother tissues. For collagenous tissues, the relevant length
is the diameter of collagen fibrils. The relevant length in
non-collagenous (e.g. neural) tissues is not clear.
What do these new calculations predict for the
performance of the 6.45-µm tabletop source currently
under development? Assuming this laser will be focusedto similar spot sizes as the FEL, its pulse intensity will lie
in the range of 109 W/cm2 [12]. According to the model
calculations, this intensity is high enough to drive truly
remarkable protein-saline temperature differences,
yielding an FDV of order one. While the prospects forthis 6.45-µm source are very promising, we must cautionthat this range of intensities has not yet been exploredexperimentally.
Because of their wavelength-tunability and relatively
long pulse length, FELs are excellent prototyping tools.
FELs can be used to investigate wide swaths of parameter
space to find optimal operating conditions for a specificapplication. The challenge, that we hope to repeatedly

face, is to then find a more economical source, dedicatedto the application of interest.

ACKNOWLEDGEMENTS
This work was supported by grants FA9550-04-1-0045
and F49620-00-1-0370 from the DOD MFEL Program.

REFERENCES[1] G. Edwards, R. Logan, M. Copeland, L. Reinisch, J.
Davidson, J.B. Johnson, R. Maciunas, M.
Mendenhall, R. Ossoff, J. Tribble, J. Werkhaven and
D. O’Day, Nature (London) 371 (1994) 416.
[2] G.S. Edwards et al, Rev. Sci. Instr. 74 (2003) 3207.
[3] M.L. Copeland, R.J. Maciunas and G.S. Edwards, In
Neurosurgical Topics: Advanced Techniques inCentral Nervous System Metastases, R.J. Maciunas,
Ed. (The American Association of Neurological
Surgeons, Park Ridge, IL, 1998), Chap. VII.
[4] K.M. Joos, J.H. Shen, D.J. Shetlar and V.A.
Cassagrande, Lasers Surg. Med. 27 (2000) 191.
[5] M.A. Mackanos, E.D. Jansen, A.N Soldatov, R.A.
Haglund and B. Ivanov, Proc. SPIE 5319 (2004) 201.
[6] G. Edwards, M.S. Hutson, S. Hauger, J. Kozub, J.
Shen, C. Shieh, K. Topadze and K. Joos, Proc. SPIE
4633 (2002) 194.
[7] J.M.J. Madey, J. Appl. Phys. 42 (1971) 1906.
[8] M.S. Hutson, S.A. Hauger and G.S. Edwards, Phys.
Rev. E 65 (2002) 061906.
[9] M.A. Mackanos, J.A. Kozub, E.D. Jansen, Proc. SPIE
5319 (2004) 209.
[10] J.A. Kozub, M.A. Mackanos, M.H. Mendenhall, E.D.
Jansen, Proc. SPIE 5340 (2004) 87.
[11] G.S. Edwards and M.S. Hutson, J. Synchrotron Rad.
10 (2003) 354.
[12] A.I. Makarov, G.A. Pasmanik, A.A. Shilov, A.G.
Spiro, L.R. Tiour and G.S. Edwards, Presented at
Solid State and Diode Laser Technology Review(2004) Albuquerque, NM, USA.
[13] J. Kampmeier, B. Radt, R. Birngruber and R.
Brinkmann, Cornea 19 (2000) 355.
[14] K.M. Meek and N.J. Fullwood, Micron 32 (2001)
261.
[15] M.J.C. van Gemert and A.J. Welch, In OpticalThermal Response of Laser-Irradiated Tissue (Plenum
Press, New York, 1995), Chap. XIII.
[16] L.D. Landau and E.M. Lifshitz, Fluid Mechanics,
2nd Ed. (Pergamon Press, Oxford, 1987), Chap. V.
[17] G.M. Hale and M.R. Querry, Appl. Opt. 12 (1973)
555.
[18] V.P. Skripov, Thermophysical Properties of Liquids
in the Metastable (Superheated) State (Gordon &Breach, New York, 1988).
[19] J.M. Auerhammer, R. Walker, A.F.G. van der Meerand B. Jean, Appl. Phys. B 68 (1999) 111.
[20] S.R. Uhlhorn, Ph.D. Thesis, Vanderbilt University,
April 2002.

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PROPOSALS FOR PUMP-PROBE EXPERIMENTS IN THE GAS PHASE
USING THE TTF2-FEL
M. Meyer, L.U.R.E., Centre Universitaire Paris-Sud, Bâtiment 209D, F-91898 Orsay Cedex, France
Abstract
A selection of experiments is discussed, which will
make use of the combination between VUV photon pulses
produced by the TTF2-FEL in Hamburg (Germany) andpulses of an optical laser for studying atomic andmolecular samples. By applying a two-photon pumpprobe excitation scheme, the proposed investigations andthe expected results will enable us, on the one hand, tocharacterize the FEL pulses and, on the other hand, togain new insight in the dynamics of the electronicinteraction in the electronic clouds of excited atoms aswell as of the molecular dissociation processes.

outer Xe 5p or Ar 3p shell can be studied. At higher
energies more tightly bound electrons can be excited, e.g.
Xe 4d at about 65 eV or Kr 3d at 90 eV.

INTRODUCTION
Many processes induced by the interaction of XUVlight with free atoms and molecules take place on a very
short time scale. Photoexcitation of a core-electron to theionization continuum or to a resonant state will, in
general, be followed by fast electronic relaxation throughautoionization or Auger process on a sub-picosecond timescale. The temporal width of the soft X-Ray pulses fromthe TTF2-FEL (100-300 fs) and of the synchronized,
tunable optical laser (about 150 fs) will therefore be
ideally suited to gain insight into the dynamics of theseprocesses. By using time-resolved pump-probe techniques
it will be possible to investigate the temporal evolution ofa variety of processes, like electronic relaxation of
autoionization states, coupling between two
autoionization states, wave-packet formation of higher
Rydberg states, coupling between electronic and nuclear
motion in molecular systems, fast dissociation ofmolecules upon inner- and outer-shell photoexcitation,
coherent population of fragment states etc.
First experiments have of course also to serve forcharacterizing the FEL pulses themselves, in particular
the intensity, frequency and time structure of theindividual pulses, since these values are only estimated on
the basis of theoretical simulations. A powerful tool to
obtain information about the shape of femtosecond pulses
is given by cross correlation experiments [1-3]. This twocolor method has been successfully applied tocharacterize the short X-Ray pulses generated by thegeneration of higher harmonics in an intense laser in a gas
jet of rare gas atoms. It uses the measurement of theionization signal induced by a XUV photon in thepresence of a strong infrared beam (Figure 1). The latter
induces sidebands on both sides of the main line in thephotoelectron spectrum. The shape, intensity and positionof the sidebands are directly correlated to the shape of thepulses and their time delay. At low photon energies, i.e. in
the region between 15 and 50 eV, the ionization of the

THCIS01

Figure 1: Schematic representation of the photoionization
process of atomic Ar by a VUV photon in the presence ofa strong IR laser field.
In addition, after excitation of a core electron it will
also be possible to measure the corresponding Auger
spectrum, where the dressing laser will give rise to thesame type of side bands [4,5]. The spectra will be
influenced by the interaction between different ionization
continua (one-photon and two-photon ionization) and theresonantly excited state, which is characterized by an
Auger lifetime of the same order as the exciting
femtosecond photon pulses.

CHARACTERIZATION OF FEL-PULSESIn order to select suitable systems for measuring andcontrolling the temporal delay between the FEL and theoptical laser pulses and to find out the potentiality of thecross correlation method, we have performed a series ofmeasurements [3] using the femtosecond laser system atthe Laser Center (LLC) in Lund (Sweden). The XUVpulses are produced in Ar gas by generation of the higher
harmonics (HHG) nof an intense (about 1 mJ at a 1 kHz
repetition rate) 800 nm laser system giving 50 fs pulses[6]. The XUV pulses are used to ionize in theexperimental chamber a sample of rare gas atoms and thephotoelectron spectrum is recorded using a magnetic
bottle spectrometer. The cross correlation measurements
have been performed with part of the fundamental 800 nm
beam, which is separated before entering the chamber forthe production of the higher harmonics. In the presence ofthe strong IR laser pulse (dressing beam) thephotoelectron spectra shows clearly some side-bands,

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655

Figure 2: Schematic representation showing the photoionization of Ar atoms by VUV photons, which areproduced through generation of higher harmonics of an intense IR laser, in the presence of the same IR laser in
the interaction region (left-hand side). The resulting photoelectron spectra as a function of the time delay
between the VUV and the IR pulses are given on the right-hand side of the figure.
which are due to an absorption or emission of an IR
photon during the ionization process (Figure 2). The
intensity, precise energy position and peak-shape of theelectron lines strongly depend on the spatial and, more
importantly, temporal overlap between the VUV and IR
pulses as well as on the intensity of the dressing beam.
Due to the expected temporal jitter between theindividual FEL pulses, the possibility to record singleshot spectra will be envisaged for the experiments at the
TTF2-FEL. Simulations show (Figure 3) that that it ispossible to determine the width and the relative positionof the VUV pulses when the IR pulses are characterized
providing a temporal resolution of better than 10fs. A
precise analysis of the peak-shape allows in addition todetermine the width of the VUV pulses. Since the IR
pulses introduce a temporally non-uniform field theionization conditions for different parts of the VUVpulses are also different, which results in an asymmetric,
but characteristic lineshape. In this way thesynchronization between fs-pulses can be analyzed andeventually also controlled.
In the experiments using the HHG source, spectra
were recorded by averaging over 30 000 shots. This was
mainly related to the intensity of the source providing
about 106-107 photons/pulse, which corresponds to about
3 electrons per pulse. With the projected FEL output of~ 1 0 1 3 photons/pulse it can be estimated that crosscorrelation spectra are achievable with a single shot, if the
IR laser can deliver ~0.5mJ. With the expected ~0.1mJ
energy of the IR laser, the low field measurements

yielding the phase shift will be possible at a 100 µm spotof the FEL. For measuring also the profile (10TW/cm2)
the experiment has to be performed with a 10µm diameterof the FEL in the interaction region. Problems might arise
from space charge effect in the source volume when ahuge amount of electrons are produce by the same FEL
pulse. Simulations of the expected effects on thephotoelectron spectra, in particular on the achievablekinetic energy resolution are under progress.

Figure 3: Simulation of the position and the shape of theAr 3p photoelectron spectrum for different position of the
VUV pulse with respect to the IR dressing pulse.

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In general, the performed test experiments havedemonstrated that the cross correlation measurements canbe used to measure precisely the temporal parameters of a
VUV pulse with respect to a well-characterized IR pulse.

APPLICATIONS TO ATOMES
Depending on the final characteristics of the FEL withrespect to photon energy range and tuneability, the pumpprobe experiments will be extended to a large number offurther experiments on atomic or molecular samples. To
list just a few of them three examples are given:(i) The investigations of resonances with same parity as
the ground state, e.g. Xe* 4d95s25p6nd, ms. Due to dipole
selection rules, these states can only be excited either by adirect two-photon one-color excitation or by a two-photon
two-color excitation via an intermediate resonant state,
like the strong Xe* 4d9 6p resonance (hν (FEL) =65.1eV). The short lifetime of the Xe* 4d9 6p resonance(Γ=0.11eV, ∆T=6fs) necessitates the combination andsynchronization of fs-pulses (XUV + Visible). Resonant
Auger spectroscopy will be used here to study therelaxation dynamics and additionally the influence ofalignment of the intermediate state when the polarizationof the two photon beams are changed in a controlled way.
The results will extend and complete conventional studies
using one-photon excitation and will provide a new andimportant basis for the theoretical treatment of electronicinteraction and correlation in atomic multi-electron
systems.

pronounced and characteristic splitting in the resonanceprofile for laser intensities of 1GW/cm2 , which will beaccessible in the planned experimental configuration.

APPLICATIONS TO MOLECULES(iii) Coherent population of excited states by fastdissociation: The photodissociation of H2 or HCl in thephoton energy region hν (FEL)>17eV leads to the
production of excited hydrogen atoms, in particular to theexcited states with principal quantum number n = 2 or 3.
Observation of the radiative decay of these states canseparate the contributions from 2s and 2p as well as 3s, 3p
and 3d levels by their different lifetimes (several
nanoseconds). In a pump-probe experiment the FEL canbe used to induce the dissociation process and the externallaser to ionize the excited hydrogen atoms. The use of
femtosecond pulses will allow the time resolution to be
increased significantly and to observe quantum beats on
the decay curve. The coherent population of the different
fine-and hyperfine levels, which are energeticallyseparated by 1 - 10 GHz, will induce a beat structure witha period of about 10 - 100ps (e.g. [10, 11]). For different
resonant excitations different dissociation mechanisms are
expected, which would lead to different, but characteristic
quantum beats patterns of the decay curve.

CONCLUSION
The given examples for experiments using the FEL
pulses in combination with a synchronized optical fs-laser
are part of working program, which has been proposed bya European collaboration including experimental groups
at HASYLAB (Germany), Lund Laser Center and MAXLab (Sweden), Dublin City University (Ireland), MaxBorn Institute for Nonlinear Optics and Short-Pulse
Spectroscopy (Germany), and LURE (France). First
experiments are schedules for spring 2005.

REFERENCES

Figure 4: Excitation scheme for the coupling of
autoionization resonances in He.
(ii) Coupling of autoionization states by a strong laser
field. Similar to the above example, the FEL and a second
synchronized fs-laser are used in a pump-probe
arrangement to excite and to couple two autoionizing
resonances, like He* 2s2p 1P and 2s3d 1 D (at photon
energies hν (FEL) of about 60eV) (Figure 4). The profileof the resonances, being strongly asymmetric for He*
2s2p 1P [7], will strongly depend on the intensity of thetwo laser beams and on small changes in the relative timedelay of the pulses and the photon energy of the second
laser (detuning). Theoretical treatments [8,9] predict a

THCIS01[1] A. Bouhal et al., J. Opt. Soc. Am 14, 950 (1998)[2] E.S. Toma et al., Phys. Rev. A 62, 061801(R) (2000)[3] P. O'Keeffe et al., Phys. Rev. A 69, 051401(R) (2004)[4] J.M. Shins et al., Phys. Rev. A 52, 1272 (1995)[5] T.E. Glover, R.W. Schoenlein, A.H. Chin, and C.V.
Shank, Phys. Rev. Lett. 76, 2468 (1996)[6] R. Lopez-Martens et al., Eur. Phys. J. D 26, 105(2003)[7] M. Domke, G. Remmers, and G. Kaindl, Phys. Rev.
Lett. 69, 1171 (1992)[8] H. Bachau, P. Lambropoulos, and R. Shakeshaft,Phys. Rev. A 34, 4785 (1986)[9] A.I. Magunov, I. Rotter, and S.I. Strakhova, J. Phys. B
32, 1489 (1999)[10] C.C. Havener, N. Rouze, W.B. Westerveld, and J.S.
Risley, Phys. Rev. A 33, 276 (1986)[11] M. Motzkus, S. Pedersen, and A.H. Zewail, J. Phys.
Chem. 100, 5620 (1996).

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PICKED FEL MICROPULSE FOR NANO-SECOND INTERACTION
WITH BIO-MOLECULE
S. Y-Suzuki*, T. Kanai, K. Ishii, Y. Naito, K. Awazu, Institute of Free Electron Laser, Graduate
School of Engineering, Osaka Univ., 2-9-5 Tsuda-yamate , Hirakata, Osaka 573-0128, Japan
Abstract
Laser pulse duration is a very important parameter todetermine the threshold between thermal and nonthermal
effects in laser surgery of biomedical tissue. Free
Electron Laser (FEL) at Osaka University, Japan, has apulse structure in which a macropulse (pulse width: 15µs) consists of equally separated micropulses, whose
width and interval are approximately 5 ps and 44.8 ns,
respectively. A precisely controlled of micropulse train
may establish fast optic processes because thermal
relaxation time in tissue is about 1µs. A pulse-picking
system was designed in order to extract a single or a few
micropulses from an entire macropulse using an acoustooptic modulator (AOM) in which the light path can betransiently diffracted by an external gate signal. The
extracted micropulse train was monitored by a mercurycadmium-telluride (MCT) photodetector with ~1 ns
response time and recorded on a digital oscilloscope. A
single micropulse was extracted as a result of adjusting
the duration of the gate signal to 50 ns which is nearly
equal to the micropulse interval. Investigation of a fastinteraction between FEL and tissue using this system is
expected.

INTRODUCTION
Many bio-molecules absorb mid-infrared (MIR) lightstrongly due to molecular vibration. Exciting a specificmolecular vibration selectively using MIR pulse laser
gives various medical treatment effects on a level ofmolecules.
In laser surgery, controlling thermal effects isimportant. The thermal and nonthermal effects are
generally classified according to the thermal relaxation
time (τtherm) of a biomedical tissue. If the interaction time(τint) which depends on the pulse width and frequency oflaser is longer than the thermal relaxation time (τint >τtherm), the heat spreads over the entire biomedical tissue
and produces macroscopic thermal effects. For example,
a surgical laser incision and coagulation in tissue using
the thermal effect. However, the thermal effect has an
influence on normal tissue due to diffusion, and theselective interaction by bio-molecular vibration is notexpectable. In the case of τint < τtherm, because a particularmolecule is excited within τtherm, the selective interaction
is caused faster than diffusion.
Biomedical applications have been studied using a freeelectron laser (FEL). FEL at iFEL, Osaka University inJAPAN, is tunable from 5 µm to 22 µm in mid-infrared(MIR) region, which is high peak power and short pulse
operation. The FEL has a unique double pulse structure;
the structure consists of a train of macropulses, and eachmacropulses contains an ultrashort 300-400 micropulses.
The width of a macropulses is about 15 µs and repetition
rate is 10 Hz. The width of a micropulse is shorter than
10 ps and the separation between micropulses is 44.8 ns.
Therefore, precise control of micropulses is required inorder to evaluate FEL irradiation effects on the biomolecule without thermal effects.
There is a number of technologies for switching thelaser beam, e.g. Pockels cell (PC) [1, 2] or acousto-optic
modulator (AOM). PC switches the polarization
direction of laser beam rapidly by high-voltage
switching. Becker et al. have achieved switch out from80ns to the full 6 µs duration of the FEL macropulse [1].
AOM can transiently diffract the light path with an
external gate signal. The switching speed of AOM isslower than PC, but has a higher switching efficiency.
We have chosen AOM control micropulse train.
A micropulse-picking apparatus was designed toswitch-out a short micropulse train from an entire
macropulse by a deflection of the light path using agermanium acousto-optic modulator (Ge-AOM). We will
discuss the nano-second interaction with bio-molecul
tissue sample.

PULSE-PICKING SYSTEM
Principle of the acousto-optic modulator
The basic principle of the acousto-optic modulator(AOM) is shown in figure 1. All AO devices are basedon a crystalline material whose one side is bonded to apiezo-electric transducer. When radio frequency (RF)signal is applied to the transducer, an acoustic wave(AW) is produced by the inverse piezoelectric effect andtravels in the crystal. The wave of condensation andrarefaction in the crystal is acted as a diffraction grating.
An incident beam to the crystal is diffracted into manyorders during the formation of the AW. If the angle ofincidence is set to the Bragg angle, the majority of thediffracted light appears in the first order. This is the
optimal setting in most practical application.
The Bragg angle (θΒ) is determined by wavelength ofincident laser λi and RF drive frequency fc.

θB =λi f c2⋅v(1), here ν is velocity of AW into the crystal.

___________________________________________* suzuki@fel.enf.osaka-u.ac.jp

Available online at http://www.JACoW.org

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S. Suzuki et al. / Proceedings of the 2004 FEL Conference, 657-660

Incident beam
wavelength: λi
Spot size:S

Diffracted order:λd

～
～

θB

θB
Bragg angle:
θB=λifs/2v

θB

Acoustic
velocity: v

Gate pulse
for RF drive ∆trf

∆td

Zero order∆trf
RF drivefrequency: fs

Figure 1: Basic principle of the acousto-optic
modulator
FEL micropulse
train ・
・
・
・

・
・
・
・

Gate pulse for RF drive

Beam spot: S
RF wave

In order to extract a signal or a few micropulses froman entire macropulse, the incident FEL beam spot sizeneeds to be about 250 µm which is estimated from theequation (2) as equivalent to ∆td =50 ns. The focusing of
FEL beam on AOM causes various problems; forexample, damage to Ge and decrease in the diffraction
efficiency. Therefore, the incident beam to AOM isbetter to be collimated.
The FEL beam which was focused with two ZnSe
convex lenses (f1 = 50 cm, f2 = 3cm) entered the GeAOM at the Bragg angle (θΒ= 38.5 mm radian). The
polarization direction of the incident beam was verticalto the diffraction grating in the operating AOM. If thepolarization is parallel to the gating, the diffraction
efficiency is significantly reduced by the consequence of
Maxwell equations. The diameter of incident beam isabout 1 mm; it is too large to extract a single micropulse.
However, it is possible to evaluate an interaction without
the thermal effect in bio-medical tissue. Although thebeam is not collimated, it is equivalent to the parallel
light within the AOM because the beam divergence at anangle of 7 mm radian is smaller enough than the Bragg
angle.

velocity:ν
delay time

Rise time∆tr =1st order light of FEL

S
ν×1.56

Flat mirror Convex lens 2
Diffracted order
AOM
f=3cm
S=1mm
MCT
Zero order∆td

Figure 2: Time chart of pulse diffraction

Figure 2 shows a time chart and image of the pulsed
diffraction. The diffracted light is produced while thepulsed AW passes the whole incident light spot. In otherwords, an adjustment of the gate pulse for the RF driver(∆trf) can control the micropulse train which is extracted
from a macropulse. The minimum temporal window ofthe diffracted light (∆td) is limited by the rise / fall time(∆tr) which depends on the AW velocity (ν) and lightspot size (S).

∆t r =

Sv ×1.56(2)(1.56=a correction factor for large beam size)

Designs
The setup for diffraction of FEL beam is shown infigure 3. As the crystalline material of AOM, we chose agermanium (Ge-AOM) which has a high transmission
and allowable input energy at MIR wavelength region.
Table 1 shows the specification and the ba
performance of the Ge-AOM (AGM-402A1, IntraCation
sicCO.) and RF driver (GE-4010, IntraCation CO.) used inour experiments. We chose the Ge-AOM with antireflection (AR) coatings limited to 5.7~7.0 µm in order
to eliminate the Fresnel reflection on the Ge surface.

FRAOS03

Convex lens 1
f=50cmRF driver

Pulse Generator

D1=5cmFigure 3: The setup for micropulse-picking
Table 1: specification and the basic performance of
AOM and RF drive
Acousto-optic modulator (AGM-402A1)
Acousto-optic material
Acoustic Velocity (v)RF Center Frequency
Optical Insertion Loss
Optical wavelength
Beam Separation
Bragg Angle
Diffraction Efficiency

Germanium
5.5 mm/µsec
40 MHz< 7 percent
10.6 µm
77 mm radian38.5 mm radian
70 percent

RF driver (GE-4010)
Oscillator Frequency
RF Output Power
Rise/Fall Time

40 MHz
10 watts
30 nsec

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S. Suzuki et al. / Proceedings of the 2004 FEL Conference, 657-660

Optical Insertion Loss(%)

Figure 4: Experiment result of micropulse train
extracted with the control signal of 1µs.

diffracted. This system can adjust the micropulse train in
the range from 5 to 335 micropulses (macropulse width:
232 ns - 15 µs).
Figure 6 shows the optical insertion loss of
wavelength 5~12 µm. The loss in the AR coatings
wavelength region is about 7%, which agrees with thespecification values. The loss in the region out of the AR
coating wavelength (< 10 µm) is also low; it is less than30%. The diffraction efficiencies at the FEL wavelengthof 6.3 µm and 9.4µm are 65~70%, also agree withspecification value (see table 1).
50

AR coatings

40
30
20
10
0
5

6

7

8

9

10

11

12

Wavelength(µm)

Figure 6: Optical insertion loss as a function of
wavelength.

APPLICATIONS OF PICKING SYSTEM
Figure 5: Experiment result of micropulse extractedwith the control signal 100ns (a) and expansion of
extreacted micropulse (b).

RESULTS OF MICROPULSEEXTRACTION
Figure 4 and 5 show the results of the experiment for
examination of the pulse-picking system using Ge-AOM.
The temporal window for the micropulse-picking
depends on the gate pulse for the RF driver. Figure 4
confirmed that about 30 micropulses (44.8 ns * 30 = ~1.3µs) are extracted from an entire macropulse by the gate
pulse of ∆trf=1µs. The diffracted light was detected about
1.2 µs after the rising edge of the gate pulse. This delay
time is caused by the response time (30ns) of the RF
driver and the travel time of AW in the crystal. Figure 5
shows the micropulse train extracted by the gate pulse of∆trf=100 ns. Figure 5 (b) is the enlarged view. Five micropulses (44.8 ns * 5 = ~230 ns) are found to be extracted
and the picking temporal window ∆td is different from∆trf. The window is limited to the rise time (tr) of theAOM. In the case of the incident beam of 1 mm indiameter tr=116 ns is estimated from the equation (2).
Therefore, a micropulse train of less than 232 ns cannot
be extracted. Furthermore, in the case of ∆td < 232 ns,
the diffracted light intensity decreased because thepulsed AW became not able to cover the entire incident
beam spot and a portion of the incident light was

Interaction with biomedical tissue
We have researched various interactions between
biomedical tissues and MIR-FEL, for example theselective removal of cholesterol ester (5.75 µm), thesurface modification of tooth dentin (9 µm band) and thecontrol of dephosphorylation (9 µm band). Control ofthermal effects is important to lead to these processes
effectively.
We showed that the infrared absorption peak of thephosphate group is reduced after the FEL wavelength 9.4µm irradiation (average power density 8.6 W/cm2) [3].
The thermal effect on the interaction between a criticaltissue and the controlled micropulse train wasinvestigated. The length of the micropulse train wasvaried by the pulse-picking system while the average
irradiation power density was adjusted to be constant.
polyacrylic acid without phosphorylation was used as the
sample in the primary experiment. polyacrylic acid isused as a model of a biomechanical material because
chemical structure is simplicity and handling is easy. The
sample was irradiated with FEL (wavelength 9.4 µm) of
macropulse width of 15us and 2us respectively. Each
irradiation effect is estimated by comparing theabsorption spectra measured by Fourier Transform
Infrared Spectrometer (FT-IR).When an entire
macropulse is irradiated (15 µs), the polyacrylic aciddissolved remarkably. In contrast, the decrease in
micropulse train (~2 µs) reduces thermal effect and the
cemical stracture is kept. Evaluate of interaction which
controlled thermal effect is expected.

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Matrix-assisted laser desorption/ionization
using UV laser and FEL
Matrix-assisted laser desorption/ionization (MALDI)
is a powerfull and robust technique for protein
identification [4]. We have developed a novel MALDI
method based on a simultaneous irradiation of a UV laserand FEL (UV/FEL-MALDI). The UV laser and FEL cancreate electronically and vibrationally excited states on asample in parallel. The results provided analyses ofmacromolecules and insoluble proteins which are notamenable to the conventional measurement [5, 6].
The typical pulse width for MALDI has been reported
to be ~100 ns, however neither of macropulse nor
micropulse of our FEL has a suitable time scale. To
achieve the optimum irradiation condition, the FEL
micropulse train and the timing of electronic andvibration excitation need to be adjusted arbitrarily.
Figure 8 shows a schematic diagram of UV/FELMALDI time-of-flight mass spectrometer (TOF-MS)
with a micropulse picking system. The irradiation of the
UV laser and FEL is controlled by synchronous trigger
signals. Figure 9 shows the timing chart of the irradiation
event. This result confirms that the diffracted FEL
micropulse train and UV laser pulse are irradiatedsimultaneously. The UV/FEL-MALDI with themicropulse picking system which is extracts a shortmicropulse train can synchronize precisely the UV andFEL laser pulses and is expect to elucidate the ion
generation mechanism and to improve the efficiency ofionization.

Macropulse Signal
15ms, 10Hz

20ns
MALDI TOFMS

TG535
22MHz

TG535
MCT

Zero order
Diffractedorder
RF drive
AOM

FEL beam

N2 LaserVideo
cameraZnSe Lens(f=120mm)

DigitalOscilloscope

Figure 8: UV/FEL-MALDI
micropulse-picking system.

ZnSe
window

Photo detector

TOFMS

required

Figure 9: Experiment result of timing control on asimultaneous irradiation of a UV laser and FEL.

CONCLUSIONSIn order to control the FEL micropulse train forclassifying thermal and non-thermal effects on
biomedical tissue, we designed a micropulse picking
system using Ge-AOM in which the light path can bediffracted to extract a few micropulses from an entire
macropulse. The pulse-picking system achieved tocontrol the diffracted micropulse train from 232 ns to 15µs. The diffraction efficiency reached to 65~70%.
The thermal effect related to the interaction between amicropulse train and phosphrylate acrylamide wasverified. The result obtained by the controlled micropulse
train, whose length was varied at the constant average
power, confirmed that limiting the micropulse train
decreases the thermodiffusion in a critical tissue. The
UV/FEL-MALDI equipped with the picking system cancontrol the timing of electronic and vibration excitation
precisely, and many achieve the optimum irradiation
condition for protein identification. The picking system
is expected to give many information about interaction
between laser and biomedical tissue.

FRAOS03

ACKNOWLEDGMENTS
We are grateful to Mr. Kuma, Mr. Marusaki and Mr.
Teranishi, operational staff of iFEL graduate school ofengineering, Osaka University.
This study was supported by a research budget of theIntellectual Cluster Project from Senri Life Science
Foundation / the Ministry of Education, Culture, Sports,
Science and Technology of Japan.

REFERENCES[1] K. Becker et al., Rev. Sci. Instrum. 65(5),1496(1994).
[2] A. V. V. Nampoothiri et al., Rev. Sci. Instrum.
69(3), 1240(1998).
[3] K. Ishii et al., Nucl. Instrum and Math. Phys. Res. A,
528, 614, (2004).
[4] K. Tanaka et al., Rapid Commun. Mass Spectrun 2,
151(1998)[5] Y. Naito et al., Nucl. Instrum and Math. Phys. Res.
A, 528(1-2), 609,(2004).
[6] S. Y. Suzuki et al., Rev. Laser Engineering, 31(12),835(2003).

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COHERENT PROTEIN DYNAMICS EXPLORED AT FELIX
R. Austin, Princeton University, Aihua Xie, Oklahoma State University
B. Redlich, Lex van der Meer, FOM Institute for Plasma Physics
Abstract−1

We have used extremely narrow (1-2 cm ), high energy pump-probe time domain spectroscopy to probe theheterogenously broadened amide I band in several proteins.
We find that the short wavelength side of the amide I band
can give rise to very large (50%) bleaching signals, indicating a very long dephasing time of at least 20 ps to theinternal amino acid amide I stretch band.

INTRODUCTION
At a recent conference, we heard an eminent theorist refer to the “original sin” committed in a talk. The theoretical talk was about self-localization of vibrational (not electronic) energy and the generation of solitons in a biopolymer, in this case DNA. It was a good talk, very clear andcarefully presented. What then was the sin? The critic
was convinced that relevant biological motions in biology
are all overdamped and therefore diffusive in nature. Ifthey are overdamped, then (perhaps) issues of energy selflocalization and solitons are simply irrelevant at least at thepicosecond time scale. So, our critic’s point was: if you
don’t address head-on issues of overdamping times in biological vibrational dynamics you do commit an original
sin: everything after that is tainted.
There is an additional issue that wasn’t mentioned in the
charge of original sin, that of dephasing time. Using thelanguage of NMR and the Bloch equations, there are twoparameters that characterize an excited state: the longitudinal relaxation time T1 which is a measure of the lifetimeof an excited state, and the transverse relaxation time (puredephasing time) T2∗ , which is a measure of how long thesystem remains in phase [1]. It could be, as we discuss
below, that the dephasing time of any coherently excited
vibrations can be much shorter than the excited state relaxation times and determine the linewidths of the transition.
In that case, it is almost as great a sin to ignore a short T2∗
as ignoring T1 , for many non-linear effects need the coherence times of the excitations to be long as well to beeffective. A short T2∗ can be as destructive as a short T1 fora beautiful theory of non-linear effects in biology.
The determination of the T1 and T2∗ ’s of a state starts
with the static spectroscopy of the state. If a particular transition is not heterogeneously broadened, the static
lorentzian linewidth Γo of the transition (in energy units ofwavenumbers, cm−1 ) is given by [1]:


1
1
1
Γo =
(1)
+
c πT2∗
2πT1
The classic problems in proteins is of course is that by static
spectroscopy it is not possible to disentangle T1 from T2∗ by

Available online at http://www.JACoW.org

static spectroscopy alone, and further that the vibrationallines in the IR spectra of a protein are inhomogenously
broadened due to complex energy landscape of a protein[2]. It is possible that within this distribution of lines that
there exist a set of states that are both spectrally narrowand have long dephasing times. In order to discover thesestates it is necessary to probe their dynamics by some formof site-selective spectroscopy.

STATIC SPECTROSCOPY
In fact, there is evidence from static spectroscopy at leastthat there exists a distribution of relatively narrow states
within the broad envelope of amide I modes in proteins.
We take as our example Mb, but other proteins show similar evidence (data not shown). Fig. 1 shows the spectrum
IR spectra of myoglobin in a D2 O-d-glycerol buffer as afunction of temperature. If we concentrate on the amide-I
band, it is clear that the short wavelength side of the amide
I band shows little temperature dependence, while the longwavelength (red) side shows the appearance of a new bandas temperature is decreased, indicative of increasing hydrogen bond strength with decreasing temperature [3]. The
amide I mode is due to the C=O stretch of the amide group,
and is moderated by a weak hydrogen bond with neighboring hydrogen atoms of the primary amine groups, andwith hydrogens of water if they are accessible to the aminoacids. Those amino acid groups which are are buried within
the protein and not in contact with the surface or the solvent
would be expected to not have this temperature-dependentchange in the amide-I frequency, thus we identify the blueside part of the amide-I band with the internal amino acids,
and the red-side amide-I band with the external, solvent exposed amino acids.

Figure 1: (A). The infrared absorption spectrum of sperm
whale myoglobin as a function of temperature from 5 K to300 K, from 2.8 to 8.0 microns. (B) The spectrum from 5.9
to 6.6 microns
We can make a further observation: the Debye-Waller
factor S, a measure of the variance of the positions of atoms
in a lattice [4], is also a function of the position of the aminoacid in a protein. S is defined by: S =< x2 >, where

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r.h.a. Austin et al. / Proceedings of the 2004 FEL Conference, 661-664< x2 > is the variance of the position x of atoms in theprotein crystal. As a general rule, the interior parts of theprotein have small S while those at the surface of the protein have large S. Thus, not only do the internal aminoacids have small Debye-Waller factors but they also showless interactions with the solvent. One might then imagine that these internal amino acids have unusual dynamical
properties compared to the amino acids at the protein surface which are held less tightly in place than the interior.

PUMP-PROBE MEASUREMENTS
At FELIX it turns out that the pulse width can be made aslong as 10 picoseconds, giving rise to a linewidth of about
2 cm−1 , while still retaining about 1 microjoule of energy
delivered to a 100 micron spot size. Further, at FELIX it
is possible to deliver this pulse as a single pulse, since as
we have painfully shown delivering too much energy via aseries of micropulses at a rate higher than the diffusionalcooling rate only leads to damaging the protein and introduction of complications [6]. Fig. 2 shows the heterodyne
mixing signal of a long pulse from FELIX. This pulse hasa duration of 10 ps and hence a spectral linewidth of 0.01
microns or 2 cm−1 . When such a long pulse is scanned
across the amide I+II spectral region of Mb, from 5.8 to
6.5 microns, a remarkable thing happens. While ordinarily
when pulses of duration 1 ps or shorter are used the typical transmission change observed for 1 uJ pulses focussed
to 100 micron spot sizes is about 1% or less, if the spectral width is narrowed the signal enormously increases, bya factor of 50! Fig. 3 shows an example of the signals observed as a narrow pulse is scanned across the amide I+II
region. Note that the huge enhancement is seen only forthe amide I band, and only on the blue side of the amide I
band.
This blue-side signal enhancement could be due to excitation of chromophore bands which lie within the amide I
band of the protein, but this is probably not the case. Fig.4
shows a scan of the amide I region of lysozyme, an enzyme
which has no chromophores. Not only does this scan showthat a similar anomalous enhancement of the pump-probe
signal occur on the blue side of the amide I band of thisprotein, it also shows that the shape of this enhanced signal
depends on the protein. Of course, narrowing the spectral
width has its costs in that the time resolution decreases.
Fig. 5 shows what happens as the pulse width is changed
to the time-domain response of the sample. When the pulse
width is long the response of the protein, in this case myoglobin, looks like the autocorrelation of the pulse with no
obvious lifetime. As the pulse is shortened, exciting moremodes and putting less energy into each mode, the shape ofthe response qualitively changes with a clear lifetime effectcoming in at longer times but less amplitude to the pulse.
If the pulses are made as long as possible and the signal isobserved at the spectral peak of the response, then varying
the energy of the pulse by use energy attenuators shows thatthe transmission change is proportional to the energy of the

FRAOS04

Figure 2: Heterodyne mixing of the pump and probe pulse
used for these experiments.

Figure 3: Wavelength scan of the transmission change vs.
wavelength of the pump-probe signal seen for Mb in a 75%
d-glycerol/25% D2 O solvent at room temperature (solidline). We have superposed the measured absorbance of thissample (dashed line).

pulse. Finally, the polarization of the pump pulse can berotated with respect to the polarization of the probe pulse,
these measurements shown in Fig. 6 reveal that the pumppolarization must be parallel to the probe polarization for
maximum signal.
It is difficult in this brief communication to reveal succinctly all of the data we have required, even more difficult to explain what is happening. We have already discussed how the heterogeneous broadening of the amide I

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r.h.a. Austin et al. / Proceedings of the 2004 FEL Conference, 661-664

Figure 4: Scan of the pump-probe signal observed for the
enzyme lysozyme (solid line). The absorbance of the sample is given by the dashed line.

band can be roughly split into a blue side distribution ofburied amino acids not in contact with the solvent and a redside distribution of solvent exposed amino acids. We also
speculated that perhaps the blue side, buried amino acids
with their small Debye-Waller factors might have long coherence times T∗2 . How can we begin to draw a quantitative connection between coherence dephasing times and theamplitude of these strange signals? The simplest model,
which does require phase coherence of the excited state, isthe phenomena called Rabi flopping [1]. In Rabi floppinga 2 level system is driven by a resonant electromagnetic
wave with electric field strength E. We denote the strengthof the electric dipole transition moment to be µ. Somewhat
counter-intuitively, when such a two level system is driven
coherently the population of the ground state ρ1 (t) and theexcited state ρ2 (t) oscillates as:
P1 (t) =Figure 5: A time scan of the Mb signal at 6.04 microns as
the pump pulse is scanned via the delay line over the probe
pulse. The two traces are for a 10 ps and a 2 ps wide pulse.

(2)

where χ = µE
h̄ is the Rabi flopping frequency. The surprising aspect of Rabi Flopping is of course the fact that a
population can completely invert with time if driven resonantly and if the dephasing time T2∗ is much longer thanχ. It is possible to characterizea pulse of such resonantlight by an angle θ = χdt which represents for example the population change it creates. For example, a π/2pulse would the equalize the ground and excited state populations. Such a pulse would of course result in a hugebleaching signal because there would be no net absorbancechanges.
It is possible to estimate θ and hence the extent of transmission change possible. The FEL pump pulse had anenergy of 1 microjoule, a pulse duration of 5 ps, and afocused diameter of 100 microns. This yields an opticalelectric field E of about 108 V/m. The amide I band is astrongly allowed transition, we assume the electric dipole
moment is approximately 1e-Å. We compute then that aπ pulse should take about 1 ps, IF the coherence time T2∗
is on the order of the longitudinal relaxation time T1 . Of
course, dont know dipole moment, so this is just a guessbut it does indicate that if a narrow state with long T2∗ exists, its population can be inverted. We can guess how theintensity of the observed bleaching signal signal will varywith θ. Since the potential transmission change in our caseis about 1000% ( a ten-fold increase in transmission since
the sample has an optical density of about 1 at the maximum wavelength). Since we observe at most 50% changes
the actual value of θ must be much less than 1 radian. Thus,
we can expand the cos(θ) term in Eq. 2 yielding:P1 (τ ) ∼ 1 −Figure 6: A time scan of the Mb signal at 6.04 microns as afunction of the relative polarization between the pump andprobe.

[cos(χt) + 1]2[(µEτ /h̄)2[µ/h̄]2] ∼ 1 − Epump
4
4

(3)

where we measure the response at the midpoint of pumppulse, τ and Epump is the energy of the pump pulse. The
prediction then is that the transmission change which is
proportional to P1 − 1 would be proportional to the energyof the pump E. In Fig. 7 we show that in fact the signal

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r.h.a. Austin et al. / Proceedings of the 2004 FEL Conference, 661-664

Figure 7: The dependence of the peak in the transmission
signal with pump pulse energy for Mb.
is linearly proportional to the pump energy as predicted by
Eq. 3.
We come back to the issue of Original Sin. We suggest that the T2∗ , the dephasing times, of the deeply buriedamino acid band is very long, at least 20 ps. IIf so, thenthis part of the protein is an inherently quantum mechanical, strongly coupled anharmonic system. system. Perhaps
we are addressing one aspect of the Original Sin problem
in protein dynamics.

ACKNOWLEDGEMENTS
We would like to thank the staff of the FOM Laserphysics facility FELIX for their dedicated help, Profs. Warren Warren and Marlon Scully of Princeton University fordiscussions, Lorand Kellerman for assistance in the FTIR
spectra and the Office of Naval Research for their financial
support.

REFERENCES[1] P.W. Milonni, and J.H. Eberley, Lasers. John Wiley and Sons,
NY, 1988.
[2] R.H. Austin, K.Beeson, L.Eisenstein, H.Frauenfelder,
I.Gunsalus and V.Marshall, Dynamics of Ligand Binding to
Myoglobin, Biochemistry 14, 5355-5373 (1975)[3] G.A. Jeffrey, An Introduction to Hydrogen Bonding; Oxford
University Press: New York, 1997.
[4] D. Mermin, J. Math. Phys. 7 (1966) 1038.
[5] H. Frauenfelder, G.A. Petsko, and D. Tsernoglou, Nature 280(1979) 563.
[6] R.H. Austin and A. Xie, Nuc. Instru. and Meth. Physics. Res.
A (1998) 504

FRAOS04

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E.J. Minehara et al. / Proceedings of the 2004 FEL Conference, 665-666

PREPARATION FEMTOSECOND LASER PREVENTION FOR THE COLDWORKED STRESS CORROSION CRACKINGS ON REACTOR GRADELOW CARBON STAINLESS STEEL*
Eisuke J. Minehara, Akihiko Nishimura*, and Takashi Tsukada**
Free-Electron Laser laboratory at Tokai, *High Peak Power Laser Laboratory at Kizu,**Research Group for Reactor Structural Materials at Tokai, JAERI, Tokai, Naka, Ibaraki
319-1195 JAPAN
Abstract
Femto-second (fs) lasers like low average power,
Ti:Sapphire lasers, the JAERI high average power freeelectron laser excimer laser, fiber laser and so on could
peel off and remove two stress corrosion cracking ( SCC )origins of the cold-worked (CW) and the cracking
susceptible material, and residual tensile stress inhardened and stretched surface of low-carbon stainlesssteel cubic samples for nuclear reactor internals as a proofof principle experiment except for the third origin ofcorrosive environment. Because it has been successfully
demonstrated that the fs lasers could clearly remove thetwo SCC origins, we could resultantly prevent the coldworked SCC in many fields near future.

INTRODUCTION
We first reported the novel method that femto-second(fs) lasers of the low average power Ti: Sapphire one, the
JAERI high average power free-electron laser, excimer
laser, fiber laser and so on [1,2] could peel off andremove both stress corrosion cracking (SCC) origins of
the cold-worked (CW) and very crack-susceptible
material, and residual tensile stress in the hardened
surface of low-carbon stainless steel cubic samples fornuclear reactor internals as a proof of principle
experiment except for the last and third origin ofcorrosive environment. Because it has been successfully
demonstrated that the fs lasers could clearly remove thetwo SCC origins, we could resultantly prevent the coldworked SCC in many field near future.
The SCC is a well known phenomenon [3, 4, 5, 6] inmodern material sciences, technologies, and industries,
and defined as an insidious failure mechanism that iscaused by the corrosive environment, and the cracksusceptible material and the surface residual tensile stresssimultaneously. There are a large number of famous SCC
examples for damaging stainless steels, aluminium alloys,
brass and other alloy metals in many different cases. In
many boiling light-water reactor (BWR) nuclear power
plants and a few pressurized light water reactor (PWR)
ones in Japan and the world [3, 4, 5, 6, 7] up to now, alarge number of the deep and wide cracks have been
recently found in the reactor-grade low-carbon stainlesssteel components of core shroud, control-blade handle, recirculating pipes, sheath and other internals in the reactor
vessel under very low or no applied stresses. These
cracks have been thought to be initiated from the cracksusceptible like very small-sized cracks, pinholes,

Available online at http://www.JACoW.org

concentrated dislocation defects and so on in the hardened
surface, which were originated from cold-work machining
processes in reactor manufacturing factories, and to beinsidiously penetrated widely into the deep inside under
the residual tensile stress and corrosive environment, andunder no applied stress during a much shorter term
operation. Most people had thought to be unavoidable
that Japanese economy would be damaged more or lessbecause most of the nuclear power plants near Tokyo
were shut-down during the last summer because of the
CWSCC failures. As it was fortunately a cold summer
last year because of global climate disorder, Japan and theJapanese domestic electric power companies could have anarrow escape from a large scale black-out in many
prefectures near Tokyo and Tokyo metropolitan area.

SAMPLE PREPERATIONS
The low-carbon type 316, 304 and other austenitic
stainless steel materials commonly used in nuclear reactor
internals were prepared and cold-worked to introduce
high residual tensile stress, crack-susceptibility andhardening in the one side using a conventional multipurpose milling machine before the cutting,characterizing the cold-worked surface hardness,susceptibility and tensile stress, and fs laser peeling-off.
As a lot of the reactor core shrouds and others have beenfound to be damaged by CWSCC during their operationand to be manufactured and cold-worked to finish by adisk-sander and a bite of a huge turning mill in thefactories, the same stainless steel material with them andthe multi-purpose milling machine were used to simulate
or to reproduce their cold-work processes like breakingdown surface grains and lattice microstructures.

FS LASER PEELING OFF
After the stainless steel material sheet was cut into
about one centimeter cubic samples of several tens,
typical depth of the hardened surface zone was measured
to be about several tens to a hundred micrometer. Eachcube of them was used as a standard test sample being
prepared in the same manner to compare with each otherin different peeling-off and testing conditions. The laser
typically irradiated to peel off about 2mm by 2mm square
area in the depth of 0.05-0.75mm without any heat effects
around the central part of the cold-worked, hardened andtensioned one in air atmosphere. Each of the irradiatedsamples was cut into 2 pieces by a sharp and thin ceramic

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E.J. Minehara et al. / Proceedings of the 2004 FEL Conference, 665-666

disc to have a rectangular 2mm by 1mm peeled-off strip
area under water-spraying and cooling. One of the half
pieces was used to measure hardness distribution along
the depth, and another of them used to measure theresidual stress strength and direction of compressing or
tensioning in the peeled-off strip and hardened side.
The half piece sample for the hardness testing waspolished carefully to peel off the damaged surface layer
spraying water and diamond powder. Then, the crosssectional surface of the half was electrochemically etched
to get rid off the damaged layer by 10% oxalic acidsolution. The etched surface was used to measurehardness distribution along the depth from the coldworked surface to the deep inside by a Vickers type micro
hardness testing machine [8]. Results of the hardness
distribution measurements have shown that the fs laser
completely peeled off the susceptible and the hardened
zone.

RESIDUAL TENSILE STRESS
A
commercially-available
small
area
X-ray
diffractometer [9] was used to analyze residual stress inthe peeled-off strip, and to confirm no effective residual
stress in it. As typically measured in the diffractometry,the residual tensile stress which was introduced to range
from 500 to 600 MPa by the cold-work were removed
from the fs laser peeled-off strip.

except for high power fs FELs have intrinsically nocapability and no future possibility to produce a fs andkW high average power [1]. It is thought that the highaverage power and fs FEL[2] has only and enoughcapability to peel off the two SCC origins and to prevent
their damages of the nuclear reactor pressure vesselinternals like the core shroud, pipes, and other structuralcomponents for realizing at least several times longer
interval than current life expectation spans of the nuclear
reactor safely, easily and quickly in low cost near future.
There is a large possibility that we could apply the novel
fs laser removal method with a large number of thesimilar boiling and steam generating plants or devices
which were made of stainless steel and other iron alloys,
and other metal alloys like Aluminium one, Brass andother ones to prevent their CWSCC damages near future
if the same or the similar origins will govern their
CWSCC failure processes.

ACKNOWLEDGEMENTS
The authors would like to express our sincere thanks to
Drs. S. Saito, T. Iwamura and T. Kimura for theircontinuous supports and encouragements, also special
thanks to all members of the research group for reactor
structural materials and FEL laboratory at Tokai Research
Establishment, JAERI for their critical helps and supports
in the work. The work is partially supported by JAERIinternal supporting funds No.20030412, and 20030413

HARDNESS TESTINGSREFERENCES

The typical value shows that the hardness one near thesurface was measured to be very high, around 470
kg/mm2, and the artificially-introduced residual stress by
the milling and other cold workings measured to betensioned along the surface. In contrast with the highhardness values, the measured hardness ones around thefs laser peeled-off area of about 2mm by 2mm square
were as low as the original low-carbon stainless steel
austenitic material deep inside, and the fs laser peeling-off
could remove the cold-worked and hardened one andmake no additional hardened zone on the strip surface.

[1]C. Momma et.al., Optics Comm.129, 134(1996).
[2]N. Nishimori et. al., Physical Review Letters, vol86,
No.25, p.5707-5710 (2001).
[3]R.M.Horn et. al., Nuclear Engineering and Design,
174(1997)313-325.
[4]O. Wacher and G. Brummer, Nuclear Engineering and
Design, 168(1997)35-52.
[5]R. A. Mulford et.al., Corrosion-NACE, 394(1983)132-143.
[6]Bushan, Bharat, and B.K. Gupta, Handbook of
Tribology. McGraw Hill Inc. New York.1991.
[7]T. Tsukada et. al., JAERI-Conf 2003-014(2003)119131.
[8]Harry Chandler, Hardness Testing, ISBN0871706407,
ASM International, 2nd edition (December 15, 1999).
[9]Victor E. Buhrke, Ron Jenkins, and Deane K. Smith, A
Practical Guide for the Preparation of Specimens for XRay Fluorescence and X-Ray Diffraction Analysis,

SUMMARY
The novel method of the fs laser-peeling off two SCC
origins of the susceptible zone and residual tensilestressed ones without additional heat effects in thestainless steel except for the corrosive and environmental
was firstly demonstrated utilizing a half watt or less TiSapphire fs laser [1] as the proof-of principle experimentto evaluate a feasibility utilizing tens kW class fs freeelectron laser (FEL) peeling and finishing. A MgCl2 SCC
test [10] for the samples has shown to be no crack of the
CWSCC and a few tens of other shallow cracks in thepeeled-off strip, and clearly indicates successful removalof the two origins.
All of the commercially-available fs ultra-fast lasers of
Ti-Sapphire laser, excimer laser, fiber laser and so on[7]THBOS02

ISBN0471194581, Wiley-VCH、(November 7, 1997).
[10]Japanese Standard Association, JIS G0576, Stresscorrosion Cracking Test for Stainless Steels, Ferrous
Materials and Metallurgy I-2004 pp.1142-1149,
ISBN4542136175, (April 20, 2001).

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Y. U. Jeong et al. / Proceedings of the 2004 FEL Conference, 667-670

THZ IMAGING BY A WIDE-BAND COMPACT FELYoung Uk Jeong, Hyuk Jin Cha, Seong Hee Park, Byung Cheol Lee, KAERI, Daejon, Korea
Grigori M. Kazakevitch, BINP, Novosibirsk, Russia
We have developed a laboratory-scale users facility
with a compact terahertz (THz) free electron laser (FEL).
The FEL operates in the wavelength range of 100–1200µm, which corresponds to 0.3–3 THz. THz radiation fromthe FEL shows well collimated Gaussian spatial
distribution and narrow spectral width of ∆λ/λ ~ 0.003,
which is Fourier transform limited by the estimated pulse
duration of 20 ps. The main application of the FEL is
THz imaging for bio-medical researches. We aredeveloping THz imaging techniques by 2-dimensional (2D) scanning, single pulse capturing with the electro-optic
method, and 3-D holography. High power, coherent, andshort-pulsed feature of the FEL radiation is expected toshow much better performance in advanced THz imagingof 3-D tomography. The coherent length of the FEL
micropulse is measured to be 8-12 mm. In this paper wewill show and discuss the main results of THz imaging
with the different methods by using the KAERI compact
FEL.

distribution. We could get the 2-D imaging of various
materials with the THz FEL beam. The measured
coherence length of the THz FEL micropulses is 8-12mm, which corresponds to 25-40 ps. The main idea for 3D coherent THz tomography with the coherent pulse is
proposed and discussed in this paper.
1.4

FEL Output Pulse Energy (Arb. Units)

Abstract

Pulse Repetition Rate : 1 Hz
Standard Deviation = 9.4%

1.2

1.0

0.8

0.6

0.4
0

INTRODUCTION
T-ray which means THz radiation imaging technology
was selected as one of ‘10 emerging technologies that willchange your world’ by a magazine named MIT’s
Technology Review of January 31, 2004. If we see theother selected technologies, e.g. universal translation,
synthetic biology, and so on, the potentiality of the THz
radiation technology might go beyond the usual
understanding of us. THz radiation has several
remarkable advantages for imaging compared with otherconventional sources, such as safe energy range without
ionization to the materials, foot-print spectral region ofmost chemicals and bio-materials, and relatively highspatial resolution for medical imaging.
There are several kinds of THz radiation sources [1–5].
Table-top THz sources generated by conventional lasers
have been developed and used for various applications in
the THz range [6–8]. However, advanced THz imaging
such as tomography of living species requires much more
power of the radiation to get information with better S/Nratio and higher speed of data acquisition. Inexpensive
and compact THz FEL [5,9] can play the important roleof encouraging the advanced THz applications due to its
higher power and spectral brightness compared to thetable-top sources.
We have developed a THz users facility based on acompact FEL [10]. The wavelength range of the FEL is100-1000 µm and we could construct a users
experimental stage for the wavelength of 100–300 µm.
The THz FEL beam shows good performance in pulseenergy stability, polarization, spectrum and spatial

Available online at http://www.JACoW.org

1000

2000

3000

4000

Time (second)

Figure 1: Measured fluctuation of the THz pulse energy
depending on time.

THZ FEL BEAM CHARACTERISTICS
FOR IMAGING
The stability of the radiation pulse energy was
improved by keeping cooling water and air temperature of
the system and laboratory within 0.1 and 1OC,
respectively. Figure 1 shows the measured fluctuation of
the THz pulse energy depending on time. The repetition
rate of the FEL macropulse was 1 Hz during themeasurement. We could not observe any drift of averagevalue of the FEL pulse energy and the fluctuation of thepulse energy is less than 10% in r.m.s value. If wemonitor and normalize the pulse energy fluctuation of the
FEL beam, the measuring error is decreased to be lessthan 1%. With the stable THz pulses, we could measure
2-D scanned imaging, interference patterns, or
spectroscopic information of species with high resolution.
The polarization of the THz FEL beam has beenmeasured by using a metal-wire polarizer having 20 µm
spacing, which is shown in Fig. 2. The FEL beam ishighly polarized with a linear component of more than
98% due to wiggling motion of the electron beam inside aplanar undulator. We could understand that thepolarization of the FEL beam is not disturbed by the long
distance (~10 m) propagation with more than 10 pieces ofmirrors, windows and lens.

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Y. U. Jeong et al. / Proceedings of the 2004 FEL Conference, 667-670

1.0Polarizer : grid (spacing 20 µm)
Linearly polarized > 98%

0.8

0.6

0.4

0.2

0.0

0

30

60

90

120

150

180

Polarizer Angle (degree)

Figure 2: Measured polarization of the THz FEL beam byusing a metal-wire polarizer having 20 µm spacing.

180

120
100

0.4

Interference Signal (Arb. Units)

140

0.5

0.5

Interference Signal (Arb. Units)

Spectral Power (Arb. Units)

160

FWHM~25 ps

0.3

0.2

0.1

0.0
-10

-5

0

5

0.4

FWHM~40 ps

0.3

Oscilloscope

Optical Delay (mm)Detector
-5

0

5

10

Optical Delay (mm)Signal

0
-0.2
-0.4
-0.6
-0.8

20

THz FEL

Detector

Detuning (mm)400Monitoring

0.1

80
60

PC

0.2

0.0
-10

10

of the Gaussian-shaped pulse. The bunch length from thecoherence length measurement agrees well with theestimation of the FEL bunch length from the calculated
value of the electron beam bunch.
The spatial distribution of the FEL beam was measured
on the experimental stage as shown in Ref. [10]. The
results show the distribution of the THz FEL beam is near
Gaussian shape. We have focused the beam having spot
size of 7 mm and wavelength of 110 mm with a parabolamirror (F/2). The focal length of the mirror is 50 mm. The
measured beam waist at the focal point is 0.3 mm, which
is close to value of the diffraction limitation from the 7mm-diameter THz FEL beam.
We could understand that our THz FEL beam has
excellent performance in power stability, polarization,
spectral width, spatial distribution and wavefront. We
hope that the THz radiation could be used for theadvanced application of THz imaging for 3-D coherence
tomography.

Aperture
SampleParabola Mirror(f=50 mm)

150

151

Beamsplitter

152

153

154

155

156

157

Aperture
Parabola Mirror(f=50 mm)
2-D Scanning stage

Wavelength (µm)

Figure 3: Measured FEL beam spectra depending on
detuning lengths of the FEL cavity. Measured results ofthe coherence lengths of the FEL micro-bunches for the
detuning lengths of 0 and -0.8 mm from the resonanceposition of the FEL optical cavity are shown in left andright insets of the figure, respectively.
Spectra of the FEL beam have been measured by a highresolution spectrometer having resolution of 10-4. And theresults were compared by the measured value of thecoherence length of the FEL micropulses. Coherent
length of the FEL micropulse could be measured by theMichelson configuration of the interferometer. Figure 3
shows measured FEL beam spectra depending on
detuning lengths of the FEL cavity. Measured results ofthe coherence lengths of the FEL micro-bunches for the
detuning lengths of 0 and -0.8 mm from the resonanceposition of the FEL optical cavity are shown in left andright insets of the figure, respectively. The FWHM of the
FEL line width is between 0.7 µm to 2 µm, whichcorresponds to 0.4-1.2% of the wavelength. The measured
coherence length from the interferogram is between 10
mm to 16 mm in FWHM, which corresponds to the FELbunch length of 25-40 ps (8-12 mm, FWHM) in the case

THBOS03

Figure 4: Schematics of the experimental setup for THz
transmitted imaging with 2-D scanning of the samples.

2-D THZ IMAGING
Figure 4 shows schematics of the experimental setup
for THz transmitted imaging with 2-D scanning of thesamples. The 2-D scanning and data acquisition areautomatically performed by a personal computer with acontroller. For the first experiment on the THz imaging,
we did not perform spectral study on the sample.
Therefore the used wavelength for the THz imaging
experiment was not optimised.
The first sample of 2-D THz imaging with our FEL
was a microchip as shown in Fig. 5. From the experiment
we could find the dynamic range of the THz imaging ismuch bigger than that of the usual vision recognition byhuman eyes. Even the dark part of the THz imaging inside
the chip contains information on its structure. Figure 6
shows a transmitted THz imaging through an invisible
paper box containing metal and silicon rings. We could
see the shape of the rings clearly. Additionally the density
information inside the silicon ring could be measured by
the THz radiation, which means that the big dynamic

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Y. U. Jeong et al. / Proceedings of the 2004 FEL Conference, 667-670

range is very useful to recognize the nature of sample
with THz spectral information. Without any additional
processing of the imaging data, we could get the dynamic
range of 105 for the measurements.

THz : 165 µm

Scale (mm)
0

0

5

1

1

2

2

THz : 110 µm
ZOOM
0

5

0

1

Scale
2
3

4

1
8

4

1

1

2

2
3

6
8

1

1

2

4

6

Figure 5: 2-D THz imaging of a microchip. From theexperiment we could find the dynamic range of the THz
imaging is much bigger than that of the usual vision
recognition by human eyes. Even the dark part of the THz
imaging inside the chip contains information on its
structure.

Fig. 7. Transmitted THz imaging of a gingko leaf, whichis compared with a visible transmitted imaging.

SampleScale (mm)

0

0

2

4

6

8

THz CCD Camera

1
Scanning
Depth and Phase

THz : 165 µm

2

Metal
ring
i

4

Mirror

B.S.

6
8
1

THz FEL

1

Figure 8: Schematics of the coherent THz tomography.

11
1O-ringFigure 6: Transmitted THz imaging through an invisible
paper box containing metal and silicon rings
Figure 7 shows a THz imaging of a gingko leaf, whichis compared with a visible transmitted imaging. You can
see the difference between the visible and THz imaging
clearly. The main difference is caused by 103-104 times
difference in absorption coefficient of liquid water
between the two frequencies.
We are constructing a fast imaging system with a single
micropulse of the THz beam by using the electro-optic(EO) detection and switching method. The linearlypolarized visible or IR laser beam is collinearly incident
to the EO crystal with the THz beam. The image of theTHz beam is transferred to the visible or IR laser beamand the transferred image can be captured by anintensified CCD camera.

PROPOSAL FOR COHERENT 3-D THZTOMOGRAPHY
The main difficulty of the THz tomography for medical
application is the huge absorption of the radiation byliquid water which is the major constitution of humanbody. To get the information from inner part of living
sample, we should remove the relatively strong signal
scattered from the surface or near the surface of thesample. The most simple and effective way to get weaksignal from strong background is to modulate theamplitude of the signal with the frequency which we canmeasure.
We have proposed a coherent 3-D THz tomography
technique by using the method of holography. Figure 8
shows schematics of the coherent THz tomography. The
THz FEL beam is divided into illuminating and reference
beams. By using the short-pulsed feature of the THz FEL
beam and controlling the optical path of the reference
beam, we can select a certain cross-section inside the

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Y. U. Jeong et al. / Proceedings of the 2004 FEL Conference, 667-670

sample to make a hologram. By changing the optical pathof the reference beam minutely, we can get modulating
signal at fixed point of the hologram.
The idea is similar with optical coherence tomography(OCT) which uses optical range source. But in thistechnique, the light source has broad-band spectrum toreduce the resolution in depth up to ~µm. The light isfocused on a point. And by modulating the path
difference of reference beam, the absolute distance of
depth is measured by the interference of the white light.
Usually they get imaging information by scanning
through x, y, and z. As you can see the detailed phase
information of the interference is not important in the
OCT technique. In our case, the THz FEL is narrow-band
coherent source. The coherence length of the FEL beam issame as the pulse length, which is 8-12 mm as shown in
Fig. 3. If we make and measure hologram with the beam,
we could get the information of the depth less than thecoherence length. With THz range light, it is much easierto get the phase information of the interference. And we
do not need to get the full phase information through thecoherence length because we only need the relative phase
information among the points in imaging plane. If wehave high power, coherent source of the THz light andsensitive measuring 2-D device for the THz light, we
could get 3-D tomography of the living species with THz
spectroscopic information.

CONCLUSION
We have developed a compact THz FEL and the main
activity of its application for THz imaging is introducedin this paper. The FEL beam showed good performance inpulse-energy stability, polarization, spectrum and spatial

THBOS03

distribution. We could get the 2-D imaging of various
materials with the THz FEL beam. To perform
spectroscopic imaging, we will develop a Fouriertransform spectrometer for THz range. The main idea for
3-D coherent THz tomography is proposed and discussed
briefly. We hope to develop the technique for bio-medical
application or non-destructive inspection.

ACKNOWLEDGEMENTS
This work was supported by Korea Research
Foundation Grant (KRF-2003-042-D00195).

REFERENCES[1] Rudeger Kohler, et al., Nature, 417 (2002) 156.
[2] Kodo Kawase, et al., Appl. Phys. Lett. 78 (2001)
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[3] Q. Wu and X.-C. Zhang, Appl. Phys. Lett. 67, (1995)
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[4] M. Abo-Bakr, et al., Phys. Rev. Lett. 88 (2003)
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[6] D.M. Mittleman, et al., Appl. Phys. B 68 (1999) 1085.
[7] K. Kawase, et al., Opt. Express 11 (2003) 2549.
[8] T. Loffler, et al., Opt. Express 9 (2001) 616.
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[10] Y.U. Jeong, et al., Nucl. Instr. and Meth. A 528(2004) 88.

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L. M. Yang et al. / Proceedings of the 2004 FEL Conference, 671-674

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675

J. Krzywinski et al. / Proceedings of the 2004 FEL Conference, 675-678

INTERACTION OF INTENSE ULTRASHORT XUV PULSES WITH
DIFFERENT SOLIDS – RESULTS FROM THE TESLA TEST FACILITY
FEL PHASE I
Jacek Krzywinski, Marek Jurek, Dorota Klinger, Robert Nietubyc, Jerzy Pelka, Andrzej Wawro,
IP/PAS, Warsaw, Poland
Marcin Sikora, AGH University of Science and Technology, Krakow, Poland
Evgeny Saldin, Evgeny Schneidmiller, Barbara Steeg, Rolf Treusch, Mikhail V. Yurkov,
HASYLAB/DESY, Hamburg, Germany
Michal Bittner, Dagmar Chvostova, Libor Juha, Vit Letal, Vladimir Vorlicek,
IP/ASCR, Prague, Czech RepublicAndrzej Andrejczuk, Henryk Reniewicz, University of Bialystok, Bialystok, Poland
Ryszard Sobierajski, Warsaw University of Technology, Warsaw, Poland
Anna Kauch, Warsaw University, Warsaw, Poland
Abstract
Key results of a study of irreversible changes induced atsurfaces of metals, semiconductors, and insulators by
ultrashort XUV pulses generated at the TTF FEL facility
are reported and discussed. Energy spectra of ions ejectedfrom the irradiated surfaces are also reported. Special
attention is paid to a difference in the ablation behavior of(semi)conductors and insulators that we have observed.
The difference is dramatic while the absorption coefficients are similar for all materials at the TTF1 FEL wavelength.

INTRODUCTION
Before the FELIS [1] experiments were performed at
TTF1 FEL in 2001-2002, the shortest wavelengths at
which laser ablation had been investigated were 46.9 nm
and 125 nm. The 46.9-nm radiation was emitted from acapillary-discharge Ne-like Ar XUV laser [2] and the125-nm radiation was generated by four-wave-sumfrequency mixing (FWSFM) of a 626-nm dye laser and its
second harmonics in Hg vapor [3]. The pulse duration inboth cases was in the nanosecond range. A few papers(for a review see [4]) have reported ablation induced ateven shorter wavelengths (i.e. in the soft X-ray region)
but the radiation used was not coherent. In the present
study, not only the laser wavelength is short (< 100 nm)
but also the pulse duration is very short (typically 50100 fs) [5]. The short wavelength and ultrafast coherent
beam represent a unique combination. The ablation behavior of a wide variety of materials has been investigatedunder these irradiation conditions.

Available online at http://www.JACoW.org

In this contribution, key results of a study of irreversible changes induced at surfaces of metals, semiconductors, and insulators by ultrashort XUV pulses generated at
the TTF1 FEL facility are reported and discussed. We
also report the mass, energy, and spectra of ions ejectedfrom the irradiated surfaces.
Special attention is paid to a difference in the ablation
behavior that we have observed for (semi)conductors andinsulators. The difference is dramatic while the absorption
coefficients are similar for all the materials at the TTF1
FEL wavelength.
Ablation characteristics, i.e. thresholds, etch (ablation)
rates, and ablated structure quality, often differ dramatically with conventional UV-Vis-IR lasers, depending onwhether the radiation energy is delivered to the material
surface in short (typically nanosecond) or ultra-short(typically femtosecond) pulses [6,7]. The FELIS experiment, together with ablation experiments utilizing plasmabased XUV lasers, makes it possible to investigate how
ablation characteristics depend on the pulse duration in
the XUV spectral region (λ < 100nm).

EXPERIMENTAL
The samples were irradiated by the SASE-FEL beamemitted by the Tesla Test Facility (TTF) at HASYLAB/DESY in Hamburg [5]. The wavelength was tuned between 85 and 98 nm. Spectral and energy characteristicsof the laser beam were measured using photon diagnostics
described in details elsewhere [8]. The beam was focusedby an elliptical mirror into the interaction chamber asshown in Fig. 1. For more details, see [9].

FEL Users Workshop

676

J. Krzywinski et al. / Proceedings of the 2004 FEL Conference, 675-678

CCD

Focusing
mirrorVUV
detectorVideomicroscope

VUV
detector

Amorphization
3000

Intensity (a.u)

TOF spectrometer

Sampleholder
X,Y,Z,ϕ

2000

1000

0

Evaporation
cell

200

400

600

800

1000

Raman shift (cm-1)

Figure 1: Schematic of the FELIS chamber [9].
Morphological changes at the surface of the exposed samples were investigated by Nomarski, conventional optical,
scanning electron, and atomic force (AFM) microscopy.
Raman spectra were made with a laser microbeam in theusual backscattering geometry, which enables probingchosen locations on the sample surface. Ion energies andmass spectra were measured using a time-of-flight (TOF)
spectrometer equipped with high pass energy filter.

Samples
A number of different samples were irradiated by the
focused FEL beam. The bulk samples were: Au, Si,
PMMA, Ce:YAG, and SiO2. We have also irradiated Si
crystals polished to optical quality and covered with thinfilms: 15-nm Au (Au-15), 10-nm and 40-nm amorphous
carbon (a-C-10 and a-C-40).

RESULTS
Surface damage
Modification of silicon surfaces exposed to FEL pulses
of increasing fluences and recorded by Nomarski microscope is presented in Fig. 2. Each spot was irradiated with11 shots. The first changes seen are due to modification of
the refractive index. An imprinted interference pattern,

50 µm

Figure 3: Raman spectra measured at different places on
an FEL-irradiated sample of monocrystalline Si.
which is due to diagnostics that were installed in front of
the focusing mirror and to slope errors of the mirror
surface, is clearly seen. The AFM and TOF measurements
do not indicate any morphological changes or ion emission, respectively. Raman spectra however show signs ofan amorphous phase in the modified region. The Raman
spectra measured at three different locations of theexcitation-micro-beam spot are shown in Fig. 3. The
amorphous fraction increases towards the center of thecrater. The first observable changes were recorded at afluence of 0.005 J/cm2.
In Table I we present two different fluence thresholds at
which we start to record modifications of the irradiatedsurface. The first (ΦI) is the fluence at which we notice achange of the refractive index and the second (ΦII) is thefluence at which deformation of the surface is indicatedby the AFM. It can be seen that, except for Au-10 and
PMMA, the ΦII values oscillate about 0.03 J/cm2. This isof the order of the fluence, Fc, at which the absorbed energy per atom is equal to the cohesive energy, Ec,
Fc = Ec n /α,
Table 1: TTF1-FEL surface modification thresholds
ΦI [J/cm2]

ΦII [J/cm2]

Au

0.02

0.02

Au-15

0.01

0.01

Material

Figure 2: Modification of monocrystalline-Si surfaces
imaged by Nomarski microscopy. The fluence increases
counterclockwise and is equal to 0.015, 0.04, 0.3, and
1.8 J/cm2 , respectively.

THCOS02a-C-40

0.01

0.03

Si

0.005

0.04

SiO2

0.03

0.03

Ce:YAG

0.02

0.02

PMMA

0.01

0.01

677

Normalized signal [a.u]J. Krzywinski et al. / Proceedings of the 2004 FEL Conference, 675-678

350
300

Z[nm]

250
200
150
100
50
0
0

10

20

30

40

50

0.8
0.6
0.4
0.2
0
0

60

X[µm]

20
0

Z [nm]

-60
-80
-100
-120
-140
-160
200

300

400

500

X [µm]

Figure 4: AFM measurements of the silicon (upper) andquartz (lower) samples. Irradiation conditions weresimilar (fluence ~ 0.04 J/cm2). The insets are the crater
profiles along the green lines.
where n is atomic density and α is the absorption coefficient. For typical values Ec ~ 3 eV/at, n ~ 5 x 1022 at/cm3,and α ~ 106 cm-1, Fc ≈ 0.025 J/cm2, which corresponds tothe values shown in Table 1.

Difference in ablation behavior between(semi)conductors and insulators
Results of the AFM investigations carried out for the
crystalline Si and SiO2 samples are presented in Fig 4.
The samples were irradiated with 11 shots at an average
fluence of 0.04 J/cm2. One can notice a dramatic difference in the morphology of both craters. The silicon crateris covered by columnar structures. The peaks of the columns are located above the sample’s surface. In the caseof crystalline SiO2 (quartz), the interior of the crater isvery smooth and the interference pattern is clearly imprinted into the sample’s surface. Exposure of all investigated insulator samples to multiple shots leads to very
similar surface pattern when the distance between thesample and the focal spot is the same. Both the morphology of the irradiated surface and the crater depth do notdepended on the FEL beam intensity. These featuresindicate that intense ultra-short pulses of XUV radiation
can be used for nano- and micro-machining of insulators.
The ion spectra measured for the Si and SiO2 samples
are presented in Fig. 5. Multiple charged ions were recorded for high-intensity irradiation of Si. The kinetic
energy of the ions increases with charge state and reaches
the keV range for highly charged ions. Again, there is aclear difference between Si and SiO2. The high charge
states and energetic ions shown for Si are typical of all(semi)conductors. Only singly charged, low-energy ions(~50 eV) were detected for the insulator SiO2 under all
irradiation conditions. Other insulators investigated

Normalized signal [a.u]

40

-40

100

200

400

600

800

1000

Ion energy/charge [eV/e]

-20

0

+1
+2
+3
+4

1

(a)

Si+

1

+
- SiO+
- O+

0.8
0.6
0.4
0.2
0
0

20

40

60

80

100

120

Ion energy/charge [eV/e](b)

Figure 5: The energy spectra of ions taken with the TOF
spectrometer for the silicon (a) and quartz (b) samples.
Signals have been normalized. The energy scale has been
divided by the ions charge state.

exhibited similar behavior. An interesting feature of theion spectra observed for all (semi)conductors is that themeasured values can be normalized to one curve if theenergy of the ion is divided by its charge. This suggests a
field emission mechanism.
It is very interesting to notice that the difference inablation behavior between (semi)conductors and insulators is very pronounced although the absorption
coefficients are similar for all the materials at the TTF1
FEL wavelength.

FEL-induced periodic surface structures
Although laser-induced periodic surface structures(LIPSS) were discovered in the middle of the 1960s [10],they remain a subject of extensive research (for a review
see [11,12]). According to the nature of their origin, twokinds of LIPSS can be distinguished on laser-irradiatedsurfaces. In the initial stage of research, most LIPSS
observed were ripples, with a spatial period related to thelaser wavelength. The ripples, which are called LIPSS of
the first kind (LIPSS-I), are created by the interference of
the incident laser beam with a wave diffracted by periodic
features in the materials’ surface. The spatial periods of
LIPSS of the second kind (LIPSS-II), however, depend
more on laser intensity than on wavelength and are significantly longer than the laser wavelength when a shortwavelength laser is used for irradiation. On the material
surfaces irradiated by the focused TTF1-FEL beam,
LIPSS-I have been found at the rim of a few of the craters
created in a-C and PMMA by 98-nm and 86-nm radiation

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Figure 6: AFM image (tapping mode) of LIPSS at the rimof a crater ablated in PMMA by the tightly focused beamof the TTF1 FEL (λ = 86 nm, φ = 0.5 J/cm2; 11 accumulated pulses, 55o incidence)
respectively [1,13,14]. In Fig. 6, ripples of 70-nm periodicity can be seen on the right side. Currently, 86-nm FEL
radiation represents the shortest-wavelength radiation
used for production of well-developed LIPSS-I. According to our best knowledge, the shortest wavelength atwhich LIPSS-I had previously been produced was that ofthe157 nm F2 excimer laser [12].
LIPSS-I have not yet been observed on the surfaces of
Si, Ce:YAG, or SiO2 (quartz) irradiated by TTF1 FEL.
How might this be explained? Although a possible
explanation was discussed in [14], the problem remains
unsolved. Contrary to the scarcity of LIPSS-I, LIPSS-II
have been found on almost all FEL-irradiated surfaces.
LIPSS-II can be attributed to capillary (surface tension)and surface acoustic waves, fixed in laser-melted nearsurface material by its re-solidification, and also toRayleigh-Taylor and Helmholtz-Kelvin instabilities,
relaxation of stress, and similar phenomena. All of theseprocesses are expected to be very common at FEL irradiated surfaces, so that the observed high abundance of
LIPSS-II is not surprising.

SUMMARY
Results of the study of irreversible changes induced atsurfaces of metals, semiconductors, and insulators by

THCOS02

ultrashort XUV pulses generated at the TTF1 FEL facility
have been reported and discussed. A distinct difference
between the behaviors of (semi)conducting materials andinsulators was observed. In the case of inorganic insulators, the morphology of the irradiated surface and thecrater depth hardly depended on the beam intensity. In
contrast, the irradiated silicon surface becomes very roughwhen the intensity exceeds the damage threshold. There isalso a clear difference between insulators and (semi)conducting materials with respect to the spectra of ejected
ions. Highly-charged, energetic ions (~ a few keV) weretypical for (semi)conductors. Only singly-charged, lowenergy ions (~50 eV) were detected for insulators under
all irradiation conditions. LIPSS-I have been found at therim of a few craters created in a-C and PMMA by 98-nm
and 86-nm radiation, respectively. LIPSS-II have also
been found. Their spatial periods depend more on laser
intensity than wavelength and are significantly longer
than the laser wavelength, for short-wavelength lasers.

REFERENCES[1] R. Sobierajski, et al.,: “Structural changes at solid
surfaces irradiated with femtosecond, intense XUVpulses generated by TTF-FEL”, Proceedings of the24th International Free Electron Laser Conference &9th FEL Users Workshop, Argonne, IL, September 913, 2002 pp. II77-78 (2003).
[2] B. R. Benware et al., Opt. Lett. 24 (1999) 1714.
[3] D. Riedel and M. C. Castex, Appl. Phys. A69 (1999)
375.
[4] L. Juha et al., Surf. Rev. Lett. 9 (2002) 347.
[5] V. Ayvazyan et al., Eur. J. Phys. D20 (2002) 149.
[6] R. Srinivasan et al.: Appl. Phys. Lett. 51 (1987) 1285.
[7] S. Küper and M. Stuke: Appl. Phys. B44 (1987) 199.
[8] R. Treusch et al., Nucl. Instrum. Meth. Phys. Res. A
467-8 (2001) 30.
[9] A. Andrejczuk, et al., HASYLAB Annu. Rep. (2001)
117.
[10] M. Birnbaum: J. Appl. Phys. 36 (1965) 3688.
[11] A. E. Siegman and P. M. Fauchet: IEEE J. Quant.
Electron. QE-22 (1986) 1384.
[12] P. E. Dyer et al.: Appl. Surf. Sci. 96-97 (1996) 537.
[13] B. Steeg et al.: Appl. Phys. Lett. 84 (2004) 657.
[14] L. Juha et al.: HASYLAB Annual Rep. 2003 Part I(2003) 763.

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EXPLORING THE SPATIAL RESOLUTION OF THE PHOTOTHERMAL
BEAM DEFLECTION TECHNIQUE IN THE INFRARED REGION
W. Seidel, H. Foerstendorf, Forschungszentrum Rossendorf, 01314 Dresden, Germany
F. Glotin, J.M. Ortega, R. Prazeres, LURE, 91898 Orsay Cedex, France
Abstract
In photothermal beam deflection (PTBD) spectroscopy
generating and detection of thermal waves occur generally in the sub-millimeter length scale. Therefore, PTBD
provides spatial information about the surface of the sample and permits imaging and/or microspectrometry. Recent results of PTBD experiments are presented with ahigh spatial resolution which is near the diffraction limitof the infrared pump beam (CLIO-FEL).

INTRODUCTION
Figure 2: Time-resolved beam deflection signals of astrong absorbing (upper trace) and a nearly transparent
sample (lower trace).
changes periodically and thus a different reflection angle
is observed by the use of a high resolution position detector. The resulting beam deflection signals are shown in
Fig. 2.
We investigated O+-implanted and untreated regions ofgermanium substrates serving as model surfaces. The
different areas of the surfaces can be distinguished by
optical absorption (i.e. the amplitude of the deflection
signal) at λ = 11.6 µm of the germaniumoxide produced
during the implantation process (Fig. 3).

RESULTS
Simple Border Range
We investigated the border range of O+-implanted anduntreated regions of a germanium substrate serving as amodel surface. The different areas of the surface can be
distinguished by optical absorption (i.e. the amplitude of

Available online at http://www.JACoW.org+-1

O -doped Germanium

1800

Figure 1: Layout of the PTBD experiment setup used at
CLIO for microspectrometry.

860 cm
11.6 µm-1

pure Germanium

1298 cm
7.7 µmTransmission [a.u.]

The PTBD technique is based on the theory of photothermal spectroscopy which describes the conversion ofabsorbed energy of a light beam incident on a sample into
heat by nonradiative de-excitation processes [1]. The distribution of this induced, exponentially decaying, thermal
field is given by the solution of the heat equation with asource term of a Gaussian beam [2]. In typical PTBD experiments the magnitude of the signal is proportional to
the slope of the induced displacement of the sample surface. Additionally, it can be shown that there is a direct
proportionality between the observed signal and the absorption coefficient of the material under investigation[2]. Therefore, a direct access to absorption spectra isprovided [3]. The detection limit is expected to be extremely low since absorptions as low as 10-6 to 10-8 havebeen measured in the visible region by this method [4].
In typical PTBD experiments a solid sample is irradiated by a modulated beam of monochromatic light produced by a tunable infrared laser and a probe beam (e.g. a
HeNe laser) which is reflected from the sample (Fig. 1).
Depending on the modulated intensity of the pump beam
the photoinduced displacement of the probe beam

1600

1400
1200
1000
-1
Wavenumber [cm ]

800

600

Figure 3: FT-IR transmission spectra of a Ge-substrate of
O+-implanted and untreated regions.

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be expected when the deflection curves are averaged over
several FEL pulses. This will probably facilitate the reproduction of more complex structures by PTBD-FEL
microspectrometry.
period [mm]:4 x 0.06
strip width [mm]:8 x 0.03

6 x 0.2
0.05 0.1 > 0.1

A

rel. pos. [mm]-0,50 -0,25 0,00 0,25 0,50 0,75 1,00 1,25 1,50
λFEL= 11.6 µm

B

t = 1.96 ms

λFEL= 11.6 µm

Ct = 1.96 ms

λFEL= 7.7 µm

Dt = 1.96 ms

Int. [a.u.]t = 1.86 ms

Revcovery of More Complex Structures
In the next series of our experiments we investigated asample showing a distinct pattern of implanted regions
which was achieved by a special stainless steal mask infront of the substrate during the implantation process. The
dimensions of the mask are given in Fig. 5A. Additionally, the implanted regions are indicated as grey stripes
throughout Figs. 5 B-D.
The profiles presented in Fig. 5B clearly reproduce thestructure of the implanted regions generated by the mask.
In Fig. 5C an enlarged range of five thin implanted regions were detected at high resolution of positioning (stepwidth: 2 µm). Again, the recovery of the pattern of implantation is of excellent quality. For demonstration thatthe deflection signal is solely caused by optical absorption
the same sample area was recorded at a wavelength of
7.7 µm where no absorption occurs (Fig. 3). This is demonstrated in Fig. 5D.
It is noteworthy, that all profiles shown in this work
were obtained with only one macropulse for each sample
position. A significantly higher signal-to-noise ratio can

THPOS05

Int. [a.u.]

the deflection signal) at λ = 11.6 µm of the germaniumoxide produced during the implantation process(Fig. 3). From the set of time curves (Fig. 2) recorded at
distinct positions of the surface of the sample profiles canbe obtained reflecting the distribution of the implanted
oxygen in the substrate as it is shown in Fig. 4.
The transition between an O+-doped and an untreatedregion of the substrate was investigated. The HeNe laser
probe beam was focused in front of the surface of thesample to about 15 µm. This leads to an enhancement of
the spatial resolution up to about 20 µm as it can be seenaround 1.65 mm rel. pos. (Fig. 4, right panel).

Int. [a.u.]

Figure 4: Mapping plot of the set of time curves of thedeflection signal at distinct sample positions and the extracted absorption profile of the border range between O+doped and pure germanium (extracted at t = 10 µs and at
λ = 11.6 µm).

-0,10 -0,05 0,00

0,05 0,10 0,15
rel. pos. [mm]

0,20

0,25

Figure 5: Dimensions of the implantation pattern for the
preparation of the Ge-substrate with O+-ions (A).
Extracted absorption profiles (B-D): Profiles (step width:
10 µm) of the whole implanted structure at different times
after the FEL pulse (black line: time of max. deflection,
red line: time before deflection occur) (B). Profiles (stepwidth: 2 µm) of five thin lines at different wavelengths(C-D). 11.6 µm: max. absorption (C), 7.7 µm: no absorption (see Fig. 3) (D).

References[1] A. Rosencwaig and A. Gersho, J. Appl. Phys. 47(1976) 64.
[2] M.A. Olmstead et al., Appl. Phys. A 32 (1983) 141.
[3] W. Seidel et al., Eur. Phys. J - Appl. Phys. 25 (2004)
39.
[4] A. Mandelis, Physics Today 53 (2000) 29.

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EXPERIMENTS ON THE SYNCHRONIZATION OF AN ULTRAFAST
CR:LISAF LASER WITH THE ELETTRA STORAGE RING AND FEL
PULSES
M. Ferianis, M. B. Danailov, G.De Ninno, B. Diviacco, M. Trovò, ELETTRA, 34012 Trieste,
ITALY
M. Coreno, CNR-IMIP, 34012 Trieste, ITALY, G. E. Afifi, NILES, Cairo, EGYPT
Abstract
The techniques for synchronizing ultra fast lasers toexternal radio frequency reference sources are wellestablished and characterized in the literature. However,data lack on the minimum light-to-light jitter that can beachieved in different synchrotron operation modes whenan external laser is locked to the storage ring masterclock. Here we present first results for thesynchronization of an ultra fast Cr:LiSAF laser withelectromagnetic radiation coming from the Elettra storage
ring in four bunch and multi-bunch mode. In addition,
data on the synchronization of the same laser with theElettra FEL pulses, both in free running and Q-switching
regime, are reported. In our experiments, laser-to-RF
locking was continuously monitored using a built-in
phase detection. The laser light to storage ring light
locking was characterized by simultaneous acquisition of
two/three pulse trains by a streak camera. In addition,pulse jitter was determined by processing of the signal offast photodiodes monitoring the different light beams.

INTRODUCTION
During the last decade, remarkable progress has beenobtained in the establishment and full-potential operationof Third Generation Synchrotron light sources. At thesame time, impressive peak powers (Terawatts) have beenachieved by continuous advances in laser techniques;
femto-second pulse duration is now available fromcommercial equipments. Current projects of fourth
generation sources in the X-ray spectral range, X-ray Free
Electron Lasers (X-FELs) integrate accelerator and laser
based technologies [1]. This process has started also at the
ELETTRA Laboratory, where the Storage Ring FreeElectron Laser SR-FEL [2] is in operation and the fourth
generation light source [3] FERMI@ELETTRA is now
ready to go.
As the synchronization of fs-lasers to the electron
bunches is crucial for the optimum operation of these newsources, we performed some synchronization experiments
using the currently available sources.

RADIATION SOURCES AT ELETTRA
Different radiation sources can be used simultaneously
at ELETTRA for “time resolved” experiments. Beside thewell-known Undulator and Bending magnet radiation,
whose temporal structure directly reflects the Storage
Ring filling pattern, the Storage Ring Free Electron Laser(SR-FEL) is now becoming available. Furthermore, table

Available online at http://www.JACoW.org

top laser oscillators can be used when the wavelength or
the energy per pulse of a specific experiment is not
fulfilled by the ELETTRA sources. In Table 1 thetemporal structures of these sources are reported.
Table 1: Temporal structure of the radiation sources.
Source type

Pulse length
tFWHM

Repetition
Frequency

Bending/
Undulator

50÷120ps
60ps

MB: 500MHz
4B: 4.26MHz

SR-FEL, free run

15ps

4.64MHz,pulsedSR-FEL, Q-switch

15ps

10Hz

Table top fs laser
Ti:Sa, Cr:LiSAF≈110fs≈100MHz

Synchrotron radiation
During user shifts the machine is operated in:multi bunch mode (MB), the standard user mode
four-bunch mode (4-B), the SR-FEL mode
In MB mode, the 90% of the available buckets arefilled consecutively, with 2ns spacing between bunches.
This mode is used by those beam lines that rely on the
average photon flux and do not exploit the time structureof the radiation. Typical electron energies are ranging
from 2 to 2.4GeV, with a maximum average current of
330mA. Synchrotron radiation pulses have duration of
typically 60psFWHM in MB operation; recently using theThird Harmonic super-conducting cavity, this value raised
up to 120psFWHM. The temporal structures of different
sources are listed in Table 1.
The four bunch (4-B) mode is used by the SR-FEL, at
1GeV, and by the Users carrying out “time resolved”
experiments, mostly at 2GeV as the photon beam isbrighter. In this mode, four bunches are evenly distributedin four storage ring buckets and the interval between them
results to be 216ns.
••

Storage Ring Free Electron Laser
In a SR-FEL, a relativistic electron beam interacts with
an electromagnetic field as it passes through a periodic
magnetic structure forcing particles to move along sinlike trajectories and, consequently, to emit radiation. The
ELETTRA SR-FEL is the first and only one installed on athird-generation synchrotron light source. As aconsequence, its performance profit from a relative low

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Figure 1: Example of the different macro-temporal structures displayed by the ELETTRA FEL when operated instandard (Figure 2a) or Q-switching (Figure 2b) mode.
emittance and short duration of the electron bunch andfrom a longer interacting region (this resulting in a higher
gain with respect to similar devices). ELETTRA holds theworld record of the shortest wavelength ever reachedusing an oscillator FEL (190 nm). The time duration of asingle pulse from the SR-FEL can be as low as 15psFWHM.
The repetition rate of the SR-FEL pulses varies according
to the operation mode of the SR-FEL: free running (fig. 1
left) and Q-switch (fig. 1 right), where the FEL power is“concentrated” into a series of giant pulses. In this case,the peak power is considerably enhanced (one to few
orders of magnitude). The giant-pulse operation on a SRFEL can be obtained by means of a radio frequency (RF)modulation, or using a gain-switching technique [4].

Instrumentation Group where the synchrotron radiation(UV-VIS-NIR) generated by the storage ring bending
magnet S12.2 is made available for diagnostic purposes.
Furthermore, the back-end of the SR-FEL is conveniently
located in the close vicinity of the same laboratory where
the installed Streak Camera is routinely used formeasuring both the synchrotron radiation pulses and the
SR-FEL pulses. The accelerating voltage radio frequency(RF) has been routed to the Optical Laboratory to feed thestreak camera timing system. Therefore, to perform theexperiment it was sufficient to move the Cr:LiSAF fs
laser to the Optical Laboratory and to synchronize it to
the same RF signal by means of a low-jitter electronic
module.

Table top fs laser oscillator

Electron beam operating conditions

The laser system used for the experiments is a homemade femtosecond Cr:LiSAF laser. The laser construction
has been optimized in order to decrease the intrinsic noise
and increase stability. The active material is a 3% doped
3mm long Brewster cut Cr:LiSAF crystal (withtemperature stabilization at 18oC by a Peltier cooler),
which is pumped at 670nm by a 350mW diode. The
phase locking to an external reference is based on thewell-established technique using a feedback loop acting
on the cavity length [5]: we have used a commerciallyavailable instrument (CLX1100, Time Bandwidth
Products) which implements this approach. The necessary
laser frequency reference signal is provided by anavalanche photodiode illuminated by a small fraction of
the laser output beam.

The experiments have been carried out in both MB and
4-B modes. As the fs laser normally operates at arepetition frequency of 100MHz, to synchronize it to the
MB beam it was sufficient to tune the length of its opticalcavity to obtain frep1= 99.9308MHz. The reference signal
at this frequency has been obtained by division modulo-5of the RF, as indicated in Table 2.

EXPERIMENT SET-UP
The objectives of the experiments were:• to synchronize the fs laser to the machine RF• to acquire in a single shot all three sources:
synchrotron bending, SR-FEL and fs laser• to measure the jitter between the sources• to observe their stability on the long-term timescale, compared to the duration of the pulses
A pre-requisite for the experiment was to have all threesources available at the same location to allow theirsimultaneous acquisition. This configuration has been
easily achieved in the Optical Laboratory of the

THPOS08

Table 2: Different frequencies used for the experiments.
Symboldiv. modulo
N

fRF
frep1

1
5

frep2

6

f4-BUNCH

Frequency

period[MHz]499.654[ns]
2.0

99.9308

10.0

83.2756

12.0

108
4.626
216.1
108/6=18 ⇒ frep2=18th harmonic (f4bunch)

In 4-B mode, being the synchrotron radiation repetition
rate equal to f4-BUNCH=4.626MHz, to lock the fs laser
pulses to the synchrotron radiation ones at eachrevolution, the fs laser repetition frequency has beenchanged to frep2=83.2756MHz. In doing so, eachsynchrotron radiation pulse had a laser pulse locked to it,
one out of 18 as frep2 has been selected to be the 18th
harmonic of f4-BUNCH.

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Synchrotron
Radiation
Pulses @Streak Camera
Timing systemfrom Storage Ring
RF generator
fRF=499.654MHz

÷2

Power
SplitterfS-SCAN=250MHz

÷N
Unit

4.626MHz

Synchroscan
StreakCameraDivide-by-6
Unit
fREF=
83.2756MHz

Phase Detector

Power
Splitter
ReferenceIN

Laser Timing
Stabilizer

Power
SplitterBand passfilter18th
harmonic

Laser
IN

LP
filterPiezo
driverPiezo
actuator

Sub-psPhase
Detector

Laser cavity

fREP2=83.2756MHz

Figure 2: Block diagram of the Synchronization experiment

Description of the block diagram
The block diagram is reported in figure 2. In the upper
left part, the low –jitter division-by-6 module can be seen.
In the lower part, the Cr:LiSAF fs laser is visible with thelock-in equipment. Finally, in the right hand part of theblock diagram, the light-to-light jitter measurement
device is shown.
Before acquiring these different sources with the streak
camera, they had to be precisely aligned onto the streak
camera input pinhole (D=50÷200µm) and separately
attenuated, using Neutral Density filters, due to theirrather different intensities.

measurements have been cross-checked in both the timeand frequency domain. In figure 3, the phase oscillationsof the fs laser with respect to its reference, and due to akick applied to the laser table, are shown. The upper traceshows the AD8302 output, the lower one the Timing
Stabilizer output: there is a very good agreement with ahigher sensitivity on the AD8302. Same results have beenobtained with spectral observations in the range 10Hz to
1MHz, showing no major laser phase noise components
above 1kHz.

JITTER MEASUREMENTS
With the term jitter, here we intend the amplitude of theshort-term time fluctuations of a signal with respect to its
reference. When dealing with signals of the same
frequency (i.e. frequency locked) the jitter turns out to be
the phase noise of a signal to its reference.
The fs laser is equipped with its Timing Stabilizer unitthat locks the repetition frequency of the laser to areference by controlling the length of the optical cavity
using a piezoelectric actuator. The Timing Stabilizer unit
outputs the phase noise instantaneous values on a front
panel display that is very useful for the fs laser set-up.
As the phase noise is a key parameter to know in our
experiment, we implemented a redundant phase noise
measurement beside the Timing Stabilizer unit. We
adopted the Amplitude and Phase Detector AD8302 from
Analog Devices [6] that performs amplitude ratio andphase difference measurements on two signals, from DC
up to 2.7GHz and with a bandwidth of 30MHz. The two

Figure 3: Phase oscillations of fs laser to reference after
applying an external kick to the laser table. Upper trace:
AD8302 phase output, 100mV/div. Lower trace: Timing
Stabilizer output, 20mV/div. Hor. Scale 100ms/div.

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STREAK CAMERA ACQUISITIONS
Several streak camera measurements have been carriedout during the experiments. The aim was not themeasurement of the fs laser pulse duration, well beyond
streak camera resolution, but rather the characterization of
the jitter and the long-term stability of the synchronizedsources. The synchro-scan streak camera with its double
sweep capability is well suited for this measurement as it
can acquire up to 70ms of light pulses while keeping theresolution of few picoseconds. The synchro-scanacquisitions of the ELETTRA streak camera show the fasttime axis horizontally and the slow one vertically, fromthe bottom to the top of the picture.
In the following figures, some examples of streak
camera acquisitions are shown with simultaneous
acquisitions of the fs laser pulses and synchrotron lightpulses, even overlapping on the same fast sweep (duration
440ps or 880ps), like in figure 4. In this acquisition the fs
laser pulse really “seats” on the synchrotron light pulse.
The duration of the fs laser pulses is greatly increased by
the limited streak camera resolution (<2psFWHM).
Synchrotron pulses are 2ns apart

In figure 5 LEFT, one bunch of the ELETTRA beam in
4-B mode has been captured with three surrounding fs
laser pulses. Now the light pulses have been “streaked”
on different sweeps. In figure 5 RIGHT, a longer synchroscan acquisition is shown with the same 4-B beam as fig.
5 LEFT: the laser-to-synchrotron jitter has been estimatedto be ≤1psRMS. In figure 6, all three sources have been
captured on a long-time scale (VERT=6.7ms;
HOR=880ps) acquisition. The fs laser and thesynchrotron pulses appear as solid lines, whereas the SRFEL is operating free running (pulsed): the stability
between the sources can be estimated.

Figure 6: all three sources on a single synchro scanacquisition (VERT=6.7ms, HOR=880ps). The fs laser andsynchrotron light pulses appear as continuous lines, the
SR-FEL is in free running mode i.e. pulsed.

LIGHT TO LIGHT JITTER MONITOR
Figure 4: Fast synchro-scan acquisition (VERT=13ns,
HOR=880ps) of seven synchrotron light pulses (MBbeam) and two overlapping fs laser pulses at frep1 (10nsapart).

As previously shown (fig. 1), a direct light to light jittermonitor is proposed here based on the AD8302 phasedetector. Relying on the integer multiplying factor (N=18)
between the 4-B beam repetition frequency and the fs
laser operating at frep2 (83.2756MHz), a narrow-band band
pass filter can be adopted to extract the 18th harmonicfrom a beam signal (pick-up or photo-diode). The twosinusoidal signals (fs laser rep. rate and filtered beam
signal) can be, then, phase-compared using an AD8302,
in a 30MHz bandwidth and with a resolution better than
0.01deg. We call it light to light, real-time, on-line jittermonitor: reliminary measurements are encouraging.

REFERENCES

Figure 5, LEFT: fast synchro-scan acquisition(VERT=34ns, HOR=440ps) of one ELETTRA bunch (4B mode) surrounded by three fs laser pulses. The laser
now operates at frep2 12ns period). RIGHT, same beam but
slower vertical axis (VERT=1380ns, HOR=880ps): six
ELETTRA bunches captured with 18 laser pulses in
between each pair, here shown as a solid line.

THPOS08[1] G. Dattoli, A. Renieri, NIM A 507 (2003) 464[2] G. De Ninno et al., Nucl. Instr. and Meth. A, 507(2003) 274[3] R. Bakker et al. “FERMI at ELETTRA: 100 nm 10nm Single Pass FEL User Facility”,
EPAC2004 conference Proceedings[4] I. V. Pinayev et al., Nucl. Instr. and Meth. A, 475(2001) 222[5] M.J.W.Rodwell et al, IEEE J.Quantum Electron. 25(1989), 817[6] LF-2.7GHz RF/IF Gain and Phase detector AD8302,
P.O. Box 9106, Norwood, MA, USA.

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LASER COMPTON SCATTERING GAMMA RAY INDUCEDPHOTO-TRANSMUTATION
D. Li*, K. Imasaki, ILT, 2-6 yamada-oka, suita, Osaka 565-0871,Japan
S. Miyamoto, S. Amano, T. Mochizuki, LASTI, 3-1-2 Koto, Kamigori, Hyogo 678-1201, Japan
Abstract
High brightness beams of gamma rays produced in themeans of laser Compton scattering have the potential toinduce photo-transmutation through ( γ ,n) reaction,
which implies an efficient method to dispose long-lived
fission products. Preliminary investigations have been
carried out in understanding the feasibility of developing
transmutation facility to repose nuclear waste. A laser
Compton scattering setup has been built on
NewSUBARU storage ring and worked steadily togenerate gamma-ray beams for studying the relevant
nuclear physics. This paper aims at exploring thedependency of nuclear transmutation efficiency on target
dimensions and gamma ray features with employing
197
Au target. The experimental results are in agreementwith the theoretical estimations.

INTRODUCTION
To repose long-lived fission products effectively is an
attractive issue in management and disposal of nuclear
waste. Recently a number of methods have beenpresented and discussed [1,2], involving transmutation bybombardment with neutrons from a reactor or a particle
accelerator, and laser-driven gamma generation for phototransmutation [3]. However, nuclear transmutation
through photonuclear reaction induced by high brightness
gamma ray generated from a storage ring based laser
Compton scattering facility is considered by us as apromising alternative [4][5]. In accordance to theconceptual scheme, we carried out relevant researchesboth on laser Compton scattering to produce highbrightness gamma ray and photonuclear reaction throughnuclear giant resonance. We have reported the laser
Compton scattering setup built on NewSUBARU storage
ring elsewhere [6][7].
In this paper, we concentrate on exploring the nuclear
transmutation efficiency and its dependency on target
geometrical dimensions and properties of laser Compton
scattering gamma rays, which is a key point forrealization of nuclear transmutation facility.

LASER COMPTON SCATTERINGGAMMA RAY
Our laser Compton scattering setup was built on one of
the straight section of NewSUBARU storage ring, which
provides 1GeV electron beam with average current up to
200 mA. A laser light of 1.064 μ m wavelength from___________________________________________*lidazhi@ile.osaka-u.ac.jp

Available online at http://www.JACoW.org

Nd:YAG laser was guided into the vacuum chamber tocollide with the electron beam in a head-to-head manner,and scattered gamma ray photons with maximum energyof 17.6 MeV. The gamma ray goes along the incident
electron moving direction in a forward cone of angle 1/γ, whereγis the relativistic factor of electron, namely, 0.5
mrad in our experiment for the 1 GeV electron beam. Theinteraction point was designed at the center of the straightsection, where both the electron beam and laser transverse
profiles were focused to the minimum.
The gamma ray generated from our laser Compton
scattering setup is polarized, and its polarization ischangeable with inserting a wave plate in the laser lightpath [4].

ESTIMATION OF TRANSMUTATIONEFFICIENCYWhen a beam of gamma rays strikes on a target, thephotonuclear reaction rate (1/sec/m3) is given by
R = N 0σ g ( E ) I ( E , z )(1)where N0 is the number of atom per volume, σg(E) is thenuclear giant resonance cross section, and I(E, z) is the
gamma ray intensity, which is a function of photon’senergy E and penetrating depth z in a target.
According to the fact that laser Compton scattering
gamma ray features a circular transverse profile, we
considered a cylindrical target with radius of a and lengthof b, and the integration of volume gives the total reactionrate~
R = ∫ RdV = N 0 ∫ σ g ( E ) I ( E , z )dV(2)

The gamma ray intensity could be expressed as

I ( E , z ) = ξσ L ( E )e − µz(3)where ξ relates to the properties of electron beam andlaser light for collision, σ L(E) is the laser Compton
scattering cross section, and μ is the total linear
attenuation coefficient given byµ = µ PE ( E ) + µ C ( E ) + µ PP ( E ) + µ PN ( E ) (4)where μPE=σPE(E) N0 , μC=σC(E)Z N0, μPP=σPP(E) N0,
μPN=σPN (E) N0, Z is the atomic number, σPE(E), σ
C(E), σ PP(E) and σ PN(E) represent cross sections ofphotoelectron,
Compton,pair
production
andphotonuclear reactions, respectively. Consequently, Eq.
(2) could be rewritten asb a~
R = N 0ξ ∫ ∫ σ L ( E )σ g ( E )e − µz ⋅ 2πρ dρdz (5)00FEL Users Workshop

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And we also have the following expressions to determine
the energy of laser Compton scattering gamma photons
[8]
ρ
Em
(6)
θ = arctan( )
E =
L
θ 2
1+ ( )

θ0

Em =

x
mc 2
Eb θ 0 =1+ x
Ebx +1 x =that the efficiency approaches constant when the length
is longer than 5 cm. That is because all injecting
gamma photons are absorbed after they travel suchlong a distance in target. The optimum radius ofcylinder is about 0.5 cm as shown in Fig. 2, resulting ina maximum efficiency of 2.2%. And the efficiency falls

4 Ebυ 0m2c 4

where Em is the maximum gamma ray energy, L is the
distance from the interaction point to the front surface oftarget, Eb is the electron’s energy, and υ 0 is the laser
photon’s energy.
The total injected gamma photons should be writtenasa

F = ∫ I ( E ,0)ds = ξ ∫ σ L ( E ) ⋅ 2πrdr
0(7)Then, we achieved the expression for the transmutation
efficiency defined as the quantity of transmuted nuclei by
per photon,b a~
N 0 ∫ ∫ σ L ( E )σ g ( E ) e − µ z ⋅ 2π rdr dz
R
0 0
(8)
η =
=
F
σ ( E ) ⋅ 2π rdr∫

L

From Eq.(8) we understand that the efficiency depends
on not only the parameters of the target itself, such as
target species, radius and length, but also thecharacteristics of laser Compton scattering setup
including the electron beam energy, the laser photon’senergy and even the distance from interaction point to thetarget.

Fig. 2 Transmutation efficiency vs. radius oftargetdown when the radius continues growing, because a lotof low energy gamma photons are involved, which
contributes little to the photonuclear reaction.
Furthermore, the efficiency is sensitive to the electron
beam energy as shown in Fig. 3, and the optimalenergy is 950 MeV to make a peak of ~2.5%.

Calculations and pictorial illustrations oftransmutation efficiency are made for a gold (197Au)
target, positioned on axis 15.35 m away from theinteraction point. σ L(E) can be derived from kleinnishina formula [8],σPE(E), σC(E), σPP(E) and σPN(E)are same as in reference [5].The dependency ofefficiency on target length is shown in Fig. 1, depicting

Fig. 3 Transmutation efficiency vs. electron
beam energy

EXPERIMENT

Transmutation Efficiency

Fig. 1 Transmutation efficiency vs. the lengthof target

THPOS14

We use 197Au samples for the nuclear transmutation
experiment. The target was placed on axis receiving
gamma ray irradiation, 15.35 m away from the interaction
point, in front of a Germanium detector. In experiment,
the Germanium detector was used to estimate theabsorption ratio of gamma ray by the target. An example

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D. Li et al. / Proceedings of the 2004 FEL Conference, 685-688

of measured energy spectra is shown in Fig. 4, where theFig. 4 Laser Compton scattering gamma rayenergy spectrum with and without target,
respectively.

errors come from the loss evaluation and statisticalprocess, and with the promotion of our detecting system
more precise measurement will be reached in the future.

Fig. 5 Gamma ray energy spectrum ofradioactivity of irradiated target

difference between those two signals depicts the absorbed
portion of gamma photons. Thus, one can deduce the total
absorbed gamma photons in the duration of irradiation.
The 197Au nucleus releases a neutron to undergotransmutation to 196Au when absorption of gamma
photons leads to (γ, n) reaction. 196Au is unstable, andeventually transmuted to 196Pb and 196Hg in the way ofradioactive decay. The transmutation from 196Au to 196Pb
predominates and emits gamma ray of energy 355.73
KeV, which was able to be measured by a NaI(TI)
detector. Through the measurement of radioactivity ofirradiated target, the number of transmuted nucleus at the
moment of end of irradiation can be deduced according todecay lawN0 =∆Ne λt,1 − e −λ∆twhere N0 is the number of undecayed nuclei, ΔN is thenumber of decays in the duration of Δ t, λ is the
decay constant, and t is the time interval from the end of
irradiation to the beginning of activity measurement.
Two samples of cylinder gold target were employed inour experiment, with 5 cm long and radius of 0.25 cm and0.5 cm, respectively. Both of them were irradiated withduration of 8 hours, and were processed with activity
measurement separately. An example of emission
spectrum was given in Fig. 5, showing the gamma ray
rising from the decay process. The loss of theradioactivity inside the target was estimated by using
EGS4 code [9]. And after data processing, we achieved
the transmutation efficiency shown in Fig. 6, together
with the calculation curve. The experimental results
illustrate a little higher than the calculation, which might
be the reason of secondary transmutation induced byelectron-gamma showers occurring inside target. The

Fig. 6 Comparison of transmutation efficiency
for experimental data and calculation curve

Secondary Gamma Ray
The interaction of high energy photons with mattersraises secondary gamma rays, which is from the Compton
scattering, bremsstrahlung and else effects. We performedexperiments on measuring the secondary gamma rays.
A Germanium detector, with crystal measuring 64.3
mm in diameter and 60 mm in length, exhibiting 45%
efficiency, was positioned 4 cm away the target, verticalto the beam line. The measurement was conducted for twotargets, with radius of 0.5 cm and 0.25 cm, respectively.
Their energy spectra (removed background) are shown in
Fig. 7. It is known that the secondary gamma ray yield issmall, especially the high energy photons. Generally
speaking, the photonuclear reaction is induced by thephotons with energy spanning from 8 MeV to 30 MeV,FEL Users Workshop

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D. Li et al. / Proceedings of the 2004 FEL Conference, 685-688

therefore, the secondary gamma ray will not contribute to
the photo-transmutation.

order to investigate the feasibility of developing anefficient nuclear transmutation scheme to dispose thelong-lived radioactive waste. We carefully analyzed thereaction rate of gamma ray with the nuclear giant
resonance, and gave out the relation of transmutation
efficiency with target dimensions and gamma ray
properties. 197Au rod target was used in irradiation
experiments for demonstration, and the experimental
results are close to the analytical estimations.

REFERENCE

Fig. 7 Secondary gamma ray energy spectrum
for target with radius of 0.5 cm and 0.25 cm,
respectively.

CONCLUSION
Transmutation efficiency concerned with characteristics
of target and gamma ray was studied experimentally witha storage ring based laser Compton scattering system, in

THPOS14[1] S. Matsuura ,Nucl. Phys. A 654 (1999) 417c
[2] W. Gudowski, Nucl. Phys. A 654 (1999) 436c
[3] K.W.D. Ledingham, J. Magill, P.Mckenna, et.al, J.
Phys. D: Appl. Phys. 36 (2003) L79[4] K. Imasaki , A. Moon, SPIE 3886 (2000) 721[5] D. Li, K. Imasaki, M. Aoki, J. Nucl. Sci. and Tech. 39(2002) 1247
[6] D. Li, K. Imasaki, M.Aoki, etal, Int. J. Infrared Milli.
24 (2003) 1301

[7] D. Li, K.Imasaki, S.Miyamoto et.al, The Review ofLaser Engineering, 32 (2004) 211[8] V. Telnov, Nucl.Instr. and Meth. A 355, (1995) 3[9] W.R. Nelson, H. Hirayama, W.O. Roger, The EGS4
code
system,
SLAC-Report,
265(1985)

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M. Heya et al. / Proceedings of the 2004 FEL Conference, 689-691

DEVELOPMENT OF A PUMP-PROBE SYSTEM USING A NON-COATEDZnSe BEAM SPLITTER CUBE FOR AN MIR-FEL
M. Heya*, K. Ishii, S. Suzuki, K. Awazu, and H. Horiike, Institute of Free Electron Laser, Graduate
School of Engineering, Osaka Univ., 2-9-5 Tsuda-yamate, Hirakata, Osaka 573-0128, Japan
Abstract
A reliable pump-probe technique is essential to gain aproper understanding of the interaction of lasers withtissue and similar materials. Our pump-probe system
divides an incident s-polarized MIR-FEL (Mid-Infrared
Free Electron Laser) into two beams of equal intensity,and simultaneously crosses the two beams. One beam acts
as a pump beam, while the other as a probe beam with anadditional time delay. Time-resolved absorption
spectroscopy using this technique provides us withinformation about the vibrational dynamics of molecules.
We have developed this system using a non-coated ZnSebeam splitter cube. The beam splitter cube is composed of
two ZnSe prisms in the shape of a trapezoid. Two pulses
with equal intensity are generated due to Fresnel
reflection/transmission at the boundary between the two
prisms, which then simultaneously illuminate the same
position around the point of intersection of the two
divided beams. We have conducted a proof-of-concept
experiment for this system using the MIR-FEL. We
showed that this system requires no complicated or timeconsuming optical alignment, and that it is applicable fora broad MIR waveband (5~11 µm).

within the range of λ = 5~12 µm [1], we designed the
ZnSe beam splitter cube for λ = 7.5 µm. The refractive
index of ZnSe is 2.421 at λ = 7.5 µm.

PRINCIPLES
Figure 1(a) shows the principles of our pump-probe
technique involving the ZnSe splitter cube. The ZnSe
splitter cube consists of two non-coated ZnSe prisms in a
trapezoidal configuration. An air layer with a thickness of
50 µm exists between the two ZnSe prisms. The incident
MIR-FEL beam is s-polarized. The incoming MIR-FEL
pulse divides the two pulses (Beams A and B) at theboundary between the ZnSe prisms (point C). The
reflected and transmitted beams are reflected due to totalinternal reflection, and then each beam crosses
simultaneously outside the beam splitter at point D. In
order to generate two pulses A1 and B1 with equal
intensity, the angle θ3 must be set at 20.4 deg, leading toreflectance R = 0.382, as shown in Fig. 1(b). Multiple
Fresnel reflection occurs at point C. If we let the intensity(a)S-polarized
MIR-FELINTRODUCTION*

Total internalreflection
θ4 > 24

θ2

C

θ3
θ3

θ4
θ5

46.9 mm

In order to properly understand the interaction of lasers
with tissue and other materials, a pump-probe technique isrequired. Conventional pump-probe techniques using a
Michelson interferometer split an incoming pulse into two
beams; a pump beam and a probe beam with a variable
time delay relative to the pump beam. In this technique
the two beams must simultaneously illuminate the same
position, so it requires complicated and time-consuming
optical alignment. Additionally, optical alignment for
invisible mid-infrared (MIR) light is technically difficult.
From the above point of view, we have proposed anddesigned a new pump-probe system for a tunable MIRFEL (Free Electron Laser) using a non-coated ZnSe beam
splitter cube. Since one beam splitter cube divides anincoming pulse into two pulses with equal intensity,
complicated and time-consuming optical alignment is nolonger requied. We adopted the use of Fresnel
reflection/transmission and total internal reflection toequally divide the incident MIR-FEL pulse into the twopulses. Since AR coating severely limits the applicable
waveband range, no AR coating was used. In this article,
we describe the principles and features of this pumpprobe system. In order to confirm the performance of atrial pump-probe system, we have conducted its proof-ofconcept experiment using an MIR-FEL. Since the FEL
user facility at Osaka Univ. can provide an MIR-FEL

θ1 = 8.33 deg
θ2 = 3.43 deg
θ3 = 20.4 deg
θ4 = 37.4 deg
θ5 = 3.34 deg
θ6 = 8.12 deg
θ7 = 40.3 deg

25 mm

θ1

θ6
Beam Aθ7yz

D

ZnSe / Air / ZnSe

(b)

(c)

1
A1

A1 R

(1-R)2 B1

A2 R(1-R)2

R2(1-R)2x

Beam B

B2

A2
A3

B1

B2
B3

A3 R3(1-R)2

R4(1-R)2 B3
R = 0.382@θ3 = 20.4 degxFigure 1: Principles of the pump-probe system using a
non-coated ZnSe beam splitter cube. (a) Configurationof this system. The definitions of the x-, y-, and z-axes
are also shown. (b) Generation of Beams A1 and B1
with equal intensity at the boundary between the two
prisms (point C). (c) Typical profiles of Beams A and B
along the x-axis at the point of intersection (point D).

heya@fel.eng.osaka-u.ac.jp

Available online at http://www.JACoW.org

FEL Users Workshop

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M. Heya et al. / Proceedings of the 2004 FEL Conference, 689-691

of the incident beam at point C be unity, then theintensities for the respective divided beams are as
follows: IA1 = 3.82×10-1, IA2 = 1.46×10-1, IA3 = 2.13×10-2,
IB1 = 3.82×10-1, IB2 = 5.57×10-2, and IB3 = 8.13×10-3. Here
we neglected the forth reflection/transmission and higher.
As shown in Fig. 1(c), we can simultaneously illuminate atarget at point D by using the two pulses (Beams A1 andB1) of equal intensity. Beams A1 and B1 can be used aseither a pump or a probe beam. Note that the intensities
for Beams A1 and B1 are ~0.3 (=0.382×(1−0.3)) times theincident MIR-FEL, since the total reflectance loss at thefirst and final boundaries is ~0.3.
Figure 2 shows the configuration of a typical pumpprobe experimental set-up. The sample is located at point
D. In this case, an optical window, whose material has
good transmission characteristics for MIR-FEL, isinserted to the beam line for Beam B1, which is used as aprobe beam. The optical window (such as CaF2 and MgF)
acts as a time delay relative to Beam A1, which acts as
the pump beam. The time delay can be arbitrarily varied
within the range 1~20 ps by changing the thickness of the
optical window. The intensity of the transmitted probe
beam is time-resolved by an MCT detector. This timeresolved signal, S(t), gives us information about thevibrational dynamics of molecules during MIR-FEL
irradiation.
The main features of this pump-probe technique are as
follows.
(1) Since one beam splitter cube divides two pulses
with equal intensity and crosses them over, opticalalignment of this system is simple and not timeconsuming.
(2) ZnSe prisms have good transmission characteristics
S-polarized
MIR-FEL

Beam B1

A1
Sample1-20 ps
MCT S(t)B1ttFigure 2: Typical configuration of the pump-probe
experimental set-up. In this case, Beam A1 is the pumpbeam, while Beam B1 is the probe beam. The MIR
window acts as an optical delay.

THPOS18

PROOF-OF-CONCEPT EXPERIMENT
We have conducted a proof-of-concept experimentusing a tunable MIR-FEL in order to confirm thefollowing performances of this system: (1) the division
into two pulses (A1 and B1) with equal intensity over λ =5~11 µm and (2) the focusability of the two pulses onto
the same position.

Division
When the intensity of Beam A1 is exactly equal to thatof Beam B1, the intensity ratio of Beam A to Beam B is
1.23 (as shown in Fig. 1(b)), where Beam A (B) generally
terms multiple beams A1~A3 (B1~B3). The intensity
ratio can be controlled by the incident angle of the MIRFEL, θ1. We measured the average powers for Beams A
and B while adjusting θ1. As a result, we confirmed thatthe intensity ratio can be set at 1.23 with a possible errorof 10% over λ = 5~11 µm by only adjusting θ1.
Therefore, we can easily generate two pulses (A1 and B1)
with equal intensity within an error of 10%. This error
causes due to the uncertainty of the measurement of an
average power.

Focusability

MIR window(or Filter)
Beam A1

over both the MIR and the visible spectrum, whichenables us to use He-Ne lasers as the guide laser for
optical alignment.
(3) The variation of the refractive index for ZnSe isless than 1% over a broad waveband of 2~11 µm [2]. In
addition, non-coated ZnSe prisms are used. This meansthat tunable lasers can be utilized.
(4) This system is composed of transmittive optics.
The use of ultra-fast pulse lasers is not possible due togroup velocity dispersion within the system. This system
is applicable for picosecond MIR-FELs, since the effects
on the group velocity dispersion become significant in the
femtosecond range.
(5) The time delay is constrained by the thickness of
the MIR windows and is less than a few tens ofpicoseconds.
(6) The reflectance of the MIR windows is about 3~5%,
leading to a slight difference in intensity between the twopulses.

We examined the focusability of the two pulses onto
the same position using heat sensitive papers, which werelocated at the point of intersection (point D). We obtained
burn patterns on the papers by MIR irradiation whilemoving the target along the z direction. Note that thisexperiment was carried out after adjustment of theintensity ratio as described previously.
Figure 3 shows the burn patterns on the paper observedwith an optical microscope after MIR-FEL irradiation.
The wavelength and average power of the incident MIRFEL were 9.4 µm and ~25 mW, respectively. An increasein z means a backward movement away from the beam
splitter. We can see three burn patterns for Beams A1, A2,
and B1. Patterns for the other beams were not observed
because of their weaker intensities. As z increases, the691

M. Heya et al. / Proceedings of the 2004 FEL Conference, 689-691

burn patterns of A1 and A2 gradually become closer tothat of B1. Around z = 0.5 mm, patterns A1 and B1
overlap with each other, and then they separate again withan additional increase in z.
From Fig. 3, we can obtain data for the optical paths ofBeams A1 and B1. When z is changed from 0 to 0.2 mm,
the x-position of the center of Beam B1 shifts laterally by∆x = ~150 µm. We first experimentally estimated θ7’from these data using the expression: θ7’ = tan-1(∆x/∆z),resulting in θ7’ = 36.9 deg. The specification of θ7 is 40.3
deg (Fig. 1 (a)). This disagreement gives us the differencein path length between Beams A1 and B1. This differencein path length, ∆L, can be roughly evaluated by using theequation: ∆L = Ltotal(1-cos(θ7-θ7’)), resulting in ∆L =0.206 mm. This difference leads to the time difference
between the both beams, ∆t (< 1 ps in this case). ∆t is
considerably shorter than the pulse duration of our MIRFEL and is negligible. Here Ltotal is the total path lengthfrom the first ZnSe surface to point D, and was about 117
mm.
Secondly, we estimated the positional difference
between both beams in the y direction. The distance
between the centers of the both beams in the y direction isseen to be ~100 µm from the topmost image in Fig. 3. A
positional difference should be reduced down to less than
one-tenth the spot size of each beam at point D.

B1

A1

y
x
B1

A1

CONCLUSIONSIn order to establish a useful pump-probe techniqueusing a ZnSe beam splitter cube, we have designed it andhave carried out its proof-of-concept experiment using an
MIR-FEL. We demonstrated that this pump-probe
technique is a wavelength-independent system and isapplicable for a broad MIR waveband.
We will further measure the dynamic absorption
properties [4] of soft tissue using this pump-probe
technique. The dynamic absorption properties are thoseduring laser irradiation and strongly dominate the extent
of the heating, coagulation, and cutting of tissue. For noninvasive and predictable laser surgery, a knowledge of the
dynamic absorption coefficients is essential.

A2

z = 0 mm

0.2 mmFrom these observations, the following can be derived.
(1) The pump-probe technique using the ZnSe beam
splitter cube does not require complicated and timeconsuming optical alignment and is applicable for atunable MIR-FEL system. Especially, we can divide twopulses with equal intensity by only adjusting the incident
angle of the MIR-FEL even over a broad waveband (λ =5~11 µm).
(2) The time difference between both pulses was lessthan 1 ps and can be neglected.
(3) The positional difference in the y direction was~100 µm, meaning that the spot size of the beams should
be set at 1000 µm or more at point D.

A2

ACKNOWLEDGEMENTS
The authors thank A. Ueguchi at Sumitomo ElectricIndustries, Ltd. for many useful discussions. We also give
thanks for excellent technical support from all staff at theInstitute of Free Electron Laser, Osaka Univ.

REFERENCES
0.4 mm[1] K. Awazu, M. Asakawa, and H. Horiike, “Status
report and biomedical applications of the Institute of
FEL, Osaka University,” Nucl. Instr. and Meth. in
Phys. Res. A, 507, 2003, p. 547.
[2] H. Landolt and R. Bornstein, “Landolt-Bornsteinnumerical data and functional relationships in scienceand technology,” Springer, Berlin, 1982, p. 147.
[3] Y. Ishida, T. Yajima, and A. Watanabe, “A simple
monitoring system for single subpicosecond laser
pulses using an SH spatial autocorrelation method
and a CCD image sensor,” Opt. Commun., 56, 1985,
p. 57.
[4] J. P. Cummings and J. T. Walsh Jr., “Erbium laser
ablation: The effect of dynamic optical properties,”
App. Phys. Lett., 62, 1993, p. 1988.

0.5 mm

0.7 mm

A1

A2

B1

A1

A2

B1

0.9 mm500 µmFigure 3: Observed burn patterns by MIR-FEL
irradiation as a function of z. The definitions of the x-,y-, and z-axes are similar to those used in Fig. 1(a).

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MEDICAL APPLICATION OF FREE ELECTRON LASER
TRANSMITTANCE USING HOLLOW OPTICAL FIBER
S. Y-Suzuki*, K. Ishii, K. Awazu, Institute of Free Electron Laser, Graduate School of Engineering,Osaka University, 2-9-5 Tsuda-yamate, Hirakata, Osaka 573-0128, Japan
Abstract
Mid-infrared Free Electron Laser (FEL) is expected as
new application for biomedical surgery. However,delivery of MIR-FEL into the body is difficult because
the common glass optical fibers have strong absorption at
MIR region. A good operational and flexible line for
FEL is required at medical field. A Hollow optical fiber isdeveloped for IR laser and high-power laser delivery. We
evaluated the fiber for FEL transmission line. This fiber iscoated with cyclic olefin polymer (COP) and silver thinfilm on the inside of glass capillary tube. It is 700 µmbore and 1 m in length. The fiber transmission loss of themeasured wavelength region of 5.5 µm to 12 µm is lessthan 1 dB/m when the fiber is straight and 1.2 dB/m whenbent to radius of 20 cm. In additionally, the output beamprofile and the pulse structure is not so different form
incidence beam. In conclusion, the fiber is suitable fordelivery of the FEL energy for applications in medical
and laser surgery.

INTRODUCTION
A bio-molecule that constitute of the protein has strong
absorption coefficient due to molecule vibration in
infrared region. A free electron laser (FEL) is expected as
selective and low-invasive treatments because the FEL
which is able to tune in a wide wavelength range ofinfrared region excite molecule vibration selectively.
An atherosclerosis is caused by accumulation ofcholesterol ester which is ester bond of cholesterol andfatty acid. We have reported that the wavelength of 5.75
µm corresponding to C=O stretching vibration of ester
band resolves only cholesterol ester selectively [1]. The
effect was confirmed on the in-vitro which used thecholesteryl oleate, the rabbit and the human blood vesselarteriosclerosis part section [2] [3]. Since the technique isthe potential a low-invasive laser surgery in blood vesselcompared a conventional method, an in-vivo experimentis expected. However, there is no guide line fortransmitting infrared FEL. The FEL beam is usually
guided by ZnSe lenses and mirrors to target materials but
is difficult to deliver to small target in a narrow space
and/or in the body. The common medical devices are used
articulated manipulator or grass optical fiber for lasertransmission. However, the articulated manipulators areunusable in-vivo surgery. The common glass opticalfibers with IR absorption are also difficult to transmit
enough energy. Therefore, the FEL beam transmission
line is required good operationally and flexibility at___________________________________________* suzuki@fel.eng.osaka-u.ac.jp

THPOS19

medical field.
The FEL transmittance loss using chalcogenaide NSEG
fiber have been reported by Awazu et al [4]. The
transmittance could not exceed 70%. The fiber was
fabricated with GeAsSeTe glass for the core and GeAsSe
glass for the cladding is also harmful to human, thus it is
not suitable for medical applications. A Hollow opticalfiber which is developed by Miyagi and Matsuura issuitable for delivery IR laser beam and high-power laser
such as CO2 laser and Er:YAG laser which is in practicaluse [5] [6]. It is a thin tube composed of the air core andthe dielectric with high refractive index or metal cladding,and loss in the core is practically nought. Transmission
loss of wavelength 6.45 µm FEL at Vanderbilt University
has reported by Matsuura et al [7]. The 1000 µm bore
fiber, 1 m in length, gave transmission loss of 0.46 dB. In
addition, the hollow optical fiber is used for some medical
application using infrared laser. For example, Shen et al[8] reported that the hollow optical fiber is suitable fordelivering the IR FEL for intraocular microsurgicalprocedures.
We have researched various interactions between
biomedical tissues and FEL, beside the selective removalof cholesterol (5.75 µm), such as the surface modificationof tooth dentin using FEL wavelength 9 µm bands and theablation of soft tissue using FEL 6.05 µm.
This article reports the FEL transmission loss of
wavelength from 5 µm to 12 µm using hollow opticalfiber of 700 µm-bore, the guide system in a blood vesselusing the hollow optical fiber is discussed.

EXPERIMENT
We tested the FEL power transmission of the hollow
optical fibers with 700 µm-bore and 320 µm -bore,
respectively. Both the hollow fibers are coated with cyclic
olefin polymer (COP) and silver thin film on the inside ofglass capillary tube. Figure 1 shows the IR absorption of
the fiber measured using Fourier transform infrared
spectroscopy (FTIR). The large peak at around 7.0 µm
and the broad peak at 7-8 µm are due to absorption of the
COP film. However, we need the transmission line which
can be broadly covered in a mid infrared region. In
addition, 6 µm and 9 µm bands used for our research suchas surface modification and/or soft tissue ablation has
little absorption.
The setup for the FEL power transmission experiments
is shown Figure 2. The length of both the fibers is 1m. A
FEL at Institute of FEL (iFEL), Osaka University inJAPAN, is tunable from 5 µm to 22 µm in mid-infrared(MIR) region, which is high peak power and short pulse

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S. Suzuki et al. / Proceedings of the 2004 FEL Conference, 692-694

5
Loss(dB/m)

Attenuation(dB)

15
10
5
0
5

6

7

8

9

10

11

4
3
700um-bore
320um-bore

2
1
0

12

Wavelength(µm)
(µm)

5

6

7

Figure1: Typical absorption spectrum of hollow
optical fiber.
100ms

~5ps

t

44.8ns11

12

Bending loss

Dielectric (COP)silver

t

Glass

FEL
Parabolicmirror(f=254mm)

10(µm)
Wavelength(µm)

Hollow (air)Produced by Tohoku Univ.

Power
meter

Hollow Optic Fiber(bore:700µm/300µm,length:1m)

Power
meter

FIX(20cm)

Figure 2: Experiment setup for the power transmissionof the FEL.
operation. The FEL has a unique double pulse structure;
the structure consists of a train of macropulses, and eachmacropulses
contains
train
300-400
ultrashortmicropulses. The width of the macropulses is about 15 µs
and repetition rate is 10 Hz. The width of micropulses isshorter than 10 ps and the separation between micropulses
is 44.8 ns. The FEL beam focused using parabolic mirror(f = 254 mm) and enter an input end of hollow opticalfiber. The mirror with a long focus reduces the couplingloss. The diameter of a beam is small enough to the input
end of the fibers, and the input end of the fiber is notdamage.
We measured the FEL average power at input end andoutput end of the fiber using the power meter (LaserStar
2A-SH, OPHIR) and calculate the power loss.

TRANSMISSION CHARACTERISTICS
Transmittance loss
The FEL transmission loss of wavelength from 5.5 µm
to 12.0 µm in each fiber is shown in Figure 3. The
transmission loss is not dependent on wavelength and is
not influenced by IR absorption of COP. In the 700 µm bore fiber, the transmittance loss at 5.5-12.2 µm is lessthan 1.2dB/m, which corresponds to over 80 % powertransmission. The result shows that the 700 µm -bore
hollow optical fiber is low loss and is enough as the guideline of FEL. In contrast, the 320 µm -bore fiber have thelarge loss exceeding 3dB/m, which corresponds to 50 %power transmission, because the diameter of FEL beam is
no focus attention on less than 320 µm.

Figure 4 shows the bending loss of FEL wavelength
5.75, 6.0, 9.4 10.6 and 12.0 µm, which are effective inbio-molecular such as ester band [1][2], phosphoric group
and amide bond. The bending loss was increased fromstraight state (0 m-1). The max bending loss in curvature
4.5 m-1 is 1.2 dB/m. The hollow optical fiber has losses
sufficiently low for MIR-FEL transmittance.

Output beam profile
FEL beam spectrum and pulse structure after
transmission are estimated. Figure 6 (a), (b), (c) shows
beam profile of points which is distant from output end 2,
5, 10 mm, respectively. The estimated divergence angle
is 2-3 degree. The form of these output beams are thesame Gaussian as an input beam form. The distributed oflight in Figure 6 (c) may be due to propagation mode but
it is no problem because fiber come in contact withtreated area in a blood vessel.
Figure 7 shows the pulse structure of before enteringfiber and after transmission using MCT detector (R005,
Vigo System). There is not much difference between
before and after entering fiber.
5.75um
6.0um
9.4um
10.6um12um

2
Loss(dB/m)~15µs

micropulse

9

Figure3: Transmittance loss as a function of
wavelength. The bore diameter is 700 mm and 320
mm, respectively and each fibers length is 1m.

FEL at Osaka University

macropulse

8

1

0
0

1

2

3

4

5

Curvature(1/m)

Figure 4: Bending losses of FEL wavelength 5.75 µm,
6.0 µm, 9.4 µm, 10.6 µm and 12 µm.

DISCUSSION AND CONCLUSIONS
We verified the hollow optical fiber as guiding line fortransmitting FEL. The transmission efficiency achieved

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(a)

(b)

(c)

Figure 6: Beam profile of output end. Each point isdistant fram output end (a) 2 mm, (b) 5 mm, (c)10mm.

FEL Average Power [mW]

S. Suzuki et al. / Proceedings of the 2004 FEL Conference, 692-694

100
80
60
40
20
0
300 350 400 450 500 550 600 650 700 750 800

Diameter of hollow optical fiber [µm]Figure 8: the relation of the FEL average power to thediameter of beam required in order to give the power
density for removes cholesterol ester (16W/cm).

BeforeAfter

ACKNOWLEDGMENTS
-10

-8

-6

-4

-2

0

2

4

6

8

10

12

14

Time(ns)

Figure 7: Pulse form of before entering fiber and after
transmission using MCT detector
over 80 % in the case of bore diameter of 700 µm. The
form and profile of beam passed in the fiber is like
incident beam. These results confirmed that the fiber
which developed CO2 laser is applicable to the FEL witha unique pulse structure.
We have proposed the medical treatment in a bloodvessel of atherosclerosis using the hollow optical fiber. In
a previous report, we showed that the optimal power
density which removes cholesterol ester selectively is 16
W/cm2 [3]. Figure 8 shows the relation of the FEL
average power to the diameter of beam required in orderto give the power density of 16W/cm. When using thefiber of 700 µm-bore, the FEL average power exceeding
60mW is needed, but in iFEL, it is less than 50 mW. The
scale factor of the fiber of 320 µm-bore to 700 µm-bore is
4.7, thus the fiber of 300 µm-bore obtains a necessary
requirement for removes cholesterol ester by 15 mW
average power. However, the loss of 320 µm-bore fiber is
not the optimal in order to exceed 3dB by coupling loss
(see Figure 3). In addition, the guide of the light in a
blood vessel has a problem about the structure of thehollow optical fiber. Since the core of the fiber is an airhole, the blood flows in the fiber and blocks transmissionof laser beam. We are developing the fiber cap like lens.
The material of lens cap uses a diamond which has little
absorption at MIR region and is harmless to humans.
In the future we are going to evaluate about the fiberwith lens cap and to apply to clinical. Establishment of
the technique is only the guiding light in blood vessel, but
is also possible to transmit at region which it is notpossible to focus by lens and/or mirror such as vacuum
region, is useful to the FEL application.

THPOS19

We are grateful to Mr. Kuma, Mr. Marusaki and Mr.
Teranishi, operational staff of iFEL graduate school ofengineering, Osaka University.
Gratitude is expressed to Dr. Matsuura at Tohoku
University, Japan, for providing the hollow optical fiber.

REFERENCES[1] Kunio Awazu, Akio Nagai and Katsuo Aizawa,
Selective Removal of Cholesterol Esters in an
Arteriosclerotic Region of Blood Vessels with a FreeElectron Laser, Laser on Surgery and Medicine, 23,233-237, 1998
[2] Kunio Awazu and Yuko Fukami, Selective removalof cholesteryl oleate through collagen films by MIR
FEL, Nuclear Instruments and Methods in Physics
Research A 475 (2001) 650-655.
[3] Katsunori Ishii, Kouichi Iwatuki, Toshiki Yoshimine,
Kunio Awazu, The selective Removal of cholesterol
oleate in the human carotid artety by infrared freeelectron lasers, The review of laser engineering, 30,
12 (2002) 742-746.
[4] Kunio Awazu, Seiji Ogino, Akio Nagai, and Takio
Tomimasu, Midinfrared free electron laser power
delivery through a chalcogenide grass fiber, Rev. Sci.
Instrum., 68 (12), December 1997, 4351-4352[5] Yuji Matsuura and Mitsunobu Miyagi, Hollow fibers
for high-power lasers, The proceedings of SPIE
conference, 3609 (1999) 251-255[6] Yuji Matsuura, Todd Abel and James A. Harrington,
Optical properties of small-bore hollow grass
waveguides, Applied optics, 34, 30 (1995) 68426847.
[7] Yuji Matsuura, Kaori Matsuura and James A.
Harrington, Power delivery of free electron laser lightby hollow grass waveguides, Applied optics, 35, 27(1996) 5395-5397[8] J. H. Shen, K. M. Joos, J. A. Harrington, D. M.
O’Duy, and G. S. Edwards: proc. SPIE 3262 (1988)
130.

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MODIFICATION OF HYDROXYAPATITE CRYSTAL USING IR LASER
S. Satoh*, R&D Center, Saga University, Japan
A. Danjyo, M. Goto, Y. Yamaguchi, Faculty of Medicine, Saga University
C. Yamabe, N. Hayashi, S. Ihara, W. Guan, Fac. Sci. & Eng. Saga University
Abstract
To remineralize the dental surface, infrared (IR)laser was applied. The purpose of this experiment wasconcentrating to investigate crystal structure change ofhydroxyapatite (HAp) before and after laser
irradiation. The wavelength of incident laser beam ismatching the characteristic absorption peak of HAp
which ranging around 10µm. As a preliminary study
for Free Electron Laser (FEL) application in
biological field, the results we have got with the 10µm
irradiation indicated that the FEL’s capability of
precisely deliver energy over a wide band of infrared
makes it an attractive tool for further ameliorating ofhydroxyapatite crystallization.

INTRODUCTION
The first application of laser technology todentistry was for the removal of caries infectedmaterial and preparation of cavities [1]. However, eversince reports of laser application on improvement ofdental surface were emerged, much attention has been
focused on the laser’s potential to enhance enamel’s
hardness and resistance to acid [2], [3], [4].
Although many attempts have been made toalter the tooth structure in order to increase its
resistance to dental caries, little understanding on thephysicochemical mechanisms involved has beenachieved [5]. This research has pursued thephotochemical phenomenon occurred during laser
irradiation on artificial and biological HAp. In order tofind a creative method to remineralize thedemineralized enamel or the exposed coronal of
dentine, the authors developed a novel procedure
during laser irradiation [6].
Free electron laser (FEL) application is also
intended primarily to realize the same purpose. The
micro-pulse structure and duration of FEL laser was
expected to be suitable to modify dental surface
efficiency [7], [8].
In this study, slice samples of sound molar andartificial HAp pellet were irradiated with 10.6 µm CO2
laser separately. Various laser parameter and chemical
condition were applied in the experiment. There seriesof samples covered with saturation calcium ion
solution (Ca(OH)2 and CaHPO4) and their
combination were compared after irradiation. To
investigate the micro-crystal morphology of the------------------------------* e-mail : 1952sato@cc.saga-u.ac.jp

Available online at http://www.JACoW.org

samples, X-ray Diffraction (XRD) pattern weresurveyed. The comparison of XRD result shows thatthe chemical coating effected the irradiation processevidently.

EXPERIMENTAL PROCEDURE
Experimental layout
Experimental setup shows Figure 1. A
transversely excited atmospheric pressure (TEA) CO2
laser, which works at pulse width τ=1µs (FWHM) andwave length λ=10.6µm was employed. Thisequipment permits the selection of the pulse energy
from 60mJ to 500mJ, and of the repetition rare from
0.2Hz to 1Hz. The laser output beam was focused by aplano-nonvex ZnSe lens on the front side of thesamples to spot sizes of the order of 10-2 cm2, whichcorresponding energy density of 9J/cm2. Laser pulse
energy was measured with an energy meter (Gentec,
Model ED-500L) prior to and after tissue irradiationand pulse-to-pulse stability of the CO2 laser was 23%.
Some experiments show that the fluence threshold at
this parameter are 0.3J/cm2 and 0.6J/cm2 for dentin
and enamel respectively. For our experiment, theablation threshold was estimated approximately
1J/cm2. The teeth samples used in this experiment are
obtained from the Department of Oral andMaxillofacial Surgery, Faculty of Medicine, Saga
University. Extracted sound human molars wereconserved in a physiologic serum to avoid cracking
due to dryness and then embedded into polyester resinand cut into slices less than 1mm thick by a diamond
saw microtome. After sliding, the slide discs were
polished with a series of water-lubricated SiC papers
up to 5000. Thus, enamel and dentine region wereprepared flat and accessible to laser treatment.
Additionally, artificial HAp pellet was chosen
as the target material for comparison. The Ca/P molar
ratio value of the HAp pellet (PANTAX, Japan) was
1.67, which confirms the stoichiometric value. The
HAp pellet samples present a high crystallinity as it
was demonstrated by X-ray diffraction.
In the irradiation experiments, the specimen
was mounted on a motorized x-y-z translation stage
and positioned perpendicular to the direction of laser
incidence. All experiments have been performed in air.
The incidence area was constantly changed to avoid
carbonization.

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The specific experimental conditions concernedin this experiment are following;(1) XRD survey of original and CO2 laser irradiatedartificial HAp.
(2) XRD survey of dentine and enamel before andafter CO2 laser irradiation.
(3) XRD survey of enamel covered with saturated
chemical solution film after CO2 laser irradiation.

Figure 1: The scheme of irradiation experiment

The XRD analysis
The X-ray diffraction of the profile breadth andrelative intensity date were collected from the samples
on X-ray diffractomerter using Cu(Kα) radiation(RINT1100, Rigaku, Japan). The divergence slit was
1° and the receiving slit was 0.3mm. The scan range
for relative intensities was from 20º to 70º (2θ), andscan rate was 4º (2θ/min)

RESULT AND DISCUSSION
Compared with artificial HAp sample shown in
Figure 2, the (213) and (202) reflection intensity ofdentine was not so intense. After irradiation with
CaHPO4 solution film shown in Figure 3, thereflection (202) appeared. And ten relative intensity
peaks of artificial HAp pellet sample, (002), (202),(222) was modified. Most of the characteristic peaksof HAp were decreased.

THPOS25

Through the result we can suppose that HAp
may be decomposed due to the thermal effect of laser
irradiation [8], while as the product of decomposed
HAp also exists in the dentine and enamel as
amorphous calcium phosphate phase. The generalreaction of HAp infused with chemical solution under
the photo-thermal effect condition is considered asfollowing.
3Ca3(PO4)2 + Ca(OH)2→ Ca10(PO4)6(OH)2 + 2H2O+4CO2(1)

Due to the thermal effect during photo ablation
process, the temperature of the interaction surface
should raise instantaneously. HAp may be
decomposed through the reaction as formula (2).

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a”S.”. Satoh et al. / Proceedings of the 2004 FEL Conference, 695-698(2)

And CaO is easy to react with water, and the
produce tricalcium phosphate and heat.
The potential reaction under the irradiation with
Ca(OH)2 and CaHPO4 mixed saturation solution film
was considered as following.

Non-irradiated dentine

CO2 laser-irradiated enamel

Figure 2: Comparison of CO2 laser irradiation on
artificial HAp and dentine sample

Intensity (arb.u.)

Non-irradiated enamel

Intensity (arb.u.)

CO2 laser-irradiated enamel

Intensity (arb.u.)

CO2 laser-irradiated HApIntensity (arb.u.)

Non-irradiated HApIntensity (arb.u.)

Intensity (arb.u.)(3)

Intensity (arb.u.)

4 Ca(OH)2 + 6 CaHPO4→Ca10(PO4)6(OH)2 + 6 H2O

As CaHPO4 is easy to react with Ca(OH)2 to
produce various calcium phosphate formations. At thesame time, the reaction will release amount of heat.
This may delay the heat transmittal and decrease thethermal threshold of hard tissue during irradiation.
The apparent amorphous regions of XRD patter wereconsidered to be connecting with this mechanism.

CO2 laser-irradiated enamel(Covered with Ca(OH)2 solution film)

CO2 laser-irradiated enamel
Intensity (arb.u.)Ca10(PO4)6(OH)2→3Ca3(PO4)2 + CaO + H2O(Covered with CaHPO4 solution film)

Figure 3: Comparison of CO2 laser irradiation on
enamel sample, with and withoutchemical solution

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CONCLUSION
After CO2 laser irradiation, the (002) reflection
was increased significantly. It indicates the crystal
growth in c-axis. On the other hand the (222)reflection was reduced both in HAp and dentine. It
was considered relating to the thermal effect duringhigh-energy irradiation.
The intense band in the spectrum around2θ=45° (fig.3) is not a HAp band, but a strong metalreflection most possibly caused by aluminum. In thesome observation, this band has been erroneously
assigned as a HAp band in the XRD spectra ofphosphates. In the spectrum of irradiated samples, thecrystal phase show very broad peaks and highbackground. This may indicate the presence of verysmall crystallites, which will result in broad peaks.
The broadening of spectrum was assumed to becaused mainly by crystallite (domain) and latticestrain (within the domain). At the same time, we cansee the new peaks, which indicate HAp did notdissociate, but is transformed to a new ablated form
about 1000 degree. Phase transition in Ca3(PO4)2 froma tricalcium phosphate type to a HAp type structure,
which also occurs at the similar conditions, did not
induce the dissociation of HAp. However, we were
failed to assign the new peaks to these structures.
Alternatively, the diffraction peaks of a new HAppolymorph can be indexed by an orthorhombic cellwith lattice parameter a=b=9.43nm, c=0.688nm.

REFERENCE[1] M. Myers, “The effect of laser irradiation on oral
tissues”, J Prothet Dent, 66 (1991) 395.
[2] S. Kantola, “Laser-induced defects on the tooth
structure”, Acta Odontol Scand, 30(1972)475.
[3] J. Melcer, “Latest treatment in dentistry by meansof the CO2 laser beam”, Lasers Surg Med,
6(1986)396.
[4] L. Miserendin, “The laser apicoectomy:
endodontic application of the CO2 laser in apicalsurgery”, Oral Surg Oral Med Oral Pathol,66(1988)615.
[5] M. Gonzalez, et al, “Particle-induced X-ray
emission and scanning electron microscopic
analyses of the CO2 laser irradiation on dental
structure”, J. Dentistry, 27(1999)595.
[6] W. Guan, et al, “Modification of hydroxyapatite
crystallization using IR laser”, Program and
Abstracts of MAPEES’04, (2004)112.
[7] S. Ogino, et al, “The Effect of Free Electron
Laser Irradiation on Dentine”, J. Jpn. Soc. Laser
Dent, 7(1996)67.
[8] M. Tanaka, et al, “Surface Modification of Tooth
Dentine Irradiated by a 9.45µm CO2 laser”, J. Jap.
Soc. Laser Dent, 11(2000)104.

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VIBRATIONAL EXCITATION OF AMMONIA MOLECULES BY FEL-SUT
Y. Ogi*, K. Tsukiyama, Tokyo Univ. of Science, 1-3 Kagurazaka, Shinjuku, Tokyo 162-8601, Japan
Abstract
Free Electron Laser at Tokyo University of Science(FEL-SUT) was employed for exciting single vibrationalmodes of ammonia molecules. FEL is tuned to 10.5 µm,
corresponding to the X 1A1' 21 ← 20 transition of NH3.
The population of the vibrationally excited states isprobed by the (2 + 1) resonance enhanced multiphoton
ionization (REMPI) technique via the B 1E" Rydberg
state. Excitation efficiency of the 21 ← 20 transition was
about 30 %. Rotational analyses of the spectra revealed
that vibrational ladder climbing up to X 22 in NH3 wasrealized for the first time. IR-FEL excitation spectra werealso recorded.

INTRODUCTION
For chemical physicists, the most serviceable advantageof the infrared free electron laser (IR-FEL) overconventional laser light sources is its spectral range. Since
the mid infrared (MIR) spectral region falls in the rangeof excitation energy of a specific molecular vibrationalmode, IR-FEL is considered to be a powerful tool forspectroscopic study in the MIR region and bond-selective
photochemistry. Our group [1] reported on vibrational
excitation of CO molecules as the first result ofexperiment on gas-phase molecules employing IR-FEL at
Tokyo University of Science (FEL-SUT). The 4.7-µm
FEL, corresponding to the X 1Σ+ v" = 1 ← 0 transition ofCO, generated vibrationally excited CO molecules whichwere probed by (2 + 1) resonance-enhanced multiphoton
ionization (REMPI) technique via B 1Σ+ state. We foundthat ~10 % of the population in v" = 0 was excited to v" =1, but no sequential excitation to the v" ≥ 2 vibrational
levels was observed.
As a next stage, this paper describes preliminary resultson vibrational excitation of ammonia (NH3) molecules.
Ammonia and its isotopomers are one of the mostrepresentative small gas-phase molecules. From the view
point of vibrational excitation, Akagi et al. [2] reportedbond-selective dissociation of partially deuterased
ammonia excited to the overtone state of N-H or N-D
stretching mode. When the 5νNH overtone state (excitedby 650-nm visible laser) of NHD2 was photodissociatedby UV laser, the NH dissociation cross section was ~5times as large as the ND dissociation cross section per
bond. Report on the vibrational excitation of single
quantum has also been made by Ying et al. employing
FEL at Vaderbilt University [3]. Their main purpose wasto observe absorption spectrum corresponding to X 1A1"
21 ← 20. In the current study we attempted to generate alarge amount of the vibrationally excited ammonia

molecules and to investigate whether the ladder climbing
exists or not. We employed (2 + 1) REMPI schemes via
the B 1E" Rydberg state to detect vibrationally excitedammonia, because the observation of the B 1E" using
REMPI schemes has been thoroughly studied [4-8].

EXPERIMENTThe experiment was performed at laboratory III in IRFEL Research Center at Noda campus of Tokyo
University of Science. The status of the FEL-SUT facility
was reported elsewhere [9-11]. Figure 1 displays aschematic diagram of the experimental system. The
system consists of a reflectron-type time-of-flight
spectrometer (Jordan D-651) with a pulsed valve (Jordan
C-211AL), a beam duct and several mirrors for theguidance of the FEL beam to the TOF system, ananosecond dye laser (Continuum ND6000) pumped by a
Q-switched YAG laser (Lotis TII), and a microcomputer
unit for data storage and control of the dye laser
wavelength. A main chamber is evacuated by two turbo
molecular pumps (SHIMADZU TMU1500 and TMU150): The background pressure is below 10-7 Torr. The
pulsed valve with a skimmer nozzle produces asupersonic molecular beam with 60 µs duration.
Molecular beam is supplied with 5 % NH3 in Ar at theback pressure of 1 atm. This molecular beam isintersected by two counterpropagating laser lights. Bothlaser beams are focused with a lens (f = 30 cm; BaF2 for
IR and quartz for UV). The polarization plane of the IR-___________________________________________*

ogi@rs.kagu.tus.ac.jp

Available online at http://www.JACoW.org

Figure 1: Experimental apparatus.

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FEL is parallel to the TOF axis and the UV laser
polarization is perpendicular to them.
The synchronization among the pulsed molecular beam,
FEL macropulse and YAG-laser pulse was controlled
electrically by the use of several digital delay generators(SR DG535). The repetition rates of macropulse andmicropulse are 5 and 2856 MHz, respectively. As long as
the dye laser pulse is sitting in a macropulse of ~ 2 µs
duration, the dye laser pulse of 3 ns duration contains
several micropulses which have 350 ps interval. Becausea fast detector for MIR radiation is not available, wemonitored the temporal profile of visible harmonics witha photodiode (Electro-Optics Technology, ET-4000).
The wavelength of FEL was tuned around 10.5 µm,
corresponding to the X 1A1" 21 ← 20 transition of NH3.
Typical bandwidth of the IR laser, monitored by using
monochromator and a HgCdTe detector, was ~0.16 µm(~14 cm-1, FWHM). In front of the window of the mainchamber, the macropulse energy at this wavelength wasmeasured to be 8-15 mJ which is several times greaterthan that in the earlier experiment [1]. On the other hand,
315-340 nm light required for (2 + 1) REMPI via the B
1E" state of NH3 was obtained as a second harmonic ofthe dye laser output. The output of the dye laser was
frequency doubled in a KDP crystal. The UV pulse energy
was measured to be ~1 mJ.

RESULTS AND DISCUSSION
The B ← X REMPI excitation spectrum obtained byscanning UV wavelength in the range of 315-340 nm wasgoverned by the vibronic progression of ν2 as seen in
earlier reports [4-8]. This fact is based on the large changeof equilibrium geometry. Whilst the ground state ispyramidal (point group C3v) the Rydberg states are allplanar (point group D3h).
Figure 2a) shows a portion of the REMPI excitation
spectrum corresponding to the B ← X 210 transition
without introduction of IR-FEL. Rotational assignments
are performed using known molecular constants [4]. The
B ← X two-photon transition belongs to theperpendicular band and the selection rule for K is ∆K =± 1. The rS0(0) and pR1(1) lines cannot be resolved by ourlaser bandwidth. Missing of the transition from the JK = 10
level is explainable as follows. Due to the inversion
doubling, each ν2 state in the ground state has s and acomponents having A1' and A2" vibronic symmetry,
respectively. In the B state, the vibronic symmetry iseither E" or E', for even or odd ν2 level, respectively.
Two-photon transitions connect lower and upper statesaccording to the schemes E" ← A1'(s) and E' ← A2"(a).
Owing to the nuclear spin statistics, the A1' component in
the X state has only odd-numbered J for K = 0. Inversely,
the A2" component has only even-numbered J for K = 0.
For B ← X 210 transition, the lower state doesn’t have JK= 10 level since the vibronic symmetry is A2".
Figure 2a) could be reproduced consistently by asimulation taking into account rotational line strengths[12], rotational degeneracy, rotational temperature, and

THPOS26

Figure 2: REMPI spectra in the region of the B ← X 210
two-photon transition of NH3 a) without and b) with
irradiation of the IR-FEL (10.5 µm). Rotational
assignments added in traces a) and b) belong 210 and 221
bands, respectively.
nuclear spin statistics in the ground state. Rotationaltemperature was found to be ~8 K. This calculation
indicated that over 99 % of population was fell in the JK =00 and 11 in the X(a) state.
Figure 2b) is the REMPI spectrum obtained by theirradiation of both the IR-FEL and UV laser. The center
wavelength of the IR-FEL was fixed to 10.5 µm (952 cm1). Newly appeared peaks were assigned to the rotationallines in the B ← X(s) 221 two-photon transition,
demonstrating that the vibrational excitation of NH3
corresponding to the X(s) 21 ← X(a) 20 transition in the
ground state was achieved. Simultaneous observation ofrovibronic transitions from the X(s) 21 JK = 10 and 21
levels indicate that the broad spectral width of IR-FEL
covers the transition energies of the aqR0(0) (951.78 cm-1)
and aqR1(1) (971.88 cm-1) [13]. Note that the selection
rules for the rovibrational transition are A1'(s) - A2"(a) and∆K = 0 (parallel band).
Efficiency of the vibrational excitation was estimatedcomparing Fig. 2a) and b). The intensity of the each peakin Fig. 2a) apparently decreased in Fig. 2b). Average ofthe decrease in peak intensities for pQ1(1), rR1(1), rS1(1),and pS1(1) peaks suggests that 30 % of the total
population in the X(a) 20 JK = 11 was pumped to the X(s)21 JK = 21. Here the strongest peak constructed by tworotational lines was not involved in the calculation.

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701

time that the ladder climbing up to ν2 = 2 was realized in
the NH3 system. The complete paths of the vibrational
excitations are written as (i) X(a) 22 JK = 00 ← X(s) 21
JK = 10 ← X(a) 20 JK = 00, and (ii) X(a) 22 JK = 21 ←X(s) 21 JK = 21 ← X(a) 20 JK = 11. No signals could beobserved corresponding to the subsequent climbing toX(s) 23: the transition energy of the X(s) 23 ← X(a) 22
band (~ 500 cm-1) is far from the IR-FEL wavenumber
used.
Figure 4 shows the examples of IR-FEL excitation
spectra recorded by scanning IR-FEL wavelength. The
UV laser frequencies are fixed to the a) qR0(1) and b)p
R1(1) branches of the B ← X 201 transitions; the probed
levels by the UV laser are X(s) 21 JK = 10 and 11,
respectively. These two levels were pumped through theaqR0(0) and aqQ1(1) branches of the X(s) 21 ← X(a) 20
vibrational band. Though the spectral features are verybroad owing to the condition of FEL-SUT, the spectral
positions are consistent with the transition energies(calculated from ref. [14]) indicated by down arrows.
In summary, we succeeded in detecting vibrationally
hot NH3 molecules populated by light pulses from FELSUT. MIR FEL was tuned to 10.5 µm which corresponds

Figure 3: REMPI spectra in the region of the B ← X 201
and 212 two-photon transition of NH3. a) Observed
spectrum with irradiation of both the IR-FEL (10.5 µm)
and UV laser. b)c) Simulation for B ← X b) 201 and c)
212 transitions.
Figure 3a) displays REMPI spectra in the region of the
B ← X 201 and 212 two-photon transition of NH3
obtained with irradiation of both the IR-FEL and UV laser.
Since this energy region is below the B ← X band origin(~59300 cm-1), no signal appeared without the IR-FEL.
Figure 3b) represents the calculated spectrum
corresponding to the B ← X 201 transition. This trace
reproduces ten peaks in Fig. 3a) almost perfectly. The
disagreement of their intensities is mainly caused by thefluctuation of the FEL macropulse intensity. The
rotational levels in the X 21 state are identified to be JK =10 and 21, showing that the rotational lines in the X(s) 21← X(a) 20 band are qR0(0) and qR1(1), as same in Fig. 2.
Additionally, the signals corresponding to the B ← X
212 transition appeared in this region. The calculated
spectrum displayed in Fig. 3c) clearly shows that the X(a)22 JK = 00 and 21 levels are populated. These two levels
are excited from the X(s) 21 JK = 10 and 21 through theq
P0(1) (929.61 cm-1) and qQ1(2) (947.88 cm-1) branches,
respectively. This observation demonstrates for the first

Figure 4: IR-FEL excitation spectra corresponding to theX(s) 21 ← X(a) 20 of NH3. The UV laser frequencies are
fixed to the qR0(1) and b) pR1(1) branches of the B ← X
201 transition. Down arrows represent the known
transition energies.

FEL Users Workshop

702

Y. Ogi et al. / Proceedings of the 2004 FEL Conference, 699-702

to the X 21 ← X 20 band. The population of thevibrationally excited state was probed by (2 + 1) REMPI
method. Efficiency of the vibrational excitation of the X
21 state is as large as 30 %. Spectral assignments revealed
that vibrational ladder climbing up to ν2 = 2 in NH3 wasrealized for the first time. Experiment on the vibrational
excitation of the ν4 vibrational mode of NH3 molecules isunder way.

ACKNOWLEDGEMENTS
The authors gratefully acknowledge the skillfulsupports by the FEL-SUT staffs. The experiments weredone with the help of Mr. M. Kawashita and the otherstudents in our laboratory.

REFERENCES[1] Y. Ogi, T. Endo, K. Tsukiyama, H. Kondoh, K. Tono,
Y. Ogawa, Y. Hamada, T. Ohta and H. Kuroda J.
Electr. Spectrosc. Relat. Phenom. 128 (2003) 67.
[2] H. Akagi, K. Yokoyama, A. Yokoyama, J. Chem.
Phys. 120 (2004) 4696.
[3] Z.C. Ying, A.S. Lahamer, O. Yavas, R.F. Haglund Jr.
and R.N. Compton, Chem. Phys. Lett. 282 (1998) 268.

THPOS26[4] M.N.R. Ashfold, R.N. Doxpn, N. Little, R.J. Stickland,
and C.M. Western, J. Chem. Phys. 89 (1988) 1754.
[5] M.N.R. Ashfold, R.N. Dixon, R.J. Stickland, C.M.
Western, Chem. Phys. Lett. vol. 138 (1987) 201.
[6] B.D. Kay, A.J. Grimley, Chem. Phys. Lett. 127 (1986)
303.
[7] J. Bentley, B.J. Cotterell, A. Langham, and R.J.
Stickland, , Chem. Phys. Lett. 332 (2000) 85.
[8] W.E. Conaway R.J.S. Morrison, and R.N. Zare, Chem.
Phys. Lett. vol. 113 (1985) 429.
[9] M. Kawai, H. Kuroda, in: Free Electron Lasers,
Proceedings of the 21st international FEL conference
and 6th FEL application workshop II-67 (1999).
[10] M. Yokoyama, F. Oda, A. Nakayama, K. Nomaru, H.
Koike, M. Kawai, H. Kuroda, Nucl. Instr. and Meth. A
445 (2000) 379.
[11] M. Yokoyama, F. Oda, K. Nomaru, H. Koike, M.
Sobajima, M. Kawai, H. Kuroda, K. Nakai, Nucl.
Instr. and Meth. A 507 (2003) 261.
[12] K. Chen, E.S. Yeung, J. Chem. Phys. 69 (1978) 43.
[13] S. Urban, V. Špirko, D. Papousek, R.S. McDowell,
N.G. Nereson, S.P. Belov, L.I. Gershstein, A.V.
Maslovskij, A.F. Krupnov, J. Curtis, K.N. Rao, , J.
Mol. Spectrosc. 79 (1980) 455.
[14] S. Urban, R. D'Cunha, K. N. Rao, and D. Papousek,
Can. J. Phys. 62 (1984) 1775.

703

M. Y. Yasumoto et al. / Proceedings of the 2004 FEL Conference, 703-705

PHOTO-ACOUSTIC SPECTROSCOPY WITH INFRARED FEL
M. Yasumoto*, H. Ogawa, N. Sei, K. Yamada
Research Institute of Instrumentation Frontier, National Institute of Advanced Industrial Scienceand Technology (AIST), AIST Tsukuba Central 2, Tsukuba, Ibaraki, 305-8568, Japan
Abstract
We are proposing a new photo acoustic spectroscopy(PAS) method with an infrared free electron laser (FEL).
The FEL-PAS, using the infrared FEL as the light source,
can be applied in various samples with high sensitivity,
because the FEL has continuous tunability in the infrared
wavelength range. We measured the photo-acoustic
spectrum of a polyethylene terephtarate (PET) film using
the FEL-PAS method and confirmed a high level ofagreement as compared to the absorption spectrum by a
Fourier transform infrared (FTIR) spectroscope. In
addition, we constructed an imaging system of the FELPAS. The imaging system can make a map of the PAS
signal with a high spatial resolution that is a diffraction
limit of the IR-FEL.

INTRODUCTION
Free-electron laser (FEL) is a useful laser having two
advantages: continuously coverage of a wide wavelength
range from infrared (IR) to ultra violet (UV); very shortpulse duration. The FEL in the IR wavelength region is
expected to be applied in various researches because there
are few lasers that can cover a wide range of wavelengths
continuously. The 5 ~ 15-µm wavelength range, known
as the molecular fingerprint region, is especially useful
because it corresponds to the unique absorption featuresof various molecular structures. Thus, the IR-FEL of the
wavelength range has been applied to research using
excitation of specific molecular vibration [1].
We applied the IR-FEL to the photo acoustic process,known as photo acoustic spectroscopy (PAS). In ordinaryPAS, a modulating laser beam at a wavelength thatoverlaps with a spectral feature of the target molecule
excites the target molecule by absorption of the incident
radiation. The excited molecule is deactivated via
collisions during which the absorbed radiation energy isconverted into periodic local heating at the modulation
frequency. We then monitor the resulting acoustic waves
with a microphone. In this study we used the IR-FEL as
the modulating laser radiation. The IR-FEL irradiation
excites the target molecule more efficiently than an
ordinary laser pulse by matching the photon energy of the
IR-FEL to the excitation energy. In addition the sensitive
PAS method can be developed to make a PAS image by
micro-spectroscopy. Thus, we measured the PA spectrumof a polymer sample for the preliminary experiment of the___________________________________________*m.yasumoto@aist.go.jp

Available online at http://www.JACoW.org

new PAS method and constructed the PAS imaging
system in this paper.

PHOTO ACOUSTIC SPECTROSCOPY
WITH FREE ELECTRON LASERThe PAS is a sensitive method of measuring theabsorbance of various samples [2]. In the PA process, theconversion of heat input from the incident laser radiation
into acoustic waves is described in the following equation
1.

∇2 p −1 δ2p(γ − 1) δH
=− 2
2
2
δt
c δ t
c

(1)

where p is the pressure, H is the generated heat, and γ isthe ratio of specific heat.
The heat will be modulate, if the laser radiation ismodulated (δp/δt is not 0). The magnitude of the photo
acoustic signal is described in the following equation 2.
(2)
S = CPN ∆ t σ S mwhere C is a cell specific constant, P is the incident laser
power, N is the number density of absorbing molecules, σ
is absorption cross section of the transition that is being
interrogated, ∆t is the cycle period of the modulated
radiation and Sm is the sensitivity of the microphone.
The signal magnitude (S) is proportional to theabsorption cross section (σ) of the transition. Carbon
dioxide (CO2) lasers have long been used in thelaboratory because of the ability to produce discrete
wavelengths that are effectively absorbed by a variety ofmolecules. CO2 lasers have approximately 120 discrete
wavelengths between 9 µm and 11 µm with high output
power. They have nearly coincident with one of thetarget spectral line, because the CO2 lasers are not acontinuous tunable laser. On the other hand, the IR-FEL
is a continuous tunable laser and can be matched perfectlywith the absorption line of the target molecule. Thus, thePAS with the IR-FEL is a more highly-sensitive methodthan ordinary PAS methods.
In this study we used MIR-FEL at the FEL user facilityof Osaka University in Japan as the infrared FEL. The
MIR-FEL is one of the four FEL machines (MIR-, NIR-,
UVV-, FIR-FEL) at the facility and that covers the
wavelength range of 5 ~ 18 µm [3, 4]. The wavelength
range corresponds to the fingerprint region. Table 1
shows the specifications of the MIR-FEL.
Another advantage of the MIR-FEL is short pulse
duration with high power. The MIR-FEL has a double
micropulse structure of ~3-ps duration and a macropulse

FEL Users Workshop

M. Y. Yasumoto et al. / Proceedings of the 2004 FEL Conference, 703-705

of ~20-µs duration. The short duration pulse is sensitive
to the surface of the sample.
Table 1: Specifications of the MIR-FEL.
Wavelength
5 ~ 20 µm

Peak power~3 MW

Average power~20 mW

Pulse duration~3 ps (micropulse)~20 µs (macropulse)

Pulse repetition rate

22.3 MHz (micropulse)
10 Hz (macropulse)
Although many kinds of PAS methods using otherspectroscopic lights such as the Fourier Transform
Infrared (FTIR), the synchrotron infrared radiation areproposed in the past, the FEL-PAS proposed in this paper
has other advantages.
(1) The FEL-PAS has a sensitivity of the sample surface
comparing with the synchrotron radiation (SR) in
the infrared wavelength region, because the pulse
duration of the FEL is much shorter than one of theSR.
(2) In the FEL-PAS method the PAS spectrum can bemeasured in a short time, although in the FTIR-PAS
the enough time is needed for storing the data. Thus,
the FEL-PAS enables real-time diagnosis of thesample.

FEL-PAS SPECTRA OF POLYMER FILM
We measured a FEL-PAS spectrum of the polyethylene
terephtarate (PET) film to show the feasibility of the FELPAS. The spectrum was detected by a developed PA cellwith a microphone. The output signal from themicrophone was recorded by a digital oscilloscope under
the FEL irradiation. The PA cell has a transparent
window (ZnSe) for introducing the IR-FEL to the sample.
The irradiation power of the IR-FEL is ~5mW. The PA
signals were detected from 9.2 to 12.2 µm by 0.1-µm
steps. Figure 1 shows the normalized PA signals of the
PET with the IR-FEL and the normalized absorption
spectrum measured by the FTIR (Nicolet 750). The film
thickness was about 100 µm. The FEL-PA signals almost
correspond to the curve of the FTIR spectrum.

THPOS30

1

PA signal / FTIR signal (a.u.)

704

0.8

0.6

0.4

0.2
FEL-PAS
FTIR

0

9.5

10

10.5
11
11.5
Wavelength (µm)

12Figure 1: Spectra of PAS signal and FTIR signal from thePET film. The solid line and the dashed line are the PAS
spectrum and the FTIR spectrum, respectively. Both arenormalized with the maximum value.

FEL-PAS IMAGING SYSTEM
We constructed a new FEL-PAS imaging system with
the IR-FEL. The new FEL-PAS imaging system isdesigned for making a PAS image with the infrared FEL.
The FEL-PAS imaging system takes a full infrared PA
spectrum at each point on the sample. A spatial resolution
is limited to the diffraction limit of the IR-FEL,
approximately equal to the wavelength. The spatial
resolution of the system is one of the importantparameters for making PA image. Samples are precisely
scanned by a XY-stage for producing magnitude maps of
the PA signal corresponding to the absorption coefficientof the wavelength.
The FEL-PAS imaging system consists of an optical
microscope, a PA cell and a focusing mirror of the IRFEL shown in Figure 2. The sample cell has a
microphone to detect the PA signal and placed on the XYstage. The focusing mirror, an off-axis parabolic mirror,is placed upon the PA cell. After observation of themeasuring area using the optical microscope, we canirradiate the sample using the parabolic mirror. The
sample can be moved with the raster scanning.
Simultaneously, the PAS signal from the irradiated points
can be detected by the microphone. The signal value canbe reformed to the PAS image of the sample. Eliminationof the mirror aberrations leads to better confinement of
the beam and the spot size is almost equal to thediffraction limit of the IR-FEL.

M. Y. Yasumoto et al. / Proceedings of the 2004 FEL Conference, 703-705

Digital Oscilloscope+PC

Visible light

705

FEL

ParabolicmirrorObjective lens for
microscope
MicrophoneFlatmirrorSampleXY stage
Pre-amp.

Figure 2: Schematic of optical path inside the FEL-PAS
system. A parabolic mirror is removed and the objective
lens is installed, when observed with microscope.

SUMMARY
We have proposed a new PA spectroscopy with the IRFEL (FEL-PAS) in this paper. The FEL-PAS offers
unique capabilities that allow analysis of very broad rangeof sample types with high sensitivity. In the case of a
PET film, the signals from the FEL-PAS are good
agreement with absorption spectra from the FTIR
between 9.2 µm and 12.2 µm. In addition, the FEL-PAS
imaging system is also described. The FEL-PAS imaging
system is useful for microscopic analysis of a sample
surface. The spatial resolution is more or less limited by
the wavelength of the IR-FEL. Although the PET sample
is stable in time, the FEL-PAS will be especially useful intime resolved analysis of the sample because of its highpower during short pulse duration. Thus, the FEL-PAS is
expected to play an important role in the field of biomedical research and semiconductor research.

ACKNOWLEDGEMENTS
We would like to thank all staff of the FEL user facility(iFEL) at Osaka University for their efforts in maintaining
an excellent FEL beam quality.

REFERENCES[1] Proceedings of AFEL97, Osaka, Jan. 1997.
[2] A. Rosencwaig, Rev. Sci. Instrum. 48 (1977) 1133.
[3] T. Tomimasu et al. Nucl. Instrum. And Meth. B144
(1998) 1.
[4] H. Horiike et al., Jpn. J. Appl. Phys. 41 (2002)
Suppl.41-1, 10.

FEL Users Workshop

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W. B. Colson et al. / Proceedings of the 2004 FEL Conference, 706-710

FREE ELECTRON LASERS IN 2004
W. B. Colson* and B. W. Williams
Physics Department, Naval Postgraduate School, Monterey CA 93943 USA
Abstract
Twenty-seven years after the first operation of the freeelectron laser (FEL) at Stanford University, there
continue to be many important experiments, proposed
experiments, and user facilities around the world.
Properties of FELs operating in the infrared, visible, UV,
and x-ray wavelength regimes are listed and discussed.

INTRODUCTION
The following tables list existing (Table 1) andproposed (Table 2) relativistic free electron lasers (FELs)
in 2004. Each FEL is identified by a location or
institution, followed by the FEL’s name in parentheses;
references are listed in Tables 3 and 4.
The first column of the table lists the operating
wavelength λ, or wavelength range. The large range of
operating wavelengths, six orders of magnitude, indicatesthe flexible design characteristics of the FEL mechanism.
In the second column, σz is the electron pulse length
divided by the speed of light c, and ranges from almost
CW to short sub-picosecond pulse time scales. The
expected optical pulse length can be 3 to 5 times shorteror longer than the electron pulse depending on the opticalcavity Q, the FEL desynchronism, and the FEL gain. If
the FEL is in an electron storage-ring, the optical pulse istypically much shorter than the electron pulse. Most FEL
oscillators produce an optical spectrum that is Fouriertransform limited by the optical pulse length.
The electron beam energy E and peak current I
provided by the accelerator are listed in the third andfourth columns. The next three columns list the numberof undulator periods N, the undulator wavelength λ0, andthe undulator parameter K=eBλ0/2πmc2 where e is theelectron charge magnitude, B is the rms undulator fieldstrength, and m is the electron mass. For an FEL klystronundulator, there are multiple undulator sections as listed
in the N-column. Note that the range of values for N, λ0,
and K are much smaller than for the other parameters,
indicating that most undulators are similar. Only a few of
the FELs use the klystron undulator at present, and therest use the conventional periodic undulator. The FEL
resonance condition, λ=λ0(1+K2)/2γ2 where γ is therelativistic Lorentz factor, provides a relationship that canbe used to derive K from λ, E, and λ0. The middle entryof the last column lists the accelerator type (RF for Radio
Frequency Linear Accelerator, MA for Microtron
Accelerator, SR for Storage Ring, EA for Electrostatic———

Accelerator), and the FEL type (A for FEL Amplifier, O
for FEL Oscillator, S for SASE FEL, H for a high-gainhigh harmonic HGHG FEL). Most of the FELs are
oscillators, but recent progress has resulted in shortwavelength FELs using SASE (Stimulated Amplificationof Spontaneous Emission).
For the conventional undulator, the peak optical power
can be estimated by the fraction of the electron beam
peak power that spans the undulator spectral bandwidth,
1/4N, or P≈EI/4eN. For the FEL using a storage ring, theoptical power causing saturation is substantially less than
this estimate and depends on ring properties. For thehigh-gain FEL amplifier, the optical power at saturation
can be substantially greater. The average FEL power isdetermined by the duty cycle, or spacing between
electron pulses, and is typically many orders ofmagnitude lower than the peak power. The TJNAF
IRFEL has now reached an average power of 10 kW withthe recovery of the electron beam energy insuperconducting accelerator cavities.
In the FEL oscillator, the optical mode that best
couples to the electron beam in an undulator of length
L=Nλ0 has Rayleigh length z0≈L/121/2 and has a mode
waist radius of w0≈N1/2γλ/π. The FEL optical mode
typically has more than 90% of the power in thefundamental mode described by these parameters.

ACKNOWLEDGMENTS
The authors are grateful for support from ONR,NAVSEA, and the JTO.

* Corresponding Author: 831-656-2765, Colson@nps.edu

THPOS58

Available online at http://www.JACoW.org

707

W. B. Colson et al. / Proceedings of the 2004 FEL Conference, 706-710

Table 1: Free Electron Lasers (2004)
EXISTING FELs
Italy (FEL-CAT)
UCSB (mm FEL)
Novosibirsk (RTM)
Korea (KAERI-FEL)
Himeji (LEENA)UCSB (FIR FEL)
Osaka (ILE/ILT)Osaka (ISIR)
Tokai (JAERI-FEL)
Bruyeres (ELSA)
Osaka (FELI4)
UCLA-Kurchatov
LANL (RAFEL)
Stanford (FIREFLY)
UCLA-Kurchatov-LANL
Maryland (MIRFEL)
Beijing (BFEL)
Dresden (ELBE1)
Korea (KAERI HP FEL)
Newport News (IR demo)
Darmstadt (FEL)
BNL (HGHG)
Osaka (iFEL1)Tokyo (KHI-FEL)
Nieuwegein (FELIX)
Duke (MARKIII)
Stanford (SCAFEL)
Orsay (CLIO)
Vanderbilt (FELI)Osaka (iFEL2)
Nihon (LEBRA)
UCLA-BNL (VISA)BNL (ATF)
Dortmund (FELICITAI)BNL NSLS (DUVFEL)
Orsay (Super-ACO)
Osaka (iFEL3)
Okazaki (UVSOR)
Tsukuba (NIJI-IV)
Italy (ELETTRA)
Duke (OK-4)
ANL (APSFEL)DESY (TTF1)

λ (µm)
760
340
120-180
97-1200
65-75
60
47
40
22
20
18-40
16
15.5
15-80
12
12-21
5-20
3-22
3-20
3, 6, 10
6-8
5.3
5.5
4-16
3-250
2.7-6.5
3-13
3-53
2.0-9.8
1.88
0.9-6.5
0.8
0.6
0.42
0.1
0.3-0.6
0.3-0.7
0.2-0.6
0.2-0.6
0.2-0.4
0.193-2.1
0.13
0.08-012

σz(ps)
15-20
25000
70
25
10
25000
3
30
2.5-5
30
10
3
15
1-5
5
5
4
10
10-20
0.2
2
6
10
2
1
3
0.5-12
0.1-3
0.7
10
<1
0.5
6
50
0.7
15
5
6
14
28
0.1-100.3
0.04

E(MeV)
1.8
6
12
4.3-6.5
5.4
6
8
17
17
18
33
13.5
17
15-32
18
9-14
30
40
20-40
160
25-50
40
33.2
32-40
50
31-41.5
22-45
21-50
43
68
58-100
70.9
50
450
300
800
155
607
310
1000
1200
399
250

I(A)
5
2
10
0.5
10
2
50
50
200
100
40
80
300
14
170
100
15-20
8
30
270
2.7
120
42
30
50
20
10
80
50
42
10-20
250
100
90
500
0.1
60
10
10
150
35
400
3000

N
16
42
2x33
80
50
150
50
32
52
30
30
40
200
25
100
73
50
2x34
30x2
25
80
60
58
43
38
47
72
38
52
78
50
220
70
17
256
2x10
67
2x9
2x42
2x19
2x33
648
492

λ0(cm)
2.5
7.1
12
2.5
1.6
2
2
6
3.3
3
8
1.5
2
6
2
1.4
3
2.73
3.5
20
3.2
3.3
3.4
3.2
6.5
2.3
3.1
5
2.3
3.8
4.8
1.8
0.88
25
3.9
13
4
11
7.2
10
10
3.3
2.73

K(rms)
0.75
0.7
0.71
1.0-1.6
0.5
0.1
0.5
1
0.7
0.8
1.3-1.7
1
0.9
1
0.7
0.2
1
0.3-0.8
0.5-0.8
4.5
1
1.44
1
0.7-1.8
1.8
1
0.8
1.4
1.3
1
0.7-1.4
1.2
0.4
2
0.7
4.5
1.4
2
2
4.2
0-4.75
2.2
0.81

RF,O
EA,O
RF,O
MA,O
RF,O
EA,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,A
RF,O
RF,O
RF,A
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,A
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,O
RF,S
RF,O
SR,O
RF,SH
SR,O
RF,O
SR,O
SR,O
SR,O
SR,O
RF,S
RF,S

Tables of Operating and Proposed FELs

708

W. B. Colson et al. / Proceedings of the 2004 FEL Conference, 706-710

Table 2: Proposed Free Electron Lasers (2004)
PROPOSED FELs

λ(µm)σz(ps)

Tokyo (FIR-FEL)
Netherlands (TEUFEL)
Rutgers (IRFEL)
Novosibirsk (RTM1)
Dresden (ELBE)
Daresbury (4GLS-IRFEL)
Novosibirsk (RTM)
Frascati (SPARC)
TJNAF (UVFEL)
Hawaii (FEL)
Harima (SUBARU)
Shanghai (SDUV-FEL)
Frascati (COSA)
Daresbury (4GLS-VUV)
Daresbury (4GLS-XUV)Duke (OK-5,VUV)DESY (TTF2)
Italy (SPARX)BESSY (Soft X-ray)
Trieste (FERMI)RIKEN (SPring8 SCSS)
MIT (Bates X-Ray FEL)SLAC (LCLS)DESY (TESLA)Pohang (PAL X-FEL)

300-1000
180
140
3-20
30-750
5-100
2-11
0.533
0.25-1
0.3-3
0.2-100.5-0.088
0.08
0.4-0.1
0.1-0.01
0.03-10.006
0.00150.00120.001-0.1
0.000360.00030.000150.00010.0003

5
20
25
10
1-5
0.2-1
20
0.1
0.2
2
26
1
10
0.1-1
0.1-1
0.1-10
0.17
0.1
0.08
0.1
0.5
0.05
0.07
0.08
0.1

THPOS58

E(MeV
)
10
6
38
50
10-40
50
98
142
160
100
1500
300
215
600
600
1200
1000
2500
2300
3000
1000
4000
14350
30000
3000

I(A)

N

30
350
1.4
20-100
30
100
100
500
270
500
50
400
200
300
2000
50
2500
2500
3500
2500
2000
1000
3400
5000
4000

25
50
50
3x33
45
100
4x36
6x71
60
84
33,65
400
400
150
1000
4x32
981
1000
1450
570-1140
1500
1500
3328
4500
6000

λ0(c
m)
7
2.5
20
6
5
4
9
3
3.3
2.4
16,32
2.5
1.4
5
2
12
2.73
3
2.75
3.5
1.5
1.8
3
6
1.5

K(rms)
1.5-3.41
1
2
0.4-1.6
2
1.6
1.3
1.3
1.2
8
1.025
1
2
1
3
0.9
1.2
0.9
1.2
1.3
2
3.7
3.2
1.1

RF,O
RF,O
MA,O
RF,O
RF,O
RF,O
RF,O
RF,S
RF,O
RF,O
SR,O
RF,O
RF,O
RF,O
RF,S
SR,O
RF,S
RF,S
RF,S
RF,S
RF,S
RF,S
RF,S
RF,S
RF,S

W. B. Colson et al. / Proceedings of the 2004 FEL Conference, 706-710

709

Table 3: References and Websites for Existing FELs
EXISTING FELs
ANL (APSFEL)
Beijing (BFEL)BNL NSLS (DUVFEL)BNL (ATF)
BNL (HGHG)
BNL (VISA)
Bruyeres (ELSA)
Darmstadt (FEL)DESY( TTF1)
Dortmund (FELICITAI)
Duke (MARKIII)
Duke (OK-4)
Himeji (LEENA)
Italy (ELETTRA)
Italy (FEL-CAT)
Korea (KAERI HP FEL)
Korea (KAERI-FEL)
LANL (RAFEL)
Maryland (MIRFEL)
Newport News (IR demo)
Nieuwegein (FELIX)
Nihon (LEBRA)
Novosibirsk (RTM)
Okazaki (UVSOR)
Orsay (CLIO)
Orsay (Super-ACO)
Osaka (FELI4)
Osaka (iFEL1)Osaka (iFEL2)
Osaka (iFEL3)
Osaka (ILE/ILT)Osaka (ISIR)
Stanford (FIREFLY)
Stanford (SCAFEL)
Tokai (JAERI-FEL)
Tokyo (KHI-FEL)
Tsukuba (NIJI-IV)
UCLA-Kurchatov
UCLA-Kurchatov-LANLUCSB (FIR FEL)UCSB (mm FEL)
Vanderbilt (FELI)Internet Site or Reference
J. W. Lewellen et. al., NIM A483, 40 (2002).
http://bfel.ihepa.ac.cn
http://www.nsls.bnl.gov/organization/Accelerator/DUVFEL
K. Batchelor et. al., NIM A318, 159 (1992).
A. Doyuran et. al., NIM A475, 260 (2001).
A. Tremaine et. al., NIM A483, 24 (2002).
P. Guimbal et. al., NIM A341, 43 (1994).
http://linaxa.ikp.physik.tu-darmstadt.de/richter/fel
http://www-hasylab.desy.de/facility/fel
http://www.delta.uni-dortmund.de/pub/fel/FEL.html
http://www.fel.duke.edu/lightsources/mk3.html
http://www.fel.duke.edu
http://www.lasti.himeji-tech.ac.jp/NS/LEENA/LEENA_HP.html
http://www.elettra.trieste.it/projects/euprog/fel
A. Doria et. al, Phys. Rev. Lett. 80, 2841 (1998).
http://www.kaeri.re.kr/fel/index.php
http://www.kaeri.re.kr/fel/index.php
http://www.lanl.gov/orgs/ibdnew/usrfac/userfac03.html
http://www.ireap.umd.edu/FEL
http://www.jlab.org/FEL
http://www.rijnh.nl/n4/n3/f1234.htm
http://www.lebra.nihon-u.ac.jp
http://www.inp.nsk.su
http://uvsor-ntserver.ims.ac.jp
http://www.lure.u-psud.fr/CLIO.HTM
M. E. Couprie et. al., NIM A407, 215-220 (1998).
T. Takii et. al., NIM A407, 21-25 (1998).
http://www.fel.eng.osaka-u.ac.jp/english/index_e.html
http://www.fel.eng.osaka-u.ac.jp/english/index_e.html
http://www.fel.eng.osaka-u.ac.jp/english/index_e.html
N. Ohigashi et. al., NIM A375, 469 (1996).
http://www.ei.sanken.osaka-u.ac.jp
K. W. Berryman and T. I. Smith, NIM A375, 6 (1996).
H. A. Schwettman et. al., NIM A375, 662 (1996).
R. Hajima et. al., NIM A507, 115 (2003).
M. Yokoyama et. al., NIM A475, 38 (2001).
K.Yamada et. al., NIM A475, 205 (2001).
http://pbpl.physics.ucla.edu
http://pbpl.physics.ucla.edu
http://sbfel3.ucsb.edu
http://sbfel3.ucsb.edu
http://www.vanderbilt.edu/fel

Tables of Operating and Proposed FELs

710

W. B. Colson et al. / Proceedings of the 2004 FEL Conference, 706-710

Table 4: References for Proposed FELs
PROPOSED FELs
BESSY (Soft X-ray)
Daresbury (4GLS)DESY (TESLA)DESY (TTF2)
Dresden (ELBE)
Dresden (ELBE1)
Duke (OK-5,VUV)
Frascati (COSA)
Frascati (SPARC)
Harima (SUBARU)
Italy (SPARX)
MIT (Bates X-Ray FEL)Netherlands (TEUFEL)
Novosibirsk (RTM)
Novosibirsk (RTM1)
Pohang (PAL X-FEL)
RIKEN (SPring8 SCSS)
Rocketdyne/Hawaii (FEL)
Rutgers (IRFEL)
Shanghai (SDUV-FEL)
SLAC (LCLS)
TJNAF (UVFEL)Tokyo (FIR-FEL)
Trieste (FERMI)THPOS58

References for Proposed FELs
M. Abo-Bakr et. al., Nucl. Inst. and Meth. A483, 470 (2002);
Tsukuba Mo-P-07,Mo-P-08,We-P-51 (Sept 2003).
M. W. Poole and B. W. J. McNeil, Nucl. Inst. and Meth. A507,
489 (2003).
R. Brinkmann et. al., Nucl. Inst. and Meth. A393, 86 (1997);
TESLA Technical Design Report.
W. Brefeld et. al., Nucl. Inst. and Meth. A375, 295 (1996).
F. Gabriel et. al., Nucl. Inst. and Meth. B161, 1143 (2000).
F. Gabriel et. al., Nucl. Inst. and Meth. B161, 1143 (2000).
V. N. Litvinenko et. al., Nucl. Inst. and Meth. A358, 369 (1995).
F. Ciocci et. al., A. Torre, IEEE J.Q.E. 31, 1242 (1995).
A. Renieri et. al., Nucl. Inst. and Meth. A507, 507 (2003).
S. Miyamoto et. al., Report of the Spring-8 International
Workshop on 30 m Long Straight Sections, Kobe, Japan(August 9, 1997).
A. Renieri et. al., Nucl. Inst. and Meth. A507, 507 (2003).
W.S. Graves et. al., Nucl. Inst. and Meth. AXXX, xx (2004);
Twenty-Fifth International Free Electron Conference, Tsukuba,
Japan (Mo-P-49, Sept 2003).
J. I. M. Botman et. al., Nucl. Inst. and Meth. A341, 402 (1994).
N. G. Gavrilov et. al., Status of Novosibirsk High Power FEL
Project, SPIE Proceedings, vol. 2988, 23 (1997); N. A.
Vinokurov et. al., Nucl. Inst. and Meth. A331, 3 (1993).
V. P. Bolotin et. al., Nucl. Inst. and Meth. A475, II-37 (2001).
pal.postech.ac.kr/kor
T. Shintake et. al., Nucl. Inst. and Meth. A507, 382 (2003);
Tsukuba We-P-59 (Sept 2003).
R. J. Burke et al, Proc. SPIE: Laser Power Beaming, Los
Angeles, Jan. 27-28, 1994, Vol 2121.
E. D. Shaw et. al., Nucl. Inst. and Meth. A318, 47 (1992).
Z. T. Zhao et. al, Nucl. Inst. and Meth. AXXX, xx (2004);
Twenty-Fifth International Free Electron Conference, Tsukuba,
Japan (We-P-65, Sept 2003).
M. Cornacchia, Proc. SPIE 2998, 2-14 (1997); LCLS Design
Study Report, SLAC R-521 (1998).
S. Benson et. al., Nucl. Inst. and Meth. A429, 27-32 (1999).
H. Koike et. al., Nucl. Inst. and Meth. A483, II-15 (2002).
C. J. Bocchetta et. al., Nucl. Inst. and Meth. A507, 484 (2003);
Tsukuba We-P-53 (Sept 2003).

Author Index

Proceedings of the 2004 FEL Conference – Trieste, Italy

Author Index
Bold paper codes mean primary author.
A
Abo-Bakr, M. . . . . . . . . . . . . . . . . . . . . . . . 104, 112, 116
Abrahamyan, K. . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Ackermann, W. . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 399
Afifi, G.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
Aghahosseini, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Agustsson, R.B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Alesini, D. A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Alessandria, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Amano, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685
Andersson, x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Andonian, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Andrejczuk, A.A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Andrews, H. L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Armstead, R. L. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75, 241
Asaka, T.A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Asakawa, M.R. . . . . . . . . . . . . . . . . . . . . . . . . . . 251, 618
Asova, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Assoufid, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
Austin, r.h.a. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661
Awazu, K.. . . . . . . . . . . . . . . . . . . . . . 251, 657, 689, 692
BBaba, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Babzien, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325, 530
Bacci, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Baehr, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Bahrdt, j.b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610
Baik, S.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Bakker, R.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Balkcum, A.J.B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Barton, D.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Basam, A.B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Beard, K.B.B. . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 558
Beavis, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Behre, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . 222, 229, 363
Bellaveglia, M. . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Ben-Zvi, I. . . . . . . . . . . . . . . . . . . . . . 325, 355, 570, 594
Benson, S. V. . . . . . . . . . 222, 229, 363, 554, 558, 562
Bentson, L.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
Berden, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Bertolucci, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Bessonov, E.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
Bevins, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Biagini, M.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Biallas, G. H. . . . . . . . . . . . . . . . . . . . 229, 363, 554, 558
Biedron, S.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216, 530
Biscari, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Bittner, M.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

713

Blaskiewicz, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Blau, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . 75, 78, 241, 274
Bluem, H.P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Bocchetta, C.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . 159, 163
Bohlen, H. P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Bohnet, I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385
Boller, K.-J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53, 314
Bolotin, V. P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Boni, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Borland, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
Boscolo, I. . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 325, 407
Boscolo, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Boucher, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Boulware, C. H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Bowler, M.A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270, 511
Boyce, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229, 363
Boyce, R.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
Brandin, x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Brau, C. A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Brennan, J.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Broggi, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Buettig, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Bulfone, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Bullard, D.B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222, 558
Burger, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Burrill, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
C
Calaga, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Cameron, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Candel, A.C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Cao, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
Carneiro, J.-P. . . . . . . . . . . . . . . . . . . 120, 347, 385, 399
Carpanese, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Carr, G.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
Carré, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Casalbuoni, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Castellano, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Castro, J.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Catani, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Cha, H. J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Chae, Y.-C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100, 523
Chalut, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322, 640
Chang, C.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
Chang, X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Cheever, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
Chen, C.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Chen, Chen Nian. . . . . . . . . . . . . . . . . . . . . . . . . 487, 490
Chen, H.B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Chen, H.Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Chen, J. E. . . . . . . . . . . . . . . . . . . . . . . . . . . 478, 481, 671
Chen, J.R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Chen, w. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

714

Proceedings of the 2004 FEL Conference – Trieste, Italy

Cheng, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Cheng, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Chiadroni, E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Chin, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
Cho, M.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Chu, X. Q. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Chvostova, D.C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Cialdi, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 325, 407
Cianchi, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Ciocci, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Clendenin, J.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Clozza, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Cole, M.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Coleman, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Colson, W. B. . . . . . . . . . . . . . . . . 75, 78, 241, 274, 706
Connolly, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Coreno, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
Couprie, M.-E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Craievich, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159, 403
Crooker, P. P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241, 274
Csorna, S.E. C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546

Doria, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . 155, 163, 407
Dou, YH. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Douglas, D. . . . . . . . . . . . . . . . . 229, 363, 558, 562, 590
Dowell, D.H. . . . . . . . . . . . . . . . . . . . . . . . . 163, 205, 538
Doyuran, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Drago, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Du, Q. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Du, t.b. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Du, Y.Ch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Dylla, H. F. . . . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 558E
Ebadpoor, F.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Edwards, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648
Einat, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Eliran, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Elliott, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Elzhov, A.V. . . . . . . . . . . . . . . . . . . . . . . . . . 68, 187, 318
Emma, P. . . . . . . . . . . . . . . . . . . 163, 333, 395, 407, 582
England, R.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Erdmann, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100, 523
Eriksson, x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Esposito, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
D
D’Angelo, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Evans, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 558
D’Auria, G. . . . . . . . . . . . . . . . . . . . . . . . . . 159, 163, 403 Evtushenko, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 359
Dai, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
FDai, Z.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .494 Faatz, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120, 270
Danailov, M.B. . . . . . . . . . . . . . 163, 233, 237, 243, 681 Fahmy, K.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
Danjyo, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695 Fan, T.C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262, 501
Dattoli, G.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407 Fantini, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Davoud-Abadi, G.R.D. . . . . . . . . . . . . . . . . . . . . . . . . 578 Favale, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
de la Fuente, M.I. . . . . . . . . . . . . . . . . . . . . . . . . . 53, 314 Fawley, W. M. . . . . . . . . . . . . . . . . . . . . . . . 515, 582, 637
de Loos, M.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 Feldhaus, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
De Martinis, C. . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407 Feldman, D. W.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .574
De Ninno, gdn. . . . . . . . . . . . . . . . . . 159, 237, 243, 681 Feng, B.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546
De Silvestri, S. S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407 Ferianis, M. . . . . . . . . . . . . . . . . . . . . . . . . . 163, 237, 681
Dehler, M.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602, 606 Ferrario, M. . . . . . . . . . . . . . . . . . . . . . . . . . 163, 325, 407
Dejus, R.J. . . . . . . . . . . . . . . . . . . . . . . . . . . 367, 519, 523 Feshchenko, R.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
Dekorsy, R.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 389 Filippetto, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Delayen, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570 Fiorito, R.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
Demske, D. L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574 Flacco, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Den Hartog, .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .367 Floettmann, K. . . . . . . . . . . . . . . . . . . 120, 347, 385, 399
Dewa, H.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431 Flora, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Di Mitri, S.D.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159 Foerstendorf, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679
Di Pace, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407 Forchi‘, V.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Di Pirro, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407 Frentrup, W.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610
Di Salvo, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163 Freund, H.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
Dillon-Townes, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222 Froehlich, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Dimitrov, G. . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399 Funk, W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Ding, Y. T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478, 481 Fusco, V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Diviacco, B. . . . . . . . . . . . . . . . . . . . . 159, 237, 243, 681
Dohlus, M.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
G
Donohue, J. T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30, 34 Gabella, G.E. G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546

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Gabriel, F.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Gallerano, G.P. . . . . . . . . . . . . . . . . . . . . . . 163, 216, 407
Gallo, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Ganter, R.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602, 606
Garzella, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Gassner, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Gatto, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Gaupp, A.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610
Ge, Y.Ch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Geloni, G. A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22, 26
Gensch, U. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
Gerth, Ch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
Ghigo, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Giannessi, L. . . . . . . . 37, 155, 163, 237, 243, 407, 411
Gierman, S.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . 205, 538
Gill, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
Gillespie, W.A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Ginzburg, N.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68, 318
Giove, D.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .163, 407
Giovenale, E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Glotin, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297, 679
Gobrecht, J.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . 602, 606
Gorbachev, E.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Goto, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Gough, C.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Gover, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Grabosch, H.-J. . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Graves, W.S.. . . . . . . . . . . . . . . . . . . . . . . . . . . . .339, 542
Grimm, O.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Grippo, A. . . . . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 558
Grosse, E.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 389
Guan, W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Gubeli, J. . . . . . . . . . . . . . . . . . . . . . . 222, 229, 363, 558
Guenster, St. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Guiducci, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
H
Hahn, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Hahn, U. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Hajima, R. . . . . . . . . . . . . . . . . . . . . . . . . . . 255, 301, 304
Han, J.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
Han, J.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Hanaki, H.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Hansen, T.N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Hao, J. K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Hara, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155, 439
Hardy, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . 222, 229, 363
Hartrott, M.v. . . . . . . . . . . . . . . . . . . . . . . . 104, 347, 399
Hayakawa, K. . . . . . . . . . 247, 427, 443, 447, 450, 454
Hayakawa, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247, 427
Hayano, Dr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Hayashi, N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
He, He Duohui. . . . . . . . . . . . . . . . . . . . . . 487, 490, 494

715

He, X.Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Helm, M.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Hernandez-Garcia, C.H.G.. . . . . . . . . . . .229, 363, 558
Hershcovitch, A. . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Hettel, R.O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
Heya, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251, 689
Hiatt, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
Hidume, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Hodgson, J.A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
Holldack, K.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Holmes, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Honkavaara, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
Horiike, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251, 689
Hseuh, H.C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Hsiao, F.Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Hsu, K.T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Hua, J.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Huang, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Huang, J.Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179, 325
Huang, S.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478, 481
Huang, w.h. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Huang, Z. . . . . . . . . . . . . . . . . . . . . . . 193, 201, 333, 582
Hutson, M.S.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648
Hwang, C.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262, 501
I
Ihara, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Iijima, I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
Ilday, F. O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Imasaki, K. . . . . . . . . . . . . . . . . . . . . . . . . . 614, 618, 685
Inagaki, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Incurvati, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Ingold, G.I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Isaka, S.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Ishii, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657, 689, 692
Ishiwata, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Isoyama, G.I. . . . . . . . . . . . . . . . . . . . . . . . 167, 458, 462J
Jaeschke, E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
Jaleh, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Jamison, S.P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Janssen, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Jaroszynski, D.A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
Jarvis, J. D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
Jastrow, U. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Jensen, K. L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
Jeong, Y. U. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Jia, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60, 64, 494
Jiao, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Jie, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
John, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
Johnson, E. D. . . . . . . . . . . . . . . . . . . . . . . . . . . . 282, 285

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Johnson, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Jordan, K. . . . . . . . . . . . . . . . . . 222, 229, 363, 558, 590
Joshi, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Juha, L.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Jurek, M.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
K
Kachel, T.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Kaertner, F. X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Kaiser, N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Kaminsky, A.K. . . . . . . . . . . . . . . . . . . . . . . 68, 187, 318
Kamps, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
Kanai, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
Kanno, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Kanter, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Kapilevich, BY. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Kashiwagi, S.K. . . . . . . . . . . . . . . . . 167, 458, 462, 466
Kato, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167, 458, 462
Kauch, A.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Kayran, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Kayran, D. A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Kazakevitch, G. M. . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Kewisch, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Khan, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Kii, T. . . . . . . . . . . . . . . . . . . . . . . . . . 443, 447, 450, 454
Kikuzawa, N. . . . . . . . . . . . . . . . . . . . . . . . 255, 301, 304
Kim, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45, 49
Kim, D.E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171, 179
Kim, E.-S... . . . . . . . . . . . . . . . . . . . . . . . . .171, 179, 183
Kim, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Kim, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151, 151, 175
Kitamura, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155, 439
Klinger, D.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Klose, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Knobloch, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
Knyazev, B. A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Ko, I. S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151, 175, 179
Kobayashi, K.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
Kobayashi, T.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Kolobanov, E. I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Kondo, H.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Kordbacheh, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Korhonen, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Kosukhin, V.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Kotenkov, V.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Krämer, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108, 347
Krasilnikov, M. . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Krenz, M.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Krinsky, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282, 285
Kruchkov, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Krzywinski, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Kubarev, V. V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Kulipanov, G. N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

Kuo, C.C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Kurennoy, S.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
Kuroda, Dr. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Kuske, B. . . . . . . . . . . . . . . . . . . . . . . 104, 112, 116, 610
Kuzikov, S.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Kuzmin, A.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
L
Lambert, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Lambiase, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Larsson, x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Lassiter, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
Lau, W.K.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .262
Lee, B. C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Leemann, S.L.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .602
Lehnert, U. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 359
Lenci, S. J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Letal, V.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Levi, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Lewellen, J.W. . . . . . . . . . . . . . . . . . . . . . . 100, 523, 530
Li, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614, 685
Li, K.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602, 606
Li, Li Ge. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487, 490
Li, LiYuhui. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64, 487
Li, W.P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
Li, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523, 530
Li, y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
Li, Y.X.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Li, Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
Ligi, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Limberg, T.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Limborg-Deprey, C. . . . . . . . . . . . . . . . . . . . . . . 163, 538
Lin, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Lin, Lin. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
Lin, P.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
Lin, Y.Zh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Lindgren, x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Lipka, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Litvak, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Litvinenko, V.N. . . . . . . . 322, 325, 355, 570, 594, 640
Lonza, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
Loos, H. . . . . . . . . . . . . . . . . . . . 209, 282, 285, 329, 586
Lu, H. H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
Lu, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
Lu, X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481, 484
Lumpkin, A. H. . . . . . . . . . . . . . . . . . 100, 515, 519, 523
Luo, G.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Lurie, Yu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14, 289
M
MacDonald, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
MacLeod, A.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Madey, J.M.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

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Mairesse, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Malkin, A.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Mansfield, R. P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Maraghechi, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Marcellini, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Maroli, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Marusaki, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618
Masuda, K. . . . . . . . . . . . . . . . . . . . . . 443, 447, 450, 454
Matsumoto, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Mattioli, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Matveenko, A.N. . . . . . . . . . . . . . . . . . . . . . . . . . 226, 629
Mauri, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
McCormick, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
McIntyre, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
McNeil, B.W.J. . . . . . . . . . . . . . . . . . . . . . . 270, 598, 633
Medici, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Medvedev, L. E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Meng, W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Merminga, L. . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 590
Meseck, A.M. . . . . . . . . . . . . . . . . . . 104, 112, 116, 610
Messina, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Meyer, M.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654
Mezi, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Michel, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 359, 389
Michelato, P. . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Miginsky, S. V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Migliorati, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Milardi, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Miltchev, V.V. . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Milton, S.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
Minamiguchi, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Minehara, E.J. . . . . . . . . . . . . . . . . . . 255, 301, 304, 665
Ming, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
Mironenko, L. A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Mitzner, R.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Miyamoyo, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685
Mizuhara, A.X.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Mizuno, A.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Mochizuki, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685
Monaco, L. . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Moncton, D. E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Moody, N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
Moog, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
Mori, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Moricciani, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Mostacci, A. M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Muecke, O. D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Mueller, W.F.O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
Murakami, M. . . . . . . . . . . . . . . . . . . 443, 447, 450, 454
Muratori, B.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
Murokh, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325
Murphy, J.B. . . . . . . . . . . . . . . . . . . . . . . . . 209, 282, 285
Musumeci, P. M. . . . . . . . . . . . . . . . . 163, 407, 504, 644

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Myskin, O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
NNagai, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . 255, 301, 304
Nagl, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Naito, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251, 657
Nakao, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Nam, S.-K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45, 49
Nam, S.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Namkung, W. . . . . . . . . . . . . . . . . . . . . . . . 151, 175, 179
Nehring, T.C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Neil, G. . . . . . . . . . . . . . . . . . . . 222, 229, 363, 554, 558
Neumann, J.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
Nicoletti, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Nicolosi, p. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Niles, S. P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Nishimori, N. . . . . . . . . . . . . . . . . . . . . 41, 255, 301, 304
Nishitani, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301, 304
Nisimura, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
Nisoli, M. N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Noda, T.N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
Nogami, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
O
O’Shea, P.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574, 586
Ogawa, H. O. . . . . . . . . . . . . . . . . . . . 258, 307, 311, 703
Ogi, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
Oh, J. S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151, 175, 179
Ohgaki, H. . . . . . . . . . . . . . . . . . . . . . 443, 447, 450, 454
Ohigashi, N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618
Okamoto, C.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Onoe, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Oppelt, A. . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Oreshkov, A. D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Ortega, J.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297, 679
Ottaviani, P.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Ovchar, V. K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Owen, H.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
P
Pagani, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
Pagnutti, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Palmer, D.T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Palumbo, L. . . . . . . . . . . . . . . . . . . . . . . . . . 163, 325, 407
Paraliev, M.P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Parisi, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Park, J.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
Park, S. H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
Park, S.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171, 179
Parvin, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Pate, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Pedrozzi, M.P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Pekeler, MP. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
Pelizzo, m.g. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415

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Pelka, J.P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Pellegrini, C. . . . . . . . . . . . . . . . . . . . . . . . . 325, 504, 644
Pellegrino, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Penn, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71, 637
Perelstein, E.A. . . . . . . . . . . . . . . . . . . . . . . . . . . 187, 318
Perrott, M. H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
Peskov, N.Yu. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68, 318
Petelin, M.I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Peters, O. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Petrillo, V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Petrosyan, B. . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Phillips, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Picardi, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Pilyar, N.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Pinayev, V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322, 640
Pinhasi, G. A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
Pinhasi, Y. . . . . . . . . . . . . . . . . . . . . . . . 14, 289, 419, 423
Ploenjes, e.p. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Poletto, l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Poole, M.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598
Popik, V. M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Pose, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Pozdeyev, E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590
Prazeres, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297, 679
Preble, J. . . . . . . . . . . . . . . . . . . . . . . . 229, 355, 363, 570
Preger, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Q
Qian, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
Quan, S. W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481, 484
Quast, T.Q. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Quattromini, M.Q. . . . . . . . . . . . . . . . . . . . 163, 407, 411
Quinn, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
R
Raguin, J.-Y.R. . . . . . . . . . . . . . . . . . . . . . . . . . . 602, 606
Raimondi, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Rakowsky, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209, 282
Ralph, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Rank, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Rathke, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Redlich, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343, 661
Reiche, S. . . . . . . . . 163, 193, 197, 201, 325, 407, 582
Reinsch, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71, 637
Renieri, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Reniewicz, H.R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Ricci, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Richter, D. . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Riemann, S. . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Ristau, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Rivkin, R.L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602, 606
Robb, G.R.M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598
Romè, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407

Ronci, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Ronsivalle, C. . . . . . . . . . . . . . . . . . . . . . . . 163, 407, 411
Roper, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
Rose, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209, 282
Rosenzweig, J.B. . . . . . . . . . . . 163, 325, 407, 504, 644
Roser, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Ross, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Rossbach, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 395
Rukoyatkina, T.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Rule, D.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515, 519
Rullier, J. L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
Russo, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
S
Sabia, E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Saito, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Sajad, S.B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Sakai, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Sakaki, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
Saldin, E.L..22, 26, 96, 123, 127, 131, 135, 139, 143,
147, 212, 375, 675
Salières, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Salikova, T. V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Sandner, W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
Sanelli, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Sarto, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
Sasaki, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
Sashalmi, T.R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546
Sassi, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Sato, I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247, 427
Satoh, aS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Sawamura, M. . . . . . . . . . . . . . . . . . . . . . . . 255, 301, 304
Scaduto, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Schaerf, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Scheer, M.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610
Scheglov, M. A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Schilcher, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Schlarb, H.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Schlott, V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392, 602
Schmüser, P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Schmerge, J.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . 205, 538
Schneider, Ch. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Schneidmiller, E.A. . . 22, 26, 96, 123, 127, 131, 135,
139, 143, 147, 212, 375, 675
Schnepp, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 399
Schreiber, S. . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Schultheiss, T.J. . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Schwarz, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
Sedykh, S.N. . . . . . . . . . . . . . . . . . . . . . . . . . 68, 187, 318
Sehr, h.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Sei, N. S. . . . . . . . . . . . . . . . . . . . . . . . 258, 307, 311, 703
Seidel, W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 389, 679
Seidov, Z.F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419, 423

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Senf, F.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
Serafini, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Serednyakov, S. S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Sergeev, A.P. . . . . . . . . . . . . . . . . . . . . . . . . . 68, 187, 318
Sergeev, A.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68, 318
Serio, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Sertore, D. . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Setzer, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 399
Sgamma, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Shaftan, T. . . . . . . . . . . . . . . . . . . . . . 282, 285, 329, 586
Sheehy, B. . . . . . . . . . . . . . . . . . 209, 282, 285, 329, 586
Shen, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209, 285, 586
Shevchenko, O.A. . . . . . . . . . . . . . . . . . . . 226, 266, 629
Shi, c. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
Shinn, M.D. . . . . . . . . . . . . . . . 222, 229, 363, 558, 562
Shintake, T. . . . . . . . . . . . . . . . . . . . . . . 90, 155, 351, 439
Shu, XJ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Shvedunov, V.I.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .625
Sidorov, A.I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Sigg, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Siggins, T. . . . . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 558
Sikora, M.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Simrock, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Skaritka, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209, 282
Skrinsky, A. N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
Smith, K.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Smith, T.I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590
Smith, T.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
Snyder, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
Sobierajski, R.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Socol, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
Solar, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
Son, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Spataro, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Srinivasan-Rao, T.. . . . . . . . . . . . . . . . . . . . . . . .355, 570
Stagira, S. S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Staykov, L. . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Stecchi, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Steeg, B.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Steffen, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Stella, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Stephan, F. . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 385, 399
Stephan, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Streun, A.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Stupakov, G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
Su, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
Suemine, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167, 462
Suetterlin, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Sung, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Suzuki, S. . . . . . . . . . . . . . . . . . . . . . . 251, 657, 689, 692
Suzuki, S.S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Szarmes, E. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550

719

T
Tanaka, T. . . . . . . . . . . . . . . . . . . . . . . 247, 351, 427, 435Tang, Ch.X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Taniuchi, T.T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Tarasov, V.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Tarawneh, x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
Tazzari, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Tazzioli, F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Teichert, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
Tennant, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590
Thompson, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . 270, 633
Tiedtke, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
Tochitsky, Ya. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Todd, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Togawa, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
Tolmachev, S.V. . . . . . . . . . . . . . . . . . . . . . . . . . . 504, 644
Tomizawa, H.T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Tonutti, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Tornoe, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Torre, A. T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
Tosi, L.T.Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Toyokawa, H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
Trakhtenberg, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
Travish, G. . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 325, 644
Treusch, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Trovò, M.T. . . . . . . . . . . . . . . . . . . . . 233, 237, 243, 681
Tsakov, I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 399
Tsubouchi, N.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
Tsuchiya, K.T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
Tsukada, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
Tsukiyama, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
Tsunawaki, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618
U
Uesaka, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Ueyama, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Urakawa, Prof. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
Ursic, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
V
v. Hartrott, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
Vaccarezza, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
van der Geer, C.A.J. . . . . . . . . . . . . . . . . . . . . . . . . . . 470
van der Geer, S.B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
van der Meer, A.F.G. . . . . . . . . . . . . . . . . . . . . . 343, 661
van der Slot, P.J.M. . . . . . . . . . . . . . . . . . . . . . . . . 53, 314
Varfolomeev Jr., A.A. . . . . . . . . . . . . . . . . . . . . 504, 644
Varfolomeev, A.A. . . . . . . . . . . . . . . . . . . . . . . . 504, 644
Vasserman, I.B. . . . . . . . . . . . . . . . . . . . . . . . . . . 367, 527
Verzilov, V.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
Vescovi, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Vicario, C. . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 325, 407
Vinokurov, N.A. . . . . . . . . . . . . . . . . . . . . . 226, 266, 629

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Vogel, HV. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
Volkov, V.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .359
Volshonok, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
vom Stein, PS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
Vorlicek, V.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
W
Walker, R. . . . . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 558
Wan, W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
Wang, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
Wang, D.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Wang, G. M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Wang, J.P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Wang, L. F. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Wang, M.H. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
Wang, M.K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
Wang, Wang. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
Wang, X.J. . . . . . . . . . . . . . . . . . . . . . . . . . . 209, 282, 285
Wang, Y.G. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
Wang, YZ. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
Washio, Prof.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .466
Watanabe, K.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
Wawro, A.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Weiland, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 403
Werin, l. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
White, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
Will, I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347, 399
Williams, B. W. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78, 706
Williams, G. . . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 562
Williams, N.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Winter, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
Wohlfarth, D.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
Wolf, A.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 389
Wright, E.L.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
Wrulich, A.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . 602, 606
Wu, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
Wu, K.-C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Wu, Z. . . . . . . . . . . . . . . . . . . . . . . . . . 209, 282, 285, 586
Wuensch, R.W. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8, 389
Wurtele, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71, 637
X
Xia, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Xiang, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Xiao, B. P. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Xiao, L. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
Xiao, x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
Xie, a.x. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661
Xie, D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Xinfan, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
Xu, M.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Xu, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
Xumin, S. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498

YYahalom, A. . . . . . . . . . . . . . . . . . . . . . 14, 289, 419, 423
Yakimenko, V. . . . . . . . . . . . . . . . . . . . . . . . . . . . 325, 570
Yamabe, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Yamada, K. Y. . . . . . . . . . . . . . . . . . . 258, 307, 311, 703
Yamaguchi, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
Yamamoto, S.Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
Yamamoto, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167, 462
Yamauchi, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
Yamazaki, T. . . . . . . . . . . . . . . . . . . . 443, 447, 450, 454
Yanagida, K.Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
Yanan, C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
Yang, L. M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481, 671
Yang, y.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .474
Yarovoi, T.V. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504, 644
Yasumoto, M. Y. . . . . . . . . . . . . . . . . 258, 307, 311, 703
Yip, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
Yoder, R. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
Yokoyama, K. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
Yoon, M.H. . . . . . . . . . . . . . . . . . . . . . . . . . 171, 179, 183
Yoshikawa, Y. . . . . . . . . . . . . . . . . . . 443, 447, 450, 454
Yu, L.H. . . . . . . . . . . . . . . . . . . . . . 1, 209, 282, 285, 329
Yu, N. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
Yuan, X.D. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Yunn, B. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229, 363, 558
Yurkov, M.V. . . . . 22, 26, 96, 123, 127, 131, 135, 139,
143, 147, 212, 375, 675
Z
Zagorodnov, I.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .403
Zaitsev, N.I. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
Zaltsman, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Zamanipour, Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
Zelenika, S.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
Zen, Z. . . . . . . . . . . . . . . . . . . . . . . . . . 443, 447, 450, 454
Zhang, B. C. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Zhang, S. . . . . . . . . . . . . . . . . . . 222, 229, 363, 558, 562
Zhang, Zhang Pengfei. . . . . . . . . . . . . . . . . . . . . . . . . 487
Zhang, Zhang Shancai. . . . . . . . . . . . . . . . . 64, 487, 494
Zhao, K. . . . . . . . . . . . . . . . . . . . . . . . 478, 481, 484, 671
Zhao, Y. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355, 570
Zhao, Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
Zheng, J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
Zheng, Sh.X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Zholents, A.A. . . . . . . . . . . . . . . . . . . . . . . . . . . . 582, 637
Zhou, Q. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
Zhou, X. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
Zhu, Z. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
Zhuang, J.J. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474, 478
Zobov, M. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
Zolfaghari, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
Zucchini, A. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163, 407
Zwart, T. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339, 542

Index of Paper ID’s

Proceedings of the 2004 FEL Conference – Trieste, Italy723. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197
Index of Paper ID’s MOPOS60MOPOS63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201
FRAIS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 648
FRAOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 657
FRAOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 661
FRBIS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
FRBIS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216
MOAIS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
MOAIS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
MOBIS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
MOBOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
MOBOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
MOCOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
MOCOS05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
MOPOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
MOPOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
MOPOS05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
MOPOS06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
MOPOS07 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
MOPOS08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
MOPOS09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
MOPOS10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
MOPOS11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
MOPOS12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
MOPOS14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
MOPOS15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
MOPOS16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
MOPOS17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
MOPOS18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
MOPOS21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
MOPOS22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
MOPOS23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
MOPOS25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159
MOPOS26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
MOPOS27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163
MOPOS29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
MOPOS30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
MOPOS32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
MOPOS33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
MOPOS34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
MOPOS36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
MOPOS37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179
MOPOS38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
MOPOS39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
MOPOS40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
MOPOS41 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
MOPOS42 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
MOPOS47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
MOPOS49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
MOPOS51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
MOPOS57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
MOPOS59 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193

MOPOS64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
MOPOS65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
MOPOS66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
MOPOS67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 209
MOPOS69 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
THBOC02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347
THBOC03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351
THBOC04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
THBOC05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 359
THBOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665
THBOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 667
THBOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 671
THCIS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 654
THCOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
THPOS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 602
THPOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 606
THPOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 610
THPOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293
THPOS05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 679
THPOS06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297
THPOS08 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681
THPOS09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 243
THPOS13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614
THPOS14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685
THPOS15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 247
THPOS16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 618
THPOS17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251
THPOS18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 689
THPOS19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 692
THPOS21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301
THPOS22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 255
THPOS23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304
THPOS25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695
THPOS26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699
THPOS27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 258
THPOS28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 307
THPOS29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 311
THPOS30 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 703
THPOS33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314
THPOS35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
THPOS36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
THPOS37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318
THPOS38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
THPOS45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 629
THPOS46 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266
THPOS47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 270
THPOS48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 633
THPOS51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
THPOS53 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 640
THPOS54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322
THPOS56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

724

Proceedings of the 2004 FEL Conference – Trieste, Italy

THPOS57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644
THPOS58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706
THPOS59 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
THPOS60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 278
THPOS62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
THPOS65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 375
THPOS66 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
TUAOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
TUAOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
TUBIS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
TUBOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363
TUBOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 222
TUBOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367
TUBOS05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371
TUCOS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226
TUCOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
TUCOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233
TUCOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
TUCOS05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
TUPOS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 379
TUPOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 381
TUPOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 385
TUPOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 389
TUPOS06 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392
TUPOS07 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 395
TUPOS09 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399
TUPOS10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403
TUPOS11 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
TUPOS12 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 411
TUPOS13 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
TUPOS14 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 419
TUPOS15 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 423
TUPOS17 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 427
TUPOS18 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 431
TUPOS19 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435
TUPOS20 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 439
TUPOS21 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443
TUPOS22 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447
TUPOS23 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 450
TUPOS24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 454
TUPOS25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 458
TUPOS26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 462
TUPOS27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466
TUPOS29 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470
TUPOS32 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474
TUPOS33 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 478
TUPOS34 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481
TUPOS35 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
TUPOS36 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
TUPOS37 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
TUPOS38 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494
TUPOS39 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 498
TUPOS40 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501

TUPOS43 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504
TUPOS45 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508
TUPOS47 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 511
TUPOS48 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515
TUPOS49 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
TUPOS50 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523
TUPOS51 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 527
TUPOS52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 530
TUPOS54 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534
TUPOS56 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538
TUPOS57 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542
TUPOS58 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546
TUPOS59 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 550
TUPOS60 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554
TUPOS61 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 558
TUPOS62 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562
TUPOS63 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 566
TUPOS64 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 570
TUPOS65 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 574
TUPOS67 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578
WEAIS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 282
WEAOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285
WEAOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
WEBOS01 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582
WEBOS02 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586
WEBOS03 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 590
WEBOS04 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594
WEBOS05 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 598

Proceedings of the 2004 FEL Conference – Trieste, Italy

Producing the Conference Proceedings
The Proceedings of the 2004 edition of the FEL Conference have been produced thanks to the long experience and deep knowledge matured among
the Joint Accelerators Conference Website’s “working group” (JACoW – see
http://www.JACoW.org).
The JACoW collaboration has recently developed the SPMS, a new Open
Source tool that aims to automate as many tasks a conference like this requires
to perform. This includes full abstracts treatment (collecting, accepting, editing, etc.), generic conference management (sessions, speakers, posters, etc.)
and production of final proceedings.
This SPMS, achronym that means “Scientific Programme Management System” has been adopted by and customised for FEL 2004: being founded on a
back-end database with a web interface, it has recorded all the proposed abstracts (pure text plus simple formulæ), helped put them into sessions, produced the Abstract Booklet, kept all the information about the scientific contributions and produced the proceedings.
Every single contribution has been submitted to the SPMS in Adobe PostScript(PS) format and, for most of the cases, in ‘source’ format (mostly Microsoft
Word files and LATEX): a well-motivated and extremely effective group of
persons from Sincrotrone Trieste, during and after the conference, has thenchecked the files for fonts/graphics (un-)readability and adherence to proposed conference templates, hence transforming all the contributions in Adobe
Portable Document Format (PDF) files.
With all the metadata (titles, list of authors and related institutes, etc.) in a
database and all the accepted PDF files on a server, going to the production of
the Proceedings was very easy. A novel package in the SPMS, developed forthis conference, permitted to generate a LATEX source file that, when compiled,merged all the contribution files into one and in the proper order, inserted running page numbers, inserted different headings and footers for different pages,
created the Table Of Contents and various other indexes. As a result, one PDF
file has been produced to print this book, together with several HTML and PDF
files to publish on the web and on the CD.
Commercial software was only needed to create the PDF’s (Acrobat Distiller), touch up the PDF’s (Adobe Acrobat and Enfocus PitStop – see
http://www.enfocus.com), seldom to change the source files (if generated by Microsoft Word). All the other steps have been performed using Open Source tools: LATEX, pdfTEX with the pdfpages, fancyhdr
and multind packages, vim for editing (http://www.vim.org), Perlscripts for a couple of global changes in PDF files, GNU/Linux for the
Operating System. Even if the SPMS is currently based on Oracle,
its code has been released under the GNU General Public License (seehttp://www.gnu.org/licenses/licenses.html).
I hope that this information will be of use to future conference organisers.
Ivan Andrian, Nov. 2004
<ivan.andrian@elettra.trieste.it>

Trademarks or service marks mentioned here have been capitalised and belong to their respective
owners. Neither JACoW nor Sincrotrone Trieste S.c.p.a. will claim any rights on them.

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