FEL 2007 – Novosibirsk, Russia

WelcomeDear colleagues,
I am happy to open the 29th International Free Electron Laser Conference here, in
Budker Institute of Nuclear Physics.
During 30 years from the first operation of FEL this activity has grown to a big
international branch of accelerator physics and technology. Looking at our conference
programme one can see a lot of very prospective directions of the FEL development. X-ray
FEL projects are close to the final stage, and the German soft x-ray facility has realized firstuser experiments. Terahertz radiation sources allow new research approaches. Numerous
technology achievements provide good prospects for further increase of FEL power andimprovement of radiation quality. Due to good theoretical understanding of FEL physics,
several novel schemes are under examination.
Our Institute has a long history of participation in the FEL and synchrotron radiation
activity, but it is the first time when we hold the International FEL conference. It is a great
pleasure for us to be the hosts of this extraordinary meeting of world best experts. I wish us agood conference with fruitful exchange of ideas and discussions.
Gennady N. Kulipanovii

PrefaceFEL 2007 – Novosibirsk, Russia

Contents
Prefacei
Foreword . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iii
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
v
Committees . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
Pictures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
MOBAU01 – Self-Force-Derived Mass of an Electron Bunch . . . . . . . . . . . . . . . . . . . . . . . . .
1
MOBAU02 – Technology Challenges Towards Short-Wavelength FELs . . . . . . . . . . . . . . . . . . .
9
MOPPH003 – VOLC: Volume Free Electron Laser Simulation Code . . . . . . . . . . . . . . . . . . . . .
14
MOPPH004 – Measurement and Analysis of CSR effects at FLASH . . . . . . . . . . . . . . . . . . . . .
18
MOPPH005 – Improvements of the Tracking Code Astra for the Simulation of Dark Current Losses in the
FLASH Linac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
22
MOPPH006 – Longitudinal Wake Field for an Electron Beam Accelerated through a Ultra-High Field Gradient 26
MOPPH007 – Theory of Nonlinear Harmonic Generation in Free-Electron Lasers with Helical Wigglers .
30
MOPPH009 – Undulator Radiation in a Waveguide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
34
MOPPH010 – Three-Dimensional Analysis of the Surface Mode Supported by a Reflection Grating . . . .
38
MOPPH011 – Comparison Between Kinetic and Fluid Description of Plasma-Loladed Free-Electron Laser
42
MOPPH012 – Conservation Laws in Quasilinear Theory of Raman Free-Electron Laser . . . . . . . . . .
46
MOPPH015 – Limit for Harmonic Conversion in a Single Cascade of Coherent Harmonic Generation . . .
50
MOPPH017 – 1D Linear Intensity Spiking Evolution in a Single Shot of a SASE FEL . . . . . . . . . . . .
54
MOPPH019 – Optimized Designs for CAEP IR Free-electron Laser . . . . . . . . . . . . . . . . . . . . .
58
MOPPH020 – FEL with Orotron Type Feedback . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
61
MOPPH022 – A Description of Guided FEL Radiation Using Dielectric Waveguide Eigenmodes . . . . . .
65
MOPPH023 – Enhancing FEL Power with Phase Shifters . . . . . . . . . . . . . . . . . . . . . . . . . .
69
MOPPH025 – Three-dimensional Theory of the Cerenkov Free-Electron Laser . . . . . . . . . . . . . . .
73
MOPPH026 – Three-Dimensional Theory of the Smith-Purcell Free-Electron Laser . . . . . . . . . . . .
77
MOPPH028 – On NMR probing of the kinetics of a free-electron laser-induced chemical exchange . . . .
81
MOPPH030 – Terahertz Imaging and Radioscopy with 160x120 Microbolometer 90 fps Camera . . . . .
83
MOPPH031 – Spectroscopy and Spectrally Resolved Radioscopy of Biological Substances Using Terahertz
Free Electron Laser Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
86
MOPPH032 – Development of Metal Mesh Based Quasi-optical Selective Components and Their Application in High-power Experiments at Novosibirsk Terahertz FEL . . . . . . . . . . . . . . . . . .
89
MOPPH033 – Diffraction Optical Elements and Optical Systems with a High Power Monochromatic Terahertz Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
93
MOPPH034 – Diagnostics of an Electron Beam using Coherent Cherenkov Radiation . . . . . . . . . . .
95
MOPPH036 – First Experiences with the FIR-FEL at ELBE . . . . . . . . . . . . . . . . . . . . . . . . .
97
MOPPH040 – A Study of Detection Schemes in Electro-Optic Sampling Technique . . . . . . . . . . . . 101
MOPPH041 – Comparative Study of Electro-Optic Effect between Simulation and Measurement . . . . . 104
MOPPH042 – Losses in Optical Resonator of Novosibirsk Terahertz Free Electron Laser: Theory andExperiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
MOPPH043 – Control and Diagnostic System of Novosibirsk FEL Radiation . . . . . . . . . . . . . . . . 111
MOPPH046 – Operation of Near-infrared FEL at Nihon University . . . . . . . . . . . . . . . . . . . . . . 114
MOPPH048 – ARC-EN-CIEL Project Electron Beam Dynamics . . . . . . . . . . . . . . . . . . . . . . . 118
MOPPH050 – Status of the Undulator System of the Seeded HGHG-FEL Test Bench at MAX-lab . . . . . 122
MOPPH051 – Nonlinear Harmonic Generation in the BESSY Soft X-Ray FEL . . . . . . . . . . . . . . . 126
MOPPH052 – Output Performance of the STARS HGHG Demonstrator at BESSY . . . . . . . . . . . . . 130
MOPPH054 – Small-Aperture Vacuum-Chamber Design for STARS . . . . . . . . . . . . . . . . . . . . . 134
MOPPH055 – Measurements of the Projected Normalized Transverse Emittance at PITZ . . . . . . . . . 138
MOPPH058 – Status of the SPARX Project . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142
MOPPH060 – The Drive Laser System for CFEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
MOPPH061 – Design of the PAL Test FEL Machine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149
MOPPH062 – Features of the PAL-XFEL Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
MOPPH063 – Potentialities of ELMI Device for Submillimeter Generation by Stimulated Intercavity Scattering in Planar FEM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
MOPPH064 – A Project of SC ERL at KAERI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160
MOPPH068 – The NCAS-FEL: an FEL Oscillator with High Slippage . . . . . . . . . . . . . . . . . . . . 163
Contentsv

FEL 2007 – Novosibirsk, Russia
MOPPH069 – 3D Modelling of the ERLP IR-FEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167
MOPPH072 – The IR-Beam Transport System from the ELBE-FELs to the User Labs . . . . . . . . . . . 171
MOPPH073 – Thermal and Non-thermal Laser Cutting Utilizing Advanced Industrial Lasers and ERL-FELs 175
MOPPH074 – Preliminary Design of the Proposed IR-FEL in India . . . . . . . . . . . . . . . . . . . . . 179
MOCAU01 – Short Wavelength Regenerative Amplifier FELs . . . . . . . . . . . . . . . . . . . . . . . . 182
MOCAU02 – Numerical Solution of the FEL Correlation Function Equation . . . . . . . . . . . . . . . . . 188
MOCAU03 – Numerical Propagation Simulations and Coherence Analysis of SASE Wavefronts . . . . . 192
MOCAU04 – Impact of Longitudinal Space-charge Wake from FEL Undulators on Current-enhanced SASE
Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 196
MOCAU05 – Space Charge Effect in an Accelerated Beam . . . . . . . . . . . . . . . . . . . . . . . . . 200
TUAAU02 – Electron Outcoupling Scheme for the Novosibirsk FEL . . . . . . . . . . . . . . . . . . . . . 204
TUAAU05 – Modelling Mirror Aberrations in FEL Oscillators Using OPC . . . . . . . . . . . . . . . . . . . 207
TUBAU01 – FLASH Upgraded - Preparing for the European XFEL . . . . . . . . . . . . . . . . . . . . . 211
TUBAU02 – Status of SCSS & X-ray FEL Project in Japan . . . . . . . . . . . . . . . . . . . . . . . . . . 216
TUBAU03 – STARS – an FEL to Demonstrate Cascaded HGHG . . . . . . . . . . . . . . . . . . . . . . 220
TUBAU04 – Towards a Low Emittance X-ray FEL at PSI . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
TUPPH002 – High Order Mode Analyses for the Rossendorf SRF Gun . . . . . . . . . . . . . . . . . . . 228
TUPPH006 – FEL Potential of the High Current ERLs at BNL . . . . . . . . . . . . . . . . . . . . . . . . 232
TUPPH008 – Beam Dynamics Studies on the UVSOR-II Free Electron Laser . . . . . . . . . . . . . . . . 236
TUPPH011 – Analytical Studies of Transverse Coherence Properties of X-ray FELs . . . . . . . . . . . . 240
TUPPH012 – Compact X-ray Free-Electron-Laser Based on an Optical Undulator . . . . . . . . . . . . . 244
TUPPH013 – Production of Ultra-short Radiation Pulses in Frequency Doubler . . . . . . . . . . . . . . . 248
TUPPH014 – Generation of X-ray FEL Light Using Laser Wakefield Accelerated Electron Beams . . . . . 252
TUPPH015 – Diffraction Effects in the Coherent Transition Radiation Bunch Length Diagnostics . . . . . 256
TUPPH019 – Simulations for the LCLS Injector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 260
TUPPH020 – Quiet Start Method in small signal HGHG FEL Simulation . . . . . . . . . . . . . . . . . . 264
TUCAU01 – FELs and High-energy Electron Cooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 268
WEAAU01 – Commissioning Results of the SLAC LCLS Gun . . . . . . . . . . . . . . . . . . . . . . . . 276
WEAAU02 – Direct Measurement of Phase Space Evolution in the SPARC High Brightness Photoinjector 284
WEAAU04 – Superconducting Photoinjector for High-Power Free Electron Lasers . . . . . . . . . . . . . 290
WEAAU05 – A Compact Electron Spectrometer for an LWFA . . . . . . . . . . . . . . . . . . . . . . . . 294
WEBAU01 – Adaptive 3-D UV-laser Pulse Shaping System to Minimize Emittance for Photocathode RF
Gun . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
WEBAU03 – Performance Tests of the Photon Monochromator for Self-seeding at FLASH . . . . . . . . . 306
WEBAU04 – Single-Shot Longitudinal Bunch Profile Measurements at FLASH Using Electro-Optic Detection: Experiment, Simulation, and Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . 310
WEBAU05 – Magnetic Measurements, Tuning and Fiducialization of LCLS Undulators at SLAC . . . . . . 314
WEPPH003 – Magnetic Measurements of the FLASH Infrared Undulator . . . . . . . . . . . . . . . . . . 318
WEPPH004 – Numerical Calculations of the Radiation Emitted from the FLASH Infrared Undulator . . . . 322
WEPPH005 – Magnet Sorting for the European XFEL Hybrid Undulator - Comparing Study . . . . . . . . 326
WEPPH006 – Study of Undulator Deformation Tolerance for the European XFEL . . . . . . . . . . . . . 330
WEPPH007 – MCP-based Photon Detector with Extended Wavelength Range for FLASH . . . . . . . . . 334
WEPPH008 – Measurements of Projected Emittances at FLASH . . . . . . . . . . . . . . . . . . . . . . 338
WEPPH009 – Recent Measurements of the Longitudinal Phase Space at PITZ . . . . . . . . . . . . . . 342
WEPPH011 – Photocathode Laser Pulse Diagnostics at PITZ . . . . . . . . . . . . . . . . . . . . . . . . 346
WEPPH012 – Investigations on the Thermal Emittance of Cs2Te Photocathodes at PITZ . . . . . . . . . 350
WEPPH013 – Status and Perspectives of the PITZ Facility Upgrade . . . . . . . . . . . . . . . . . . . . . 354
WEPPH014 – Performance of the FERMI FEL Photoinjector Laser . . . . . . . . . . . . . . . . . . . . . 358
WEPPH015 – Modeling of a Laser Heater for Fermi@Elettra . . . . . . . . . . . . . . . . . . . . . . . . . 362
WEPPH017 – UV Performances of Pulsed Laser Deposition Grown Mg Photocathodes . . . . . . . . . . 366
WEPPH018 – A High Brightness X-band Split Photoinjector Concept and Related Technological Challenges 370
WEPPH019 – Determination of the Wakefield Budget for the FERMI FEL Undulator System . . . . . . . 374
WEPPH021 – Wide Band Seeding and Wavelength Compression . . . . . . . . . . . . . . . . . . . . . . 378
WEPPH022 – Feasibility Test of Shottoky Effect-Gated Photocathode RF Gun . . . . . . . . . . . . . . . 382
WEPPH023 – Beam Properties from S-band Energy Compensated Thermionic RF Gun and Linac for KUFEL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386

vi

Contents

FEL 2007 – Novosibirsk, Russia
WEPPH024 – Numerical Evaluation of Oscillator FEL with Multi-Bunch Photo-Cathode RF-gun in Kyoto
University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 390
WEPPH025 – Progress in the FEL Lasing in Kyoto University . . . . . . . . . . . . . . . . . . . . . . . . 394
WEPPH026 – Design Study of the Triode-Type Thermionic RF Gun . . . . . . . . . . . . . . . . . . . . . 398
WEPPH027 – Beam Diagnostics for the First Lasing of the KU-FEL . . . . . . . . . . . . . . . . . . . . . 402
WEPPH028 – Development of a Compact Cherenkov Free-Electron Laser Operating Terahertz Wave Range 406
WEPPH029 – Development of the Longitudinal Phase-Space Monitor for the L-band Electron Linac at ISIR,
Osaka University . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 409
WEPPH030 – Development of a Precise Timing System for the ISIR L-Band Linac at Osaka University . . 413
WEPPH031 – Development of A Low Emittance DC Gun for Smith-Purcell BWO FEL . . . . . . . . . . . 417
WEPPH032 – Electron-Linac Based Femtosecond THz Radiation Source at PAL . . . . . . . . . . . . . . 421
WEPPH033 – Stabilization of a Klystron Voltage at 100 PPM Level for PAL XFEL . . . . . . . . . . . . . 424
WEPPH034 – Fourier and Non-Fourier Models for Photoemission . . . . . . . . . . . . . . . . . . . . . . 428
WEPPH037 – Coherence of Space Charge Vibrarion and Parameters of Electron Guns . . . . . . . . . . 432
WEPPH038 – Low Power Consuming Hybrid Bending Magnet at the XFEL Beam Dump . . . . . . . . . 435
WEPPH039 – The Optical Replica Synthesizer in FLASH . . . . . . . . . . . . . . . . . . . . . . . . . . 438
WEPPH041 – 7th Harmonic Buncher Experiment at Neptune Laboratory . . . . . . . . . . . . . . . . . . 441
WEPPH043 – The UCSB MM-FEL Injection Locking System . . . . . . . . . . . . . . . . . . . . . . . . 445
WEPPH046 – A Superconducting RF Photo-Injector for Operation at the ELBE Linear Accelerator . . . . 449
WEPPH047 – Electro-Optic Spectral Decoding for Single-Shot Characterisation of the Coherent Transition
Radiation Time Structure at FLASH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453
WEPPH048 – XPS Studies of Cs2Te Photocathodes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457
WEPPH049 – Test of a Wiresanner in the Diagnostic Section of PITZ . . . . . . . . . . . . . . . . . . . . 461
WEPPH051 – Development of a Beam Current Transformer for the X-FEL Project in SPring-8 . . . . . . 464
WEPPH052 – In-situ Undulator Field Measurement with the SAFALI System . . . . . . . . . . . . . . . . 468
WEPPH053 – Non-Destructive Single-Shot 3-D Electron Bunch Monitor with Femtosecond-Timing AllOptical System for Pump & Probe Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . 472
WEPPH054 – Coherent THz Light Source Using Very Short Electron Bunches from a Thermionic RF Gun 476
WEPPH055 – Experimental Investigation of Smith-Purcell Radiation From Gratings of Different Profile . . 480
WEPPH056 – Gain and Coherence Enhancement for SASE FEL using Laser pre-modulated Electrons . 484
WEPPH058 – Modeling a RF Linac Based Short Pulse Waveguide FEL . . . . . . . . . . . . . . . . . . 487
THAAU01 – Experience and Plans of the JLAB FEL Facility as a User Facility . . . . . . . . . . . . . . . 491
THAAU03 – Experimental Study of Volume Free Electron Laser Using a "Grid" Photonic Crystal with Variable Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496
THBAU01 – Research Highlights from FLASH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499
THBAU04 – Millimeter Waves Sensing Behind Walls - Feasibility Study with FEL Radiation . . . . . . . . 501
FRAAU01 – Source of Radiation on ARC-EN-CIEL Proposal . . . . . . . . . . . . . . . . . . . . . . . . . 505
FRAAU02 – Status of the FEL Test Facility at MAX-lab . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513
FRAAU03 – Compact Ring FEL as a Source of High Power Infrared Radiation . . . . . . . . . . . . . . . 517
FRAAU04 – Re-Commissioning of the Far-Infrared Free Electron Laser for Stable and High Power Operation after the Renewal of the L-Band Linac at ISIR, Osaka University . . . . . . . . . . . . . . 521

Contentsvii

FEL 2007 – Novosibirsk, Russia

Conference Committees
Conference Chair
G.N. Kulipanov (BINP)International Executive Committee
I. Ben-Zvi (BNL)
W.B. Colson (NPGS)
M.E. Couprie (CEA/DSM)
J. Galayda (SLAC)
A. Gover (Tel Aviv University)
H. Hama (Tohoku University)
E. Jaeschke (BESSY)
K.-J. Kim (ANL & University of Chicago)
V. N. Litvinenko (BNL & Duke Uni.)
G. R. Neil (TJNAF)

C. Pellegrini (UCLA)
M.W. Poole (ASTEC)
A. Renieri (ENEA)
C.W. Roberson (ONR)
J. Rossbach (DESY & Hamburg Uni.)
T. Smith (Stanford University)
A.F.G. van der Meer (FOM)
N.A. Vinokurov (BINP)
R. Walker (DLS)

Scientific Programme Committee Chair
N.A. Vinokurov (BINP)
Scientific Programme Committee
R. Bakker (SLS)
C. Bochetta (Elettra)
M.E. Couprie (Soleil)
J. Dai (IHEP-Bejing)
J. Feldhaus (DESY)
M. Ferrario (INFN-LNF)
L. Giannessi (ENEA)
W. Graves (MIT)R. Hajima (JAEA)
J. Hastings (SLAC)
I. Lindau (Stanford University)
V. Litvinenko (BNL)
A. Lumpkin (APS)
B. McNeil (Strathclyde)
L. Merminga (TJNAF)
A. Meseck (BESSY)

P. Michel (FZR)
E. J. Minehara (JAEA)
J. S. Oh (PAL)
J. Pflüger (DESY)
M. Poole (ASTeC)
A. Renieri (ENEA)
J. Rossbach (DESY & Hamburg Univ.)
J. Schmerge (SLAC)
L. Serafini (INFN)
T. Smith (Stanford University)
F. Stephan (DESY)
T. Tanaka (RIKEN)
S. Werin (MAXLAB)
Y. Wu (Duke University)
L. H. Yu (BNL)
A. Zholents (LBL)

Local Organizing Committee Chair
M.V. Kuzin (BINP)
Proceedings Editors
B.Goldenberg (BINP)
V.Eliseev (BINP)
PrefaceCommittees

A.Zhirkova (BINP)
P.Budz (BESSY)ix

FEL 2007 – Novosibirsk, Russia

Conference Pictures not foundx

Preface
PicturesProceedings of FEL 2007, Novosibirsk, Russia

MOBAU01

SELF-FORCE-DERIVED MASS OF AN ELECTRON BUNCH
E. Saldin, DESY, Hamburg, Germany
Abstract
We study an electron bunch together with its self-fields
from the viewpoint of basic dynamical quantities. This
leads to a methodological discussion about the definition ofenergy and momentum for fully electromagnetic systems
and about the relation between covariance of the energymomentum pair and stability. We show here that, in thecase of unstable systems, there is no mean to define, in aphysically meaningful way, a total energy-momentum fourvector: covariance of the energy-momentum pair follows
from the stability of the system and viceversa, as originallypointed out by Henry Poincaré. Another version of this paper by G. Geloni and the author can be found in [1].

It is worth to mention here that the factor 4/3 in Eq. (2)and the term proportional to 1/3β 2 in Eq. (1) depend on
the choice of spherical symmetry made on the charge distribution: had we chosen, for instance, an infinitely longline distribution in the direction of v , we would have found

Ee = γU  (1 + 1/3β 2 )(1)Pe = 4/3γvU  /c2 ,

(2)

and

where the index e indicates the electromagnetic nature of
the energy Ee and momentum Pe , γ is the usual Lorentz
factor, β is the velocity v/c (normalized to the speed oflight in vacuum c), and U  indicates the electromagnetic
energy in the electron rest frame [5],  2 dV  ,U = 0 /2 E
(3)where 0 is the free space permittivity. U  is purely an electrostatic quantity (in this paper the prime will always indi
cate quantities calculated in the rest frame; therefore Eand dV are, respectively, the electric field and the volume
element in the rest frame of the system).

(4)Pe2 = 2γvU  /c2 ,

(5)

and

while, in the case of a line charge oriented perpendicularly
to the direction of v ,INTRODUCTION
Nearly one hundred years have passed since Abrahamand Lorentz calculated their famous expressions for the energy and momentum of a purely electromagnetic, spherically symmetrical distribution of charges [2], [3]. This distribution constitutes an attempt to build a classical modelof the electron: according to Lorentz’s initial idea, mass,energy and momentum of the electron could, indeed, be ofcompletely elecromagnetic nature.
Nevertheless, the energy (divided by the speed of lightin vacuum, as we will understand through this paper) andmomentum of such an electromagnetic electron do not constitute a four-vector. In fact (as Abraham [4] pointed out
already in 1904 probably, at that time, without a clear understanding of what a four-vector is), in a frame moving
with velocity v with respect to the system rest frame, wehave

Ee2 = γU  (1 + β 2 )

Ee3 = γU 

(6)Pe3 = γv U  /c2 ,

(7)

and

which only incidentally, due to the particular choice of the
distribution, behaves as a four-vector.
Henry Poincaré solved the problem of the lack of covariance shown in Eq. (1) and Eq. (2) by introducing, in the electron model, energies and momenta of nonelectromagnetic nature [6]. These are actually due to nonelectomagnetic interactions which keep the electron together. By doing so he strongly related the covariance ofenergy and momentum with the stability of the system:
the electomagnetic energy-momentum pair alone is not afour-vector, but the total energy-momenum pair, accounting for the non-electromagnetic interaction, is a regularfour-quantity.
In 1922, Enrico Fermi developed an original, early relativistic approach to the 4/3 problem [7]; about forty years
later a redefinition of the energy-momentum pair related toFermi’s work was proposed by Rohrlich [8], which leaves
untouched the total energy-momentum vector, but splits
it into electromagnetic and non-electromagnetic contribution in such a way that covariance is granted for both theelectromagnetic and the non-electromagnetic part of theenergy-momentum pair.
It is possible to show [9], [10] that the treatments by
Poincaré and Rohrlich are not in contradiction.
Nevertheless, the approach by Rohrlich [8] was sometimes taken (see e.g. [11]) as the proof that stability andcovariance are unrelated matters since, upon redefinition,
the electromagnetic part alone is a four-vector.
We will show here, that such a conclusion is incorrect.
The stability of the system is related to the covariance of

FEL Prize and New Lasing

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Proceedings of FEL 2007, Novosibirsk, Russia

the total energy-momentum vector, according to the original work by Poincaré: the redefinition procedure mentioned above is indeed acceptable only in the case one isinterested in the total energy-momentum vector of a stable system (i.e. a system whose constituents are and stayat rest in a particularly chosen frame), and not in the separate electromagnetic and non-electromagnetic part. Onlyin that case the arbitrariness included in the recombinationof these two contributions does not affect the equation of
motion for the system (which deals, in fact, with the totalenergy-momentum vector).
Some time ago, we were addressing the problem of describing the transverse self-fields originating within an ultrarelativistic electron bunch moving in a fixed trajectory[12].
This is a particularly relevant problem in modern particle
accelerator physics, in view of the need for very high-peakcurrent, low emittance beams to be used, for example, in
self-amplified spontaneous emission (SASE)-free-electron
lasers operating in the x-ray regime (see for example [13],[14]): in fact, the good quality of the beam may be spoiled
by self-interaction occurring within the bunch.
Besides practical relevance (which stresses how, after
one hundred years, pure academical problems become relevant also to applied physics), an electron bunch is also avery good example of an unstable system subject to purely
electromagnetic interactions. For such a system, the totalenergy and the total momentum in any frame, are just ofelectrodynamical nature. We will show that (according toour previous statement about the relation between stability
and covariance) there is no way, in this case, to define thetotal energy-momentum pair in a covariant way. In fact, incontrast to what happens for stable systems, there is no way
to describe the evolution of an unstable system without theknowledge of the (electromagnetic) field theory governing
the (self-)interactions between its constituents.

A PARADOX AND ITS SOLUTION
Let us consider a short electron bunch moving, in a given
laboratory frame, in a circular orbit. We can simplify thedescription of this system accounting only for two electrons
which will represent the head and the tail of our bunch.
Imagine that the two particles are moving, initially withthe same Lorentz factor γ  1, in a circular orbit of radiusR, and separated by a (curvilinear) distance Δs  R/γ 3 .
In this situation the two electrons are near enough to beconsidered travelling with the same velocity vector: indeed it can be shown [15], that they radiate as a single
particle of charge 2e (e being the electron charge) up to
frequencies much above the synchrotron radiation criticalfrequency (note that, from a quantitative viewpoint, theexpression ”much above” is trivially connected to ”howmuch” Δs  R/γ 3 ). The requirements specified before
consist, from a geometrical viewpoint, in assuming that, atthe beginning of the evolution, the two particles world-lines
are very close: actually, considering our resolution in space
FEL Prize and New Lasing2

equal to R/γ 3 , they initially coincide.
This assumption justifies the presence of an inertial
frame in which both particles are, with good approximation, at rest during the initial part of their evolution. We
will refer to it simply as the rest frame. A quantitative definition of the initial part of the evolution may be given whena choice is made about close to zero are the velocities ofthe particles in the rest frame. Note that the existence ofthe rest frame is central for our study because, referring toit, one can easily analyze the energy and momentum of thesystem constituted by the two particles together with theirelectromagnetic fields.
By means of a Lorentz transformation, then, we can recover the same quantities in the laboratory frame.
Starting with the study in the rest frame we will refer,separately, to mechanical and electromagnetic quantities.
Obviously, in the rest frame, the mechanical momentumof the system, P  ne , is zero, and the mechanical energy,, is just equal to 2mc2 , where m is the electron rest
Ene
mass.
The study of the electromagnetic contributions to energy
and momentum is also trivial. Since the electrons are at rest
they produce electric field only. Therefore the Poynting
vector vanishes and P  e = 0. On the other hand, E e isgiven, simply, by the work U  done against the field to bring
the two particles together (quasistatically) from a situationin which they are separated by an infinite distance.
By doing so, of course, we are neglecting, in both P  e
and Ee , the contributions from the acceleration (self-)fields
generated by the system.
This approximation is justified by the fact that we are
discussing the asymptotic behavior for the two particles
separated by a very small distance: then, as it will be clear
from Eq. (16) and Eq. (25), we may assume that the acceleration field contribution are unimportant, when comparedwith the Coulomb one. In fact acceleration effects saturate
in the asymptotic limit of small distance between the twoparticles [15], while Coulomb ones are singular; once again
it must be clear that we are discussing the asymptotic casefor small distance between the two particles. Therefore wehave:
Ee = U  = e2 /(4π0 γΔs)

(8)P  e = 0.

(9)

and

Summing up the electromagnetic and mechanical contributions one gets the total energy and momentum for thesystem:


Etot
= Ene
+ Ee = 2mc2 + U (10)P  tot = P  ne + P  e = 0.

(11)

and

Proceedings of FEL 2007, Novosibirsk, Russia
As already said one may, now, use a Lorentz transformation in order to calculate these quantities in the laboratory
frame. Again, since we are interested at the beginning of
the evolution, it follows from our assumptions that the twoparticles evolve with the same four-velocity vector. Therefore a direction of motion (which we will designate with z)
is well defined for the system in the laboratory frame andthe Lorentz transformation from the rest frame is, indeed,a simple boost in the −z direction (note that a good definition of the z direction is equivalent to a good definition of
the rest frame). We will represent this boost with a matrix
with components Λ μν with μ, ν = 0...3 (where the third
component corresponds to the z direction):⎛⎞
γ 0 0 βγ
⎜ 0 1 0 0 ⎟⎟Λμν = ⎜
(12)
⎝ 0 0 1 0 ⎠.
βγ 0 0 γ
The use one makes of Λ μν is a critical point in our derivation. If one (erroneously) assumes that energy and momentum constitute a four-vector, then he gets, straightforwardly:(Etot /c, Ptot )μ = Λμν (Etot/c, P  tot )ν

(13)and, therefore,
Etot /c = γ 2mc2 + U  ,(14)Ptot = γ 2m + U  /c2 βc ,

(15)

and

where Ptot is a scalar quantity, since we understand thatPtot is oriented along the z direction.
We can now project the equation of motion, Fsyst =dPtot /dt, onto the transverse direction (perpendicular toz and lying on the orbital plane) thus getting, within our
approximations:e2F⊥syst = 2eBβc +4πε0 RΔsMOBAU016¶ β6¶

5

567)
3

6

ΔV
7

φ

β7

2

Figure 1: Geometry for the two-particle system in thesteady state situation, with the test particle ahead of thesource. Here T is the present position of the test particle, S
is the present position of the source, while S’ indicates theretarded position of the source.

F⊥ 

e2 γ 3Φ(φ̂) ,
4πε0 R2(17)

where Φ is defined byΦ(φ̂) =

2 + φ̂4 /8
φ̂(1 + φ̂2 /4)3

,

(18)

Here φ̂ is the retarded angle φ (which expresses the angular distance between the retarded position of the source thepresent position of the test electron, see Fig. 1, normalized
to the synchrotron radiation formation angle at the criticalfrequency, 1/γ, i.e. φ̂ = γφ. Eq. (18) is completely independent of the parameters of the system.
It is straightforward to study the asymptotic behaviorsof Φ. In order to do so, just remember that the retardation
condition linking Δs and φ is given by (see [12], [15]):
φ
,
2

(19)

Rφ3
.
24

(20)

Δs = Rφ − 2βR sin
or by its approximated form

(16)

As already mentioned in the Introduction (with in mind theapplications in the physics of particle accelerators and theone of SASE-FELs, see [13], [14]) we addressed the description of the transverse self-fields originating within anelectron bunch moving in a circle in [12]. In that paper anapproach has been proposed which involves purely electrodynamical considerations, based on the retarded Greenfunction solution of Maxwell equations.
In particular, in part of [12] we treated the case of two
particles separated by a distance Δs (non necessarily muchsmaller than R/γ 3 ), moving rigidly in a circle (see Fig. 1)of radius R. Our results disagree with Eq. (16).
Let us briefly justify the latter statement. The total transverse force (orthogonal to its velocity and lying on the orbital plane) felt by the head electron and due to the tailelectron source turned out to be (see, again [12]):Δs = (1 − β)Rφ +It is now evident that Φ(Δŝ) → 1/(3Δŝ) when φ̂  1 andΦ(Δŝ) → 1/(Δŝ) when φ̂  1, having introduced thenormalized quantity Δŝ = (γ 3 /R)Δs. This normalization
choice is, again, linked with the fact that the critical synchrotron radiation wavelength, R/γ 3 , is also the minimal
characteristic distance of our system: as we said before,
two particles nearer than such a distance can be considered
as a single one radiating, up to the critical frequency, withcharge 2e (see [12], [15]).
The asymptotic behavior above suggests to study thefunction Φ(Δŝ)Δŝ. We plotted such a function in Fig. 2(and the contribution from the acceleration field alone) forvalues of Δŝ running from 0 to 5.
As it is seen from the figure, the contribution from thevelocity field is not important in the asymptotic limit for

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Proceedings of FEL 2007, Novosibirsk, Russia
S is almost parallel (and equal) to βT
In this situation, βand antiparallel to n̂ (which is the unit vector oriented as
the line connecting the retarded source to the present test
particle): it turns out that the only important contribution
to the transverse force results from the acceleration field
and reads:) )Φ(Δ8)Δ8






F⊥ 










)
Δ8

Figure 2: Plot of Φ(Δŝ)Δŝ (solid line) and comparison with the asymptotic values, 1 and 1/3. The dashedline shows the contribution from the acceleration field,
ΦR (Δŝ)Δŝ, alone.
Δs
βT
^
RSTn

T

S’
S

βS’

R

φ
O

Figure 3: Geometry for the two-particle system in thesteady state situation, with the source particle ahead of thetest one. Here T is the present position of the test particle,
S is the present position of the source, while S’ indicatesthe retarded position of the source.
particles very nearby (our case) or very far away. When, inparticular, Δs  Rγ 3 we can approximate Eq. (17) by
F⊥ 

e2
.
4πε0 RΔs(21)

On the other hand, as regards the force felt by the tailparticle (see Fig. 3), it is easily seen that (see [12], [15]) thetest electron, which now is the tail particle, ”runs against”
the electromagnetic signal emitted by the source (while in
the previous case it just ”runs away” from it). Therefore therelative velocity between the signal and the test electron isequal to (1+β)c (instead of (1−β)c in the other situation).
Hence the retardation condition readsφΔs = Rφ + 2βR sin ,2(22)or, solved for φ in its approximated form,φ
FEL Prize and New Lasing

4Δs.
R(1 + β)

(23)

e2
.
4πε0 RΔs(24)

In the case under study, since Δs  R/γ 3 , the total selfforce acting on the system is given by the sum of Eq. (21)and Eq. (24):F⊥  2e2,
4πε0 RΔs(25)

which is in disagreement of a factor 2 with respect to theself-force term in Eq. (16). In other words, had we erroneously assumed covariance, we would have encountereda paradox. Again, note that we are treating the asymptotic limit of a small distance between the two electrons:in this limit we can neglect the contribution from the acceleration field in the equation of motion Eq. (16). In fact thiscontribution saturates for small distance between the twoparticles (see [15]), while the term missing by comparison
between Eq. (16) and Eq. (25) is singular (and, therefore,
dominating) in the limit when Δs goes to zero.
This situation should not be too much surprising for thereader familiar with the works [2]... [4] which led to Eq.
(1) and (2): the derivation of Eq. (16) is, in fact, performed
under the explicit assumption that energy and momentum
constitute a four-vector.
As we will immediately see, in the case of unstable systems (like the one we deal with), the use of correct transformation laws for the electromagnetic stress tensor solves the
problem but spoils the covariance of the energy-momentum
pair.
The energy and momentum of an electromagnetic system in the laboratory frame is given bydV 
E = T μν Λ0μ Λ0ν
(26)
γ

1
dV 
Pi =
T μν Λiμ Λ0ν
,
(27)
c
γ
where T μν are the components (in the rest frame) of theelectromagnetic stress tensor of the system, which contains
all the information about the (electromagnetic) field theory governing the interactions between the particles. The
process of lowering and raising indexes is governed in theusual way by the metric tensor. Here the latin index i runs
from 1 to 3 and, as already said, the quantities with prime
refer to the rest frame. In our case we will consider the only
important component, i.e. the third (along z).
Note that the integrals in Eq. (26) and Eq. (27) include
both a single-particle term and an interaction term (compare also [10]). Here we are interested in the interaction
term alone: in fact we will treat the (trivial) mechanicalProceedings of FEL 2007, Novosibirsk, Russia
contributions to the energy-momentum pair separately and,once again, we will neglect the acceleration-field contributions. Therefore, in the following, we will understand thatT  refers to the interaction term alone.
Then, since the mechanical energy-momentum pair of asingle particle is a 4-vector, one gets: ν/c, Pne) ,(Ene /c, Pne )μ = Λμν (EneMOBAU01

particles world lines are very close and are roughly characterized by the same Lorentz factor, that is, once again, atthe beginning of the evolution.
Then we can use Eq. (28)... Eq. (32) to get, by summation, the total energy and momentum of the system in thelaboratory frame and in the direction of motion (see also
[5] and [17]):

(28)
2



Etot = γ 2mc + U + β

hence
Ene = 2γmc2

(29)

(30)

while
Ee = β 2 γT 33 dV  + γU  ,Pe = γβU  /c + γβ/cT 33 dV  ,

(31)
(32)

We should note, here (but this is a valid methodologicalremark also as regards the previous, incorrect approach),that the particles are subject to a long-range interaction (theelectromagnetic interaction) and, therefore, a covariant definition of the total energy and momentum is not straightforward even when one is considering the two particles alone,
without including (as we did, instead) the electromagnetic
fields in the system. Therefore, strictly speaking, one may
object that Eq. (28) does not make any sense at all.
Indeed, if the interaction occurred at a single point inspace-time (short-range scattering case), the particle velocities would have been constant, in the view of any inertial
observer, before and after the scattering took place. Then
if two observers related by a Lorentz boost compared their
judgments about the particles velocities, they would havefound that these are linked by a Lorentz transformation,
the same which transforms from one observer to the other.
Nevertheless, this is a particular case. We must remember
that, in general, according to the Theory of Relativity, theconcept of simultaneity depends on the observer. Therefore, when (as in the situation under study) one deals witha long-range interaction, the velocities of the particles, inthe judgment of the two observers above, are not related
by a Lorentz transformation anymore (see [16]): the objection about the correct definition of the mechanical energymomentum vector follows directly from this observation.
A good definition of the energy-momentum vector of thetwo-particle system alone (without their fields!) can, in
fact, be recovered using more subtle geometrical methods
only, like a regular correlated representation of the worldlines (see [16]).
However this objection does not concern us, here, since,as already implicit in the definition of the z direction, we
discuss about that region of space-time in which the twoT 33 dV  ,(33)

T 33 dV  βc .

(34)

and

and
Pne = 2βγmc.

2Ptot = γ 2m + U  /c2 +

1
c2



Note that Eq. (33) and Eq. (34) can be used to obtain Eq.
(1) and Eq. (2), as well as Eq. (4)... Eq. (7): different
distributions of charge give different expressions for theelectromagnetic stress tensor and for the electromagnetic
energy.
In our case of two electrons we already know the explicit
expression for U  . In fact we remind that, as has alreadybeen said, the electromagnetic interaction energy is simply
given by the work done against the field to bring the twoparticles together, quasistatically, from a situation in which
they are separated by an infinite distance:
U 

e2
.
4πε0 γΔs(35)

On the other hand it is easy to calculate T  33 (in the rest
frame, since we need to integrate over V  ). To this purpose we remind that, in the rest frame (and at short distanceγΔs  R/γ 2 , so that the acceleration field contributions
are unimportant), the space-space components of the total(comprehensive of both single particle and interaction part)symmetric energy-momentum tensor read (see [5]):ijTtot= −ε0 (Ei Ej − δij E 2 /2) ,(36)

where, here, i, j = 1.. 3. The discussion above shows that,. It can befor us, the only interesting component is T 33
proven that the interaction part alone is justT 33 dV  = U  .
(37)
Note that Eq. (37) describes also the case of a charged line
distribution oriented in the direction of motion (in the caseof a charged line, of course, the single-particle term is notpresent at all).
The equations for the energy and momentum of the system in the laboratory frame now read:Etot = γ 2mc2 + U  (1 + β 2 )(38)

Ptot = γ 2m + 2U  /c2 βc ,

(39)

and

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Proceedings of FEL 2007, Novosibirsk, Russia

whose electromagnetic parts are the same of Eq. (4) andEq. (5).
From the transverse component of the equation of motion for the system one getsF⊥syst  2eBβc + 2e2
4πε0 RΔs(40)

Eq. (40) is now in perfect agreement with our result in
Eq. (25).
Both the terms on the right hand side of Eq. (40) are centripetal as well as in Eq. (16) (although, of course, Eq. (16)and Eq. (40) are in disagreement as concerns the magnitude of the self-interaction term); the first describes the motion of the system under a magnetic field, while the second
is linked with the presence, in the system, of electromagnetic fields: an extra centripetal (external) force is needed,
if one wants to keep the system moving in a circle of radiusR, compensating for the centrifugal self-field contributions
calculated in [12].

DISCUSSION
In order to reach the agreement between Eq. (40) andEq. (25), one has to give up the covariance of the energymomentum pair of our system, as it is seen directly from
Eq. (38) and Eq. (39).
We can sum up the discussion in the previous Section bysaying that the assumption of covariance for the transformation of the energy-momentum pair of an unstable system leads to a paradox. Such a paradox can be solved introducing the correct transformation laws for the energymomentum tensor. In this way, it is seen that the energymomentum pair for an unstable system (particles and electromagnetic field) is not a four-vector. We already mentioned in the Introduction that the non-covariant characterof energy and momentum is also present when one discusses some classical problems which involve the relativistic dynamics of a charged particles stable system. Nevertheless, in these cases, covariance can be always restored
by introducing non-electromagnetic stresses which keep
the system together or, equivalently, by redefinition (see[8]) of the energy-momentum pair. In particular we can refer to the 4/3 problem in the classical electron model (asdone above in the Introduction) but also to other problems
like, for example, the explanation of the Trouton-Noble
paradox, which has been treated extensively in literature(see [9], [18].. [21]) all over the last century.
As we already said in the Introduction, there is one majordifference with respect to our case, though: our system, incontrast with the latter ones, is, by nature, unstable; there is
no reference frame such that its components are and stay atrest. This fact leads to a major difference in the treatmentof the total energy and momentum.
In the case of a stable system, the total energy andmomentum of the system (including non-electromagnetic
binding forces) constitute a four-vector, a well-defined geometrical entity.
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6

On the contrary, in the case of an unstable system, thispair of quantities has no geometrical meaning, although it
is possible to give, of course, separate definitions of totalenergy and momentum in the judgment of any observer.
In the situation discussed in the previous Section this isa direct consequence of the fact that we deal with a fully
electrodynamical system and there is no way to introduce,in a straightforward way, an analogue of Poincaré stresses.
As a result we must conclude that stability of the systemand covariance of the energy-momentum pair are bound together.
Let us discuss the latter statements in detail, starting witha review of well-known arguments for stable systems.
Stable systems are characterized by a zero (total self) four-force density. When the four-force density can bederived from an energy-momentum tensor T μν , the latter
property is equivalent to:T μν;μ = 0 ,(41)which is the requirement for a zero-divergency energymomentum tensor.
However, Eq. (41) refers to the total energy-momentum
tensor, while the electromagnetic part of it is not divergenceless at all (its divergence is, simply, the Lorentz fourforce density).
On the other hand, since stability is characterized by azero total four-force density, non-electromagnetic stresses
must be present (Poincaré stresses), which balance theLorentz four-force density, thus insuring stability for thesystem. Poincaré stresses also insure covariance for theenergy-momentum pair which is, therefore, a well-defined
four-vector: to prove this, one can remember the definitionof the total energy-momentum pair (see [5], [9]):
1Pμ =T μν dσν(42)c σwhere the integration is carried out over any hypersurface
at t = constant (actually σ may be, more generally, any
spacelike surface, see [9]) for any inertial observer.
It can be easily proved (see [9]) that Eq. (42) is independent from the choice of the integration hypesurface. Sucha proof is based on Eq. (41).
The choice of different inertial observers is equivalent tothe choice, on the space-time manifold, of different timelike unit vectors. The different families of hypersurfaces
orthogonal to these vectors represent the physical space ata certain time in the judgement of different observers. Fromthe independence of the definition in Eq. (42) of the choiceof the integration hypersurface follows, therefore, the independence of P μ on the reference frame used to evaluate
it, and this constitutes the proof that P μ is a well-defined
four-vector.
Since P μ is independent from the choice of the integration hypersurface, one is free to choose the one which helps
better in solving problems. Historically, two choices havebeen used in explaining, for example, the Trouton-NobleProceedings of FEL 2007, Novosibirsk, Russia
paradox. The first (see [9]) consists in considering the surface at t = constant for any observer. This leads to theusual expressions for the electromagnetic energy and momentum in a given frame:
1
Ee= Pe0 =
c
2c

 

2
B
0 E +
μ0



2

dV

(43)

and
Pe =

1
μ0 c2

 

 ×B
 dV,
E

(44)

where μ0 is the free space permeability.
While Eq. (43) and Eq. (44) do not constitute a fourvector, one can straightforwardly solve the problem of thelack of covariance by introducing Poincaré stresses.
The second choice consists in selecting t = constant in
the rest frame of the system:Ee1= Pe0 =
c
c



  
 ×B

2
1
E
B
2
 +
0 E
− v ·
dV
2
μ0
μ0 c2
(45)

and
γ
Pe =
c



 

2
v
E×B
B
2
 +
− · 0 E
+
μ0 c
2
μ0

 E
 + (v · B)
 B dV+0 (v · E)
μ0

(46)

In this case it can be easily shown (see [8], [9]) that theelectromagnetic part of the total energy-momentum pair is,
actually, a four-vector. This is, in fact, the same redefinitionof the four-momentum that Rohrlich used to deal with theelectron problem [8]. One can easily check (see [9]) that, in
this case, the non-electromagnetic part of the total energymomentum pair is zero.
All this illustrates the well-known fact that the introduction of Poincaré stresses or the Rohrlich redefinition of energy and momentum are, in fact, equivalent inessence. The choice of the integration hypersurface isa matter of taste for stable systems, since the only important quantity from a geometrical viewpoint is the total energy-momentum four-vector, given by the sum of
the electromagnetic and the non-electromagnetic part; thissum, by definition, is independent from such a choice.
In other words, different choices of the hypersurface justsplit the same, total quantity onto two parts (electromagnetic and non-electromagnetic) in two distinct ways but, as
quoted from [9] : ”The split into electromagnetic and nonelectromagnetic parts is quite arbitrary”.
Our point is that this situation is completely different in
the case of unstable systems, where only electromagnetic
forces are present and Poincaré stresses are not.

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In the case of unstable systems there is no way one candefine the total energy-momentum four-vector. This statement is justified, from a mathematical viewpoint, by thefact that
μν
μν
Ttot
;μ = Te ;μ = 0 ;(47)

in fact, from the previous discussion, we know that divergenceless is an essential ingredient for the independenceof the total energy-momentum pair from the choice of theintegration hypersurface.
Note that Eq. (47) means that there is a non-vanishingfour-force density field over the space-time. In the case discussed in the previous Section we gave a practical exampleof the latter statements.
Of course, also for unstable systems, we may consider
an observer and find out the energy and momentum of thesystem with respect to that observer, but this quantities will
not be covariant, nor we can recover covariance by integrating the energy-momentum tensor over a suitable hypersurface (as done with stable systems), since the electromagnetic energy-momentum pair (which coincides now withthe total energy-momentum pair) would change Eq. (38)and Eq. (39), thus giving an unphysical result on the second term of Eq. (40), when compared with Eq. (25). The
latter discrepancy, to the authors view, is similar to the one
encountered in [10]. In that paper a system composed by
two electron is studied too and a comparison is proposed
between energy-derived mass m u (electrostatic energy divided by c 2 ), momentum derived mass m p (momentum divided by γv, being v the system velocity) and self-forcederived mass ms (self-force divided by γ 3 a, a being thesystem acceleration). The authors of [10] point out that
ms = mp = mu and that the inequality between m p andmu can be solved by redefining, following Rohrlich (see[8]) the energy-momentum pair. Nevertheless, in this case,one is left with a discrepancy between m s and mu . This
fact is perceived by the authors of [10] as an unsolved paradox. Actually the derivation of Eq. (16) (or equivalently,of mu , treated with Rohrlich’s method) is performed underthe explicit assumption that energy and momentum constitute a four-vector which is true only in the case of a stablesystem. As a result, by comparing Eq. (16) and Eq. (25)or, which is the same, m u (treated by Rohrlich’s methodor, equivalently, by introducing Poincaré stresses) with m s ,one is comparing quantities which refer to a stable systemwith quantities which refer to an unstable one, thus givinga paradoxical result.
Consider, as a last example, an unstable system formedby different subsystems initially at rest in a certain frame(as in the case discussed in the previous Section). In general, while dealing with unstable systems, the knowledge ofdynamical quantities for the subsystems cannot bring any
information about the behavior of the system as a whole,unless we have knowledge of the (electromagnetic) field
theory governing the interactions (which make the system
unstable).

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In our example of the previous Section, even if we canmeasure, in a certain frame, the particle velocities when
they are far away from each other (thus no more interacting) and if we know their rest masses, we cannot say anything about energy and momentum of the total system without the knowledge of the stress tensor, and the reason forthat is the presence of a non-zero four-force density field(which we can account for only knowing the stress tensor, i.e. the interaction theory) on that part of the fourdimensional manifold on which we want to have information.
Suppose our system was stable (think about an ideal”rope” responsible for Poincaré stresses, or think, insteadof the case of two electrons, about a nuclear fission process in which electromagnetic fields are, before the fission
event, balanced by the strong interaction). Put ourselvesin the laboratory frame, and imagine that, at a certain moment, for a certain reason (a collision with a neutron, forexample) the Poincaré stresses are not present anymore.
Thus the system becomes unstable, it breaks in two subsystems and the electromagnetic interaction (if you’re thinking
about the nucleus imagine we are talking about a chargedion) takes over. If we wait for enough time the two particles will get far away from each other and we can consider
them no more interacting.
At this point, the kinetic energy of the particles is equal
to the energy previously stored in the electromagnetic field
when the system was stable: thus we are able to get information about the total energy-momentum vector of thestable system even if we do not know anything about thestress tensor and the theory of the interaction between thesubsystems. In fact, the sum of the momenta of the two freeparticles and the sum of their energies will give us, respectively, the energy and the momentum of the stable system,
which form a four-vector again.
The reason is, simply, that there is no four-force density
field in that part of the space time on which we want tohave information: from a general viewpoint we can conclude that the presence of a four-force density, which characterizes unstable systems, spoils without remedy the covariance of the energy-momentum pair. The only way torecover such covariance would be to introduce a balancing
four-force density, i.e. to make the system stable.
In other words, in agreement with Poincaré, from thestability of the system follows the covariance of the system and, vice versa, from covariance follows stability: theenergy-momentum pair of an unstable system does not constitute a four-vector. This conclusion may seem, at firstglance, of academical importance only. It has, indeed, verypractical consequences in modern electron beam physics.
Energy and momentum of an electron bunch are physicallymeasurable quantities and an electron bunch itself is a practical example of an unstable system. Nowadays, technology allows the production of ultra high-brightness, intenseelectron beams (to be used, for example, in self-amplified
spontaneous emission (SASE)-free-electron lasers operating in the x-ray regime). The production of such bunches
FEL Prize and New Lasing

8

is one of the most challenging activities for particle accelerators physicists. The description of these systems
would be completely incorrect without accounting for selfinteractions in the right way. We can conclude that, forexample, simulation codes (as well as analytical considerations: actually, as already reminded, we wrote this paper after studying the self-interactions within an electron bunch)which rely on the covariance of the energy-momentum pairwould give, a priori, wrong results which may be immediately confuted by experimental control. Technological developments often transform, as in this case, purely methodological issues into very practical ones.

REFERENCES[1] G. Geloni and E. Saldin, On energy and momentum of an ultrarelativistic unstable system,DESY 02-201, ISSN 0418-9833, online available at
http://arxiv.org/abs/physics/0211093 .
[2] M. Abraham, Theorie der Elektrizitat, vol II: Elektromagnetische Theorie der Stralung, Teubner, Leipzig, 1905
[3] H.A. Lorentz, The Theory of electrons, Leipzig, Teubner,
1909[4] M. Abraham, Phys. Z., 5, 1904
[5] J. D. Jackson, Classical Electrodynamics, Wiley, N.Y.
[6] H. Poincaré, On the dynamics of the electron, Rendicontidel Circolo Matematico di Palerma 21, 129, 1906
[7] E. Fermi, Il Nuovo Cimento, 25, 159-170, 1923
[8] F. Rohrlich, Classical Charged Particles (Addison-Wesley,
Reading, Mass., 1965), Sec. 6-3[9] S. A. Teukolsky, Am. J. Phys. 64 (9), 1104, 1996
[10] D. J. Griffiths and R. E. Owen, Am. J. Phys. 51 (12), 1120,
1983[11] M. H. Mac Gregor, The enigmatic electron (Kluwer Academic Publishers, Dordrecht /Boston/London, edited by Alwyn van der Merwe), pp. 19-24[12] G. Geloni et al., DESY 02-048, May 2002; also, to be submitted to Phys. Rev. E[13] TESLA Technical Design Report, DESY 2001-011, edited
by F. Richard et al. and http://tesla.desy.de/[14] The LCLS Design Study Group, LCLS Design Study Report, SLAC reports SLAC -R521, Stanford (1998)
and http://www-ssrl.slac.stanford.edu/lcls/CDR[15] E. L. Saldin, E. A. Schneidmiller and M. V. Yurkov, Nucl.
Instr. Methods A 398, 373 (1997)[16] M.A. Trump at al., Classical Relativistic Many-Body Dynamics, Kluwer Academic Publishers, Dordrecht, 1999[17] C. Möller, The theory of relativity, second edition, Chapter
7, Clarendon press, Oxford (1972)[18] M. v. Laue, Ann. Phys. 35, 524, 1911
[19] W. Pauli, The thory of relativity, (Pergamon, New York,1958)[20] A. K. Singal, Am. J. Phys. 61, 428, 1993[21] J. W. Butler, Am. J. Phys. 36, 936, 1968

Proceedings of FEL 2007, Novosibirsk, Russia

MOBAU02TECHNOLOGY CHALLENGES TOWARDS SHORT-WAVELENGTH FELS
J. Rossbach, Universität Hamburg and DESY, 22603 Hamburg, Germany
Abstract
The paper sheds some light on achievements inaccelerator technology that paved the way towards shortwavelength FELs, specifically the FLASH facility at
DESY. Also, a few of the technical challenges are discussed which we are facing in view of future X-ray FELs.

INTRODUCTION
Free-electron lasers (FEL) operating in the SASE mode
(self-amplified spontaneous emission) at wavelengths far
below the visible are now with us since several years, andmore, and even more ambitious, projects are ahead of us.
Although most of the basic theory is known since theearly eighties, it took more than twenty years until FEL
saturation was demonstrated experimentally at
wavelengths below the visible. Even more, it took almost
30 years until a user facility was put in operation in the
VUV regime, although it was clear from the very
beginning, that such a radiation source would open up an
entirely new world of possibilities for experimenters.
The major reason for this long time span was related tothe unprecedented electron beam quality needed toachieve saturation within a reasonable undulator length.
Considerable R&D on accelerator physics and technology
was indispensable to come to a credible and reliable
design of a (soft) X-ray FEL. In particular, it was not only
necessary to develop technologies for producing ultrarelativistic electron bunches with high charge (typically
1 nC), small normalized emittance (typically 1 mrad mm)
small energy spread (order of 100 keV after compression)and very short bunch length (10 fs range, thus achieving
both the kA peak current needed for the FEL and the shortradiation pulses desired by users), but it was as important
to invent novel beam diagnostics tools to verify andcontrol the beam properties at a micrometer precisionlevel – in all three dimensions. This broad scope of tasks
could only be accomplished by big accelerator centres,
being able to initiate and conduct a coordinated effort of
the full spectrum of accelerator scientists and engineers.
This broad spectrum of expertise was traditionallycultivated at big labs dedicated to high-energy particle
physics (HEP), for their permanent demand of more
powerful and more sophisticated accelerators. It is thus
not by accident that the first X-ray FEL programs were
initiated mainly by such labs like DESY and SLAC. It
will be a most awarding science management task (and, inview of the more and more project oriented funding
policies, a very challenging one) to keep alive and evenextend the fruitful collaboration of accelerator scientists
from both HEP and FEL communities.
The present paper is not considered a review article on
this extremely broad subject. It is rather a personal
review, mainly referring to the almost 14 years of R&D

effort conducted at DESY, Germany towards the FLASH
user facility. To a large extent, this effort was based on,
and conducted by, the international TESLA collaboration,with the superconducting accelerator called “TESLA Test
Facility” still being the backbone hardware. In the spirit
mentioned above, part of the accelerator beam time is still
allocated to HEP-related accelerator R&D towards theInternational Linear Collider (ILC), being based on thesame TESLA superconducting accelerator technology.
The list of technology issues mentioned in thefollowing is by far not complete. It represents a personal,
partly arbitrary selection of topics that are FEL specific,
where considerable progress has been made, but whichshould keep us busy for another while.

TRANSVERSE SPACE CHARGE
In linear 1D theory [1], the power e-folding length Lgof the high-gain FEL can be expressed by

Lg =1 ⎡ 2m γ 3λu ⎤
⎢

⎥

2
2
3 ⎣ πμ0 e K ne ⎦

1/ 3

−

1

∝ ne 3(1),

where λu is the undulator period, K the undulator

parameter, γ the electron energy in units of its rest
energy, andne is the electron density in the lab frame. In

order to achieve a sufficiently short power gain length
Lg , there is little alternative to calling for very highcharge density. Taking into account that particles withlarge betatron amplitudes fall out of FEL resonance, large
ne must be realized in a combination of small radial
beam emittance ε r and large peak current Iˆ . Such an
electron beam is subject to considerable space charge
forces, even though such forces are largely suppressed at
ultrarelativistic energies. The impact on transverse
electron focusing can be estimated from the focal length f
generated by the linear defocusing forces on a beamdrifting along the accelerator over a distance z (f > z
assumed):f ≈ec βε norm γ 2
re
z
Iˆ

(2)

With typical numbers for the normalized emittanceε norm = βγε r ≈ 1 mrad mm , the average beta functionβ ≈ 10 m , the peak current Iˆ ≈ 1 kA , and the beamenergy γ ≈ 200 , we get a focal length as small asf ≈ 10 m already after a few meters of passage length z.

FEL Prize and New Lasing

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Proceedings of FEL 2007, Novosibirsk, Russia

As a consequence, the electron beam carries its own
focusing system, i.e. it is difficult to control the transverse
beam size just by external quadrupole magnets. This is
illustrated in Fig. 1, where the beta functions at FLASH
are calculated for different assumptions on the peakcurrent [2]. Note that the peak current inside the bunch isby far not constant (see below) such that different parts ofthe bunch acquire different focusing. It is then difficult totell whether the lasing part of the beam has the desired
focusing inside the undulator.

βxβyFigure 1: Optics beta functions at FLASH for the
beamline after the final bunch compression at 380 MeV,

calculated for different peak currents: Iˆ = 0 kA (red),
1 kA (green), 2 kA (blue), 3 kA (black). It is assumed
here that space charge forces are negligible before thecompression where the peak current is much lower.

Generation of low emittance electron beams
The reliable generation of electron beams with thedesired small emittance is of outmost importance for theover-all design and for the performance of an X-ray FEL.
In particular, the requirement that the emittance should
fulfil (at least approximately) the condition
ε r ≤ λ Light 4π is extremely demanding if radiation
wavelengths (first harmonics) around λ Light ≈ 1 Angstrom
are to be achieved. Generally this is the major reason forchoosing a rather high electron beam energy beyond
10 GeV at LCLS and at the European XFEL. The electron
source is thus the single component where improvements
would have the largest impact on the overall design,
performance and costs of an X-ray FEL. An overview ofthis subject is beyond the scope of this paper and can befound in Ref. [3].
At present, most of the FEL projects are based on a RF
gun [4]. Through appropriate choice of cathode material
and RF frequency, RF guns have been developed both forsuperconducting and normal conducting linacs, i.e.
FEL Prize and New Lasing

10

serving for a wide range of duty cycles and bunch
repetition rates. It is of particular importance, that very
recently both R&D lines have reported success inachieving the design emittance of approx. 1.0 mrad mm(normalized) for 1 nC charge [5,6]. In order to reduce thenonlinear part of space charge forces, it is beneficial inthese guns that the drive laser pulses are shaped towards
flat transverse and longitudinal profiles.
It was pointed out before that the lower the beamemittance the better. It is thus exciting that there arealternative concepts potentially performing even better
than RF guns:• A thermionic gun based on a single crystal CeB6
cathode is used at SCSS [7] and has alreadydemonstrated promising results.
• An array of nanometer size field emittersimmediately followed by a high voltage pulsed diodeis under study at PSI in order to significantly reduce
the thermal emittance and to suppress emittance
growth due to space charge forces directly after theemission process [8].
• A dramatic progress might be achieved by plasmabased laser-wakefield acceleration on which a real
break-through was demonstrated recently by demontrating an electron beam of up to 1 GeV and only a
few % momentum width [9] with a tabletop setup.
Momentum spread, stability, and the transport of thebeam into an FEL undulator remain critical issues.
Whatever the electron gun is, precise measurement of theemittance is very critical, in particular since the phasespace distribution will be everything else but trivial. Thus,
measurements of phase space distribution at resolution in
the 10 μm range (in all three dimensions!) are desired.
But even if the measurement is restricted to thelongitudinal projection of the bunch, it is not trivial tofind a parametrization of the distribution adequate for the
FEL physics, the reason being that the phase space
distributions are generally by far not Gaussian. The
general approach is to describe the beam quality in termsof the rms-emittance ε x =

x

2

2

x′ − x ⋅ x′

2

. Fig. 2

illustrates a few phase space distributions measured at
FLASH with almost the same rms emittances. The
question remains whether all these distributions are really
equivalent in terms of FEL performance, or whether more
appropriate figures of merit should be developed.

Figure 2: Various phase space distributions measure at
FLASH. Are they all equivalent in terms of FEL
performance?

Proceedings of FEL 2007, Novosibirsk, Russia

SHORT BUNCH ISSUES
From FEL point of view
As mentioned before, in terms of emittance preservation ahigh peak current in the kA range is only tolerable atultrarelativistic beam energies. As a consequence, the kA
peak current is generated by magnetic bunch compression
at some 200 MeV beam energy. In practice it is anunavoidable consequence that this leads to a very shortbunch length in the 0.1 mm range. Very strong coherent
fields are generated which have a large and detrimental
effect on the beam dynamics. As an example, Figure 3
illustrates the longitudinal phase space distribution 1 m
after the exit of the first bunch compressor of FLASH as
predicted by numerical simulation. It is seen that thephase space distribution is distorted at the head of thebunch due to combined interaction of the electrons withspace charge Coulomb forces and coherent synchrotron
radiation (csr) generated in the bending magnets of thechicane. For details on beam dynamics simulation inpresence of csr, see Ref. [10].
This interaction becomes even more pronounced during
final compression. Figure 4 shows the calculated
longitudinal phase space distribution in front of theundulator. csr effects are very pronounced in the head of
the bunch, which is the only part of the bunch achieving
high enough peak current as to expect FEL gain
saturation.

MOBAU02consequence, not all the particles within the head of thebunch have an emittance sufficiently small for lasing.
Figure 5 indicates the current distribution resulting from
Figure 4 (colours representing the respective particles in
Figure 4). The black curve indicates that fraction of theparticles located within an emittance smaller than thetolerable one ( ε x , y ≤ 3 ⋅ 10 π m ). This part of the bunchn−6achieves a peak current of 1400 A and is only approx.
60 fs (FWHM) long. According to FEL simulation [11],such a beam would generate a radiation pulse approx.
30 fs (FWHM) in length, which agrees nicely with thepulse length measured at FLASH.
Various techniques have been established at DESY todetermine the longitudinal bunch current profile
experimentally. One of the most powerful ones makes useof a transverse deflecting mode cavity resonator(“LOLA”)[12,13]. LOLA’s capability of resolving very
detailed longitudinal features of the bunch is illustrated in
Figure 6.

<

60

Figure 5: Predicted current distribution in front of theundulator according to beam dynamics calculations.

Figure 3: Longitudinal momentum distribution 1 m after
the first bunch compressor of FLASH. The head of thebunch is to the right.

Figure 4: Longitudinal momentum distribution in front of
the undulator. The plot on the r.h.s. shows the head of thebunch zoomed.
Csr effects do not only distort the momentum
distribution but also the transverse phase space. As a

Figure 6: Longitudinal charge distribution within a single
electron bunch of FLASH at DESY. Upper part: Image ofthe bunch on an observation screen, located downstreamof the transverse mode cavity LOLA streaking the bunchtransversely by a time dependent electro-magnetic field.
The horizontal direction corresponds to the time. Only thepart containing the spike at the head of the bunch isshown. The (green) solid curve shows the charge density
profile projected onto the longitudinal position, i.e. thecurrent profile. In this particular setting of bunch
compression parameters, the spike is actually split into
two parts approx. 300 fs apart, each part being shorter
than 120 fs /(FWHM). The lower part of the figure shows
the prediction of numerical beam dynamics simulation.

FEL Prize and New Lasing

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Proceedings of FEL 2007, Novosibirsk, Russia

Due to the pronounced beam dynamics effects in thevicinity of the high peak current spike, not only the
distribution of electron not only in the longitudinal, butalso the transverse phase space can be heavily distorted.
The transverse phase space distribution thus varies
considerably along the internal bunch coordinate at
FLASH, see Figs. 7,8 [14] illustrating that a capability ofmeasuring properties of bunch slices is essential at an Xray FEL.
Slice emittance and current:

Horizontal phase space(selected slice) :

2
-0.2

60

1.5

1
5

-0.15

current [kA]

10

0.5

γε = 2.22 μ mx
Q = 6.84 pC-0.1
x′ [mrad]normalized emittance [μ m]

15

50

-0.05

40

0

30

0.05
20

0.1

0

-0.15

-0.1

-0.05
Δ z [mm]

0

0.05

0.15

0
0.1

90% core: 1.5 μm

0.2
-2

-1

0
x [mm]

1

10

2

Longitudinal slice position

Figure 7: Horizontal phase space distribution of thoseelectrons in the bunch located at the longitudinal positionindicated by the green arrow, measured with LOLA at
FLASH. Since this a position with relatively small current(blue solid line), the emittance is undistorted.
15

Slice emittance and current:

2

-0.2

10
1
5

Horizontal phase space(selected slice) :γεx = 10.9 μ m
Q = 31.2 pC-0.1x′ [mrad]1.5
current [kA]

normalized emittance [μ m]-0.15Size of lasing spike

60

50

-0.05

40

0

30

0.05
20

0.5

0.1
10

0.15
0

shows the single bunch spectrum at FLASH taken under
SASE conditions. While a unique reconstruction of thelongitudinal charge profile is hardly possible due to theloss of phase information, it is easy to identify evidence
for substructure inside the bunch occurring at lengthscales well below the size of the lasing spike.
The coherent IR signal seems to be a good candidate
for providing input signal for a SASE feedback loop. In
principle, one might think that the maximum total IR
power should be correlated with optimum compression
and thus maximum SASE. It is, however, not so simple
as seen from Fig. 10 [16]. While there is indeed a clear
correlation between SASE and IR power within somerange, maximum IR power is observed with only little
SASE left, most like due to over-compression.
Achieving ultrashort bunches in a reliable way requires
not only precise understanding of beam dynamics and lotsof advanced diagnostics. In the first place, high stabilityof rf phase regulation in the 0.1º is needed which is very
challenging ti achieve, see. Fig. 11.

-0.15

-0.1

-0.05
Δ z [mm]

0

0.05

0
0.1

0.2
-2

-1

0
x [mm]

1

Substructure
inside spike

2

Longitudinal slice position

Figure 9: Single shot infrared spectrum taken at FLASH.

Figure 8: Same conditions as Fig. 7, but now a slice issampled where the bunch current is high. The distributionof particles within this slice is heavily distorted.
In principle, we should know the bunch properties at alongitudinal resolution smaller than the cooperation
length, i.e. for X-ray FELs in the sub-fs range. This ispresently not accessible with time-domain beamdiagnostics techniques. As an alternative, the coherent
part of the infrared (IR) spectrum dU / d λ radiated by
the electron bunch when traversing magnetic fields or
discontinuities like metallic foils contains information
about the longitudinal structure function F (λ ) [15]:(SASE optimum

No SASEfactor 2

Maximum IR power does NOT
correspond to max. SASE!
(rather to over-compression)

No SASE

Figure 10: SASE power (vertical axis) versus total IR
power measured at FLASH with a pyro detector [16].
Rms phase jitter: 0.07 deg

Rms momentum jitter: 1.3×10-)

dU ⎛ dU ⎞2(3)=⎜⎟ N + N ( N − 1) F (λ )d λ ⎝ d λ ⎠1Here, (dU / d λ )1 is the spectral density of a single
electron, and N is the total number of electrons radiating.
Such measurements should cover the spectral range down
to 1 μm wavelength, and they should be, preferably,
single shot measurements since some effects taking placeat the micrometer-scale are likely to fluctuateconsiderable from bunch to bunch. As an example, Fig. 9
FEL Prize and New Lasing

12

Figure 11: RF phase jitter and rms momentum jitter after
first bunch compression at FLASH.

Proceedings of FEL 2007, Novosibirsk, Russia

From FEL User point of view

MOBAU02

CONCLUSION

What has been said so far results from requirements of the
SASE process – almost independent of user needs. For
many users, it is the capability of generating ultra-short,powerful X-ray pulses what makes FELs so attractive.
They are thus interested in pulses as short as possible. The
lower limit is obviously determined by the cooperation
length lc . At FLASH, with lc ≈ 1.3 μ m at 13 nm, thislimit has been almost achieved with a pulse length
l pulse ≈ 3 μ m , i.e. the radiation puls length is almost
Fourier limited. At Angstrom FELs, lc will be as short as

0.03 μ m . This opens up the possibility to generate

attosecond pulses [17,18], and calls for electron bunch
diagnostics at sub-femtosecond resolution, both big
challenges not yet met.

Synchronization Issues
The radiation pulses length being in the 20 fs range, it isimportant for users to have the pulses arriving at a time
jitter well below 100 fs with respect to a reference clockthat can be used for a pump-probe set-up. The underlying
problem is that a state-of-the-art rf microwave oscillator
represents an excellent master clock, but it is impossible
to distribute rf signals by rf cables over long distances at
fs stability. Techniques are under development toovercome this limitation [19-21], involving electrooptical detection of bunch arrival time, a stabilized opticalfibre transmission line and an optical-only master clock
system. Presently, a bunch–to-bunch time arrival stabilityof 200 fs rms has been verified [19, see Fig. 11. It is
worth noting that the bunch arrival time is measured at~10 fs resolution. With the help of an all-opticalsynchronization system it should become possible tostabilize many accelerator subsystems and lasers withrespect to each other at <50 fs precision, even overdistances some 1 km apart.

200 fsFigure 11: Fluctuation of bunch arrival time of 300
consecutive, compressed bunches at FLASH, measured
by electro-optic modulation [19].

Impressive progress in accelerator technology made overthe past 10-20 year was the backbone of the successful
implementation of FELs in the VUV-and soft X-ray
regime. Still it is not yet possible to measure the electron
beam properties at the undulator entrance at such
precision and resolution that the FEL radiation could be
inferred from this information at sufficient precision. In
particular in view of X-ray FELs being under way, thereis thus good reason to support even more refined beam
dynamics investigations as well as precise beamdiagnostics with micrometer and femtosecond resolution.

ACKNOWLEDGEMENT
The author. wishes to thank the entire FLASH team andnumerous colleagues from the TESLA collaboration for
their dedication, enthusiasm and hard work which was thebasis for the success of FLASH. He also profited a lot
from the supportive and friendly spirit within theworldwide FEL community. In particular, he wants tothank his colleagues E.L. Saldin, E.A. Schneidmiller, and
M.V. Yurkov for numerous and always inspiring
discussions.

REFERENCES[1] R. Bonifacio, C. Pellegrini, L.M. Narducci, Opt.
Commun. 50, 373 (1984).
[2] V. Balandin, N. Golubeva,[3] M. Ferrario, Proc. 2006 EPAC Conf. (2006)[4] J.Fraser, R. Sheffield, Nucl. Instr. Meth. A250, 71(1986).
[5] F. Stephan, et al, this conference[6] D. Dowell, et al., this conference[7] T. Shintake, this conference[8] A. Oppelt, this conference[9] W P Leemans et al., Nature Physics 2, 699 (2006)[10] M. Dohlus, Proc. 2006 EPAC Conf. (2006)[11] E.L. Saldin et al., DESY Print TESLA-FEL 2004-06(2004)[12] P. Krejcik, et al., Proc. 2003 Part. Acc. Conf, 423(2003)[13] R. Akre et al., Proc. 2002 EPAC Conf. (2002)[14] M. Roehrs, Proc. 2006 Part. Acc. Conf. (2006)[15] O. Grimm, Proc. 2006 Part. Acc. Conf. (2006)[16] H. Delsim-Hashemi, unpublished data (2007)[17] E.L. Saldin, et al., Opt. Commun. 212, 377 (2002)[18] A.A. Zholents, W.M Fawley, PRL 92, 22, 224801(2004)[19] B. Steffen, et al., this conference, WEBAU04[20] A. Winter, et al., Proc. 2006 Part. Acc. Conf. (2006)[21] F. Löhl, Proc. 2006 Part. Acc. Conf. (2006)[22] H. Schlarb, this conference, TUBAU01

FEL Prize and New Lasing

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MOPPH003

Proceedings of FEL 2007, Novosibirsk, Russia

VOLC: VOLUME FREE ELECTRON LASER SIMULATION CODE
S. Sytova∗ , Research Institute for Nuclear Problems, Belarusian State University
Abstract
First lasing of Volume Free Electron Laser (VFEL) in
mm wavelength range was obtained recently [1]. Multiwave volume distributed feedback (VDFB) where electromagnetic waves and electron beam spread angularly one
to other in a spatially-periodic structure (resonator) is the
VFEL distinctive feature [2]. Mathematical model and numerical methods for VFEL nonlinear stage simulation were
proposed [3] and implemented in computer code VOLC
that allows to simulate different geometries of two- andthree-wave VFEL in amplifier and oscillator regimes. Electron beam is modelled by averaging over initial phases ofelectrons. VOLC dimensionality is 2D (one spatial coordinate and one phase space coordinate) plus time. A description of VOLC possibilities and representative numerical results are presented.

INTRODUCTION
Principles and theoretical foundations of VFEL operation based on VDFB [4] put the beginning of experimental developing of new type of electronic generators. Creation of VFEL solves the problem of current threshold reduction, frequency tuning in a wide range, miniaturizationof resonators. All these problems present some difficulties for widely used schemes of free electron lasers (FEL),
backward wave tubes (BWT), travelling wave tube (TWT)and other electronic devices. As a rule, these high efficient devices have optimally specified parameters (electron
beam, waveguides, resonators and undulators periods etc.).
Changing of one of these parameters to tune frequency
leads to abrupt reduction of efficiency of the system. VFEL
design features allow to move and rotate diffracting gratings, change the distance between gratings and the gap between gratings and electron beam as well as orientationof grating grooves with respect to electron beam velocity. These aspects provide possibility to tune conditions ofdiffraction. VFEL threshold current for an electron beampassing through a spatially-periodic structure in degeneration points decreases essentially in comparison with singlewave systems [4]. This is valid for all wavelength ranges
regardless the spontaneous radiation mechanism and as aconsequence this means the possibility to reduce significantly system sizes.
In VFEL operation the linear stage investigated analytically [5]-[7] quickly changes into the nonlinear one where
the most part of the electron beam kinetic energy is transformed into electromagnetic radiation. Nonlinear regimeof VFEL operation can be investigated only using meth∗ sytova@inp.minsk.by

FEL Theory14

ods of mathematical modelling. Experiments on VFEL go
on [8]–[9] and need optimal geometry determination andresult processing.

MATHEMATICAL FORMULATION OF
VFEL PHYSICAL MODEL
The scheme of VFEL resonator of the experimental installation [1] formed by two diffraction gratings with different periods and two smooth side walls the same as thescheme of the volume resonator (so-called ”grid” volume
resonator) built from the metallic threads inside a rectangular waveguide of the installation [8]–[9] can be considered as the following scheme of VFEL. Here an electron
beam with electron velocity u passes through a spatially periodic structure. Under diffraction conditions some strong
coupled waves can be excited in the system. If simultaneously electrons of the beam are under synchronism condition, they emit electromagnetic radiation in directions depending on diffraction conditions in oscillator regime. In[10]–[12] different two-wave and three-wave schemes of
VFEL were considered in amplifier and oscillator regimes.
System of equations for all cases of VFEL is obtained fromMaxwell equations in the slowly-varying envelope approximation. For two-wave VFEL it has the following form:∂E∂E+ γ0 c+ 0.5iωlE − 0.5iωχτ Eτ =
∂t
∂z
 2π
2π − p(exp(−iΘ(t, z, p)+= 2πjΦ
8π 2
0+ exp(−iΘ(t, z, −p)))dp,∂Eτ∂Eτ
+ γ1 c+ 0.5iωχ−τ E − 0.5iωl1Eτ = 0.
∂t
∂z

(1)
Here E(t, z) and Eτ (t, z) are amplitudes of transmitted and diffracted waves with wave vectors k and k τrespectively.
k 2 c2 − ω 2 ε0 /ω 2 and l1 = l0 2 = 2 2
2kτ c − ω ε0 /ω are system parameters. l = l 0 + δ.
δ is a detuning from synchronism condition. γ 0 , γ1 are
VDFB
cosines. β = γ0 /γ1 is an asymmetry factor. Φ =
l0 + χ0 − 1/(u/cγ)2. γ is the Lorenz factor. χ 0 , χ±τ
are Fourier components of the dielectric susceptibility ofthe target.
System (1) must be supplemented with proper initial andboundary conditions which can contain conditions for external reflectors. Equations for the phase dynamics of elec-

Proceedings of FEL 2007, Novosibirsk, Russia
tron beam are written with respect to electron phase:d2 Θ(t, z, p)
= eΦ
dz 2
mγ 3 ω 2kz −dΘ(t, z, p)
dz

·
(2)

·Re (E exp(iΘ(t, z, p)) ,dΘ(t, 0, p)= kz − ω/u,dz

3

Θ(t, 0, p) = p.

It was proposed in (2) that the electron beam is synchronous with the transmitted wave E only. The integral
form of beam current in the right-hand side of the firstequation of (1) is obtained by averaging over the following initial phases of electrons in the beam: entrance time ofelectron in interaction zone and transverse coordinate of its
entrance point. Method of averaging over initial phases ofelectrons is well-known and widely used in simulation of
BWT, TWB, FEL etc. Equations (1)-(2) are more complicated than usually used (see e.g. [14]). System (1)-(2) takes
into account two-dimensional distributions with respect tospatial coordinate and electron phase p. So, these equations
allow to simulate electron beam dynamics more precisely.
This is very important when electron beam moves angularly to electromagnetic waves.

NUMERICAL METHODS AND
DESCRIPTION OF VOLC POSSIBILITIESAt present time there are a wide number of different
computer codes for FEL simulation. A comparison of existing FEL codes on dimensionality, time-dependent simulation, models of particle beam [15] shows that beam description by collective variables allows the faster calculation in time than by method of the Particle-in-Cell. We
used the beam description by collective variables in VFEL
simulation too.
Numerical algorithms proposed for solving (1)-(2) allow
to use parallel processing and can be started up on standard
symmetric multi-processor (SMP) computing systems withsome parallel processors based on common memory. The
big volume of processor work takes the computation of gridvalues of Θ in (2). In algorithm proposed their calculation
is not locked-in with respect to spatial coordinate z, so it
can be executed parallel. Finite difference system in thealgorithm has the form AE = F. Matrix A is inverted once
before the main computation and then it is multiplied to
the vector of right-hand sides F recalculated in each point
in time.
Numerical methods for all possible two-wave and threewave geometries including external reflectors are implemented in computer code VOLC, version 1.0 [10], [11].
VOLC means ”VOLume Code”. It was developed on thebasis of multiple Fortran codes, created in 1991—2005
years. Dimensionality is 2D (one spatial coordinate andone phase space coordinate) plus time. Theree-wave geometries were considered to confirm all main VFEL physical laws and mechanisms.

MOPPH003

New version 2.0 of VOLC allows for two-wave VFEL
geometries to obtain distributions of VFEL intensities withrespect to current density j, resonator length L, diffraction
asymmetry factor β, system parameters l 0 or l1 , detuningfrom Cherenkov condition δ, as well as dynamical regimes
recognition and intensity Fourier transforms. Reduction of
VOLC possibilities to two-wave case is connected with geometry of experimental installation [8] for which VOLC
simulation was designed. Interface of VOLC, version 2.0
is presented in Fig.1. Its block-scheme is depicted in Fig.2.
Interface of VOLC is a standalone program written in
Borland C++ Builder 6.0 for use in the Windows Operating environment. Interface allows to define input parameters, check their validity with corresponding messages, callthe main routine for VFEL simulation and output some results in the window including 2D plots and summary tableof results. The main routine for VFEL simulation was elaborated in Compaq Visual Fortran and can operate without
VOLC interface. In this case only the file with input parameters should be filled. Numerical results are written in
specified files.
VOLC interface uses the standard MS Windows dialog
and are supplied by screen tips. All wrong user actions
are stopped with corresponding messages. Computation of
distributions of intensities with respect to some parameters
can take much of computer time, so at any moment user
can stop computation without losses of calculated data.

Figure 1: Interface of computer code VOLC
VOLC was tested with carping. Numerical results obtained were reported in [3], [10]–[13]. There were investigated different regimes such as oscillator and amplifier
regimes, SASE (Self-Amplified Spontaneous Emission),
VFEL as BWT, TWT, BWT-TWT and others. All resultscorrespond to physical theory predictions. Some results ofnumerical experiments are presented below.

NUMERICAL RESULTS
One of the main VFEL physical laws [4] is the following dependence of threshold current in degeneration points:jth ∼ 1/((kL)3 (kχτ L)2s ), where s is a number of surplus

FEL Theory

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MOPPH003

Proceedings of FEL 2007, Novosibirsk, Russia

Input initial parameters andcheck their validity

Computation ofsystem coefficients AE=Fand others
Left-hand side matrix A
inversionComputation ofright-hand sides Fof the system

Computation of amplitudes
E=A-1F

VOLC
interfaceComputation of phases q
and integral I

Data output

Check for the endof time cyclenoyesCheck for the endof parameter cycles

no

yes

Figure 2: Block-scheme of VOLC
waves in diffraction. So, threshold current can be significantly decreased when modes are degenerated in multiwave diffraction geometry if k|χ τ |L  1. On the other
hand interaction length L can be reduced at given current
value j. This was confirmed in numerical experiments anddemonstrated in [11].
In [13] theoretically derived dependence of the thresholdcurrent on asymmetry factor of VDFB was presented. This
relation confirms that VDFB allows to control the thresholdbeam current. Numerical results presented in [11] are inclose agreement with the theory. Example of successful
simulation with help of code VOLC of VFEL experimentwith ”grid” volume resonator was proposed in [9].
In electronic devices such as FEL, TWT, BWT etc. selfoscillations are due to interaction of electron beam andelectromagnetic field under distributed feedback. Investigation of chaos in such devices is of great interest in modern physics [14], [16]–[18]. In VFEL simulation we facedwith chaotic behaviour of electromagnetic field intensities
too. Here chaotic dynamics is induced by complicated interaction of electron beam bunches with electromagnetic
field under VDFB. Investigation of chaos in VFEL is important in the light of its experimental development.
FEL Theory

16

Two points of beam current threshold exist in VFEL theory. First threshold point corresponds to beginning of electron beam instability. Here regenerative amplification starts
while the radiation gain of generating mode is less than radiation losses of the coupled feedback mode. Parameters
at which radiation gain becomes equal to absorption correspond to the second threshold point. When electron current exceeds the second threshold value, generation progresses actively. In simulations carried out an important
VFEL feature due to VDFB was shown. This is the initiation of quasiperiodic regimes at relatively small current
near first and second threshold points that are bifurcation
points. This is depicted via intensity plots in Fig.3 withcorresponding intensity Fourier transforms in Fig.4. Curve
1 depicts regime under regenerative amplification. Current
j is less than the value of the first threshold point. Valuej for curve 2 is a little larger than this threshold. Lines 3
and 4 depict 1T periodic regimes that pass to quasiperiodic
ones (lines 5-7).
Numerical investigations of chaotic lasing in VFEL
show the possibility of complicated transitions between
following chaotic regimes: stationary generation, selfmodulation and periodicity, quasiperiodicity, intermittency,
chaotic self-modulation or ”weak” chaos and chaotic selfoscillations or ”developed” chaos. Two-parameter analysis of VFEL chaotic lasing was carried out with respect tobeam current density j and (1) diffraction asymmetry factor
β, (2) detuning from synchronism condition δ, (3) length of
the resonator L. One of possible roots to chaos in VFEL ispresented in Fig.5 and Fig.6. Windows of periodicity andquasi-periodicity exist between chaos. Larger number ofprinciple frequencies for transmitted wave can be explainedby the fact that simultaneous generation at several frequencies is possible in VFEL. In the case considered electrons
emit radiation namely in the direction of transmitted wave.
As we have more than ten control parameters (see explanations for (1)-(2)) it seams to be very difficult to investigate the full picture of possible chaotic behavior in
VFEL. The aim of this investigation is to show the possibility to choose more precisely domains with periodic selfmodulation instead of chaotic one.

CONCLUSION
The original software for VFEL simulation is released
and allows to obtain all main VFEL physical laws and dependencies. VOLC overriding goal is to investigate thenonlinear stage of its operation. In simulation VFEL wasconsidered as a dynamical system. Two-parameter analysis
shows the complicated root to chaos. Author is grateful toProf. V.Baryshevsky for permanent attention to her work.

REFERENCES[1] V.Baryshevsky, K.Batrakov et al., Nucl. Instr. Meth. 483A
(2002) 21.
[2] V.Baryshevsky, Nucl. Instr. Meth. 445A (2000) 281.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH003

|E|

120

2500

6
5
4

2000

3

j, A/cm 2

80

7

I

9.00

C

6.00

Q

1500

4.00

40

2
1

0
0

200

400

t, ns

600

800

Figure 3: Transition from periodicity to quasiperiodicity
for transmitted wave in amplification regime. j is equal to:1) 350 A/cm 2 , 2) 450 A/cm 2 , 3) 470 A/cm 2 , 4) 515 A/cm 2 ,5) 525 A/cm 2 , 6) 528 A/cm 2 , 7) 550 A/cm 2 .

P

1000

1.00

0

500
-20

0.00

-15

-10

-5

b

Figure 5: Dependence of the threshold current on asymmetry factor of VDFB for transmitted wave. 0 depicts a domain under beam current threshold. P, Q, C, I correspondto periodic regimes, quasiperiodicity, chaos and intermittency, respectively.
2500

j, A/cm

2

2000

1500

1000

500
-20

-15

-10

-5

b

Figure 4: Intensity Fourier transform for curves 4-7 from
Fig.3
[3] K.Batrakov and S.Sytova, Computational Mathematics andMathematical Physics, 45 (2005) 666.
[4] V.Baryshevsky and I.Feranchuk, Phys. Lett. 102A (1984)
141.
[5] V.Baryshevsky, K.Batrakov, I.Dubovskaya, J. Phys. D. 24(1991) 1250.
[6] V.Baryshevsky, K.Batrakov, I.Dubovskaya, Phys. Stat. Sol.
B169 (1992) 235.
[7] V.Baryshevsky, K.Batrakov, I.Dubovskaya, Nucl. Instr. Meth.
358A (1995) 493.
[8] V.Baryshevsky, K.Batrakov et al., Nucl. Instr. Meth. B252
(2006) 86[9] V.Baryshevsky et al., ”Experimental study of a Volume Free
Electron Laser with a ”grid” resonator”, FEL2006, August
2006, Berlin, p.3311, http://www.JACoW.org[10] K.Batrakov and S.Sytova, Mathematical modelling andanalysis, 11 (2006) 13; 10 (2005) 1.

Figure 6: Dependence of the threshold current on asymmetry factor of VDFB for diffracted wave.
[11] K.Batrakov and S.Sytova, ”Numerical simulation of nonlinear effects in Volume Free Electron Laser (VFEL)”,RUPAC2006, September 2006, Novosibirsk, p.141,
http://www.JACoW.org[12] K.Batrakov and S.Sytova, Nonlinear Phenomena in Complex Systems, 8 (2005) 359; 8 (2005) 42.
[13] K. Batrakov K. and S. Sytova, ”Generation regimes of FEL
with volume distributed feedback”, FEL2006, August 2006,
Berlin, p.41, http://www.JACoW.org[14] N.S.Ginzburg, R.M.Rosental, A.S.Sergeev, Tech. Phys.
Lett., 29 (2003) 71[15] S. Reiche, ”Computation of FEL processes”, PAC2003,
May 2003, Portland, Oregon, p.203, http://www.JACoW.org[16] M.E.Couprie, Nucl. Instr. Meth. A507 (2003) 1[17] R.Bachelard et al., ”Control of the intensity of a wave interacting with charged particles”, FEL2006, August 2006,
Berlin, p.83, http://www.JACoW.org[18] M.S.Hur, H.J. Lee, J.K.Lee., Phys. Rev. E58 (1998) 936

FEL Theory

17

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Proceedings of FEL 2007, Novosibirsk, Russia

MEASUREMENT AND ANALYSIS OF CSR EFFECTS AT FLASH
Bolko Beutner, Winfried Decking, Torsten Limberg, and Michael Röhrs
DESY, Hamburg, Germany
Abstract
The vacuum-ultra-violet free electron laser in Hamburg(FLASH) is a linac driven FEL. High peak currents are produced using magnetic bunch compression chicanes. Suchpeak currents are required for the SASE process in the undulators. In these magnetic chicanes, the energy distribution along an electron bunch is changed by effects of
Coherent Synchrotron Radiation (CSR). Energy changes
in dispersive bunch compressor chicanes lead to transverse displacements. These CSR induced displacements
are measured using a transverse deflecting RF-structure.
Recent experiments and simulations concerning the charge
dependence of such transverse displacements are presented
and analysed.

INTRODUCTION
Electron bunches in magnetic bunch compressor chicanes are subject to CSR self-forces. CSR induced energychanges along the bunch give rise to different trajectories
for different longitudinal slices. Measurements of such effects were done at FLASH in 2006 [1][6]. We present results of CSR induced centroid shift measurements, in thefirst chicane, as a function of bunch charge.
For an undisturbed measurement of CSR effects, spacecharge fields are reduced by over-compressing the bunch.
The longitudinal energy correlation (chirp) introduced in
the accelerating module upstream of the first bunch compressor chicane is chosen to reach minimum bunch lengthand a peak current of about 1.2 kA toward the end of thesecond magnet in the chicane. Due to over-compression,
the bunch will exit the chicane with a length comparable toits incoming length of about 2 mm RMS, corresponding toabout 50 A peak current (see Fig. 1). The integrated effectof space-charge from the exit of the chicane to the observation point ≈ 60 m downstream is then small compared to
the CSR effects.

Figure 1: Top: Beam current along the bunch compressor
chicane in over-compression mode. Dipoles are indicatedas dashed boxes. Bottom: longitudinal phase space at theentrance, the middle, and the end of the bunch compressor.

TDS

Figure 2: Sketch of FLASH. The blue triangles indicate
dipole magnets, the yellow boxes symbolise TESLA accelerator modules.

MEASUREMENTS
A layout of FLASH is given in Fig. 2. We vary thephase offset of acceleration module ACC1 and keep thebeam on crest in the modules ACC2/3 and ACC4/5. The
expected CSR effects are created in BC2. Downstream, thetransverse deflecting RF-structure (TDS) is used to analyse
the longitudinal-horizontal beam profile. The experimental
setup is as in [1][6].
Starting from a stable SASE working point, we achieved
good transmission of the beam in the over-compression
FEL Theory

18

range (ϕACC1 = 23◦ − 26◦ ), while keeping the beam energy constant by adjusting the RF-amplitude.
To optimise the resolution of the measurements, a special beam optics between BC2, the transverse deflecting
cavity and the screen is used.
To ensure a proper optics set-up, the emittance and Twiss
parameters of the beam were measured in the diagnostic
section downstream the first bunch compressor [7]. The
measured Twiss parameters are used to determine correc-

Proceedings of FEL 2007, Novosibirsk, Russia

IMAGE ANALYSIS
The measured longitudinal-horizontal beam profiles areanalysed to obtain information about the general beam dynamics and CSR effects in BC2. We observe a horizontal
deformation of the beam profile (see Fig. 3).
In the first step of the analysis, we determine the maximal horizontal displacement of the centroid curve along thebunch and use it as a measure for the strength of the CSR
interactions. This maximal centroid displacement is related
to the maximal energy loss per longitudinal bunch slice due
to CSR in BC2.
Each picture is divided into slices along the longitudinalaxis. Only the central part of the picture is analysed. The
head and tail sections are omitted because of the noise inthese low charge regions.
The horizontal charge profiles of these slices are calculated. Within these horizontal charge profiles the centre
position has to be determined. The maximum or the centreof mass can be used for such a definition. The centre ofmass within such a slice is strongly influenced by noise in
the empty regions of the picture, drawing this value to thegeometrical centre of the slice. The maximum of a profile
does not underestimate the centroid shifts but is unstable
due to noise in the charge profiles. A Gaussian fit to thecharge profile is also not completely appropriate to our situation. The horizontal charge profiles are not Gaussian but
asymmetric in the regions of the picture with strong centroid shifts which lead to an underestimation of the centre.
A double Gaussian x−a 2
 x−a 2
− 2a 2− 2a 63
7f (x) = a1 e
+ a4 + a5 e
(1)
is used to fit the data. As initial values for the fit of a 2 anda6 we use the maximum and the mean of the transverse
charge profile. a 2 is then a good choice for the centre position. It is close to the maximum but more stable than theposition of the maximum value.
The centre position of each slice together with the meanof its longitudinal position defines the centroid curve. The
centroid curves corresponding to different fit methods areshown in Fig. 3.
In general, the bunch does not line up exactly parallel tothe screen axis (see next section). The linear correlation of
the different centroid curves, as indicated by the green line
in Fig. 3, is subtracted.
After subtraction of the tilt the horizontal peak to peakshifts of the centroid curves are calculated. A summary ofthese data is shown in Fig. 4.

−3

x 10

1
horizontal [m]tions to the five quadrupoles upstream of this diagnostic
section, after BC2, to achieve a matched beam optics in the
diagnostic section FODO lattice.
Due to space charge effects in the injector, the beam optics depends on the bunch charge. To ensure a good transmission up to the transverse deflecting cavity, the matchingin the DBC2 section was redone for every bunch charge.

MOPPH004

2
3
4
5
1

2

3

4
5
6
longitudinal [m]

7

8
−3

x 10

Figure 3: An example of a TDS measurement with bunchcharge q = 0.65 nC. Longitudinal charge profile (red line),
FWHM lines (white solid) and the lines corresponding to”full width of 1/6 maximum” (white dashed) are shown, indicating the omitted head and tail parts of the bunch. Different centroid curves (black - Gaussian fit; white - maximum value; magenta - mean value; red - double Gaussianfit) are plotted as dashed lines. The green line represent an
overall linear slope determined from the edge points of thecentroid curves. Bunch head is to the left.

SIMULATIONS
Tracking calculations were done to simulate
longitudinal-horizontal beam projections at the TDS.
Photo emission and beam transport through ACC1 wascalculated with the space charge tracking code ASTRA[2]. After ACC1, wake fields are applied as a discrete
effective kick [4]. The tracking code CSRTrack [3] is used
to simulate CSR effects in BC2. Downstream of ACC1
linear transport theory is used. The actual currents of thequadrupoles were used to calculate the transport matrices.
Transverse and longitudinal wake fields are added as
perturbations [4]. From the resulting particle distributions
at the TDS beam images are obtained by representing eachparticle with a 2D Gaussian.
The simulated images are analysed with the same methods as the measured ones. In Fig. 4 simulated maximal
centroid shifts vs. bunch charge for different threshold intensities are compared with measured data.
To simulate the minimum intensity observable with thecamera system, a lower threshold of charge density is usedin the image calculation. An image intensity threshold ischosen as a charge density ρ(T ) for a given charge T . The
intensity of each pixel is reduced by ρ(T ) = T /(total number of pixels), while negative values are set to zero.
Considering the space charge effects on bunch lengthand uncorrelated energy spread, one can predict the behaviour of peak current, and thus the centroid shift, withincreasing charge. The peak current is not increasing linearly with charge, it saturates beyond 1 nC and for higher
total bunch charges, the peak current is decreasing.
Two effects play a role here. First the bunch length

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Proceedings of FEL 2007, Novosibirsk, Russia
−4

x 10
11
10

centroid shift [m]

9
8
7
6
5
Simulations − upper bound T=0nC
Simulations − lower bound T=2nC
Simulations − T=1nC
measurements

4
3
2

0.4

0.6

0.8

1
1.2
1.4
Bunch Charge [nC]

1.6

1.8

2

Figure 4: CSR induced centroid shifts as a function ofbunch charge. The measured centroid shift is plotted andcompared with the simulated obtained from the image analysis for three different image intensity cutoffs.

increases with higher bunch charge due to space charge
forces in the RF-Gun, which reduces the charge density andthus the peak current. Second, the space charge interaction in the injector increases the uncorrelated slice energy
spread towards higher bunch charges. Due to this increaseof the energy spread the width of the charge spike after the
chicane is increased. As a result the peak current is reduced
even further. While the maximum centroid shift is an important property to identify the strength of the CSR effects,
it is not sufficient for the analysis of the beam dynamics.
Hence, in a second step of this analysis, the whole centroid
curves are compared with simulated data.
The comparison of the measured and simulated centroid
curves is summarised in Fig. 5. The measured curves are
determined using the Gaussian method described earlier.
Error bars are calculated as the standard deviation using
the set of 20 pictures taken at each machine setting and asystematic error of the image analysis algorithm.
Different self-field effects act on the beam and cause additional distortions downstream of BC2. A model of transverse wake fields in the acceleration modules ACC2 andACC3 is included to simulate the observed beam tilt. Together with the spurious dispersion [5] this has an important impact on the centroid curve tilt.
Cavity misalignment and cavity tilts inside an acceleration module yield similar transverse wake fields as a beam
offset. On the other hand, the effect of the transverse wakefields and of horizontal dispersion is similar. Images fromthe TDS can not distinguish between transverse deformations caused by transverse wakes induced by an orbit offset
and horizontal dispersion.
Vertical dispersion leads to changes in the longitudinal
profile observed at the screen after the TDS because the
TDS streaks the longitudinal beam axis in vertical direction. Therefore, one can not distinguish between verticaldispersion at the TDS and errors in the longitudinal disFEL Theory

20

persion of the transport matrices or phase errors in ACC2ACC5.
In this sense, the vertical dispersion and the horizontal
beam position offset assumed in these simulations are effective parameters, which can not be directly be identified
with the real properties of the beam orbit during the measurements.
Other studies on orbit errors and spurious dispersion givea reasonable upper limit estimate of these effects. Orbit
errors up to 10 mm and spurious dispersion up to 200 mm
have been measured in 2006 [5]. With assumptions of thisorder the simulated centroid curves can be matched to themeasured ones (Fig. 5).

SUMMARY AND OUTLOOKWe did extensive studies on the beam dynamics ofFLASH using both numerical simulations and experiments.
In normal SASE operation the overall effects on the beam
are complicated due to a commingling of different self-field
effects, like space charge, CSR, and wake fields. Studies on
CSR effects are done in an special over-compression mode.
In this compression scheme CSR interactions are the dominant self-field effect.
A quantitative comparison of CSR simulations and measurements was done with a dedicated experiment. CSR induced energy loss throughout the bunch can be observed asa horizontal sag on the TDS screen. The measurement was
performed for different bunch charges to compare parameter dependencies with those predicted by simulations. The
magnitude of the effect is expected to be up to 130 keV,leading to a trajectory offset of up to 1 mm after the bunch
compressor chicane. With proper settings of the optics between the chicane and the TDS (involving 4 more accelerating modules, the 2nd bunch compressor, diagnostic andmatching sections) the sag in the longitudinal-horizontal
beam profile is of the same order. The sag (i.e. the largest
offset of the slices from the nominal position) is derived
for different bunch charges. The sag gets smaller for large
bunch charges because the bunch length and the uncorrelated energy spread at the entrance of the bunch compressor increases, resulting in a smaller maximal peak current
inside the chicane.
A numerical model of the FLASH linac with the same
conditions as the real machine was constructed. Despite
the limited knowledge of all machine parameters, a good
agreement between numerical results and experimental
data was achieved. We demonstrated that the numerical
tools as well as the beam diagnostics at FLASH are suitable for quantitative studies on CSR.

REFERENCES[1] B. Beutner and W. Decking and M. Dohlus and T. Limberg
and M. Roehrs: Beam Dynamics Experiments and Analysis
on CSR Effects at FLASH, FEL 2006 - Proceedings BESSY,
Berlin, Germany.

Proceedings of FEL 2007, Novosibirsk, Russia

0.01

−0.5

−3

x 10

−1
−2
0

0.005
longitudinal [m]horizontal [m]
−4

0.01

x 10

0.005
longitudinal [m]q=1.8nC

0

−1
0

−5
0

0.005
longitudinal [m]

0.01

2
4
6
8
longitudinal [m] x 10−3
q=1.4nC−40.005
longitudinal [m]
q=2nC

0
−1

10

0

−3

x 10

−2
0

0.01

5

q=0.8nC

−0.5

1

−1

x 10

0.5

2
4
6
8
longitudinal [m] x 10−3
q=1.2nC

0

10

0

x 10

−2
0

2
4
6
8
longitudinal [m] x 10−3
q=1.6nC

horizontal [m]−10

horizontal [m]

−10
0
1

0

1

−5

−3

0.5

−3

1

0

horizontal [m]

1

x 10

0.005
longitudinal [m]
q=1nC

x 10

horizontal [m]−3q=0.65nC

−4

5

0

−5
0

horizontal [m]q=0.4nC

horizontal [m]horizontal [m]x 10

horizontal [m]−45

MOPPH004

x 10

0.01

5
0
−5
0

2
4
6
8
longitudinal [m] x 10−3

Figure 5: Comparison of centroid curves obtained from measurements (blue) and simulations (red). ACC1 phase offset isϕ = 24.9◦. The centroid curves obtained by the image analysis of measured profiles are shown. Bunch heads are to theleft.

[2] K. Flöttmann: ASTRA user manual,
http://www.desy.de/mpyflo/Astra dokumentation.
[3] M. Dohlus, T. Limberg: CSRtrack: Faster Calculation of 3D
CSR effects, FEL 2004, 2004
[4] T. Weiland and I. Zagorodnov: The Short-Range Transverse
Wake Function For TESLA Accelerating Structure, TESLA
Report 2003-19[5] E. Prat and W. Decking and T. Limberg: Measurement andCorrection of Dispersion in the VUV-FEL, Proceedings of
EPAC 2006, Edinburgh, Scotland[6] B. Beutner: Measurement and Analysis of Coherent Syn
chrotron Radiation Effects at FLASH, PhD Thesis, University Hamburg 2007, to be published[7] F. Löhl et al.: Measurements of the Transverse Emittance atthe FLASH Injector at DESY, Phys. Rev. ST Accel. Beams 9,092802 (2006)

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Proceedings of FEL 2007, Novosibirsk, Russia

IMPROVEMENTS OF THE TRACKING CODE ASTRA FOR DARKCURRENT STUDIES AT FLASH
L. Fröhlich∗ , University of Hamburg and DESY, Hamburg, Germany,
S. Meykopff, DESY, Hamburg, Germany
BC2

Abstract
At the Free Electron Laser in Hamburg (FLASH), the activation of components due to dark current emitted by thegun has become a serious problem. To improve the understanding of dark current transport in the linac, we haveused extensive tracking simulations. To reduce the required
amount of computing time, we have used a novel parallelized version of the Astra tracking code. We present themain parallelization scheme and investigations on the scalability of the code. We also introduce a new library for thedescription of complex three-dimensional aperture models.
Finally, a brief overview of the simulation results and anevaluation of possible remedies of the activation problem
are given.

INTRODUCTION
The FLASH linac accelerates electron bunches from a
photoinjector to beam energies of up to 700 MeV [1]. The
bunch length is reduced in two magnetic chicanes, BC2 andBC3, at energies of 127 MeV and 380 MeV. In front of
the undulator, a four-stage collimation system consistingof two transverse and two energy collimators removes particles deviating excessively from the designated reference
orbit and momentum (Fig. 1).
Because it is operated at a high electric field amplitudeof 40–44 MV/m, the normal conducting RF gun is a major source of dark current. Measurements with a Faraday
cup have shown an average current of 200–300 µA exiting
the structure during the RF pulse. A substantial part of it
is picked up by the first superconducting acceleration module ACC1 and transported through the linac, leading to increased losses and activation of components along the machine. This has become a problem especially near the first
dipole magnets of bunch compressor BC2, where the narrow vacuum chamber intercepts a major fraction of the incoming dark current. Equivalent dose rates above 16 mSv/hdue to activated material have been measured in this place,requiring an increased radiation protection effort [2].
To investigate possible remedies for this problem, thetransport of dark current through the linac has been studied with particle tracking simulations. The space charge
tracking code Astra [3] was the natural choice for this task
because a good model of the FLASH injector was alreadyavailable for it [4]. Originally covering only the initial 14 mof the machine, this model has been extended to include thecomplete beamline of about 250 m length. The scope of∗ lars.froehlich@desy.de

FEL Theory

22

BC3

Gun
ACC1

ACC2 ACC3

ACC4 ACC5

Bypass line
Undulator
Collimation
sectionPhotonbeamline
Dump

Figure 1: Schematic of the FLASH linac. The five acceleration modules ACC1-5 are shown in yellow, dipole magnets in blue, and collimators in orange color.
these simulations required substantial changes to the codein order to reduce execution times as well as the development of a new aperture modelling language capable of describing the complex geometries found in the accelerator.
In this paper, we provide only a rough outline of simulation setup and results; details are found in [5]. Instead, we
focus on the computational aspects of the work.

SIMULATION SETUP
The main simulation is divided into three steps:
1. Beam tracking: A bunch of 105 macroparticles is
extracted from the cathode by photoemission andtracked to the dump. The step is iterated several times
to match the beta function to the design optics.
2. Dark current tracking: 106 macroparticles are extracted from the cathode by field emission according
to the Fowler-Nordheim model [6] and tracked to thedump. The phase space is saved in intervals of 8 cm,
resulting in about 100 GB of data.
3. Aperture check: The saved phase space data are compared against a three-dimensional aperture model ofthe machine with a separate tool.
While space charge effects have to be included in the
tracking of the beam in step 1, they are negligible in step 2
due to the low charge density of the dark current. The
number of macroparticles required in step 2 is determinedby the desired precision of the results. With a million
macroparticles, relative dark current losses down to thelevel of 10−5 – 10−4 can be simulated.
We found the conventional single-processor version of
Astra to be ill-suited for a work load of this magnitude;a single run would take several days to complete on theProceedings of FEL 2007, Novosibirsk, Russia

MOPPH005

50
40
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speedup

execution time (s)

8000

4000
2000

30
20
10

0

0
0

10

20

30

40

50

number of processors

0

10

20

30

40

50

number of processors

Figure 2: Parallel performance benchmark. The dottedline indicates the best theoretically possible execution time
based on the measurement for a single processor, i.e. withassumed full scalability.

Figure 3: Speedup achieved by running Astra on multiple processors. The dashed line indicates the ideal case offull scalability, the dotted line corresponds to Amdahl’s law
with a sequential code fraction of α = 1.4 %.

fastest available computer. Instead, we decided to makeuse of parallel computing with a new version of the code.

To exploit this form of data parallelism, we have chosena classical “single program multiple data” (SPMD) approach; the existing serial source code has been extended
by calls to the MPICH2 message passing interface library[8]. It is therefore possible to run the executable on a single
processor as usual, or to spawn multiple processes within
the framework of an existing MPICH2 installation.

PARALLELIZATION OF THE ASTRA
TRACKING CODE
Astra provides several particle-in-cell (PIC) algorithms
to calculate the space charge field generated by themacroparticles. The most frequently used one employs acylindrically symmetric grid in which the single cells are
addressed by a radial and a longitudinal bin number, r andl. The code iterates over all N macroparticles to determine
the charge present in each cell, Qrl . Afterwards, the main
tracking loop iterates over all particles again, for each one
summing up the contributions of all partial charges Qrl to
the local space charge field as well as external electric andmagnetic fields. The forces exerted on each particle areintegrated with a fourth-order Runge-Kutta algorithm [7].
Many parallel PIC codes divide the computation work by
distributing the grid cells among the available processors,which is especially advantageous in the case of grids withhigh resolution and with computationally demanding fieldcalculations. However, Astra’s cylindrically symmetric algorithm is frequently used with coarse grids (under 1000
cells), and the field calculation is comparatively simple dueto the absence of complicated boundary conditions. Investigations with a code profiler also confirm that only a minor
part of the execution time is spent in the space charge routines.
On the basis of these considerations, it was decided toachieve parallelization by distributing the macroparticles
among the processors. In a run with N particles and P
processors, the initial assignment would follow the pattern:
process 0:
process 1:...
process N :particles
particles

0 . . . N/P − 1
N/P . . . 2N/P − 1

particles (P − 1)N/P . . . N − 1

Parallel Performance
Figure 2 shows the measured execution times on a cluster with 23 nodes of two CPUs each. Shared memory isused for communication between the twin CPUs, gigabit
ethernet for communication between the nodes. The input
file used for benchmarking contains the complete model ofthe FLASH linac, but simulates only the first 20 m of themachine with 105 macroparticles including space charge
effects. There are no emittance calculations or file outputs
except for the saving of one phase space file at the end of
tracking.
The speedup ξ achieved by using P processors is defined as the ratio of parallel to sequential execution time,ξ(P ) = Δt(P )/Δt(1). Figure 3 shows that the measured
speedup increasingly deviates from ideal behavior with increasing number of processors—the maximum achieved on
the cluster is ξ(46) = 28.4. This behavior is described wellby Amdahl’s law [9] which states that if a program can beseparated into a parallelizable part and a sequential part thattakes a fraction α of the total execution time, the speedup
by running it on P processors is given by
−1

1−α
.
ξ(P ) = α +P
By fitting to the data, we obtain a sequential fraction of
α = 1.4 % for this benchmark case. The maximum possible speedup is then given bylim ξ(P ) ≈ 71 .

P →∞FEL Theory

23

MOPPH005

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 4: Horizontal section of the FLASH aperture model. The blue dots mark the positions of lost dark current particles.
Losses in the gun region are not shown.
However, it is obvious that these figures depend strongly
on the specific application—generally, a higher numberof macroparticles will increase the speedup, and a higher
number of sequential operations like file saving or emittance calculations will decrease it.

APERTURE MODELLING
To obtain reliable information about dark current losses
from a tracking simulation, a good knowledge of the apertures along the machine is required. It is also necessary tohave tools that can reproduce this geometry in an adequate
way. Unfortunately, the built-in capabilities for modelling
apertures in Astra and in most tracking codes are limited tobasic shapes like circular openings or parallel plates.
To facilitate a coherent and exact description of aperture models, we have developed the portable ApertureLib
library. It is written in C++ and allows integration to C and
Fortran projects by a set of wrapper functions. The libraryallows to read aperture models from XML files like the following:<aperture-list><circle z="0" name="drift"><r>0.017</r></circle><include z="2.4" name="acc. module"><filename>acc_module.xml</filename></include></aperture-list>
In this example, two aperture elements are specified alongwith their longitudinal positions in the machine. The first
one describes a circular aperture with a radius of 1.7 cm,
the second one includes another XML file that defines thegeometry of cavities and vacuum chambers inside a cryomodule.
A wide variety of element types is available, allowing tomodel even complicated geometries:• Primitive profiles (circle, ellipse, rectangle, . . . ), rotatable to any direction in space
FEL Theory

24• Elements delimited by an arbitrary number of planes,
specified by position and normal vectors• Combination of other apertures by a logical AND or
OR, e.g. to model alternative beamlines or new shapes
like semicircles• Inclusion of other XML files as “building blocks” forrepetitive structures• Inclusion of existing Astra aperture files• Import of 2-dimensional CAD drawings in DXF format for complex planar geometries
In addition to the library, a set of tools has been createdthat allows validation and inspection of aperture models aswell as generation of plots and checking of phase space
files against the model.
With this toolkit, the geometry of the FLASH vacuum
chambers shown in Fig. 4 was set up and compared against
the phase space files from the previous Astra simulations.

SIMULATION RESULTS
The simulation shows that about 70 % of the emitted
dark current are lost in the region from the gun cavity to
the first cavity of module ACC1. Many particles arrive
there on the wrong phase of the RF wave and are reflected
or lost in the module. By scaling to the measured value of∼250 µA at a Faraday cup behind the gun, we can conclude
that roughly 100 µA of dark current are transported throughACC1 (Fig. 5).
After passing the acceleration module, the dark current
has reached an energy of about 127 MeV. Since this is well
above the giant nuclear resonance threshold, losses maylead to activation of accelerator beamline and components.
As expected, the entrance of bunch compressor BC2 with
its low vacuum chamber of only 8 mm height intercepts thebiggest part of the remaining current, more than 50 µA. The
simulation predicts other hot spots at the exit of ACC1, atthe entrance and exit of BC3, and at the collimators, whichis qualitatively confirmed by the measured radiation levelsin these locations [2].
We can also estimate the remaining amount of dark cur-

MOPPH005

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400

10000

300

1000

200

100

100

10

dark current (µA)

lost macroparticles

Proceedings of FEL 2007, Novosibirsk, Russia

0
0

25

50

75

100

125

150

175

200

225

z (m)

Figure 5: Simulated dark current losses along the FLASH linac. Red (logarithmic scale): lost number of macroparticles
per phase space file. Blue (linear scale): remaining gun dark current.
rent traversing the FEL undulator to be about 5 µA. With
the machine set to default optics, it oscillates between rms
beam sizes of 250 µm and 1.5 mm in both planes while
the beam is smaller than 100 µm. Therefore it is easy tolose some dark current in the undulator chamber by wrong
beam steering. Calculations with the particle transport code
Fluka [10, 11] have shown that a complete loss of the darkcurrent would deposit a local dose rate of 30 Gy/minute in
the permanent magnets.
To reduce the amount of gun dark current that is transported through module ACC1, it has been proposed to increase the drift length between gun and module by 30 cm[12], and to insert a collimator with a circular aperture of
8 mm diameter behind the gun. From simulations with ourmodel, we expect a reduction of transported dark current
by about two thirds.

CONCLUSION
The investigation of dark current transport and losses
with detailed tracking simulations is computationally demanding. We found the parallelized version of the Astracode well suited for this task. It has been demonstrated thatsimulation times can be reduced drastically by distributing
the work load over several processors. The scalability of
the code makes it well suited for multicore-/multiprocessor
machines or small clusters with up to 64 processors.
In order to set up a detailed three-dimensional aperturemodel of the FLASH linac, we have developed the portable
C++ library ApertureLib and a set of necessary tools. We
have used this toolkit to compare phase space files generated by the Astra runs against the aperture model. This
allowed us to check variations of the model quickly without having to repeat the tracking. However, the library has
also been integrated into Astra as an optional component
and can be used directly during the tracking run.
The simulation has provided an insight to the beam dynamics of dark current transport in the linac and allowed
to evaluate possible counter measures for the problem of
beamline activation. Based on these data, we can predict a

reduction of dark current losses at bunch compressor BC2
to about one third of their former amount by the proposed
relocation of the gun and the use of a transverse collimator.

ACKNOWLEDGEMENTS
We highly appreciate K. Flöttmann’s assistance with theoriginal Astra source code. We also wish to thank him,
B. Beutner, and J.-H. Han for many helpful discussions.

REFERENCES[1] The TESLA Test Facility FEL team, “SASE FEL at
the TESLA Facility, Phase 2”, TESLA-FEL 2002-01,
June 2002, Hamburg.
[2] A. Leuschner, DESY, private communication.
[3] K. Flöttmann, “Astra—A Space Charge Tracking Algorithm”, available at http://www.desy.de/~mpyflo/.
[4] K. Flöttmann, E. Schneidmiller, Y. Kim, private communication.
[5] L. Fröhlich, “Dark Current Transport in the FLASH Linac”,
PAC’07, June 2007, Albuquerque, USA, pp. 956–958.
[6] R. H. Fowler, L. Nordheim, “Electron Emission in IntenseElectric Fields”, Proc. R. Soc. A, 119, May 1928, London,
pp. 173–181.
[7] K. Atkinson, “An Introduction to Numerical Analysis”, 2nded., Wiley, 1989.
[8] MPICH2, an implementation of the message-passing interface, http://www-unix.mcs.anl.gov/mpi/mpich2/.
[9] G. Amdahl, “Validity of the Single Processor Approachto Achieving Large-Scale Computing Capabilities”, Proc.
AFIPS, (30), pp. 483–485, 1967.
[10] A. Ferrari, P. R. Sala, A. Fassò, et al., “Fluka: A MultiParticle Transport Code”, CERN-2005-00X, August 2005,
Geneva.
[11] A. Fassò, A. Ferrari, S. Roesler, et al., “The Physics Modelsof FLUKA: Status and Recent Developments”, CHEP’03,
March 2003, La Jolla.
[12] J.-H. Han, K. Flöttmann, “Dark Current Collimation and
Modified Gun Geometry for the European X-Ray FEL
Project”, FEL’06, August 2006, Berlin, pp. 579-582.

FEL Theory

25

MOPPH006

Proceedings of FEL 2007, Novosibirsk, Russia

LONGITUDINAL WAKE FIELD FOR AN ELECTRON BEAM
ACCELERATED THROUGH A ULTRA-HIGH FIELD GRADIENT
G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
The impact of longitudinal wake fields on an electron beam accelerated through a ultra-high field gradient is discussed, based on solution of Maxwell’sequations for the longitudinal field. We consider anacceleration distance much smaller than the overtaking length, as for laser-plasma devices. We give expressions for impedance and wake function that may
be evaluated numerically. A limiting expression isfound for a large distance of the electron beam fromthe accelerator compared with the overtaking length.
We derive analytical solutions for a Gaussian transverse and longitudinal bunch shape. We apply our
analytical asymptote by studying the feasibility of a
Table-Top VUV FEL (TT-VUV-FEL) based on laserplasma driver. Numerical estimations indicate a serious threat to the operation of this device. A detailed
report with relevant references is given in [1].

INTRODUCTION
In this paper we study longitudinal wake fields produced within electron beams accelerated with highgradient fields. We assume that the acceleration distance da is much smaller than the the overtaking
length. This is the distance travelled by the electrons
as a light signal from the tail of the bunch overtakes
the head of the bunch. Given a bunch of rms length σz ,the overtaking length is 2γ2 σz , and corresponds to theradiation formation length 2γ2  calculated at  = σz ,
 = λ/(2π) being the reduced radiation wavelength.
When da  2γ2 σz , electrons can be assumed to be accelerated at position zA down the beamline. This is
the case for laser-plasma devices, since accelerationin the GeV range takes place within a few millimeter,
but not for conventional accelerators. The assumptionda  2γ2 σz simplifies wake calculations. When thiscondition is verified, the wake generated along thepart of the trajectory following the acceleration pointzA is independent of any detail of the accelerator. Thus
our study is valid independently of the particle accelerator technology chosen, provided that da  2γ2 σz .
One may also have contributions to the wake generated before zA . These depend on the physical natureof the accelerator, can be separately calculated, andwill be neglected here because they do not aﬀect thebunch in the case of a laser-plasma accelerator. We
base our study on solution of Maxwell’s equations forthe longitudinal field. Our consideration is valid in
FEL Theory

26

free-space. This approach gives accurate results if thetypical dimension of the vacuum pipe a is larger thanγ = γσz , that is the typical transverse size relatedwith the longitudinal electric field. Paraxial approximation can be applied to describe electromagnetic
sources up to the observation point, while sources
after the observation point in the beam propagation
direction can be neglected. We make use of the paraxial approximation to calculate the Fourier transformof the longitudinal field produced by fixed electromagnetic sources (current and charge densities) at a
certain observation plane down the beamline. This
constitutes the basis of our treatment, because it allows to calculate the longitudinal impedance and thewake function. Impedance and wake function yieldan analytical expression in the asymptotic limit of alarge distance of the electron beam from the accelerator compared with the overtaking length, i.e. in
the far-field zone for all wavelengths of interest (upto  ∼ σz ). This asymptotic limit allows simple estimations of the impact of the longitudinal wake on
the electron beam energy change. We apply our theory by studying the feasibility of TT-VUV-FELs basedon parameters described in [2], and finding a serious
threat.

FIELD IN SPACE-FREQUENCY
Let zA be the exit of the accelerator. After z A , thenominal Lorentz factor of electrons is γ. Acceleration
happens on a scale da  2γ2 . Significant emission
is present for wavelengths longer than the longitudinal bunch length σz , up to transverse beam sizesσ⊥  γσz . For typical ultra-relativistic beams, condition da  2γ2  can be read as d a  2γ2 σz . We picture
the fast acceleration process as a sudden ”switch-on”
of both harmonics of the electromagnetic sources andof the field. When the switching distance (the acceleration distance) da  2γ2 σz , the description of the wake
generated after the switching point (the acceleration
point) zA , is independent of the nature of the switcher.
As long as sources are rapidly switched-on, it does
not matter whether we are considering a fast longitudinal acceleration or other switching mechanisms.
We first calculate Ēz (zo , r⊥o , ω), that is the longitudinal
electric field at frequency ω from given electromagnetic sources in vacuum. It is detected at longitudinal
position zo > zA and transverse position r⊥o . We de¯fine ∞ the Fourier transform of a function f (t) as f (ω) =dt f (t) exp[iωt], and we follow analogous conven−∞Proceedings of FEL 2007, Novosibirsk, Russia
tion in the definition of the Fourier transform in two
dimensions. The field in the space-frequency domain
 , r , ω) is the Fourier transform of the field in the
Ē(z
o ⊥o
 o , r⊥o , t). As is well-known, one
space-time domain, E(zmay use the field in the space-frequency domain fora given frequency and yet think of the amplitude ofa monochromatic field or viceversa. We should solve
the paraxial equation for sources located in [zA , zo ]: ρ̄ − 4πiωj.¯
c2 exp[iωz/c] · [∇2⊥ + 2iω/c∂/(∂z)]E= 4πc2 ∇Since electrons are moving along the z-axis, we write
the harmonic components of the charge density asρ̄(z , r ⊥ , ω) = ρo (r ⊥ ) f¯(ω) exp[iωz /v]u(z − zA ), whilej¯z (z , r ⊥ , ω) = βcρ̄. Notation u(z − zA ) indicatesa Heaviside step function centered at position zA ,whose presence signifies that there are no sources
before the plasma accelerator. Functions ρo and f¯are specified once a model for the beam is chosen.
The quantity ρo has the meaning of transverse electron beam distribution. It may depend on the harmonic ω, but we will assume it does not. Thus, allinformation about the longitudinal electron density
distribution f (t) is included in its Fourier transformf¯(ω). A typical Gaussian beam model is definedby ρo (r ⊥ ) = 1/(2πσ2⊥c) exp[−r⊥2 /(2σ2⊥)], and f (t) =√(−e)N/( 2πσt ) exp[−t2 /(2σ2t )], whose Fourier transform is given by f¯(ω) = (−e)N exp[−ω2 σ2t /2], N being
the number of electrons in the beam and (−e) the electron beam charge. Here σt is the rms bunch duration,connected σz by σz = βcσt , so that in terms of lengths√
f (s) = (−e)N/( 2πσz ) exp[−s2 /(2σ2z )]. The wake generated along the part of the trajectory following zA , isindependent of the nature of the switcher. However,
the above expressions for ρ̄ and j¯z violate the continuity equation, and should be completed by extracontributions depending on the switcher. For example, if one thinks of an acceleration process where alow energy bunch with Lorentz factor γo is accelerated on a distance da up to a Lorentz factor γ, one
should add to ρ̄ and j¯z the contribution of the harmonic at frequency ω associated with the beam withLorentz factor γo . In that way, the continuity equation
can be satisfied. However, these extra-contributions
depend on the switching process. Here we will notconsider them. We will focus, instead, on the switchindependent part of the problem. Moreover, in thecase of a plasma accelerator, the switch-dependent
contributions have no eﬀect on the longitudinal wakefield acting on the electron beam. For zA → −∞, corresponding to the steady state solution, we obtain thefollowing expression:
z
E

=



iωzo ¯2iω
− 2 exp
f (ω)
γc
2γ2 c



|ω| | r⊥o − r ⊥ |× dr ⊥ ρo (r ⊥ )Ko
. (1)
γc

MOPPH006

z depends on zo through a phase factor only. WhenEzA = 0, corresponding without loss of generality to
the switch-on case, we have:ω f¯(ω)Ez (zo , r⊥o , ω) = − 2dr ⊥ ρo r ⊥
γc


 zo
| r⊥o − r ⊥ |2
dz
iωz
exp
+ iω
× i

2c(zo − z )2γ2 c
0 (zo − z )

2
2

γ c
| r⊥o − r ⊥ |exp iω
+
.
(2)
ωzo
2czo
Eq. (1) and Eq. (2) can be used to estimate the impact of the field generated by the electron beam on
any particle in the beam. We do so with the helpof the concepts of wake fields and impedances. By
definition of impedance Z(ω, z) we have Z(ω, z) =1/| f¯(ω)|2 V j¯z∗ Ēz dV, where | f¯(ω)|−2 accounts for thefact that test and source disks have total charge (e), while j¯z∗ ∝ f¯∗ and Ēz ∝ f¯. Here the volume V encloses the beam up to position z. Relation between
impedance Z and wake G is given by∞
Z = −∞ d(Δs)/(βc) G(Δs) exp[iωΔs/(βc)]. An explicit
expression for Z(ω, z) is


 z
ω
dr ⊥
dr ⊥ ρo∗ (r ⊥ )ρo (r ⊥ )
dz
Z=− 2
γ
0
⎧  
  
z⎪⎪iω z − z | r⊥o − r ⊥ |2
dz
⎨
i
exp
+
⎪
⎪
⎩ 0 (z − z )2cz − z
γ2


⎫

⎪
γ2 c
iωz ⎪| r⊥o − r ⊥ |2⎬
exp − 2 ⎪+  exp iω
.
(3)

⎭
ωz
2cz
2γ c ⎪
Eq. (3) constitutes a practical algorithm to computeboth real and imaginary parts of the impedance (and,subsequently, of the wake).
Since ρo is a real quantity, Z(ω) has the property
Z(ω) = Z ∗ (−ω). Then, Re[Z](ω) is an even function of
ω, while Im[Z](ω) is odd. The property Z(ω) = Z ∗ (−ω)
follows, more in general, from the fact that G(Δs, z) is areal function. If we split the wake function in the sum
G = GS + GA of a symmetric and antisymmetric part,the Fourier transform of GS gives back Re[Z], while theFourier Transform of GA yields Im[Z]. The symmetricpart of the wake, GS , is also known as active part andis related with the energy lost by the bunch throughradiation. The antisymmetric part GA is known asreactive part and is related with energy redistribution
within the bunch.

ANALYTICAL ASYMPTOTES
Impedance
With the help of Eq. (3) we calculate asymptotesof the real and imaginary parts of the impedance forz
2γ2  (see [1]). The real part is:

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27

MOPPH006

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 1: Plot of ζRe (left) and plot of ζIm (right).

Re[Z](ω) = −

c
π




2
 ρ̃o (θ, ω) 
dθ

γ θ

4 2

1 + γ 2 θ2

2 .

Figure 2: (a) Plot of HS and (b) plot of HA .

(4)

We now choose a Gaussian model for ρo , substituting ω) = 1/c · exp[−θ2 ω2 σ2 /(2c2 )] in Eq. (4). Thisρ̃o (θ,⊥gives Re[Z] = Zo ζRe (α), whereζRe (α) =1 
1 − (1 + α2 ) exp[α2 ]Γ(0, α2 ) ,4π(5)Γ(0, x) being the incomplete gamma function, Zo =4π/c the free-space impedance and α = ωσ ⊥ /(γc). A
plot of the universal function ζRe (α) is given in Fig.
1 (left plot). Re[Z] exhibits a singular behavior forσ⊥ −→ 0 (i.e. for α −→ 0 in Fig. 1 (left plot)). Thisis linked with our particular model, where we choseda −→ 0. The imaginary part is:1
Im[Z](ω) = − ωz
π




2
 ρ̃o (θ, ω) dθ1.
1 + γ 2 θ2

(6)

Similarly as for the real part, use of a Gaussian beammodel allows to give an explicit expression for Im[Z].
Namely, Im[Z] = (Zo ẑ) ζIm (α), whereζIm (α) = −1
exp[α2 ] Γ(0, α2 ) ,2π(7)where and ẑ = z/(2γ2 ). A plot of the universal function ζIm (α) is given in Fig. 1 (right plot).

Wake function
Analytical results given for zγ2 . GS (Δs)
can be found calculating the inverse Fourier transform of Re[Z](ω) with respect to Δs/βc. Using notation Δξ = γ(Δs)/σ⊥ , one obtains√ G√S (Δξ) = γ/σ⊥ ·HS (Δξ) where HS (Δξ) = −1/(4 π){ π |Δξ| + π[1 −(Δξ)2 /2] exp[(Δξ)2 /4] · erfc[|Δξ|/2]}. A plot of the universal function HS as a function of Δξ is given in the
FEL Theory

28

left plot of Fig. 2 (a). The energy gained or lost bya single particle at position s within the bunch dueto the active (symmetric) part of the wake, averaged
over transverse coordinatesis given by the convo∞lution ΔES (s) = (−e) −∞ GS (Δs) f (s − Δs)d(Δs). An explicit expression for ΔES /Eo as a function of ξ = γs/σ⊥ ,Eo = γme c2 being the nominal energy of an electron(with rest mass me ) is
Imax
ΔES
=
Eo
γIA



(Δξ)2
d(Δξ)HS (ξ − Δξ) exp −
,
2η2
−∞

 ∞

(8)

where we introduced the new parameter η = γσz /σ⊥ ,and we called the Alfven current IA√= e/(mc3 ) 17 kA
and the beam current Imax = eNc/( 2π σz ).
GA can be found calculating the inverse Fouriertransform of iIm[Z](ω) with respect to Δs/βc. One
obtains √GA (Δξ)√= γηẑ/σ⊥ · HA (Δξ), where HA (Δξ) =−Δξ/(2 π) {2 π/|Δξ| − π exp[(Δξ)2 /4] · erfc[|Δξ|/2]}
and we redefined ẑ = z/(2γ2 σz ). A plot of the universal function HA is reported in Fig. 2 (b). The energy
gained or lost by a single particle at position s within
the bunch due to the reactive part of the wake (averaged over transverse coordinates)
is given by the∞convolution ΔEA (s) = (−e) −∞ GA (Δs) f (s − Δs)d(Δs).
ΔEA /Eo as a function of ξ = γs/σ⊥ is given by :


ΔEA s
;η =
Eo σz



Imax ẑ
s
F
;η .
γIA
σz

(9)

where Eo = γme c2 , and



  ∞


(Δξ)2
s
s
F
;η =
d(Δξ) η HA η − Δξ exp −
.
σz
σz
2η2
−∞
(10)
A plot of F is given as a function of s/σz in Fig. 3 fordiﬀerent values of η.
Plots for ΔES /Eo and ΔEA /Eo as a function of ξ canbe computed with the help of numerical techniques.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH006

very large eﬀect. Note that the energy chirp in Fig. 4(right plot) depends on the electron beam profile but
also on time, because it develops along the undulator.
This eﬀect is fundamental, and is directly linked withthe feasibility of the proposed FEL scheme. Radiation
generated in one part of the undulator cannot interact
in resonance in another part of the undulator, and theamplification process is destroyed.

CONCLUSIONS

Figure 3: Plot of F at diﬀerent η.

Figure 4: ΔEs /Eo (left) and ΔEA /Eo (right) for the TTVUV-FEL at z = 0.8 m.

IMPACT ON TT-VUV-FEL
One of the applications envisaged for nextgeneration plasma accelerators is as drivers for tabletop FELs [2]. Here we will apply our theory to the
VUV case in Table I of reference [2]. The undulator parameter K is smaller than unity. Thus, wake field calculations in vacuum can still be used inside the undulator. In the TT-VUV-FEL case 2γ 2  18 cm, several
times smaller than the size of the planned undulator,that is about 0.8 m. Therefore we are well-within theapplicability region of the our asymptotic expressions.
Needed parameters are γ = 300, η = 10 and I = 50 kA.
Also, we need to fix a position along the longitudinalaxis. Here we set z 0.8 m, corresponding to the foreseen undulator length. The relative energy change
ΔES,A /Eo are presented respectively on the left and on
the right plot in Fig. 4 as a function of the longitudinalcoordinate inside the bunch. While travelling down
the undulator, a correlated energy change develops
along the electron beam. For estimations of the eﬀect
on the FEL gain we can use the linear energy chirpparameter α̂ = −(γωρ21D )−1 · dγ/dt. The eﬀect of linear
energy chirp starts to play a significant role on the FEL
gain when α̂  1. One finds α̂ 10, that indicates a

We studied the impact of longitudinal wake fields
on the quality of electron beams produced with highfield-gradient accelerators. Our consideration does
not depend on the particular realization of the accelerator. However, given present technological developments, one of the most relevant applications of ourstudy should come from the realm of laser-plasma
accelerators. We calculated longitudinally symmetric and anti-symmetric parts of the wake function as
well as real and imaginary part of the impedance withthe help of paraxial approximation within a spacefrequency domain formulation of Maxwell’s equation. While the general expressions for wakes and
impedances need numerical techniques to be evaluated, it is possible to present analytical expressions
for the asymptotic limit when the electron bunch hasreached a position, down the beamline, that is far
from the acceleration point with respect to the overtaking distance. Then, the wake and the impedance
are proportional to universal functions. Our results
can be used as analytical benchmarks for computercodes. Taking advantage of similarity techniques we
presented such result in terms of a complex dependent on the problem parameters (γηẑ/σ⊥ ) multiplied
by a universal function HA . Our expression for GA
can further be used to calculate the relative energychange of a particle within a given bunch. In caseof a Gaussian longitudinal profile the relative energy
spread reduces to Eq. (9). Plots presented in Fig. 3
will help the reader to perform a fast estimation of
the influence of the space-charge wake at the stageof planning of experiments. As a particular example, we used our results to estimate the impact of thelongitudinal wake fields on the energy change of theelectron beam for the TT-VUV-FEL setup in [2]. The
total energy deviation is found to be critical.
For details on our work we refer the interested
reader to [1].

REFERENCES[1] G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov,
Nucl. Instrum. and Methods in Phys. Research A
578 (2007) 3446, preprint version DESY 06-222 at
http://arxiv.org/abs/physics/0612077[2] F. Gruener et al., Appl. Phys. B 86, 431 (2007)

FEL Theory

29

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Proceedings of FEL 2007, Novosibirsk, Russia

THEORY OF NONLINEAR HARMONIC GENERATION IN FELS WITH
HELICAL WIGGLERS
G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
Nonlinear Harmonic Generation (NHG) is of importance for both short wavelength FELs, in relation
with the achievement of shorter wavelengths with afixed electron-beam energy, and high-average power
FEL resonators, in relation with destructive eﬀects ofhigher harmonics radiation on mirrors. We present atreatment of NHG from helical wigglers with particular emphasis on the second harmonic. Our study isbased on an analytical solution of Maxwell’s equations, derived with the help of a Green’s function
method. We demonstrate that NHG from helical wigglers vanishes on axis. Our conclusion is in contrast
with literature, that includes a kinematical mistakein the description of the electron motion. A detailed
report with relevant references is given in [1].

INTRODUCTION
NHG is of undisputed relevance in the field of FELs.
It is generated by bunching of the electron beam at
higher harmonics, driven by interaction with the fundamental. In general, NHG can be treated in terms ofan electrodynamical problem where Maxwell’s equations are solved with given macroscopic sources inthe space-frequency domain. These sources are obtained through the solution of self-consistent equations for electrons and fields. Further on, solutionof Maxwell’s equations characterizes harmonic radiation in the space-frequency domain. The dependence of sources in the space-frequency domain ontransverse and longitudinal coordinates is complicated because is the result of the above-mentioned
self-consistent process. However, here we deal withan FEL setup where an ultrarelativistic electron beam
is sent, in free space, through an undulator with many
periods. Then, paraxial and resonance approximation
can be applied. In particular, for a fixed transverse position, the longitudinal dependence is always slow on
the scale of an undulator period. NHG has been dealt
with in the case of a planar wiggler, both theoretically and experimentally. Odd harmonics have maximal power on axis1 and are linearly polarized. Even
harmonics have been shown to have vanishing onaxis power and to exhibit both horizontal and verticalpolarization components. Here we present the first
theory of NHG from helical wigglers, based on a so1
Here we assume that the bunching wavefront is perpendicular
to the (longitudinal) FEL axis.

FEL Theory30

lution of Maxwell’s equations in the space-frequency
domain, obtained with a Green’s function technique.

NHG IN HELICAL WIGGLERS
Analysis of the harmonic generation mechanism
We use paraxial Maxwell’s equations in thespace-frequency domain to describe radiation fromultra-relativistic electrons. Let us call the transverse electric field in the space-frequency domainĒ⊥ (z, r⊥ , ω), where r⊥ = xex + ye y and z identify a pointin space. From the paraxial approximation follows
that the electric field envelope E= Ē exp [−iωz/c]⊥⊥does not vary much along z on the scale of the reduced
wavelength  = λ/(2π). Maxwell’sequationin parax
ial approximation reads: D E⊥ (z, r⊥ , ω) = f (z, r⊥ , ω),
where D ≡ ∇⊥ 2 + (2iω/c)∂/∂z, ∇⊥ 2 being the Laplacian operator over transverse cartesian coordinates.
The source-term vector f(z, r⊥ ) is specified by the
trajectory of the source electrons, and can be written
in terms of the Fourier transform of the transverse
current density, j¯⊥ (z, r⊥ , ω), and of the charge density, ⊥ ρ̄] exp[−iωz/c].
ρ̄(z, r⊥ , ω), as f = −4π[(iω/c2 )j¯⊥ − ∇In this paper we will treat j¯ and ρ̄ as macroscopic⊥

quantities, without investigating individual electron
contributions. j¯⊥ and ρ̄ are regarded as given data,that can be obtained from any FEL code. Codes
actually provide the charge density of the modulated
electron beam in the time domain ρ(z, r⊥ , t). A
post-processor can be used in order to perform theFourier transform of ρ that can always be presented
as ρ̄ = −ρ(z, r⊥ − r o⊥ (z), ω) exp [iωso (z)/vo ], where theminus sign on the right hand side is introduced for notational convenience only. Quantities r o⊥ (z), so (z) andvo pertain a reference electron with nominal Lorentz
factor γo that is injected on axis with no deflection andis guided by the helical undulator field. Such electron
follows a helical trajectory r o⊥ (z) = roxex + roye y .
We assume that rox (z) = K/(γo kw )[cos(kw z) − 1] androy (z) = K/(γo kw ) sin(kw z), where K = λw eHw /(2πme c2 )is the undulator parameter, λw = 2π/kw being
the undulator period, (−e) the negative electron
charge, Hw the maximal modulus of the undulator
magnetic field on-axis, and me the rest mass of theelectron. The correspondent velocity is describedby vo⊥ (z) = voxex + voye y . Finally, so (z) is the curvi-

Proceedings of FEL 2007, Novosibirsk, Russia
linear abscissa measured along the trajectory of is useful
the reference particle. Introduction of ρ is a slowly varying function of z on thewhen ρ
wavelength scale. This property is granted by thefact that the charge density distribution under study
originates from an FEL process. From this fact it
 is slowly varying on the scale ofalso follows that ρ
the undulator period λw and is peaked around eachharmonic of the fundamental ωr = 2kw cγ̄2z , that isfixed imposing resonance condition between electricfield and reference particle. The word ”peaked”
means that the bandwidth of each harmonic component obeys Δω/(hωr )  1 for each positive integer
value h. Here γ̄z = 1/ 1 − v2oz /c2 is the longitudinal
Lorentz factor. Finally, the relative deviation of theparticles energy from γo me c2 is small, i.e. δγ/γo  1.
It follows
motion we have f =
  zthat for a generic

2
2
⊥ ρ
[z; r⊥ −4π exp i 0 dz̄ω/(2γ̄z c) iω/(c )vo⊥ (z) − ∇r o⊥ (z)]. We account for a possible deflection angle
(c) in the the trajectory of the reference electron.
η(c)Therefore r o⊥ (z) −→ r⊥ (z, η(c) ) = r o⊥ (z) + 
η(c) z
(c)
(c)



and vo⊥ (z) −→ v⊥ (z, η ) = vo⊥ (z) + c
η . Usingv⊥ (z, η(c) ) in place of vo⊥ (z) implies that γz (z, η(c) ) is(c)
now a function of both z and η . In particular,
1/γ2z (z, η(c) ) = 1 − v2z (z, η(c) )/c2 , where v2z = v2 − v2⊥
is the square of the electron longitudinal velocity.
It follows that 1/γ̄2z in f should also be substituted
η(c) ). With these prescriptions, we find aby 1/γ2z (z, solution to paraxial Maxwell’s equation with the helpof a Green’s function technique, without any otherassumption about the parameters of the problem.
We are interested in the total power emitted andin the directivity diagram of the radiation in the
far zone. Thus, we introduce the observation angle = r⊥o /zo , setting θ ≡ |θ|, taking the limit for zo  Lw ,θ
where Lw = Nw λw is the undulator length. Moreover,
we are interested in studying frequency near thefundamental harmonic ωr = 2kw cγ̄2z or its h-th integer
multiple. We specify ”how near” the frequency ω is tothe h-th harmonic by defining a detuning parameter
Ch = ω/(2γ̄2z c) − hkw = Δω/ωr kw . Here ω = hωr + Δω.
Altogether, using Anger-Jacobi expansion, we find
∞

∞

L /2

w
iω

 z , lx , ly
E⊥ =
dlx
dly
dz ρ
czo −∞−∞−Lw /2
⎤⎫
⎧ ⎡
2
2
(c)
⎪
⎢
⎥⎥⎪
z
+
θ
θ
⎪
⎪
o
⎢
K(θ
−
η
)
x
y
ω
x
⎨ ⎢⎢
x

 ⎥
⎥⎬
i
× exp ⎪
+
−
(θ
l
+
θ
l
)
⎢
⎪
x x
y y ⎥
⎢
⎥
⎪
⎦⎪
⎩ c ⎣
⎭
2
k γ

w




iπn
exp [i(n + m + h)kw z ]2m,n=−∞
 
 
ω
ω
(c) 2
(c) 2 × exp i Ch +zθx − ηx +θy − ηy
2c
2c


K 
(c)
×
exp[ikw z ] − exp[−ikw z ] + θx − ηx ex
2iγ

×

∞


Jm (u)Jn (v) exp

MOPPH007




K 
(c)
−
exp[ikw z ] + exp[−ikw z ] − θ y − η y e y
2γ
with

=

u

−Kω(θy − η(c)y )/(cγkw )

and

!
(1)
v

=

(c)
−Kω(θx − ηx )/(cγkw ). Whenever Ch + ω/(2c)[(θx −
(c) 2
(c)
ηx ) + (θ y − η y )2 ]  kw , the second phase factor in z

in Eq. (1) (the one containing Ch ) is varying slowly
on the scale of the undulator period λw . As a result,simplifications arise when Nw  1, because fast
oscillating terms in powers of exp[ikw z ] eﬀectively
average to zero. We further select frequencies suchthat |Δω|/ωr  1, i.e. |Ch |  kw . Note that this condition on frequencies automatically selects observation
−η(c) )2  1/γ̄2z . Independently
angles of interest h(θof the value of K and for observation angles of interest
we have |v|  1 and |u|  1, and we can expand J n (v)and Jm (u) in Eq. (1).
From now on we consider the case h = 2. Performing expansion, and accounting for terms giving
a non-zero contribution after integration in dz we obtainiω ex + ie y K 


(c)
(c)

E⊥ =
θx − ηx + i θ y − η y22czo ωr (1 + K )
2

∞

2

∞

Lw /2

 z , lx , ly exp [iC2 z ]
dlx
dly
dz ρ
−∞
−∞
−L
/2
w
⎤⎫
⎧ ⎡
2
2
⎪
⎥⎥⎪
⎪
⎪
⎨ ω ⎢⎢⎢⎢ zo θx + θ y
⎬

 ⎥
i ⎢⎢
− θx lx + θ y l y ⎥⎥⎥⎪
× exp ⎪
⎪
⎦⎪
⎩ c ⎣
⎭
2




ω
(c) 2
(c) 2 × exp iz .
(2)θx − ηx + θ y − η y2c×The electric field is left circularly polarized and van = η
(c) . Polarization characteristics are theishes at θsame as for the fundamental harmonic, although the=η(c) .
fundamental does not vanish at θ
We conclude our analysis of NHG in helical wigglers studying on-axis harmonic generation. We cando so in all generality, i.e. for any harmonic number,−with the help of Eq. (1). We set θη(c) = 0. It follows
that Eq. (1) can be rewritten as
Lw /2
iω


 z , l exp [iCh z ]
dl
E⊥ =
dz ρ
czo
−Lw /2
#"K×exp[i(h + 1)k w z ] − exp[i(h − 1)k w z ] ex
2iγ

# !
"
K
+ −
exp[i(h + 1)k w z ] + exp[i(h − 1)k w z ] e y .
2γ(3) is a slowly function of z on the scale of theSince ρundulator period and Ch  kw , we see by inspection
that, after integration in dz , one obtains non-zero onaxis field only for h = 1. This result is in open contrast
with what reported in reference [2]: we will address
this fact in the discussion section.

FEL Theory

31

MOPPH007

Proceedings of FEL 2007, Novosibirsk, Russia

Analysis of a simple model
We treat a particular case to exemplify our results.
We consider the case when C2 = 0 (i.e. ω = 2ωr ) = Io a2 /(2πcσ2⊥) exp [−l 2x + l 2y /(2σ2⊥)] exp[i2ωr /c ·and ρ

(ηx lx + η y ly )]HLw (z), with HLw a window function
equal unity inside the undulator and zero everywhere
else. Here Io is the bunch current, a2 is a constant determining the strength of the bunching and σ⊥ the rms
transverse size of the electron beam. This corresponds
to a modulation wavefront perpendicular to the direction of motion of the beam. Direct substitution in Eq.
(2) and calculations yield
(c)

(c)

$
%
2iIo a2 Lw ωr ex + ie y
K2

E⊥ =
c 2 zo
1 + K 2



ωr
(c)
(c)
× θx − ηx + i θ y − η y exp i zo (θ2x + θ2y )c!
2σ2⊥ ω2r 
(c) 2
(c) 2
× exp − 2
θx − ηx + θ y − η y
c



2
2
Lw ωr
+ θ y − η(c)
×sinc
.
(4)
θx − η(c)xy2cFigure 1: Directivity diagram for the intensity.

Going back to our particular case in Eq. (4), a
subject of particular interest is the angular distribution of the radiation intensity, which will be denoted with I2 . Upon introduction of normalized√√2ωr Lw /c θx,y =8πNw γ̄z θx,y ,quantities θ̂x,y =
√
√
(c)
(c)
(c)
η̂x,y = 2ωr Lw /c ηx,y = 8πNw γ̄z ηx,y and of the Fresnel number N = 2ωr σ2⊥ /(cLw ), one obtains

 &
&
&!
& !
&&
&&
(c) &2(c) &2(c) &2
&
1



2
&
&
&
&
&
I2 ∝ &θ̂ − η̂ & exp −N &θ̂ − η̂ & sinc&θ̂ − η̂ &&4(5)
In the limit for N  1, Eq. (5) gives back the directivity diagram for the second harmonic radiation from asingle particle. The directivity diagram in Eq. (5) isplotted in Fig. 1 for diﬀerent values of N as a func(c)tion of |θ̂ − η̂ |, normalized to the maximal intensity
I2max at each value of N. The next step is the calculation of the second harmonic power that is given by
∞
∞

2
W2 = c/(2π) −∞ dxo −∞ dyo |E⊥ (zo , xo , yo )| . It is convenient to present the expressions for W2 in a dimensionless form. After appropriate normalization it is afunction of one dimensionless parameter only, that is(2)Ŵ2 = F2 (N) = ln [1 + 1/(4N 2 )]. Here Ŵ2 = W2 /Wo is
the normalized power, while the normalization con(2)(2)
stant Wo is given by Wo = (2K2 /1 + K2 )2 (Io2 /c)a22 . The
function F2 (N) is plotted in Fig. 2. The logarithmic
divergence in F2 (N) in the limit for N  1 imposes alimit on the meaningful values of N. However, in thecase N < Nw−1 we deal with a situation where the dimensionless problem parameter N is smaller than theaccuracy of the resonance approximation ∼ Nw−1 , andfor estimations we should replace ln (N) with ln (Nw−1 ).
FEL Theory

32

Figure 2: Illustration of the behavior of F2 (N).

DISCUSSION
NHG in a helical wiggler has been addressed in [2],where a numerical study-case guarantees that paraxial and resonance approximation can be applied. The
main result of [2] is that characteristics of helical undulator radiation from an extended source, i.e. abunched electron beam, are drastically diﬀerent compared to those from a single electron. In particular,
NHG does not vanish on-axis, in open contrast withour conclusions. In our understanding, results in [2]are incorrect. Any linear superposition of a given
field harmonic from single electrons conserves singleparticle characteristics like parametric dependence on
undulator parameters and polarization. In particular,
since field harmonics from a single electron vanishes
on-axis, they must vanish on-axis for the linear superposition as well. This also applies in the case of NHG,
because the dependence of charge and current density
distributions of the bunched beam on the longitudinal coordinate is slow on the scale of the undulator

Proceedings of FEL 2007, Novosibirsk, Russia
period. This argument suggests that results in reference [2] are incorrect. A flaw can be pinpointed in
the azimuthal resonance condition proposed in [2]:”The azimuthal electron motion in helical wigglers isθ = kw z (kw is the wave number for the wiggler period
λw ), which couples to circularly polarized waves thatvary as exp(iφh ), where φh = kz + hθ − ωt is the wave
phase. Hence, the phase along the particle trajectories varies as φh = (k + hkw )z − ωt, and the hth orderazimuthal mode corresponds to the hth harmonic resonance [i.e., ω ≈ (k + hkw )vz ]”. There θ indicates anazimuthal position as in Fig. 3. Note that the phaseφh = kz + hθ − ωt pertains a circularly polarized wave
whose electric field is written in terms of unit vectors
eρ and eθ and not of ex and e y (eρ , eθ , ex and e y are
shown in Fig. 3). In fact one may write the electricfield of a (e.g. left) circularly polarized plane wave at
position r and time t as Eo (er + i eθ ) exp[iφh ], Eo being a
constant field strength. We argue that it is incorrect touse relation θ ≈ kw z in the expression for φh as done in[2]. On the one hand, the radiation
diﬀraction size for√a single particle is of order Lw . On the other hand,the electron rotation radius is given by rw = (K/γ)w .
It follows that r2w /Lw  1, that holds independentlyof the value of K, because Nw  1. Thus, the electron rotation radius is always much smaller than theradiation diﬀraction size. Moreover, straightforward
geometrical considerations show that it makes sense
to talk about a transverse beam size σ⊥ only whenσ2⊥  r2w . This is the case in practical situations ofinterest. There is still room to compare the beam
size σ⊥√with the radiation diﬀraction size. In the caseσ⊥  Lw we deal with a filament electron beam.
In the opposite case the filament beam approximation breaks down. We are interested in this last case,where single-particle results cannot be used. We havetherefore established a hierarchy in the characteristic
scales of interest: σ2⊥  Lw  r2w . It follows that theazimuthal coordinate of each electron, θ, is fixed during the motion inside the undulator with the accuracyof the resonance approximation, scaling as 1/Nw . In
contrast to this, the identification θ ≈ kw z is made in[2]. This is a kinematical mistake. If θ ≈ kw z eachelectron would be rotating around the origin of thecoordinate system, that is not the case. Thus, theazimuthal resonance condition is a misconception following from this mistake. This misconception is subsequently passed on to simulations in [2], resulting
in incorrect outcomes. Harmonic emission exists for asingle electron, and it also exists for an electron bunch.
However, qualitative properties are diﬀerent with respect to what has been predicted in [2]. In particular,
as we have seen before, on-axis power vanishes.

MOPPH007
y

y

P

r
eθ

x

r

r
ey

r
er
θ

z

r
ex

x

Figure 3: Cylindrical coordinate system and setup.

CONCLUSIONSIn this paper we discussed NHG in helical undulators, with particular emphasis on second harmonic
generation. First we considered the NHG mechanism
in helical undulators in all generality. Then we specialized our study to the case of second harmonic generation. Finally, to exemplify our results, we treated asimplified model where the beam modulation wavefront is orthogonal to the z axis, has a Gaussian transverse profile and is independent on the position inside the undulator. Our results show that on-axis harmonic generation from helical wigglers vanishes. Thisapplies to any harmonic of interest with the exclusionof the fundamental, and independently of the form of
the electron beam modulation (assuming that the electron beam as a whole propagates on-axis). Importantconsequences follow regarding the two mainstream
development paths in FEL physics. First, as concerns
short wavelength (x-ray) SASE FEL devices, vanishing on-axis harmonics make the option of a helicalundulator less attractive as regards the exploitationof NHG radiation. Second, as concerns high averagepower FEL oscillators, vanishing on-axis harmonics
suggest that helical undulators carry relevant advantages over planar undulators, as potential for mirror
damage is reduced. Previous studies reported nonvanishing on-axis power, due to the nature of a particular azimuthal resonance condition. We showed that
this resonance condition is a misconception, arisingfrom a kinematical mistake. This misconception was
passed on to simulations, that confirmed the presenceof on-axis power out of NHG from helical wigglers.
Such result is incorrect.
For details on our work we refer the interested
reader to [1].

REFERENCES[1] G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov,
preprint DESY 07-058, http://arxiv.org/abs/0705.0295,
accepted for publication in Nucl. Instrum. and Methods in Phys. Res. A[2] H.P. Freund, P.G. O’Shea and S.G. Biedron, PhysicalReview Letters, 94, 074802 (2005)

FEL Theory

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MOPPH009

Proceedings of FEL 2007, Novosibirsk, Russia

UNDULATOR RADIATION IN A WAVEGUIDE
G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
We propose an analytical characterization of undulator radiation near resonance, when the presence ofthe vacuum-pipe aﬀects radiation properties, as forthe far-infrared undulator beamline at FLASH, that isdesigned to deliver pulses in the THz range. Suchline can be used for pump-probe experiments whereTHz pulses are naturally synchronized to the VUVpulse from the FEL, as well as the development ofnovel electron-beam diagnostics techniques. Since theTHz radiation diﬀraction-size exceeds the vacuumchamber dimensions, characterization of infrared radiation must be performed accounting for the presence of a waveguide. We developed a theory of undulator radiation in a waveguide based on paraxial
and resonance approximation. We solved the field
equation with a tensor Green’s function technique,and extracted figures of merit describing the influence of the vacuum-pipe on the radiation pulse as afunction of the problem parameters. Our theory, thatmakes consistent use of dimensionless analysis, allows treatment and physical understanding of many
asymptotes of the parameter space, together with theirregion of applicability. A more detailed report of ourstudy is given in [1].

INTRODUCTION AND THEORY
The accelerator complex at FLASH produces ultrashort bunches approaching sub-100 fs duration.
FLASH will soon operate together with a FIR electromagnetic undulator providing coherent FIR radiation intrinsically synchronized with the VUV pulses.
The wavelength range (λ = 60 ÷ 200 μm) will overlap with a large part of the THz-gap. This will allow
pump-probe experiments combining FIR and VUV radiation, and non-destructive electron beam diagnostics. Vacuum chamber eﬀects are expected to play
an important role at longer wavelengths. Optimization of the radiation transport system calls for a precise characterization of THz pulses along the photon
beamline. In the present work we focus on the characterization of undulator radiation from a filament
beam (as for the FIR line at FLASH) in presence of awaveguide. One should solve the field equations inparaxial approximation with proper boundary condi⊥ )| = 0
tions, e.g. D[Er⊥ )] = f(z, r⊥ ), where (n × E⊥ (z, S
and (∇⊥ · E⊥ )|S = 0. Here S is the internal surface of thepipe, D ≡ (∇⊥ 2 + 2iω/c · ∂/∂z), ∇⊥ 2 being the LaplaFEL Theory

34

cian operator over transverse cartesian coordinateszand f = 4πe/c · exp{i 0 dz̄ω/[2γ2z (z̄)c]}[iω/c2 · v⊥ (z) − ⊥ ]δ(r⊥ − r ⊥ (z)). Solution must accounting for the ten∇sorial nature of the Green’s function. In the UR case,the resonance approximation can be exploited too. We
thus consider planar undulator with a large number ofundulator periods and a frequency range of interest
close to the fundamental harmonic, where the freespace field exhibits horizontal polarization (for undulator field in the vertical direction) and azimuthal
symmetry. An explicit expression for the field is calculated as a superposition of TE and TM modes. Weintroduce normalized units: Ê⊥ = [−c2 /(A JJ ωeθs )]E⊥,√Ĉ = 2πNw Δω/ωr , ẑ = z/Lw , r̂ = r/ Lw , Ω = R2 /Lw ,μ
Ĉk μ21k /(2Ω) and Ĉνk = ν21k /(2Ω). Here Ω = R2 /(Lw )is the main parameter of our theory, comparing thepipe area with the radiation diﬀraction area, while
μmk and νmk are, respectively, solutions of Jm(μmk ) = 0
and Jm (νmk ) = 0. We obtain for Êx,y (r̂, φ, ẑ):



 
∞ 

μ1k r̂
μ1k r̂μAk (ẑ) Jo √+ J2 √
cos(2φ)Êx = i
Ω
Ω
k=1



 
ν1k r̂
ν1k r̂
ν− J2 √
cos(2φ)(1)+Ak (ẑ) Jo √
Ω
Ω
and




∞ 

μ1k r̂
ν1k r̂
μνÊ y = iAk (ẑ)J2 √− Ak (ẑ)J2 √sin(2φ),
Ω
Ω
k=1
(2)
μ

μ

μ

where we set Ak (ẑ) = Ĉk exp[−iĈk ẑ]/[(μ21k − 1)J12 (μ1k )]μsinc[1/2(Ĉk + Ĉ)] and, moreover, Aνk (ẑ)=
Ĉνk exp[−iĈνk ẑ]/[ν21k J02 (ν1k )]sinc[1/2(Ĉνk + Ĉ)].
The
μ,ν
sinc(·) functions in the expressions for Ak is consequence of instantaneous switching of the undulator
field. However, our theory applies with a finite
accuracy related to the use of the resonance approximation. We thus introduce a spatial frequency filterin the field by redefiningμ

Ak (ẑ) =
and

μ

μ

Ĉk exp[−iĈk ẑ](μ21k − 1)J12 (μ1k )μF S(ẑ ), Ĉk + Ĉ(3)

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH009

Hard-Edge Case
X-polarization

Y-polarization

Î

Î

1
2
1

2

0
0
-2
0

x̂

ŷ

-2
2

0.75
0.5
0.25
0

2
0
-2
0

x̂

ŷ

-2
2

Figure 1: Three-dimensional view of the virtual sourcein the free-space limit for Δ = 0 (hard-edge case) andĈ = 0 (perfect resonance) .

Figure 3: Intensity profiles of the virtual source (ẑ = 0)
at diﬀerent values of Ω = R2 /(Lw ) for Δ = 0.1 andĈ = 0 (perfect resonance).

Figure 2: Intensity profiles of the virtual source (ẑ = 0)
at large values of Ω = R2 /(Lw ) for diﬀerent valuesof Δ and Ĉ = 0 (perfect resonance). This 2D plot is
obtained cutting the 3D intensity profile at ŷ = 0 (i.e.
at φ = 0).

Aνk (ẑ) =Ĉνk exp[−iĈνk ẑ]ν21k J02 (ν1k )μ,ν

F S(ẑ ), Ĉνk + Ĉ.

We also studied the impact of wall-resistance eﬀects.
We concluded that propagation through the pipe isstrongly aﬀected by wall-resistance eﬀects even for relatively large values of Ω. This eﬀect strongly depends
on the material considered. Estimations allowed us toformulate the recommendation that the internal partof the vacuum pipe for the infrared undulator line at
FLASH should be copper-coated.

RESULTS(4)

Here F {S(ẑ ), (Ĉk + Ĉ)} is the Fourier transform of theμ,ν
function S with respect to (Ĉk + Ĉ). The where function S(z ) introduces some smoothing of the rectangular undulator profile on a scale of λw . We model S(ẑ )as a constant function along the undulator length withexponentially decaying edges on a typical distance Δ.
The value of Δ is chosen to cut oﬀ high spatial frequencies that are outside the region of applicabilityof the resonance approximation, i.e. Δ ∼ 1/Nw . A
three-dimensional view of the virtual source in the
middle of the undulator in the free-space limit Δ = 0(hard-edge case) is presented in Fig. 1, while intensity
profiled for diﬀerent values of Δ are given in Fig. 2.

Some figure of merit should be extracted from thefull information carried by the expression for the field
about how the metallic pipe influences radiation properties. We separately studied, for horizontal and vertical polarization components, two-dimensional intensity distributions on a transverse plane at arbitrary
distance from the undulator, for diﬀerent choices ofthe problem parameter. These plots are shown in Fig.
3 and Fig. 4. Another figure of merit of interest is theratio between the power density for a specific valueof Ω integrated over the waveguide cross-section andthe angle-integrated power density in free space:

Ŵ =


2 
2  









dr̂⊥  lim Ê⊥  .
dr̂⊥ Ê⊥ (Ω)
Ω→∞

(5)

FEL Theory

35

MOPPH009

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 6: Plot of Ŵ as a function of Ĉ = 2πNw Δω/ωrfor Ω = 2.0 at Δ = 0.1.

Figure 4: Intensity profiles of the virtual source (ẑ = 0)
at diﬀerent values of Ω = R2 /(Lw ) for Δ = 0.001 andĈ = 0 (perfect resonance).

Figure 7: Plot of Ŵ as a function of Ĉ = 2πNw Δω/ωr forΩ = 2.0 at diﬀerent values of Δ = 0.01 and Δ = 0. The
far-field limit (Ω −→ ∞) is also shown for comparison(dotted line).

We studied Ŵ as a function of Ω at perfect resonance(see Fig. 5). Conversely, once Ω is fixed, one caninvestigate how the total power changes as a functionof the detuning from resonance (see Fig. 6 and 7).
We also proposed a comparison between the magnitude of the horizontally and vertically polarized fields,
defined as

Figure 5: Plot of Ŵ as a function of Ω = R2 /(Lw ) forĈ = 0 (perfect resonance) at diﬀerent values of Δ.

Px (r̂) = Abs Êx (r̂, 0, 0) 

Ω−→∞

(6)

π
P y (r̂, Ω) = Abs Ê y r̂, , 0 .

4

(7)

and

Ω

FEL Theory36

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH009

Figure 8: Comparison of Px (dotted line) and P y (solidline) for Δ = 0.1 at diﬀerent values of Ω = R2 /(Lw )and Ĉ = 0 (perfect resonance). Plots refer to the virtual
source position (ẑ = 0).

Figure 10: Intensity profiles at diﬀerent values of ẑ =z/Lw for Ω = 2, Ĉ = 0 (perfect resonance) and Δ = 0.1.

Figure 9: Comparison of Px (dotted line) and P y (solidline) for Δ = 0.01 at diﬀerent values of Ω = R 2 /(Lw )and Ĉ = 0 (perfect resonance). Plots refer to the virtual
source position (ẑ = 0).

Plots are given in Fig. 8 and Fig. 9.
Finally, evolution of the intensity profiles at Ω = 2
and Ĉ = 0 is given in Fig. 9.

CONCLUSIONS

a tensor Green’s function, complicating equations thatnow depend on the undulator type and on the waveguide geometry. We treated a circular waveguide inparticular, and we implemented the planar undulator case within the applicability region of the resonance approximation. The electric field was foundas a superposition of the waveguide modes, and wasstudied for diﬀerent values of parameters. The main
parameter involved in the problem is the waveguideparameter Ω. When Ω is comparable, or smaller thanunity, waveguide eﬀects become important, under theassumption of a perfect conductor.
For details on our work we refer the interested
reader to [1].

REFERENCES[1] G. Geloni, E. Saldin, E. Schneidmiller and M.
Yurkov,submitted to Elsevier Science, also DESY 0731 (2007) http://arxiv.org/abs/physics/0703049.

We presented a theory of undulator radiation withina waveguide and we exemplified it in the case of
the infrared undulator beamline at FLASH. Relation
between current electromagnetic sources and field ismore complicated with respect to the free-space case.
Analysis of the problem is performed with the help of
FEL Theory

37

MOPPH010

Proceedings of FEL 2007, Novosibirsk, Russia

THREE-DIMENSIONAL ANALYSIS OF THE SURFACE MODE
SUPPORTED BY A REFLECTION GRATING
Vinit KumarÝ , RRCAT, Indore, M.P. 452013, India
Kwang-Je Kim, ANL, Argonne, IL 60439, USA
Abstract
In a Smith-Purcell Free-Electron Laser (SP-FEL), theelectron beam interacts with the surface mode supported
by a metallic reflection grating to produce coherent radiation. All the previous analyses of SP-FEL had considered
the localization of the surface mode only in the direction
perpendicular to the grating surface and assumed translational invariance along the direction of grooves of the grating. In this paper, we include the localization of the surface
mode along the direction of grooves as well and study thethree-dimensional structure of the surface mode in order toinclude diffraction effects in the analysis of SP-FELs. Fullthree-dimensional Maxwell-Lorentz equations are derived
for the self-consistent nonlinear analysis of SP-FELs.

interaction of the electron beam with the three-dimensionalsurface mode.
In the next section, we discuss the dispersion relationof an off-axis nonlocalized surface mode supported by areflection grating. The construction of three-dimensional
localized surface mode using a combination of off-axis
nonlocalized modes is discussed in the following section.
Maxwel-Lorentz equation for the interaction of the electron beam with the three-dimensional surface mode is discussed after that and finally, we present some conclusions
in the last section.

DISPERSION RELATION OF A SURFACE
MODE PROPAGATING OFF-AXISINTRODUCTION
Smith-Purcell Free-Electron Laser (SP-FEL) is seen as
an attractive option for a compact coherent terahertz source
using low energy electron beam. In an SP-FEL, coherent
electromagnetic radiation is generated due to the interaction of an electron beam with the surface electromagnetic
mode supported by a reflection grating. Several authors
have recently studied this interaction using analytical aswell as numerical techniques [1-4]. In all the previous analyses, the three-dimensional effects have been either ignored
or included only approximately. This is because these analyses consider the interaction of the electron beam with thetwo-dimensional surface mode, where the electromagnetic
field has no variation along the direction of grooves of thereflection grating. The two-dimensional surface mode istherefore not localized in the direction of grooves, although
it is localized in the direction perpendicular to the grating
surface. We call such surface modes as nonlocalized surface modes in this paper. The diffraction of surface modealong the direction of grooves, which affects the overlap
with the electron beam and hence the build-up of poweris therefore not included in these analyses. It is important
to include three-dimensional effects in the analysis to accurately study the performance of the system and also toaccurately calculate the start current, which is the threshold electron beam current for coherent growth of power. In
this paper, we study the three-dimensional surface mode,
which is localized in both the transverse directions that areperpendicular to the direction of propagation. We also discuss the coupled Maxwell-Lorentz equation to describe the£ Work supported by the U.S. Department of Energy, Office of Sci-ence, Office of Basic Energy Sciences, under Contract No. DE-AC0206CH11357.
Ý vinit@cat.ernet.in

FEL Theory

38

x

y

λg
Z
d
w

Reflection Grating

Figure 1: Schematic of a rectangular reflection grating. The
top surface of the grating is in the plane = 0.

Figure 1 shows the schematic of a rectangular metallic reflection grating having period  , groove depth ,and groove width . We want to study the self-consistentelectromagnetic field supported by this structure. All theprevious analyses of this problem assumed the system tohave translational invariance in the -direction and hence
these are two-dimensional analyses. Here, we assume anexp() type variation in EM field along the -direction.
In order to find out the dispersion relation of the surface
mode, we follow our earlier approach [3, 5], where the surface mode appears in terms of singularities of the reflection matrix . The EM field in the region  is composed of the incident and reflected wave having the following Floquet-Bloch expansion for the -polarization:

 

 










          (1)          (2)

Proceedings of FEL 2007, Novosibirsk, Russia                






                  

(3)
(4)



     

 

(6)

   (7)

where            
. The remaining components of EM field inside the groove
can be determined in the same way as described above by
Eqs. (3-6). In the metallic portion of the grating, the electromagnetic field can be assumed to be vanishing. The following expression for the reflection matrix  is obtainedby satisfying the boundary condition at the interface =0
for  and  :  !  "   !  " (8)where ! is the identity matrix and " is the impedance matrix given by
" 



 
 




#



(9)

        

Here,  in the complex conjugate of , #    #   , and  is given by     $ 





$ 

 %
 % $·
%
%

0.3

0.2

0.1

(5)

where  is the permeability of vacuum. Note thatsince we are considering -polarization as opposed to -polarizationn due to its strong interaction with copropagating electron beam, we take   = 0.
The electromagnetic field inside the grooves can be expressed as a superposition of cavity modes, and the expression for  in the  groove         , where      can be written as [8]  

2 2 2 1/2



where %    . The above expression for 
has the same form as given in Ref. [8] except that it is now
generalized to include non-zero value of   . We make animportant observation here that the effect of introducing afinite value of  is that in earlier expression simply gets
    . With the help of this replacereplaced withment rule, we can use the earlier calculation performed forthe  = 0 case even for a finite   case.

(ω -c kx )Here  is the spectral order,   ,      ,    ,   ,    ,           , and the sign of the square root is chosen such that Re    Im    , which is essentiallythe outgoing wave condition [6]. The phase velocity of thezeroth-order component along the -axis is  in the unitof the speed of light . Note that the plane wave components described by Eqs. (1-2) are in general, propagating
off-axis in the  plane. The total electromagnetic field andin the region  is obtained by combining thecontribution from the incident and reflected waves. In addition to  , the EM field will have   ,  ,  and           
components also. Defining and          , these components are
given by [7]

MOPPH010





0.0
0.0

0.2

0.4

0.6

0.8

kz/kg

Figure 2: Typical dispersion relation for a rectangular reflection grating for a surface mode propagating off-axis.

Next, we discuss the dispersion relation of the surface
mode. The surface mode appears as a singularity in the reflection matrix. For example, for a given value of and , we can find a value of   for which the reflection matrix becomes singular. This means that reflected components given by Eq. (2) are supported self-consistently by
the grating without the need of incident waves. Also, thereflected components corresponding to different values of in Eq. (2) add in a certain fixed ratio of amplitudes suchthat the boundary conditions are satisfied on the grating surface [3]. In this way, by studying the singularity of , we
can find out the dispersion relation of the surface mode. We
have earlier discussed the calculation of dispersion relationfor  = 0 case in Refs. [3,5]. The same calculation can beused to get the dispersion relation for a finite   case, using
the replacement rule that we have discussed in this section.
Fig. 2 shows a typical dispersion relation plotted for a certain set of grating parameters. For a given value of and , there is a certain fixed value of   and also the values of   for all values of  are fixed and can be calculated.
As has been discussed earlier [1, 3], the group velocity ofthe surface mode co-propagating with low energy electron
beam is negative, meaning that the energy flows backward
if the phase velocity is in the forward direction.
Hence, in this section, we have discussed surface mode
which propagates off-axis, but is still nonlocalized in the 
direction. In the next section, we use this to construct a setof fully localized surface modes.

FEL Theory

39

MOPPH010

Proceedings of FEL 2007, Novosibirsk, Russia

THREE-DIMENSIONAL STRUCTURE OF
THE LOCALIZED SURFACE MODE
In the last section, we have discussed the surface modethat is composed of plane waves which propagate, in general, off-axis in the  plane. We can combine such surface
modes with suitable weight function in   to obtain a modethat is localized in the  direction as follows
 





       (10)Note that it is here understood that all the field quantities
have   type time dependence. Here,   stands
for the total longitudinal electric field and  is real, meaning that the field decays and is localized in the direction.
Note that for a given   , the relative magnitudes of the amplitude  (i.e., the ratio    for all values of ) as
well as the relation between   and can be calculated as
mentioned in the last section. The   and  are therefore
functions of   in the above integral for a given value of .
In the above expression, only the zeroth-order component
corresponding to   term interacts strongly with theco-propagating electron beam and we will therefore focus
on this term only in the remaining of the paper. However,
all other components are present there with an amplitudein a fixed ratio with the amplitude of the zeroth-order component such that boundary conditions are satisfied at thegrating surface.
Let us introduce the angle & in the  plane via     &. Under the paraxial approximation &, weobtain the following expressions for the &-dependence of and  : &    

&



  & &        


(11)
(12)

where we have simplified the notations by writing      and     . Here  is the magnitude of thegroup velocity (   for   ) of the surface modein the unit of c. As mentioned earlier, the group velocity
is negative. We can substitute the above expressions for  and  in the Eq. (10) and only retain the   term andget the following expression for the field in the zeroth-ordercomponent:  $ ¼  $ 





¾
¾ ¾
       ½  
 &$ ¾ $ ¾ ¼
$  & (13)

We note that  appears as a Fourier transform in &of the underbraced term in the above expression. We cantake the orthonormal set of Gauss-Hermite functions for & and obtain a set of Gauss-Hermite orthonormal surface modes which are localized in the  direction. This isexactly the same way in which one can get the localized
FEL Theory

40

Gauss-Hermite modes for a laser beam in free space [9].
Here, we consider only the fundamental Gaussian mode bychoosing  &  & '  for which we obtain thefollowing expression for the rms beam size   [10]              (14)Note that the above equation is in the form of paraxial
diffraction with a waist at = 0, the rms waist beam sizeof    , and an rms diffraction angular divergence of  . The quantities on the right-hand side of Eq. (14)are determined by the following relations:     ' 
' '



     







  



 





(15)
(16)





 

(17)

These reduce to the well-known relations between the rms
size and angular divergence in free space when   .
Eq. (14) can also be written in a form familiar in paraxial
optics discussions:    "  

 
"

(18)

where the Rayleigh range "  is given by    (19)
We have thus derived in this section the threedimensional structure of fully localized surface mode. The
fundamental Gaussian mode is discussed in detail and theanalysis can be easily extended to derive the structure ofhigher order Gauss-Hermite surface modes. Note that compared to Gauss-Hermite modes propagating in free space,
the wavelength  is here replaced with  .
" 

THREE-DIMENSIONALMAXWEL-LORENTZ EQUATIONS
We now discuss the interaction of the localized modethat we discussed in the last section with the copropagating electron beam. For the two-dimensional case,where the system is assumed to have translational invariance in the  direction, we had earlier derived the coupled
nonlinear Maxwell-Lorentz equation for the interaction of
the surface mode with the sheet electron beam [3]. Using the Maxwell equation with the source term and using
the slowly varying envelope approximation and the paraxial approximation, we can write down the equation for theevolution of the electromagnetic field given by Eq. (13).
Leaving the details of the derivation to another publication [11], we present here the final result:  
 




    " ( * $ ¼  $  
)







(20)

Proceedings of FEL 2007, Novosibirsk, Russia
where "   is the characteristic impedance of freespace, ( is the residue of the singularity associated withthe surface mode as defined in Ref. [3], *  is the electronvolume current density at the given location, % is the phaseof the electron anddenotes averaging over electrons.
Note that  is the amplitude of the electric field in the
zeroth-order component of the surface mode at the grating surface, i.e.,  . Once   is known, one can calculate  & using Eq. (13) and then as discussed earlier
in this paper, we can calculate  & for all . Substituting these in Eq. (10), we get the total electromagnetic
field. Note that by construction, this electromagnetic fieldsatisfies the boundary condition on the grating surface andalso evolves due to interaction with co-propagating electron beam as given by Eq. (20). It is interesting to observethat the structure of this equation is similar to that for thecase of conventional FELs. The second term on the left
side this equation represents diffraction and compared tothe conventional FEL case, here  is replaced with  .
This is same as we observed in the last section, where thesame replacement occurs in the formula for the Rayleighrange in Eq. (19).
The equation for the evolution of phase and energy ofthe electrons, as derived earlier [3] are given by

MOPPH010

CONCLUSIONSIn this paper, we have discussed the three-dimensionalsurface electromagnetic modes supported by a reflection
grating that are localized along the direction of grooves aswell as in the direction perpendicular to the grating surface.
We have then discussed the nonlinear three-dimensional
time-dependent coupled Maxwell-Lorentz equations forthe interaction of the surface mode with the electron beam.
These equations can be numerically solved to study theevolution of power in an SP-FEL taking diffraction effects
into account, which has so far not been accurately studied. We can linearize the corresponding Maxwell-Vlasov
equation and solve it approximately to get an analytic expression for start current taking three-dimensional effects
into account. This will be taken up in the future.

REFERENCES[1] H. L. Andrews and C. A. Brau, Phys. Rev. ST Accel. Beams
7 (2004) 070701.
[2] J. T. Donohue and J. Gardelle, Phys. Rev. ST Accel. Beams
8 (2005) 060702.
[3] V. Kumar and K.-J. Kim, Phys. Rev. E 73 (2006) 026501.
[4] D. Li et al., Phys. Rev. ST Accel. Beams 9 (2006) 040701.

)
 )

 

%
 %

 





$ $  + )   )  

 )
)

(21)

[5] V. Kumar and K.-J. Kim, Proceedings of PAC05 (2005)
1616.

(22)

[6] Electromagnetic Theory of gratings, edited by R. Petit(Springer-Verlag, Berlin, 1980).

where ) is the energy of the electron resonant with thesurface mode in the unit of rest mass energy, )  is the energy of the  electron in the unit of rest mass energy
and % is the phase of  electron. Note that here wehave ignored space-charge term in Eq. (21) for simplicity. Eqs. (20-22) are the coupled three-dimensional timedependent Maxwell-Lorentz equations, which describe theinteraction between the surface mode and the electron
beam. If there are focusing forces, there will be equations
for the evolution of transverse dynamical variables of electrons, in addition to Eqs. (21-22).
Finally, we give the expression for the power flowing inthe surface mode in the backward direction. In general,
power will flow along  direction also in addition to direction in 3-D case. However, under paraxial approximation, we can assume that power flowing along the  direction is not very significant. The expression for the power, flowing along the (negative) direction, which is further
generalization of the expression obtained for 2-D case inRefs. [3,12] is given by
)
, 
" (





 

[7] P. M. Van den berg, Appl. Sci. Res. 24, (1971) 261.
[8] L. Schachter and A. Ron, Phys. Rev. A 40, (1989) 876.
[9] A. Seigman, Lasers, University Science Books, Sausalito,
1986.
[10] K.-J. Kim and V. Kumar, to appear in Phys. Rev. ST Accel.
Beams.
[11] V. Kumar and K.-J. Kim, under preparation.
[12] V. Kumar and K.-J. Kim, Proceedings of FEL05 (2005) 274.

(23)

Note that the above expression is for the total power corresponding to EM field in all the components corresponding
to diiferent values of  in Eq. (10).
FEL Theory

41

MOPPH011

Proceedings of FEL 2007, Novosibirsk, Russia

COMPARISION BETWEEN KINETIC AND FLUID DESCRIPTION OF
PLASMA-LOADED FREE-ELECTRON LASER
B. Maraghechi* , S. Babaei, Department of Physics, Amirkabir University of Technology,
P.O. Box 15875-4413, Tehran, Iran
Abstract
In the kinetic treatment of the plasma-loaded FEL
single particle equation of motion for both beam andplasma electrons in the radiation fields are used.
Therefore, interaction terms between the wiggler and thespace-charge wave, in the transverse velocity of electrons,
which are important elements in the fluid model, areneglected. A dispersion relation of a plasma-loaded FEL
with kinetic theory is used that takes into account thevelocity spread of both beam and plasma electrons. In thepresent analysis a dispersion relation is obtained, by thefluid theory, with the interaction terms between the
wiggler and the space-charge wave in the transverse
velocity of electrons taken into account. Since theseinteraction terms are inherently missing in the kinetic
theory the two dispersion relation are compared to findout about the importance of these terms. It was found that
although the absence of these terms has considerable
effects on the growth rate, the general kinetic dispersion
relation may be used to study the temperature effects of awarm beam/plasma on the instability of a free-electron
laser with a plasma background.

INTRODUCTION
The effects of background plasma on the interaction ofelectrons with the radiation have been of considerable
interest in devices for the generation of coherent
electromagnetic radiation.
There are several
investigations on the plasma loaded FEL[1-11]. A kinetic
dispersion relation (DR) of a plasma loaded FEL isderived in Ref. 1 that takes into account the velocity
spread of both beam and plasma electrons
In all of the above fluid methods[1-9] and in the kinetic
treatments,[1,12,13] of the plasma- loaded FEL, single
particle equation of motion for beam or plasma electrons
in the radiation fields are considered.
Therefore,
interaction terms between the wiggler and the spacecharge wave, in the transverse velocity of electrons,
which are important elements in the fluid model, areneglected.
In the present work, the kinetic theory of Ref. 1 and its
DR of a plasma-loaded FEL is considered. Since in thiskinetic model single particle treatment of electrons in theradiation field is inherent in the theory a fluid model isused to find a DR that takes into account the interaction
terms between the wiggler and the space-charge wave inthe transverse velocity of electrons. The fluid DR iscompared with the kinetic DR to find the importance of
these interaction terms. It is found that the absence of____________________________________* Electronic mail: behrouz@aut.ac.ir
FEL Theory

42

these interaction terms in the kinetic treatment has
considerable effects on the growth rate. However,characteristic behaviour of the kinetic DR is found to besatisfactory and, consequently, the general kinetic DR
may be used to study the temperature effects of a warm
beam/plasma on the instability of a plasma–loaded FEL.

KINETIC DESCRIPTION
Consider a relativistic electron beam propagating in thez direction through background plasma and a helicalwiggler magnetic field. A general DR for a plasmaloaded FEL, using kinetic theory, is derived in Ref. 1 asc 2 k 2 D L ( k , ω ) D T ( k − k0 , ω ) D T ( k + k0 , ω )1 2 T
aw [ D (k − k0 , ω ) + DT (k + k0 ,ω )] ×
2×{[ χ (1) ( k , ω )]2 − c 2k 2 D L ( k , ω )[α 3ωb2 + χ (2) (k , ω )]} .
=(1)

In order to compare the kinetic DR with that of the fluid
model a relatively weak wiggler is assumed. In this case,the resonant space-charge wave D L ( k , ω ) ≈ 0 couples tothe resonant right circular wave DT (k − k0 , ω ) ≈ 0 , whichleaves the left circular wave nonresonant, i.e.,DT ( k + k0 , ω ) ≠ 0 .

Moreover, terms containing

aw2 arealso neglected in the coupled equations and the cold beamand plasma is assumed to obtain the following DR
ω2
ω2
ωb2
(ω 2 − c 2 kr2 − b − ω p2 )(1 −− p2 )22γˆbγˆbγ z [ω − kV|| ] ω
1 2 ωb4 (ωβ|| − ck ),aw
2 γˆb4 (ω − kV|| ) 4
2

=

(2)

where, kr = k − k0 is the radiation wave number and allother quantities are defined in Sec. III and in Ref. 1.
Kinetic model DR (2) has been solved numerically to findthe imaginary part of the frequency. Figure 1 shows thevariation of growth rate with radiation wave number for-3
Bw = 1 kG, γˆb = 4 , and nˆb = 1 × 1013 cm . Curves 1, 2, 3,
4, and 5 corresponding to the density of backgroundplasma at 0.8, 1.25, 1.75, 2, and 2.3, respectively (in unitsof 1013 cm-3).

FLUID DESCRIPTION
We now consider the fluid theory description of a
relativistic and cold electron beam that passes through abackground plasma and a static helical wiggler magnetic

Proceedings of FEL 2007, Novosibirsk, Russia

The transverse component of the momentum equation for
the electron beam and plasma will be found as follows∂∂∂
γˆb m( + V|| ) δ vb ⊥ + γˆb mδ vbz v*w
∂t
∂z
∂z
V
e
∂
+ mγˆb3 2|| ( V|| .δ v bz + δ v b ⊥ .v w ) v *w − 2 v*w ( v w .δ Er )
c
c
∂z
e ∂
= ( δ A − V|| × δ B − δ v bz × B*w ) ,
(10)
c ∂t
∂
e ∂
m δ v p ⊥ = ( δ A − δ v pz × B*w ) .
(11)
∂t
c ∂t

25

20

Im( /ck0)×10 ³

¯

15

ω

1

2

4

3

10

3

MOPPH011

2 1

5Neglecting the terms proportional to aw2 , Eqs. (10) and(11) will yield5

δ vb ⊥ =eγˆ β 2 ck a*
δ A − b ze 0 w δ vbz ,γˆb mc2 (ω − krV|| )(12)δ vp⊥ =eck a*
δ A + 0 w δ v pz ,
mc
2ω

(13)

0
4

6

8

10

12

16

14

18

20

(k-k0)/k0

Fig. 1. Kinetic-model growth rate verses radiation
wave number

where aw = eBw / mc 2 k0 .
The wave equation for the radiation field is(ω 2 − c 2 kr2 ) δ A = 4π cδ J ⊥ ,where δ J ⊥ = enˆbδ v b ⊥ + enˆ pδ v p ⊥ + eδ nb v w , δ nb is thefield B w . The unperturbed state consists of
B w = Bw (eˆ x + ieˆ y )exp(ik0 z ) + c.c. ,(3)v w = vw (eˆ x + ieˆ y )exp(ik0 z ) + c.c. ,(4)with equilibrium velocity given by

v w + v|| , where

vw = −eBw / γˆb mck0

velocityisγˆb = [1 − (vw2 + vz2 ) / c 2 ]−1/ 2thetransverseandis the total beam electronenergy.
The perturbation quantities associated with the rightcircularly polarized electromagnetic wave (radiation) andthe space-charge wave areδ E, δ B, δ A ~ (eˆ x − ieˆ y )exp[i (kr z − ωt )] ,(5)

δ E z , δ v bz , δ v pz ,δ nb , δ n p ~ exp[i (kz − ωt )] ,(6)

where k = kr + k0 . In Eq. (5) subscripts minus, like δ A− ,is removed in transverse field quantities for brevity. The
relativistic momentum equation in the lab frame, for theelectron beam,
mγ b

dv
dγ
e
+ mv b = −e E − ( v × B) ,
dt
dt
c

(7)

with
d
e
γ b = − 2 ( v. E) ,
dt
mc

(8)

can be linearized using the linearized relativistic factor

γ b = γˆb +

γˆb3
c

2

( V|| .δ v bz + v w .δ v b ⊥ ) .

(14)

(9)

electron beam density, and v w , δ v b ⊥ are transverse
velocities of the electron beam due to the wiggler andradiation field, respectively.
The longitudinal
electrostatic field, i.e., space-charge wave, is produced by
the perturbed electron density of the beam andbackground plasma and is given byik δ Ez = −4π e(δ nb + δ n p ) .

(15)

The longitudinal component of the momentum equation
for the electron beam and plasma will be found as followsiγˆb m(ω − kV|| ) δ vbz =

e

γ z2

e
c

δ Ez + ( v w × δ B).eˆ zee+ (δ v b ⊥ × B w ).eˆ z − 2 V|| ( v w .δ E) ,ccei mωδ v pz = eδ Ez + (δ v p ⊥ × B w ).eˆ z .
c

(16)
(17)

Substituting δ vb ⊥ and δ v p ⊥ from Eqs. (12) and (13) andv w from Eq. (4) into Eqs. (16) and (17) we haveγˆb m(ω − kV|| ) δ vbz= −ieγ z2 δ Ez + (eawγˆb−1 / 2)( k − V||c −2ω ) δ A ,(18)mωδ vPz = −ieδ E z + (ek0aw / 2 ) δ A .

(19)

Using the continuity equation, the perturbed beam andplasma densities are given byδ nb =

k(nˆbδ vbz + V||δ nb ) ,(ω − kV|| )(20)

FEL Theory

43

MOPPH011kω25nˆ pδ v pz .

(21)

With substitution of δ vbz and δ v pz from Eqs. (18) and(19) into Eqs. (20) and (21) δ nb and δ n p are obtained
to be inserted in Eq. (15). This will give¯Im( /ck0)×10 ³

δ np =

Proceedings of FEL 2007, Novosibirsk, Russia

ω

(1 −

ω2
ωb2
− p2 )δ Ez
2γˆb γ (ω − kV|| ) ω

=i

ω
aw
ωb2
[ 2
( k − β||c −1ω ) + p2 k0 ]δ A .
2ω2 γˆb (ω − kV|| )

2
z

20

15

3

4

1 2

2 1

3

10

5

2

(22)

5

Similarly, substitution of δ vb ⊥ , δ v p ⊥ from Eqs. (12) and

04(13), vw from Eq. (4), and δ n p from Eq. (21) into Eq.
(14) will give
β||2
ω2
ωb2
c2k a
(ω 2 − c 2 kr2 − b − ω p2 ) δ A = i 0 w ( 2γˆb2 γ z (ω − krV|| ) (ω − kV|| )
−

2
k ωp
ωb2
−
) δ Ez ,γ z2γˆb2 (ω − kV|| ) 2 k0 ω 2

6

8

12

10

14

25

where terms proportional to aw2 are neglected. Equations(22) and (23) will easily yield the DR as follows

20

2

γˆb

− ω 2p )(1 −γˆb γ z2 (ω − kV|| )

ω 2p
−
)=
2
2

ω

ω

ωp
β||
1 2 2
ω 2k
ωb2k0
c aw ( 2 2 b
k
+
−
)
0
2
γ z γˆb (ω − kV|| )2 ω 2
γ z2 (ω − krV|| ) (ω − kV|| )
2

1 2

15

5
10

5

0

ω 2p
ωb2
ωb2
− ω 2p )(1 − 2−)=γˆbγ z γˆb (ω − kV|| )2 ω 2−21
c 2 aw2 ωb2k
ω 2 ( k − V||c ω ) ω p[ b2+ 2 k0 ] .
22
2
2 γ z γˆb (ω − kV|| ) γˆb (ω − kV|| ) 2
ω
2

(25)

Equation (25) is the fluid model DR to second order inwiggler amplitude and with the interaction terms in thetransverse velocities of radiation, i.e., Eqs. (12) and (13),neglected. This fluid-model DR is equivalent to the

44

4
3

(24)

Equation (24) is the fluid-model DR to second order inwiggler amplitude.
In the fluid DR (24) transverse velocity components ofradiation, given by Eqs. (12) and (13), contain interaction
terms between the wiggler and space-charge wave, which
are given by the second terms in the right-hand sides(RHS) of Eqs. (12) and (13). In contrast, these interaction
terms are absent in the derivation of the kinetic DR (2). In
order to asses the importance of these interaction terms
the fluid DR is derived with the second terms in the RHS
of Eqs. (12) and (13) removed, which will yield

FEL Theory

1

3

2

2
−2
ω 2 ( k − V||c ω ) ω p
k0 ] .
×[ b2+γˆb (ω − kV|| ) 2 ω 2(ω 2 − c 2 kr2 −¯Im( /ck0)×10 ³(ω 2 − c 2 kr2 −

ωb2

20

Fig. 2. Fluid-model growth rate verses radiation wave
number with the interaction terms in the transverse
velocities of radiation neglected.

(23)

ωb2

18

16

(k-k0)/k0

4

6

8

10

12

14

16

18

20

(k-k0)/k0

Fig. 3. Fluid-model growth rate verses radiation
wave number with the interaction terms in thetransverse velocities of radiation retained.
kinetic DR (2) and, therefore, they can be compared.
Figure 2 shows the growth rate found from fluid DR (28)with the same parameters as in Fig. 1. Since interaction
terms in the transverse velocities of radiation are absent inboth Figs. 1 and 2 they compare quite well with eachother. The highest value for the kinetic growth rate ataround 0.0144, in Fig.1, is about 10% below that of thefluid-model growth rate at around 0.016, in Fig. 2.
Moreover, location of the left (right) peak, for curve 1, in
Fig. 1 at ( k − k0 ) / k0 ≈ 7.2 ( ≈ 15.5 ) differs by only about
4% (1.3%) from the corresponding peak in Fig. 2 at
( k − k0 ) / k0 ≈ 7.5 ( ≈ 15.3 ). The critical density at around2.41 × 1013 cm-3 is about 3% higher than in Fig.1. The

widths of unstable spectrums in the two figures are also insatisfactory agreement. Therefore, due to the absence ofinteraction terms in the transverse velocities of radiation

Proceedings of FEL 2007, Novosibirsk, Russia
in the kinetic DR (2) as well as in the fluid DR (24) thetwo DRs compare quite well both quantitatively andcharacteristically.
Equation (24) is the fluid-model DR to second order inwiggler amplitude and with the interaction terms in thetransverse velocities of radiation, i.e., Eqs. (12) and (13),retained. The fluid-model growth rate, found from thisDR, is illustrated in Fig. 3. Due to the absence ofinteraction terms in the transverse velocities of radiation,in the kinetic-model growth rate in Fig.1, its peak value ataround 0.0144 is about 31% lower than that of the fluid
growth rate in Fig. 3 at around 0.021. This shows that theabsence of these interaction terms in the kinetic DR has
profound effects on its growth rate. Characteristics of thetwo figures can also be compared. Location of the left
(right) peak, for curve 1, in Fig. 1 at ( k − k0 ) / k0 ≈ 7.2( ≈ 15.5 ) differs by about 18% (7%) from thecorresponding peak in Fig. 3 at ( k − k0 ) / k0 ≈ 6.1 ( ≈ 16.7 ).
The critical density at around 2.52 × 1013 cm-3 is about 7%
higher than in Fig. 1. Therefore, characteristic behaviorof the kinetic DR compares relatively better than its
quantitative behavior with the fluid DR. Consequently,
the general kinetic DR (1) may be used to study thetemperature effects of a warm beam/plasma on the
instability of a plasma-loaded FEL.

CONCLUSION
In the derivation of the kinetic DR, in Eq. 1, thetransverse velocities of electrons in the radiation fields arefound from the conservation of the transverse componentof canonical momenta, which themselves are found fromthe single particle equations of motion. Therefore, nointeraction with the wiggler field is present. On the other
hand, in the fluid-model DR (24) the transverse velocity
components of radiation, found from the fluid momentum
equations and given by Eqs. (12) and (13), containinteraction terms between the wiggler and space-charge
wave. To first order in aw , these are the second terms in
the RHS of Eqs. (12) and (13), which are missing in the
kinetic treatment.
In order to study the importance of these interaction
terms the kinetic-model DR has been compared with thefluid-model DR. For this purpose a weak coupling
regime, i.e., small wiggler amplitude, is assumed underwhich the left circularly polarized electromagnetic wave
is nonresonant, i.e., DT ( k + k0 , ω ) ≠ 0 , and terms
containing aw2 in the coupled equations are neglected. It
was found that the resulting kinetic DR (2) compares

MOPPH011

fairly well with the corresponding fluid DR (25), which
does not contain the interaction terms in the transverse
velocities of radiation. However, the kinetic DR (2) does
not agree quantitatively with the fluid DR (24), which
does contain the interaction terms.
Nevertheless,characteristic behavior of the two DRs are of better
agreement so that the general kinetic DR (1) may be used
to study the temperature effect of a warm beam/plasma on
the growth rate of a plasma-loaded FEL. This DR is fulland contains both the Compton regime DR and theRaman regime DR. Therefore, a complete numericalinvestigation of the kinetic DR (1) should include a warm
beam/plasma in both Compton and Raman regime.

ACKNOWLEDGMENT
One of the authors (B.M) would like to thank the Centerof Excellence in Computational Aerospace Engineering
for financial support.

REFERENCES[1] S. Babaei and B. Maraghechi, Phys. Plasmas, 14,053114 (2007).
[2] P. Wen-Bing and C. Ya-Shen, Int. J. Electron. 65, 551(1988).
[3] V. K. Tripathi and C. S. Liu, IEEE Trans. Plasma Sci.
18, 466 (1990).
[4] A. Serbeto and M. V. Alves, IEEE Trans. Plasma Sci.
21, 243 (1993).
[5] V. Petrillo, A. Serbeto, C. Maroli, R. Parrella, and R.
Bonifacio, Phy. Rev. E 51, 6293 (1995).
[6] K. H. Tsui and A. Serbeto, Phy. Rev. E 58, 5013
(1998).
[7] V. Petrillo and C. Maroli, Phys. Rev. E 62, 8612
(2000).
[8] R. N. Agarwal, V. K. Tripathi, and P. C. Agarwal,
IEEE Trans. Plasma Sci. 24, 1197 (1996).
[9] B. Qian, Y. Liu, and C. Li, Phys. Plasmas 1, 4089
(1994).
[10] J. Parashar, H. D. Pandey, A. K. Sharma, and V. K.
Tripathi, J. Plasma Phys. 58, 613 (1997).
[11] K. K. Pant and V. K. Tripathi, IEEE Trans. Plasma
Sci. 22, 217 (1994).
[12] Y. Seo and E. H. Choi, IEEE Trans. Plasma Sci. 25,
360 (1997).
[13] A. Sharma and V. K. Tripathi, Phys. Fluid B. 5, 171(1993).
[14] A. Sharma and V. K. Tripathi, Phys. Plasmas. 3,3116 (1996).

FEL Theory

45

MOPPH012

Proceedings of FEL 2007, Novosibirsk, Russia

CONSERVATION LAWS IN QUASILINEAR THEORY OF RAMAN
FREE-ELECTRON LASER
B. Maraghechi, Department of Physics, Amirkabir University of Technology, Tehran, Iran
A. Chakhmachi, Plasma Physics and Nuclear Fusion Research School,
Nuclear Science and Technology Research Institute, AEOI, Tehran, Iranand Department of Physics, Amirkabir University of Technology, Tehran, Iran

PHYSICAL MODEL

Abstract
A quasilinear theory of the free-electron laser, in Raman
regime, is presented to establish that conservation laws on
number, energy, and momentum are upheld. A high density
electron beam is assumed so that the space-charge potential
is no longer negligible. A sufficiently broad band spectrumof waves is assumed so that saturation will be due to thequasilinear spread of the beam electrons. Otherwise, forthe single mode excitation, saturation will be due to theelectron trapping in the space-charge potential. It is shownthat the quasilinear slow variation of the background distribution function is in the form of the diffusion equation in
momentum space. An expression for the time evolution of
the spectral energy density is derived. Conservation laws
to the quasilinear order (second order) are derived and areproved to be satisfied. Results of the present investigation
may be used to study the quasilinear saturation of a freeelectron laser in the presence of the space-charge wave.

INTRODUCTION
Saturation and nonlinear evolution of free-electron lasers(FEL) are of considerable importance both experimentallyand theoretically. The main reason is that saturation determines the efficiency of the device.
For sufficiently broad spectrum of unstable waves, saturation is due to quasilinear energy spread of the beam electrons. This problem has been studied only in the Compton regime, where the electrostatic potential of the spacecharge wave is negligible due to low density of the electron
beam [1-5]. On the other hand, when there is only a single
exited mode, saturation of the amplification is considered
to be caused by electrons trapped in the electrostatic fieldof the space-charge wave in the Raman regime or the pondermotive wave in the Compton regime [6-8].
The purpose of the present investigation is to derive conservation laws in the quasilinear analysis of an FEL in thepresence of the space-charge field of electrons. The methodof analysis and notations are similar to Ref. 1. The quasilinear slow variation of the background distribution function is in the form of the diffusion equation in momentum
space. An expression for the time evolution of the spectral energy density is derived. Conservation laws, to thequasilinear order (second order), for particle, energy andmomentum are derived and are proved to be satisfied.
FEL Theory46

We consider a collisionless, relativistic, electron beamwith uniform cross section propagating in the z direction.
The electron beam propagates through a constant amplitude helical wiggler magnetic field specified by
B0 = −Bw cos(k0 z)ex − Bw sin(k0 z)ey ,(1)

The transverse electromagnetic and longitudinal electrostatic perturbed fields δE and δB are defined as
δE = −1 ∂δA − ∇δϕ,c ∂t

δB = ∇ × δA.

(2)

The relativistic, nonlinear Vlasov equation for the electron beam distribution function fb (z, p, t) is given byv × (B0 + δB) ∂∂∂+vz −e(δ E+). ]fb (z, p, t) = 0.
∂t
∂z
c
∂p
(3)
In the present analysis, we investigate the class of exact
solution to Eq. (3) of the form[fb (z, p, t) = n0 δ(Px )δ(Py )G(z, pz , t),(4)where n0 = const, and Px and Py are the canonical momenta transverse to the beam propagation direction. Substituting the distribution function (4) into Eq. (3) and integrating the resting equation over px and py , gives
[

∂
∂
∂
∂
+ vz
−
H(z, pz , t)]G(z, pz , t) = 0. (5)
∂t
∂z
∂z
∂pz

In this equation, H(z, pz , t) is defined by
H(z, pz , t) = γT mc2 − eδϕ(z, t)= [m2 c4 + c2 p2z + e2 (A0x + δAx )2 + e2 (A0y + δAy )2 ](1/2)−eδϕ(z, t),(6)which is the particle energy for Px = 0 = Py , and γT mc2
is the kinetic energy. In the absence of perturbed fields, theenergy is given by2/k02 )1/2 .
γmc2 = (m2 c4 + c2 p2z + e2 Bw(7)

Proceedings of FEL 2007, Novosibirsk, Russia
It is assumed that the distribution function G(z, pz , t),H(z, pz , t), and δϕ(z, t) are spatially periodic with periodicity length 2L so it is convenient to introduce the speciallyaveraged distribution function G0 (pz , t) defined by
 L

1
2L

G0 (pz , t) = G =−L

dzG(z, pz , t).

(8)

For small δA and δϕ,G(z, pz , t) = G0 (pz , t) + δG(z, pz , t),(9)H(z, pz , t) = H0 (pz , t) + δH(z, pz , t) = γmc2 + δH,(10)
and therefore
δH(z, pz , t) = (e2 /γmc2 )(A0x δAx + A0y δAy ) − eδϕ(z, t).
(11)
Equation (11) shows that the space-charge wave constitutethe electrostatic potential of the perturbed Hamiltonian orenergy. By substituting vz = pz /γT m = pz c2 /(H + eδϕ),Eq. (6) can be expressed as
G
∂
∂
∂
∂
G + pz c2 ()−(G H) = 0,∂t∂z H + eδϕ∂pz ∂z(12)

In the approximation where only linear wave-particle interactions are retained in the description, δG evolves according to [1]
pz ∂
∂
∂
∂
δG +
δG − ( δH)
G0 = 0.
∂t
γm ∂z
∂z
∂pz

(13)

Equation (13) will be recognized as the linearized Vlasov
equation for perturbations about spatially uniform distribution function G0 (pz , t), which varies slowly with time
according to Eq. (12).

TIME EVOLUTION OF DISTRIBUTION
FUNCTION AND ENERGY
We introduce the Fourier series representationsδGk (pz , t) exp(ikz), (14)G(z, pz , t) = G0 (pz , t) +k

H(z, pz , t) = H0 (pz , t)+δψ(z, t) =







δHk (pz , t) exp(ikz), (15)k

δψ(k, t) exp(ikz),

is omitted. From Eqs. (11), and (14)-(16) it follows that(for k = 0)
δHk = (e2 Bw)[δAx (k + k0 ) + iδAy (k + k0 )2γmc2 k0

+δAx (k − k0 ) − iδAy (k − k0 )] − eδϕ(k).

(17)

The time dependence of perturbed
quantities is assumed
tto be of the form exp(−i 0 Ωk (t )dt ) in circumstanceswhere the time variation of G0 (pz , t) is sufficiently slow
Ωk = ωk + iγk = −ω−k + iγ−k . By use of γ̄mc2 = const
that denotes the characteristic mean energy of the unperturbed beam electrons we can write the perturbed amplitudes in terms of dimensionless amplitudes δΦ(k) andδA±
k±k0 . In Fourier variables, Eq. (12) becomes∂∂ 
G0 = −
ikδH−k δGk .
∂t
∂pz

(18)

k

Solving Eq. (13) and neglecting free-streaming contributions to δGk (pz , t), we obtain for the perturbed distributionfunction
γ̄eBw
−
2
)(δA+
k+k0 +δAk−k0 )−γ̄mc δΦ(k)]
2γk0
 t


k∂G0 /∂pz
×() exp(−iΩk (t )dt ).
(19)
Ωk − kvz
0δGk (pz , t) = −[(which can be averaged over the spatial periodicity length
2L to obtain∂∂∂∂
G0 = G =δG δH.
∂t
∂t
∂pz
∂z

MOPPH012(16)kwhere δψ is δAx , δAy , or δϕ and k = nπ/L with n an
integer and the summations run from k = −∞ to k = +∞.
The prime on the summations denotes that the k = 0 term

Substituting Eqs. (17) and (19) into Eq. (18) yields thequasilinear kinetic equation for G0 (pz , t):∂ |δHk |2 ∂G0 /∂pz∂
G0 (pz , t) = i
k2
(
).
∂t
∂pz
Ωk − kvz(20)kNote that Eq. (20) has the form of a diffusion equation
for G0 (pz , t) in momentum space.

Linear Dispersion Relation and Energy Equation
The complex oscillation frequency Ωk (t) is obtained
adiabatically in terms of G0 (pz , t) from the linear DR. For
the present configuration the linear DR is derived in Ref. 9
and 10 as follows
TT(Ωk )Dk+k(Ωk ) =
c2 k 2 DkL (Ωk )Dk−k00TT(1/2)a2w [Dk−k(Ωk ) + Dk+k(Ωk )]
0
0
(1)

(2)

2
]},
×{[χk ]2 − c2 k 2 DkL (Ωk )[χk + α3 ωpe

(21)

T
T
where the dielectric functions DkL , Dk−k
, Dk+k, and the00(n)effective susceptibility χk are defined byT2(Ωk ) = Ω2k − c2 (k ± k0 )2 − α1 ωpe
,
Dk±k
0

dpz k∂G0 /∂pz(n)2
χk (Ωk ) = γ̄ n+1 mc2 ωpe.
γ n Ωk − kvz

DkL (Ωk ) = 1 +

(22)
(23)

(0)

χk (Ωk ),c2 k 2(24)

FEL Theory

47

MOPPH012

Proceedings of FEL 2007, Novosibirsk, Russia

2
Here ωpe= 4πn0 e2 /γ̄m, aw = eBw /γ̄mc2 k0 and αn =zγ̄ n dp
γ n G0 . We will now obtain the wave kinetic equation. The average energy density in the electromagnetic
and electrostatic fields is given by1 [|δEk |2 + |δBk |2 ] =8πk(γ̄mc2 2 1 
2
2
2
2
)
{|δA+
k+k0 | [|Ωk | + c (k + k0 ) ]
2e
4πc2
k

2
2
2
2
2 2
2
+|δA−
k−k0 | [|Ωk | + c (k − k0 ) ] + 2c k |δΦ(k)| }×exp(2

 t
0





γk (t )dt ) =k (t),(25)∂
k (t) = 2γk (t) k (t),
∂t

(26)

CONSERVATION OF PARTICLE,MOMENTUM AND ENERGY
The fully nonlinear Vlasov-Maxwell equations possess
three exact conservation relations. These are: average density, Ldz
d3 pfb (z, p, t) = const,
(27)
−L 2L
total average plasma kinetic energy density plus electromagnetic and electrostatic field energy density,d3 p(γT − 1)mc2 fb (z, p, t)

1[(δE)2 + (B0 + δB)2 ]} = const,(28)
8π
and total average plasma momentum density plus electromagnetic field momentum density,


dz
{
2L
−L

d3 ppz fb (z, p, t) +1
(δE × B0
4πc

+δE × δB)z } = const.

48

1 e4
(A0 δAx + A0y δAy )2 G0 )2 γ 3 m3 c6 x

(31)

In above equation KED is the average plasma kinetic energy density. Then the quasilinear analog of the exact energy conservation relation in Eq. (28) can be expressed as∂ 1∂
KED = −  [(δE)2 + (B0 + δB)2 ],
∂t
∂t 8π

(32)

To verify Eq. (32), we proceed by taking the derivativeof Eq. (31) with respect to time, and substituting Eq. (20)for ∂G0 /∂t into the first term on the right-hand side of Eq.
(31). The perturbed distribution function δG appearing insecond term is obtained from Eq. (19). Then by use of DR(21) we can eliminate the integrals over momentum in favorTT, Dk−k, and DkL . Relationsof dielectric functions Dk+k00
between the perturbed amplitudes and dielectric functions
are also used.
γ̄mc2 2 1∂
KED = (
)
∂t
2e
2πc2

−
T
2
T
2
{(iωk + γk )[Dk+k|δA+
k+k0 | + Dk−k0 |δAk−k0 | ]
0
−
2
2
2
α1 )[|δA++γk (ωpe
k+k0 | + |δAk−k0 | ] t+(iωk − γk )[2c2 k 2 |δΦ(k)|2 ]}exp(2γk (t )dt ). (33)0Substituting Eq. (22) into Eq. (33), and eliminating terms
in the k summations, which are odd functions of k, yields
 tγ̄mc2 2 1 ∂ ∂
KED = −()
exp(2γk (t )dt )∂t2e
4πc2 ∂t0
k(29)

We now demonstrate that the conservation relations (27)(29) are upheld by the quasilinear kinetic equations derived
in Eq. (20). The distribution function fb is taken to be of
the form of Eq. (4). In Eqs. (27)-(29), we expand quantities such as γT mc2 and retain up to second-order terms inperturbation amplitudes.
FEL Theorye2[(A0x δAx + A0y δAy )δG − (δA2x + δA2y )G0 ]
γmc2

k

+

 L

+

−

where the linear growth rate γk (t) is determined adiabatically in terms of G0 (pz , t) from Eq. (21). Equations (20),(21), and (26) then form a closed quasilinear descriptionof the system including the effects of linear wave-particle
interactions.

dz
{
2L
−L

Clearly this is true for ∂G0 /∂t given by Eq. (20) since Eq.
(20) is in the form of a diffusion equation in momentum
space and the integrand is an exact differential.
Energy conservation: To show energy conservation fromquasilinear theory, the quantity γT mc2 [Eq. (6)] is expanded to second order, by this we have

 L
dz ∞
dpz n0 ((γ − 1)mc2 G0
KED =
−L 2L −∞kwhere εk (t) is the spectral energy density. From Eq. (25),
it follows that k (t) evolves according to LParticle conservation: Substituting Eq. (4) into Eq. (27),and making use of Eq. (9), we obtain ∞∂dpz n0 G0 (pz , t) = 0.
(30)
∂t −∞

2
2
2
2
×([|δA+k+k0 | (|Ωk (t)| + c (k + k0 ) )
2
2
2
2
2 2
2
+|δA−
k−k0 | (|Ωk (t)| + c (k − k0 ) )] + [2c k |δΦ(k)| ]).
(34)
The right-hand side of Eq. (32) can be evaluated−∂ 1[ (δE)2 + (δB + B0 )2 ] =∂t 8π

Proceedings of FEL 2007, Novosibirsk, Russiaγ̄mc2 2 1 ∂ 
)
−(
exp(2
2e
4πc2 ∂t
k

 t
0





−

γk (t )dt )2
2
22([|δA+
k+k0 | (|Ωk (t)| + c (k + k0 ) )
2
2
2
2
2 2
2
+|δA−
k−k0 | (|Ωk (t)| + c (k − k0 ) )] + [2c k |δΦ(k)| ]).
(35)
Comparing Eqs. (35) and (34) completes the proof of
Eq. (32).
Momentum conservation: We will now show that the average total axial momentum is conserved in the quasilinear
theory. To obtain the quasilinear analog of Eq. (29), Eq.
(4) is substituted into Eq. (29), the resulting equation isdifferentiated with respect to time, use is made of Eq. (12),and we integrate by part with respect to pz :

n0 e
−
mc

 L

∂
dz e 0[( (Ax + δAx ) (A0x + δAx )∂z−L 2L c
 ∞
e 0
∂
dpz
0
+ (Ay + δAy ) (Ay + δAy ))
G]
c
∂z
−∞ γT
 L
∂
dz 1
(δE × B0 + δE × δB)z = 0. (36)+∂t −L 2L 4πc
 L dz 1
Where −L 2L
We can expand
4πc (δE × B0 )z = 0.
the transverse current density −e d3 p(vx êx + vy êy )fb in
powers of perturbed quantities. Thus, for the form of f0
given in Eq. (4) and by expanding G and 1/γT to firstorder perturbed amplitudes the time rate of change of theaverage plasma momentum density is given by L dz  ∞n0 e2∂
PMD =
dpz (−)∂t
mc2−L 2L −∞e2∂∂
− 3 2 4 (A0x δAx +A0y δAy )G0 (A0x δAx +A0y δAy )]
γ m c
∂z
∂z
(37)
correct to second order in the perturbation amplitude. The
analogue equation to Eq. (29) in quasilinear theory is(38)

Rearranging the terms in Eq. (37) and by use of the DR(21) and the relation between perturbed amplitudes and dielectric functions we have tγ̄mc2 2 1 ∂ ∂
PMD = −()
exp(2γk (t )dt )2∂t2e2πc ∂t0
k−2
2
×ωk [(k + k0 )|δA+
k+k0 | + (k − k0 )|δAk−k0 | ].

∂∂∂  ik(δA∗x (k, t) δAx (k, t)+δA∗y (k, t) δAy (k, t))
∂t
c
∂t
∂t
k
 t


γ̄mc2 2 1 ∂ 
)
= −(
exp(2
γk (t )dt )22e2πc ∂t0
k−2
2
×ωk [(k + k0 )|δA+
k+k0 | + (k − k0 )|δAk−k0 | ],(40)

Then, Eq. (38) is directly proved by comparing Eqs. (39)and (40).

CONCLUSION
In the Raman regime, due to the high density of the electron beam, the space-charge potential is not negligible compared to the pondermotive potential. In this paper we havederived conservation laws in the quasilinear analysis of an
FEL in the presence of the space-charge field of electrons.
The assumption of a broad spectrum of waves ensuresthat the saturation takes place through the quasilinear diffusion of electrons in the momentum space rather than by
the particle trapping.
The presence of space-charge wave, that is resonant in
the Raman regime, with the real parts of the frequency
and wave number satisfying the linear DR, modifies the
problem considerably compared to the Compton regime inwhich space-charge potential is negligible in comparison to
the pondermotive potential.
The quasilinear kinetic theory used to derive three exact conservation relations, corresponding to conservationof (average) particle density, total energy, and total axial
momentum. These results may be used to study the quasilinear saturation of a FEL in the raman regime.

ACKNOWLEDGMENT∂
1∂
1
×[ A0x δG δAx + A0y δG δAy
γ
∂z
γ
∂z

∂ 1
∂
PMD = − (δE × δB)z .
∂t∂t 4πc

MOPPH012(39)

One of the authors (B.M.) would like to thank the Centerof Excellence in Computational Aerospace Engineering for
financial support.

REFERENCES[1] A. M. Dimos, R. C. Davidson, Phys. Fluids. 28, 677 (1985).
[2] T. Taguchi, K. Mima, and T. E. Mochizuki, Phys. Rev. Lett
46, 824 (1981).
[3] W. P. Marable and P. A. Sprangle, J. Appl. Phys. 67, 3576
(1990).
[4] R. C. Davidson and Y.-Z. Yin, Phys. Fluids. 28, 2524 (1985).
[5] N. A. Vinokurov, Z. Huang, D. A. Shevchenko, and K. -J.
Kim, Nucl. Instrum. Methods. Phys. Res. A 475, 74 (2001).
[6] N. M. Kroll, P. L. Morton, and M. N. Rosenbluth, IEEE J.
Quantum Electron. QE-17, 1436 (1981).
[7] W. H. Louisell, J. F. Lam, and D. A. Copeland, Phys. Rev A
18, 655, (1978).

We can now evaluate the second term of Eq. (29) by use of
Eqs. (3), (14)-(16)[8] T. Kwan and J. M. Dawson, Phys. Fluids. 22, 1089 (1979).

1∂ 1
(δE × δB)z  =∂t 4πc4πc[10] R. C. Davidson, Physics of Nonneutral Plasmas (AddisionWesley, Redwood City, CA. 1990), Chap. 7 .

−[9] R. C. Davidson and H. S. Uhm, Phys. Fluids. 23, 2076 (1980).

FEL Theory

49

MOPPH015

Proceedings of FEL 2007, Novosibirsk, Russia

LIMIT FOR HARMONIC CONVERSION IN A SINGLE CASCADE OF
COHERENT HARMONIC GENERATION
E. Allaria, G. De Ninno, Sincrotrone Trieste, Trieste, Italy
Abstract
Harmonic generation is a reliable method for
producing coherent high-brightness photon pulses from
relativistic electron bunches. The standard process leading
to Coherent Harmonic Generation is initiated by apowerful seed laser. As a consequence, reaching shortwavelengths generally requires a high order frequency
conversion. For that reason some of the projects which
are presently under development for coherent VUV andsoft-Xray emission are based on a series of two or moreconsecutive “cascades”. In these setups, the radiation
produced into one stage is used as a seed in a following
cascade. The required number of cascades depends on the
maximum harmonic conversion which can be obtained insingle stages. In this paper we stud y the mechanism
underlying CHG, i.e. the bunching creation into themodulator, and we investigate the physical limits of thesingle-stage CHG.. The identification of the limiting
parameters may allow the implementation of new
methods for enhancing the conversion efficiency. One ofthese methods, which rely on a simple modification of thestandard CHG scheme, has been recently proposed [3]and shown to be able to significantly improve the system
performance. Results are confirmed by 3D numericalsimulations using the FERMI electron beam parameters
as initial conditions.

INTRODUCTION
It is well known that the electron bunching, which isneeded for effective High Gain Harmonic Generation(HGHG), rapidly decreases with the harmonic number,unless a strong energy modulation is produced in themodulator. However, the exponential light amplificationthat follows the first quadratic growth is strongly sensitive
to the total energy spread,i.e., the quadratic combinationof initial incoherent energy spread and of the coherent
modulation.

Figure 1: Example of Optimized output power for the
HGHG FEL setup as a function of seed power and R56.
FEL Theory50

As a consequence, the optimization of a HGHG scheme
relies on a compromise between the production of a
sufficiently high bunching in the modulator (allowing asignificant quadratic growth) and the need of keeping thetotal energy spread below the FEL parameter ρ. An
example of the dependence of the produced FEL output
power on the seed power and dispersive section strength(R56) is shown in Fig.1.
In this paper we study the possibility of optimizing the
CHG setup once the electron-beam and the radiatorparameters are given. For the presented work, electron
beam parameters have been chosen to be those of the
FERMI@Elettra project [1], see Table 1.

Figure 2: a) Schematic layout for the modulator in astandard HGHG setup. b) Proposed modified layout
considering a phase shifter in between two modulator
subsections.
The optimization is based on a modification of thestandard modulator scheme, involving both the ondulator
configuration and the power of the seed laser (Fig.2). The
study has been done by perfomring numerical simulations
with well established 3D FEL codes ginger and genesis.
Table 1: FERMI electron-beam parameters
Parameter
Electron Beam Energy
Peak current
Uncorrelated energy spread
Norm. Transverse Emittance

Value
1.2
1
200
1.5

Units
GeV
kA
keV
mm-mrad

CASCADE LIMIT IN A STANDARD CHGSCHEME
According to theoretical predictions [2], the induced
energy spread needed for efficient CHG increases withthe harmonic number.
Figs.3 and .4 show that, while the optimum value ofenergy spread increases when reducing the emitted
wavelength, the optimum bunching is approximately
constant (order of 4% in our case). This result can be
explained considering that in HGHG bunching isnecessary to induce the quadratic emission occurring in
the first part of the process, AND SIMPLY HAS TO BE
LARGER THAN SHOT NOISE. However, the main
contribution to the final output power comes from theProceedings of FEL 2007, Novosibirsk, Russia

40 nm
30 nm
24 nm
20 nm
18 nm
17 nm

9

Output power (W)

5x10

4

3

2

1

0
0.5

1.0

1.5
2.0
Starting energy spread (δγ)

2.5

3.0

Indeed, in first approximation, the required value forthe bunching is independent from the harmonic we areinterested in.

50

1

40

0.1

30
0.01

20

0.001

10
0
5

40 nm
30 nm
24 nm
20 nm
18 nm
17 nm

9

Output power (W)

5x10

4

Bunching (% )Figure 3: For each wavelength the maximum output
power, obtained after optimization, is plotted as a functionof the total energy spread (δγ) at the entrance of theradiator, which is correlated to the seed power .

for λ<20nm (N>12) and cannot be obtained for λ<17nm(fig.5).
We focus now on the 20nm case, that is the 12th
harmonic of a frequency multiplied Ti:Sa tuned at 240nm.
As shown in previous figures, a power of about 1 GW forthe considered system can be obtained. Fig.6 shows theevolution of the radiation power (red) and bunching(black) along the radiator starting from a properly
optimized initial condition. The considered radiatorparameters are those used for the first FEL of the
Fermi@Elettra project [1], with the only difference thatthe radiator period has been reduced to 55mm from theoriginal 65mm in order to extend the tunability to shorter
wavelengths.
FEL power (GW)

successive exponential growth, which is rapidly depressed
when the (total) energy spread increase.

MOPPH015

10
Radiator distance (m)1520Figure 6: Results showing the quadratic (z<5) ad theexponential growth of the FEL power in the optimized
standard setup for 20nm.

3

2

1

0
0.02

0.04

0.06
0.08
Initial bunching (B)

0.10

0.12

Figure 4: For each wavelength the maximum (optimized)
output power is plotted as a function of the bunchingproduced after the dispersive section.
The fact that shorter wavelengths require larger energy
spread implies that the final output power monotonicallydecreases (see inset of fig. 5) when going to shorter
wavelengths.

Figure 5: Form the data of figs. 3 and 4 we can see astrong dependence of the δγ necessary to optimize theoutput power as a function of the desired wavelength (redcurve). On the contrary, the bunching (black curve) shows
only a weak dependence. The inset shows the decrease of
output power as a function of λ.
A limit in wavelength for HGHG to occur is provided
by the harmonic at which it is no more possible toproduce the required amount of bunching. In theconsidered setup (see Table 1) HGHG become inefficient

The mechanism underlying the FEL process during
HGHG can be understood looking at the electron phasespace at the entrance of the radiator, as shown in fig.7a.
Figure 7b shows the localized density distribution ofelectrons, which is at the origin of initial bunching.
Bunched electrons (blue in Fig.7a) are responsible for thecoherent quadratic emission (z<5m in Fig.6). Remaining
electrons interact with the produced radiation in the restof radiator (z>5m) and are eventually responsible for the
exponential growth.

Figure 7: a) Phase-space representation of electrons at theentrance of the radiator in the optimized standard
configuration for the 20nm case. b) Histogram of theelectron density distribution. In both figures, the fieldevolution at 20 nm is reported as a reference.
Due to the energy modulation necessary for HGHG,“blue” electrons are characterized by a large energy
spread and will only participate to the initial coherent
emission. The rest of electrons (red) are characterized bya small “slice” energy spread, but their mean energy
present quite large variations along the original phase (0-FEL Theory

51

MOPPH015

Proceedings of FEL 2007, Novosibirsk, Russia

24π referring to one period of the 12th harmonic of theseed wavelength, i.e. 20nm). Such a detuning limits the
exponential growth.

necessary to induce a bunching of 4% is reported as afunction of the wavelength.

NEW OPTIMIZED CONFIGUATIONS

Figure 8: Evolution of the energy spread (a) and bunching(b) inside the modulator for the three considered setups:
standard (red curve), double modulator (black curve) anddetuned modulator (blue curve).
The modulator of a HGHG system can be optimized if
one is able to produce the needed amount of bunching by
inducing a smaller amount of coherent energy spread. For
this purpose, in [3] we have proposed a simple scheme
relying on a two-segment modulator separated by a dephasing unit (Fig.1). In the first segment, electronsinteract with the coherent radiation and coherent energy
spread is produced. After the de-phasing unit, electrons
and radiation are de-phased by about π, so that theinteraction in the second modulator section is used topartially absorb the coherent energy spread.

Figure 9: Comparison between the standard setup and theone based on the double modulator in terms of the energy
spread necessary for creating a certain amount ofbunching (4%) at the desired λ. Red curve refers to thestandard configuration while the black one refers to the
double modulator scheme.
We propose here a new setup which is able to produce
the same effect on the electron beam using a single
modulator section. The method exploits the natural dephasing that occurs to electrons moving in a detuned
undulator. As demonstrated by the data reported in Fig.8,
by properly choosing the detuning value it is possible toobtain the same effect of the two modulator sections with
π de-phasing in-between. The benefits of using one of the
proposed methods with respect to the standard one areshown in Fig.8, where the minimum energy spread
FEL Theory

52

Figure 10: Example of the improved performance at
20nm obtained by using the proposed modified
modulators. FEL power evolution along the radiator forthe setup using the standard modulator (red curve), thedouble modulator (blue curve) and the detuned modulator(black curve).
Data show that for the same wavelength the new
proposed methods allow to obtain the required bunchingwith about half of the energy spread with respect to thestandard method (Fig.9). This implies that a significantly
larger output power can be reached. This is shown in
Fig.10 where the evolution along the radiator of theoutput power and bunching for the 20nm case is shownfor the standard and two new proposed methods. A factor
two can be gained with the new modulator schemes.

Figure 11: Phase space representation of the bunchedelectrons at the entrance of the radiator in the case of thestandard modulator scheme (red dots) and the one using
the 2 modulator sections with a π de-phasing unit (blackdots).
Looking at Fig.10, one can appreciate the difference
between the standard and new methods. While thebunched electrons (φ~7), responsible for coherent
emission, are very similar for the two considered
configurations, the unbunched electrons look different.
Indeed, electrons that have been modulated by using the
double modulator setup (black dots) have in general anenergy which is closer to the nominal one.

Proceedings of FEL 2007, Novosibirsk, Russia

EXTENDING THE LIMIT
According to data shown in fig.9, using the proposed
optimized modulator setups is possible to extend the limit
for HGHG to shorter wavelengths. Indeed, data show thatwith the same induced energy spread using the new
proposed schemes it is possible to obtain a bunching of
4% at a wavelength which is about half of the one thatcan be reached with the standard method.

MOPPH015

This is confirmed by data reported in Fig.12 showing
the power evolution along the radiator using an electron
bunch which has been passed through the two- modulator
scheme for creating the bunching. Data shows that withthe proposed modified methods it is possible to go close
to saturation at 15 nm. It is important to note that better
results in terms of extracted power can be obtained atshorter wavelengths by optimizing the radiator period..

CONCLUSIONSThe limit for the harmonic conversion which can beobtained with the standard HGHG scheme in a realistic
machine has been analyzed. Moreover two methods havebeen presented allowing to extend the limit of HGHG
toward shortest wavelengths. These methods only requirea modification of the undulator used in the modulator
section and a more powerful seed laser.

REFERENCES
Figure 12: Power growth of the FEL into the radiator atthe 16th harmonic (15nm) The use of the new proposed
schemes allow to reach more than half GW, In the inset
the evolution of the bunching is shown.

[1] FERMI design technical report, in press.
[2] L. H. Yu, Phys. Rev. A 44, 5178 (1991).
[3] E. Allaria, G. De Ninno, PRL 99, 014801 (2007).

FEL Theory

53

MOPPH017

Proceedings of FEL 2007, Novosibirsk, Russia

1D LINEAR INTENSITY SPIKING EVOLUTION IN A SINGLE SHOT OF A
SASE FEL

C. Maroli, L. Serafini, INFN-Sezione di Milano,Via Celoria 16, 20133 Milano, Italy
V. Petrillo, Dipartimento di Fisica dell’Università di Milano-INFN Sezione diMilano,
Via Celoria 16, 20133 Milano, Italy
Abstract

FEL Theory

54

+∞

∫

δA(z, t) = dhδA0 (h)ei(hz−ω(h) t )−∞where ω(h) is the root of the dispersion relation
with positive imaginary part. The
ω3- hω2 -1 = 0
integral in the preceding equation is solved numericallyfor the case of a Gaussian spike at t=0 and different
values of the parameter α =L0/LC, where L0 is the
FWHM value of the initial Gaussian spike.
Fig.1 shows that the time evolution of the spike depends
on the value of its width at t=0 as compared with LC. In
particular, when L0≈LC, the spike increases exponentiallywhile its width increases only slightly. Instead, when
L0<<LC, the width of the spike increases by several ordersof magnitude starting from the very small value at t=0.
100

α=1

t=2

80

|δA|

2

60

40

t=1

20

t=0
0
-4

-2

0

2

4

6

α=0.1
80

t=4

2

60

|δA|

The intensity spiking in the radiation of a high-gain
free-electron laser starting from noise consists of asequence of random spikes with wide top-to-bottom
variations in the signal received at the end of theundulator [1-4]. The random nature of the spiking is adirect consequence of the random character of the small
electromagnetic fields created on the electron beam as itenters the undulator field and the main aspects of the
spiking are described accurately by the linear form of the
one-dimensional FEL equations.
Starting from the Maxwell-Lorentz 1D equations, thedisturbances in the radiation field δA(z,t) and bunching
factor δb(z,t) are given by the following simple linear
system in the limit of small radiation fields and when theradiation wave length λ is much smaller than thecooperation length LC = λ/4πρ (ρ is the FEL parameter):∂∂( + c(1 − β 0 ) ) δA( z, t ) = δb( z, t ),
∂t
∂z
(1)
∂2
i
δ
b
(
z
,
t
)
=
δ
A
(
z
,
t
)
∂t 2
TG3
These equations are written in the frame moving with theundisturbed beam velocity cβ0, TG = λw/4πcρ is the gain
time and λw the undulator period. The reason why wereconsider this very simple system of equations is that it
may lead to final situations in which there is no spiking
and the signal found at the end of 10-20 gain times TG
consists of one single and smooth bump, even when thelength Lb of the beam is much longer than the cooperation
length LC.

We consider the particular solution of (1)

40

20

t=2
t=0
0
0

1

2

3

4

5

16

α=0.01
14

t=6
12
10
2

INTRODUCTIONONE SINGLE SPIKE|δA|

It is shown that the simple system of equations used by
Bonifacio et al. in 1994, leads to signals characterized by
the usual spiky behaviour of the FEL radiation intensity,
as well as to “coherent” signals in which the spiking is
reduced to a small amplitude random fluctuation on asmooth and nearly constant average value. The two typesof signals are obtained with different classes of initialconditions. In particular, coherent signals correspond toinitial shot-noise configurations whose closely spaced
spikes have widths much smaller than the cooperation
length.

8
6
4
2

t=4
t=0

0
0,0

0,5

1,0

1,5

2,0

2,5

z/L C

Fig.1(color) – Values of |δA|2 vs z/LC. Top figure α = 1,
curves (a, black),(b, red),(c, green) for t/TG = 0, 1, 2,
respectively; middle figure α = 0.1, (a),(b),(c) for t/TG=0,2, 4 ; bottom figure α = 0.01, (a),(b),(c) for t/TG=0, 4, 6.

Proceedings of FEL 2007, Novosibirsk, Russia
Fig.2 shows what happens for large values of t/TG and for
α = 1, 0.1, and 0.01, while Fig.3 gives the value of theradiation intensity at the peak of the spike vs t/TG.
6x10

7

5x10

7

4x10

7

3x10

7

2x10

7

|δ A |2α =0.1t=12.5a=0.01 t=15
α =1 t=10

1x10

7

0
-5

0

5

10

MOPPH017

spikes being 5LC. At t=10TG, |δA|2 has the usual spiky
form with wide top-to-bottom variations of the signal
intensity. Fig.5 shows modulus and phase of δA at t=0
and 10 TG, for a sequence of spikes whose widths are allmuch smaller than LC. In this case the signal at t = 10 TG
has only a small amplitude fluctuation on top of a smoothand nearly constant average value. The number of“spikes” that characterise the shape of the signal intensity
at this time follows approximately the usual rule, i.e.,
number of spikes ~ bunch length/ 2πLC ~ 40/2π ~ 6-7 but
the amplitude of the spikes as compared with the averagevalue of the intensity is much reduced. The two parts (d)in figures 4 and 5 show the profile of the signal intensity
at t=10 TG for the two cases, together with thecorresponding incoherent and interference terms.
4

15

t=0

z/L C

3
2

Fig.2 (color) – Values of |δA|2 vs z/LC. Curve (a, black) α= 1, t/TG = 10; curve (b, red) α = 0.1, t/TG = 12.5; curve(c, green) α = 0.01, t/TG = 15.

phase( δ A)

1
0
-1
-2
-3

8

-4
-20

7

20

40

20

40

60

80

100

120

60

80

100

120

t=0

10

6
5

8

α=0.1

2

4
6

| δ A |2

log10(|δA| )max

0

α=1

3

α =0.01

2

4

1

2

0
0

2

4

6

8

10

0
-20

t/TG

0

z/LC

Fig.3 (color) – |δA|2 at the maximum of the spike vs t/TG
for: (a, black) α = 1; (b, red) α = 0.1; (c, green) α = 0.01

4

t=10

3

caso A2

phase( δA)

1

RANDOM SEQUENCE OF SPIKES

0
-1
-2

Infinitely long electron beam-3

 In this case we assume δA(z,0) as the following random

-4
-20

∑A e

− μ j ( z − z 0 j ) 2 + iθ jz

0j

j=1

where Nsp is the number of spikes, the peak of each single
spike being at z=z0j while the complex numbers A0j andthe real numbers μj, θj and z0j are all random functions of
the integer j defined in terms of their average values andr.m.s. deviations.
Fig.4 shows modulus and phase of the complex
number δA at t=0 and t=10TG for an initial random
sequence in which all spikes have widths comparablewith LC, the average distance Dsp between successive|δ A|

δ A ( z ,0 ) =N sp

1,4x108

1,2x108

1,0x108

8,0x107

6,0x107

4,0x1072,0x10

7

0

20

40

60

80

100

120

60

80

100

120

t=10

2

sequence of Gaussian spikes

0,0
-20

0

20

40

z/L C

Fig.4 (color) – Phase and modulus squared of δA vs z/LC
at t=0 (first column, parts (a) and (b)) and t=10TG (second
column, (c) and (d)). (d) shows the signal intensity (curve
1, black) and the incoherent part (curve 2, green).
Nsp=20, Dsp=5LC, α=1.

FEL Theory

55

MOPPH017

Proceedings of FEL 2007, Novosibirsk, Russia

While |δA|2 in Fig.4 is practically equal to its incoherent
part indicating that the interference between different
signals is always negligible, in Fig.5 the final signal
intensity is the result of a strong process of constructive
interference. If it seems appropriate to classify as“incoherent” the signal produced in the case of Fig.4, it
seems likewise appropriate to consider as “coherent” thesignal produced in the case of Fig.5.

LC), together with 15 large spikes whose widths are
uniformly of the order of LC (average distance between
large spikes 3 LC). The whole signal at t = 0 covers about
45 cooperation distances. As one can see, spiking
develops also in this case after a considerable “cleaning”
of the signal, because at t = 10 TG it is composed by 8large spikes (number of spikes ~ 45/2π ~ 7-8) with theusual wide top-to-bottom oscillations. This is due to thelong spikes at t = 0 increasing immediately with thelargest growth rates.

4
3

1400

2

1200

t=0

1000

0

800

| δ A |2

phase(δA)

1

-1

600

-2

400

-3

200

-4
4

5

6

7

8

9

0

10

-10

0

10

20

0

10

20

30

40

50

30

40

50

25

t=0

20000020t=4150000|δA|

2| δ A |2

15
100000

10
50000

5
0
-10

0
4

5

6

7

8

9

10

z/LC

z/L C

10000

4

t=2

3

8000

2

6000

0
-1

|δ A |2

phase(δA)

1

-2

4000

-3
-4
0

4x10

7

3x10

7

2x10

7

5

10

15

20

25

30

35

40

45

2000

50

0

1x10

7

0
0

10

20

30

40

50

z/LC

|δ A |2

|δ A|

2

-10
3,5x1093,0x1092,5x1092,0x109

1,5x1091,0x109

5,0x10

8

0

10

20

30

40

50

30

40

50

t=10

0,0

Fig.5 (color) – Same as Fig.6 with Nsp=1000, Dsp=0.04
LC, α=0.007. Only part of the signal has been plotted at
t=0. Part (d) shows the signal intensity (curve 1, black)and the interference part (curve 2, red).
As a third example, we consider the case in which
the signal at t = 0 contains two characteristic lengths, thefirst of the order of the cooperation length LC and thesecond much shorter than LC. Fig.6 shows what happens
in a case in which the initial signal is made up by 225
narrow spikes whose widths are uniformly of the order of
10-1 LC (the average distance between narrow spikes is 0.2
FEL Theory

56-5,0x108-1,0x10

9

-10

0

10

20

z/LC

Fig.6 (color) - |δA|2 vs z/LC at t/TG=0,2,4,10 (part(a),(b),(c),(d) respectively). (d) shows also the incoherent(curve 2, green) and interference (curve 3, red) parts ofthe total signal (curve 1, black) at t=10TG.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH017

Finite-length electron beam
System (1) has been integrated numerically also inthe case of a beam of finite length. Fig.7 shows the
behaviour of the signal intensity as obtained by solving
the system with appropriate initial and boundary
conditions. The initial condition for this case consists of8000 Gaussian spikes with the average distance between
successive spikes Dsp = 0.01LC. The bunch length is Lb =80 LC.

REFERENCES[1]R.Bonifacio,L.DeSalvo, P.Pierini, N.Piovella,
C.Pellegrini, Phys.Rev.Letters 73,70(1994)[2]L.H.Yu, S.Krinsky, Nucl.Instrum.Methods
Phys.Res., Sect.A 407,261(1998)[3] E.L.Saldin, E.A.Schneidmiller, M.V.Yurkov,
Opt.Commun. 148,383(1998)[4]K.-Je Kim, in Towards X-ray Free Electron
Lasers, edited by R.Bonifacio andW.Barletta, AIP Conference Proceedings
No.413 (AIP,New York,1997), p.3[5] Zhirong Huang, K.-Je Kim, Phys. Rev. STAB
10,034801(2007)

1,2

1,0

|δ A |2

0,8

0,6

0,4

0,2

0,0
40,0
4,0x10

6

3,5x106

3,0x1062,5x1062,0x10

6

1,5x106

1,0x106

5,0x10

5

40,5

41,0

41,5

42,0

|δ A |2

t=5

0,0
0

20

40

60

80

100

z/L C

3000

2500

2000

|δ A |2

t=1
1500

1000

500

0
0
1,0x1098,0x108

6,0x108

4,0x1082,0x10

8

20

40

60

80

100

t=10

|δ A |2

CONCLUSION
The main result of this paper is that according tosystem (1), the light emitted by an FEL is not always achaotic light even if the initial signal is noisy [5]. In fact,
this system leads to signals dominated by the spiking aswell as to signals in which the spiking is reduced to asmall amplitude fluctuation superimposed on a smoothpulse. Spiking in the usual sense is associated with initialconditions characterized by a scale-length L0 of the orderof the cooperation length LC, while absence of spiking
requires that the initial shot-noise condition consists of arandom sequence of uniformly narrow spikes with widthsof the order of 10-2 LC or smaller, i.e., that L0<<LC. Since
system (1) is based on the slowly-varying envelope
approximation (SVEA), the initial conditions are
consistent with its nature only if the characteristic length
L0 is longer than the wave-length λ of the emitted
radiation. Absence of spiking as deduced on the basis of(1), therefore, requires that L0 satisfies the inequality λ<
L0 << LC. This means small values of the FEL parameterρ, of the order of 10-4 or smaller which are typical of
FELs based on static or optical undulators and operatingin the regime of very high frequencies or even X-ray
FELs.

t=0.01

1,4

0,0
0

20

40

60

80

100

z/LC

Fig.7 – Signal intensity vs z/LC at times t/TG = 0.01, 1, 5,
10 (parts (a), (b), (c) and (d)) in the case of a finite-length
electron beam with Lb = 80 LC. Nsp = 8000, Dsp =0.01LC.
Only part of the signal is given at t=0.01.

FEL Theory

57

MOPPH019

Proceedings of FEL 2007, Novosibirsk, Russia

OPTIMIZED DESIGNS FOR CAEP IR FREE-ELECTRON LASER
Xiaojian Shu#, Yuhuan Dou, Institute of Applied Physics and Computational Mathematics, P. O.
Box 8009, Beijing 100088, P. R. China
Abstract
The characteristics of CAEP IR free-electron laser are
estimated and the optimized designs of the resonatorparameters such as the radius of output hole, the size of
mirror and the length of the resonator are carried out
using our 3D FEL oscillator code. With the appropriate
parameters, the saturated power, output power, gain andthe construction of optical modes are calculated.

INTRODUCTION
Infrared free-electron lasers (FELs) have broken
important ground in optical science for many attractive
features such as most notably wavelength tunability,
control of spectral and temporal pulse width. In order tobring along the development of correlative technologies
such as superconducting technology, linear accelerator
technology and optical cavity technology, an infrared FEL
device is built at the China Academy of Engineer Physics(CAEP) which driven by superconducting linear
accelerator. The radiation wavelength of the device will
be in the range from 3 to 8μm.
In this paper, The characteristics of CAEP IR freeelectron laser devices will be estimated and the optimized
design of the resonator parameters such as radius of
output hole, the size of mirror, the resonator length will be
carried out by using our 3D FEL oscillator code
(OSIFEL)[5-7]. The design is achieved by considering
two factors as optical cavity character and the transverse
optical modes. Based on the appropriate parameters, thesaturated power, output power, the resonator gain, theconstruction of optical modes are calculated.

THE ESTIMATE OF THE OPTICAL
CHARACTERISTICS
Table 1: CAEP IR FEL Parameters
Electron beam
Energy (MeV)37
Peak current (A)30
Micro bunch (ps FWHM)
2.5
Energy spread (%)
1
20
Emittance ( mm mrad)
Wiggler
3.2
Period (cm)
3.2
Peak field strength (kG)44
Number of periods
Optical
4.4
Wavelength (μm)
2.769Cavity length (m)1.499
Mirror curvature (m)π________________________________________#

shu_xiaojian@iapcm.ac.cn

FEL Theory

58

The electron-beam and wiggler parameters used arelisted in Table 1. The energy spread and emittance are
specified as FWHM and RMS. Using the parameters of
the optical cavity, we can attain that the Rayleigh length is
40cm, the optical waist radius is 0.7mm, and the radius of
the optical beam on the cavity mirror is 2.6mm.

THE NUMERICAL SIMULATIONS
To attain optimized the radius of the mirror of the
optical cavity and the coupling hole, the numericalsimulations are performed using the 3-D OSIFEL code. In
the simulations, the distribution functions of transverse
position and velocity, energy of the electron are assumed
as Gaussian. The corresponding initial values of thesample electrons are given by Monte Carlo method andthe initial phases are loaded according to the ‘quiet start’scheme to eliminate the numerical noise.

Selection of the Radius of Coupling HoleThe influences of the hole-coupling on the gain, power,
output and the mode construction are simulated andstudied, as shown in Table 2, where r is the radius of thecoupling hole, Gnet the net gain, Pin the saturated
intracavity power, Pout the output power, ηloss the total lossof the resonator, f00 the ratio of the fundamental mode,ηout the coupling efficiency, which is defined as the ratioof the useful loss to the total loss. It can be seen that the
total loss of resonator and coupling efficiency decrease asa reduction in the size of hole, however, the ratio of thefundamental mode increases. If the size of hole is increase,
the interaction of the optical radiation with the electrons
will become weaker so the net gain of resonator isdecreased. According to Table 2, we may select the
optimum size of radius r as 0.3 to 0.4mm.
Table 2 Characteristics of resonator as a function of
the radius of the coupling hole
f00
r
Gnet
Pin
Pout
ηout
ηloss
/mm
0.30
0. 35
0. 40
0. 50

/%
23.4
20.0
15.5
10.3

/MW
131
110
67
41

/MW
3.58
3.61
3.41
2.82

/%
52.7
53.0
54.6
56.0

/%
5.40
6.60
10.1
14.0

/%
98.0
97.1
94.2
90.0

Effects of the Mirror Size
There are mainly two aspects from the influence of thecavity mirror size. One is the influence on thecharacteristics of the resonator, the other is the influenceon the structure of transverse optical modes. That is, when
the radius of cavity mirror becomes large, the net gain andthe saturated intracavity power will increase; however, theproportion of fundamental mode will decrease because
the loss of the high order modes is small. So the optimum

Proceedings of FEL 2007, Novosibirsk, Russia

Table 3 The characteristics of resonator as a function of
the radius of the mirror of the resonator
R/cm Gnet/% Pin /MW Pout/MW ηout /%ηloss /%
0.5
0. 8
0.9
1.0
1.2
1.5

20.0
20.0
20.4
20.5
20.0
20.0

107
110
108.6
108
114
117

3.50
3.61
3.81
4.29
4.38
4.46

51.4
53.0
55.9
63.4
63.9
66.2

6.8
6.6
6.68
6.8
6.37
6.1

1.00

1.0
0.8

Power (arb.)

size of the mirror of the resonator must be selected. The
characteristics of the resonator as a function of the radiusof the mirror of the resonator R are simulated as shown in
Table 3, the evolvement curves of fundamental mode as afunction of optical pass for different radius of the mirrorof the resonator are plotted in Fig. 1. It can be seen from
Table 3 as the radius of the mirror of the resonatorincreases, the quality of resonator becomes better such as
the little loss of the resonator, lager output power, andhigher coupling efficiency. However, from Fig. 1, it canbe seen that when the radius of the mirror of the resonatorincreases, the distributing of modes becomes more
complex and the proportion of fundamental mode will
decrease. When the radius of the mirror of the resonator is
1.5cm, the proportion of fundamental mode is about 75%.
Considering the quality of resonator and structure ofmode, it is suggested that the suitable range of mirrorradius is 0.8-0.9cm. In this range, the proportion of
fundamental mode is above 90% in the whole cavity.

MOPPH019

0.6
0.4
0.2
0.0
-8

-7

-6

-5

-4

-3

-2

-1

0

1

Cavity length detuning (μm)

Fig. 2. Detuning curve of CAEP IR FEL from 3D
simulations.

Simulation Results
Based on the above numerical simulations, we selectthe radius of the coupling hole as 0.35mm, the radius of
the mirror as 0.8cm. The evolvement curves of the total
gain Gt and the net gain Gnet are shown in Fig. 3. The
evolvement curves of intracavity optical power Pin and theoutput power Pout are shown in Fig. 4. It can be seen thatafter 100 pass number, the intracavity optical power issaturated, the total gain is about 28%, the net gain is about
20%, the saturated power is about 110MW, the output
peak power is about 3.6MW. The proportion of
fundamental mode is about 97%.

0.95

0.5

0.85

Gt
Gnet

0.4
0.5cm
0.8cm
1.0cm
1.5cm

0.80
0.75

0.3

Gain

f00

0.90

0.70
0

50

100

150

200

250

0.2
0.1

pass number
0.0

Fig. 1. The evolvement of fundamental mode for different
radius of the mirror.

The Detuning Curve
Furthermore, the detuning curves of free-electron laser
oscillators are calculated using the 3-D OSIFEL. The
result is shown in Fig. 2. It can be seen that the range ofthe detuning curve is from about –0.2 μm to –7 μm andthe detuning length is about 7 μm. Note that the curve isvery sharp and the detuning length is shorter because thesmall signal gain of CAEP IR FEL device is smaller.

-0.1
0

50

100

150

200

250

Pass number

Fig. 3. The evolvement curves of the total gain (Gt) andthe net gain (Gnet).

FEL Theory

59

MOPPH019

Proceedings of FEL 2007, Novosibirsk, Russia

CONCLUSIONS
120

In general, the simulation and optimized design of the
CAEP IR FEL has been made with the help of our 3-D
OSIFEL code. Considering the quality of resonator andstructure of mode, the optimum radius of the couplinghole and the radius of the mirror of the resonator havebeen chosen. It can be attained that the range of thedetuning curve is from about –0.2 μm to –7 μm and thedetuning length is about 7 μm. With the appropriate
parameters, the saturated power, output power, theresonator gain, the construction of optical modes arecalculated.

100

Pin/MW

80
60
40
20
0
0

50

100

150

200

250

REFERENCES

Pass number

Fig. 4a. The evolvement of the intracavity power.

4

Pout/MW

3

2

1

0
0

50

100

150

200

250

Pass number

Fig. 4b. The evolvement of the output power.

FEL Theory

60[1] G.R. Neil, et al., Phys. Rev. Lett., 84 (2000) 662.
[2] C. Behre, et al., Nucl Instr And Meth, A528 (2004)
19.
[3] R. Hajima, et al., “Recent Results of the JAERI
Energy-Recovery Linac FEL”, 26th International
FEL Conference &11th FEL Users Workshop,
Trieste, Italy, August 2003.
[4] E.A. Antokin, R.R. Akberdin et al., Nucl Instr And
Meth. A528 (2004) 15.
[5] Xiaojian Shu, Yuanzhang Wang, Nucl. Instr. And
Meth. A 483 (2002) 205.
[6] Xiaojian Shu,Yuanzhang Wang, Yunqing Jiang, etal.,Optical Engineering, 39 (2000) 1543.
[7] Xiaojian Shu, Yuanzhang Wang, et al., Nucl. Instr.
And Meth. A407 (1998) 76.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH020

FEL WITH OROTRON TYPE FEEDBACK*
N.S. Ginzburg#, A.M. Malkin, N.Yu. Peskov, R.M.Rozental, A.S. Sergeev, IAP RAS, Nizhny
Novgorod, Russia
K. Kamada, R. Ando, Kanazawa University, Kanazawa, Japan.
Abstract
In this paper we discuss a novel scheme of the freeelectron laser in which the electromagnetic wave excitedby the electron beam is coupled to the mode of a twomirror quasioptical resonator by means of corrugation oneof the mirrors. The described scheme allows to combine
selective properties of quasioptical resonator withrelativistic frequency up-conversion of a free electron
laser.

THE ELECTRODYNAMIC MODEL
We consider a resonator consisting of two metallic
mirrors . One of the mirrors is corrugated with a period d.
This corrugation provides coupling between the modes
possessing longitudinal (in z direction, see Fig.1b)
wavenumbers differing by factor h = 2π / d . In thesimplest case of the sinusoidal corrugationb( z ) = b0 cos(h z ) ,INTRODUCTION

where b(z ) is the deviation of the mirror surface, 2 b0 is

In microwave electronics orotron [1] is widely used asa source of radiation in millimeter and submillimeter
wavebands. In this device an electron beam is coupled toa mode of quasi-optical resonator by means of theperiodical grating one of the resonator mirrors. In ourpaper we discuss a relativistic modification of such a
device which can be useful for providing spatial
coherence radiation from large size electron beam
In orotron (Fig.1a) a rectilinear electron beam moving
along the periodical grating on the mirror of aquasioptical cavity to be in Cherenkov synchronism to a
spatial harmonic of the resonator mode. A novel FEL
scheme (Fig. 1b) is suggested in which the slow wave
structure of orotron is replaced by shallow Bragg
corrugation which provides the coupling of the transverse(with respect to direction of beam propagation) mode of aquasi-optical resonator with longitudinally propagatingwave. The latter can be excited by the relativistic electron
beam wiggling in undulator field in condition of Dopper
frequency up-shift. It should be noted that such a scheme
is similar to FEL based on coupling between the quasi
cutoff and the propagating mode in cylindricalwaveguides which was described in [2,3] (above
interaction mechanism will be tested on a 8 mm FEL
based on high current accelerator 0.7 MeV/2 kA/200ns at
Kanazawa University, Japan). In considered case wereplace the waveguide by open quasi-optical resonatorand suggest that FEL will be driven by large size sheet
electron beam. As in [2] the transverse propagating (cutoff) mode provides the feedback in the system thus
leading to self-excitation, while the longitudinal
propagating wave is responsible for energy extraction in
the steady-state regime of operation. But additionally as
will be shown in this paper in considered geometry the
cut-off mode provides spatial coherence radiation fromsheet electron beam.

tthe corrugation depth. In the case of more complicatedcorrugation (for example, meander type corrugation ) b0___________________________________________*Work supported by RFBR under Grant 06-02-17129-a and the
Dynasty foundation.
#
ginzburg@appl.sci-nnov.ru

is equal to the amplitude of the first space harmonic We
assume corrugation to be shallow in the wavelength scale,so that h b0 << 1 .
We use coupling between the propagating in z direction
wave and the q-th mode of the quasioptical resonator (inthe system with the closed waveguide [2] this mode
corresponds to the quasi cut-off mode). Above coupling
requires that the wavenumber of the longitudinal
propagating wave h= ω / c and the wavenumber of thetransverse propagating mode quasioptical resonator( qπ / L y ) should be equal to the translation vector of the
Bragg structure:

h≈

qπ
≈h,
Ly

where ω is the operation frequency, c is the velocity oflight, L y is the distance between the mirrors (in ydirection).
Note that due to the symmetry of the consideredsystem not only the forward + z direction propagating
wave is coupled to the transverse mode, but also a

A− B

y

A+

x

z
electron beamelectron beam

Fig.1. Schematic of the orotron (a) and FEL with orotrontype feedback (b).

FEL Theory

61

MOPPH020

Proceedings of FEL 2007, Novosibirsk, Russia

backward propagating one. This wave in the FEL does notinteract with electrons but provide an additional channelof extraction of electromagnetic energy out of the system.
We present the electromagnetic fields of the coupledmodes in the following form, separating its transverse(over y-axis) structures and the slowly varying amplitudes
over z and x coordinates:rr(1)
E± = Re A± (t , z , x) EA ( y)e m ihA z e iωct()
r
E = Re (B (t ) f ( x, z ) E ( y )e )riω c tB(2)

Here z is the coordinate along the corrugation vector, y is
directed between the mirrors an x is the transverse
coordinate parallel to the mirrors (fig.1b).
The coupling equations describing the scattering of thethree modes in assumption of shallow corrugation can bederived from the Maxwell equations using the surface
magnetic current technique developed in [4]. Theseequations include the equations for the propagating modes(1) and the equation of resonator mode excitation (2).

±∂A± 1 ∂A±+
+ iδA± = iαBf ( x, z )∂z c ∂τ

(3)

∂B ω
(4)
B =icα ∫∫ f ( x, z )( A+ + A− )dXdZ ,+∂t 2Q
qπc is the geometrical detuning from theHere δ = ω −Lzwave synchronism,

α=

hb0
4Ly

1
hL z

is the coupling coefficient proportional to the depth ofthe corrugation, the factor Q describes the quality factorof the mode of regular two-mirror resonator (this factor
takes into account both diffraction losses of the mode andOhmic losses in the resonator walls).
We use the open boundary conditions for theamplitudes of the propagating modes:(5)
A+ ( z = L z ) = 0 , A− ( z = 0) = 0 .
where L z is the length of the mirrors in z direction. We
also assume that the corrugation is shallow so that the
perturbation of the quasioptical resonator modes is small
which structure specifies by the function f(x,z.) .
It should be noted that the spatial structure of the
propagating waves A± (z, x) is not fixed and can befound from simulations.

FEL INTERACTION IN THE
QUASIOPTICAL RESONATOR WITH
CORRUGATED MIRRORA FEL oscillator can be realised within the described
electrodynamic system. We consider a sheet beam ofelectrons and wiggling in the periodical undulator field
and interacting with synchronous A+ wave propagatingin +z direction Corresponding synchronism condition canbe presented as
FEL Theory62ω − hv|| ≈ Ω ,where Ω is the oscillation (bounce) frequency of theparticles in the undulator field, v|| is the electrons
longitudinal velocity. Electrons wiggling parallel to the yaxis generate RF current, which density can be written inthel form(6)j ( x, z , t ) = I 0 ( x ) J ( x, z , t ) ,J ( x, z , t ) =

1

2π

e
π∫

− iθ ( x , z , t )0dθ 0 .

Here I 0 ( x ) is the unperturbed beam current density,θ = ωt − hz − ∫ Ωdt

is the slowly varying electrons phase in the field ofsynchronous wave, θ 0 is its value in the point of entry in
the interaction space. Current (6) excites the synchronous
wave so the currant density enters the right hand part ofEq.(3) in a usual way.
Equations of electron motion can be written in the
forms
2

(

)
⎛ ∂
1 ∂ ⎞⎟⎜
θ = Re A+ e iθ+⎜ ∂Z⎟
β || ∂τ ⎠
⎝

)

(7)

Here we use the following dimensionless variables andparameters: Z = zCh , X = 2 x / Lx τ = ωCt , β || isnormalized electron velocity, Aˆ ± = eκμA± mcω γ 0 C 2
is the propagating wave norm, θ = ω t − hz − Ωdt - is∫the electron phase in the field of the synchronous wave,⎛ eI
cλ2 K 2 μ ⎞⎟C = ⎜⎜ 03
2⎟⎝ mc 4π γ 0 N A ⎠13

is the Pierce parameter, μ is an inertial bunchingparameter, K is the electron-wave coupling parameter
proportional to the amplitude of transverse oscillation ofelectrons, N A is the norm of the propagating mode.
Electron efficiency of the oscillator is defined byrelations

η=

L 2π

1 x ⎛ ∂θ
C
⎞
), )
η
=
− Δ⎟
dθ 0 dx .
η
⎜
−1
∫
∫
μ 1− γ 0
2π 0 0 ⎝ ∂Z
⎠ Z =L()

We suppose the characteristic time of the changing of
the resonator mode amplitude B to be substantiallygreater than the electrons transit time l v|| and forward
and backward waves propagation time l v gr . In this case
it is possible to assume that amplitude of the above mode
is constant during intervals l v|| and l v gr and neglect
time derivatives in the equations of electron motion (7) as
well as the propagating wave excitation equations (3).
It is convenient to overwrite the coupled-waves
equations in the form:

Proceedings of FEL 2007, Novosibirsk, Russia))∂A++ iδA+ = iα ′Bf ( x, z ) + J
∂Z
ω
∂B
+
B =iα ′∫∫ f n ( X ) A+ dXdZ∂t Qmod)

These equations form the self-consistent set describing
the dynamics of electron-wave interaction in the system
under consideration.
The function f(x,z) for the lowest mode of two-mirror
resonator can be approximated as follows:f ( z ) = sin

πz
Lx

sin

πz .

8

Lz

Deriving the equations (8) we took into account thatthe backward wave A− is not coupled to the electrons,consequently the equation for the backward wave withboundary condition (5) can be integrated. After
substitution the result of integration the cutoff mode
equation and the second integration one can get the valueof losses coefficient which takes into account the
scattering of the mode into the backward wave and write
the equation (9) entering the modified Q-factor
2 2 2
2
⎛
1 2α π L z cos (δLz / 2) ⎞⎟Qmod ≈ ⎜ +2⎜Q⎟
δ 2 L2z − π 2
⎝
⎠

(

3

longitudinal structures of the propagating wave A+ . It is
important to note that output phase distribution of
propagating wave arg A+ (x) does not depend on initialconation that actually means spatial synchronization of
output radiation associated with this wavethrough thecoupling with the cut-off mode B. Thus considered FEL
scheme provides mode control in oversized microwave
system. According to estimations the dimension of thesystem in the transverse (x and y) directions is sufficientfor using above scheme for producing powerful spatiallycoherent radiation in short millimeter and submillimeterbands from moderately relativistic sheet electron beams.

)

A+
6
A+

(

) iθ
⎛ ∂θ 2 ⎞⎜⎟ = Re A+ e
2 ⎟⎜⎝ ∂Z ⎠

(8)

4

a)

−1

.

2

Z

η̂ 3

A+ , B

0
0

2

2

1

1

3

10

20

30

40

2

3

4

5

Z

A+

b)
1

0

0

1

2

τ
0

MOPPH020

50

Fig.2. The process of establishment of steady-stateoscillations.
The equations (8) were solved numerically. The resultsof simulations are presented in Fig.2,3 at Lx = 2 ,Lz = 4.5 , Δ = −1 , δ = 1.7 , α '= 2 . In Fig 2 one can see
the process of establishment of steady-state oscillation
regime. Fig.3 demonstrates the transverse and

X
0
0

0.4

0.8

1.2

1.6

2

Fig.3. Longitudinal (a) and transverse (b) structureof the propagating wave in the steady state regime.

FEL Theory

63

MOPPH020

Proceedings of FEL 2007, Novosibirsk, Russia

Note in conclusion that it is interesting to consider
situation when the transverse (over y axis) structure of
propagating mode A+ is not fixed and is defined by its
interaction with electron beam.

REFERENCES[1] F.S Rusin,. G.D Bogomolov, in Proceedings of theIEEE vol. 57, 1969, p.720[2] N.S.Ginzburg, A.M.Malkin, N.Yu.Peskov, et. al.,Phys. Rev. ST Accel. Beams vol. 8, 2005, p. 040705.
[3] N. S. Ginzburg, A. M. Malkin, N. Yu. Peskov, and A.
S. Sergeev, Technical Physics Letters, Vol. 32, 2006,
p. 896[4] N.F. Kovalev, I.M. Orlova, M.I. Petelin, Izv. VUZov,Radiofizika vol.2, 1968, p. 783 (in Russian).

FEL Theory64

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH022

A DESCRIPTION OF GUIDED FEL RADIATION WITH
DIELECTRIC WAVEGUIDE EIGENMODES
E. Hemsing∗ , G. Andonian, J. Rosenzweig, Particle Beam Physics Laboratory, UCLA, USA
A.Gover, Deptartment of Physical Electronics, Tel-Aviv University, Israel
evaluated at the waist. This connection is useful both in
Abstract
We present a description of free-electron laser (FEL) radiation in the high-gain, small-signal regime through an expansion of eigenmodes of a virtual dielectric waveguide.
A set of coupled differential equations is derived for the
slowly-varying mode expansion coefficients and the electron beam density modulation amplitudes. The equations
are decoupled into an algebraic matrix equation for solutions of the self-similar FEL supermodes that propagate
with a self-similar profile. For a suitable choice of the formof the virtual dielectric, this virtual dielectric waveguide
expansion (VDE) approach has the advantage of describing
gain-guided FEL radiation over many Rayleigh lengths interms of a basis that parallels the standard gaussian modesof free-space paraxial optics.

characterizing the free-space propagating radiation fields
emitted from the FEL, but also in understanding input radiation coupling, as in the case of seed radiation injection.

FIELD EXPANSION AND MODE
EXCITATION IN A WAVEGUIDEIn a structure of axial translational symmetry, the radiation fields can be expanded in terms of transverse radiation
modes with amplitudes that vary only as a function of thesymmetry axis, z. Neglecting backward propagating waves
and approximating the fields as dominantly transverse, theradiation field expansion in terms of waveguide modes is,Cq (z)Ẽ ⊥q (r⊥ )eikzq zẼ ⊥ (r) =q

INTRODUCTION
The optical guiding of light in free-electron lasers(FELs) is a well-known phenomena that results during amplification as the coherent interaction between the electron
beam (e-beam) and the electromagnetic (em) field introduces an inward curvature in the phase front of the light, refracting it back towards the lasing core of the e-beam[1, 2].
During the exponential gain process the e-beam can behave like a guiding structure that suppresses diffraction, reducing transverse power losses and enhancing the em field
amplification (gain-guiding). The guided em field eventually settles into a propagating, self-similar eigenmode of
the FEL system (supermode) with a fixed transverse profile
distribution and spot size[3, 4].
Guided modes have been previously explored analytically by direct derivation of the eigenmode equations
from the coupled Maxwell-Vlasov equations[3, 5, 6], andthrough expansions of the FEL signal fields in terms of hollow, conducting-boundary waveguide eigenmodes[4], stepindex fiber modes[2], and free-space paraxial waves[7, 8].
Since, in an FEL, the e-beam operates simultaneously as
an optical source and as a wave-guiding structure, an em
mode description permits investigation of the coupling efficiency and guiding characteristics of individual modes
to the e-beam. Of particular interest is the coupling to
the well-known Hermite-Gaussian or Laguerre-Gaussianmodes that describe free-space waves in the paraxial limit.
The propagation and guiding of these modes over many
Rayleigh lengths in an FEL interaction can be investigateddirectly by an expansion of the radiation field in terms ofguided eigenmodes that have the form of paraxial modes∗ ehemsing@physics.ucla.edu

H̃ ⊥ (r) =q

Cq (z)H̃⊥q (r⊥ )eikzq z .

(1)

where H̃⊥q = (1/Zq )êz × Ẽ ⊥q , kzq is the q th mode axialwavenumber, and Zq = (k/kzq ) μ0 /0 for TE modes.
The modes are orthogonal and normalized to
 

1 
∗
[Ẽ ⊥q (r⊥ ) × H̃⊥q (r⊥ )] · êz d2 r⊥ . (2)Pq = Re2
The mode Ẽ⊥q is an eigenmode of a dielectric medium withtransverse variation in the refractive index n(r⊥ ). Assuming ∇n2  k, the eigenmode equation is2]Ẽ ⊥q (r⊥ ) = 0∇2⊥ Ẽ ⊥q (r⊥ ) + [n(r⊥ )2 k 2 − kzq(3)

where k = ω/c. With equations (1) and (3) and under
the paraxial approximation (|d2 Cq /dz 2 |  |k 2 Cq |) for the
slowly-growing coefficients, the excitation equation for themode q in the presence of a source current is given by, 
1 −ikzq zd∗
Cq (z) = −J˜⊥ (r) · Ẽ ⊥q (r⊥ )d2 r⊥
e
dz
4Pq

−i
Cq (z)e−iΔkzqq z κdq,q
(4)
q

where
κdq,q =

ω0
4Pq

 

∗

[n(r⊥ )2 − 1]Ẽ ⊥q (r⊥ ) · Ẽ ⊥q (r⊥ )d2 r⊥(5)
and Δkzqq = kzq − kzq is the difference between theaxial wavenumbers of the modes q and q  . The term κdq,qcharacterizes the mode coupling and represents the virtualpolarization currents and charges that must be subtracted
when using eigenmodes of a dielectric waveguide, since nosuch structure exists in the physical system.

FEL Theory

65

MOPPH022

Proceedings of FEL 2007, Novosibirsk, Russia

ELECTRON BEAM FLUID MODEL AND
COUPLED EXCITATION EQUATIONS
A linear plasma fluid model for a cold e-beam (negligible energy spread) can be used to describe the smallsignal excitation in an FEL interaction[4]. A relativistic e-beam in an FEL experiences transverse oscillations
driven by an interaction with a periodic structure. This
motion drives an axial ponderomotive force that modulates
the axial electron velocity such that, to first-order, the axial velocity of a cold beam within a static undulator canbe expanded as vz (r, t) = vz0 + Re[ṽz1 (r)e−iωt ] wherevz0 = βz c is the d.c. component and ṽz1 is the perturbation oscillating at signal frequency ω. Longitudinalvariations in the velocity like the half-frequency modulation found in planar undulator systems are ignored here.
The velocity modulation ṽz1 develops a density bunchingmodulation that is similarly described in a linear model
as n(r, t) = n0 (r⊥ ) + Re[ñ1 (r)e−iωt ] where n0 (r⊥ ) is
the transverse density profile of the e-beam. The a.c.
component of the longitudinal current density results fromboth the axial velocity and density perturbations and isJ˜z1 (r) = −e[n0 (r⊥ )ṽz1 (r) + vz0 ñ1 (r)]. If the transverse
divergence of the current perturbation is assumed small∇⊥ · J˜⊥1  ∂ J˜z1 /∂z, the continuity equation can be written as dJ˜z1 /dz = −iωeñ1 (r). The transverse componentof the current density that excites the signal wave is written
in terms of the density perturbation as
1J˜⊥ (r) = − eñ1 (r)ṽ ⊥w e−ikw z .
2(6)

where ṽ ⊥w is the transverse velocity vector and kw is theaxial wavenumber of the periodic undulator lattice.
From the expressions for the current density and the relativistic force equation for the axial velocity perturbation,
the density bunching can be expressed as a second orderdifferential equation[4]. It is useful to define the density
bunching parameter e −i vω z∗z0ĩq (z) =ñ1 (r)ṽ ⊥w · Ẽ ⊥q (r⊥ )d2 r⊥ . (7)e8Pq
By combining the density modulation equation from Ref[4] with Eqs (4) and (7) we obtain a coupled form for themode excitation evolution equations:dκdq,q Cq (z)e−iΔkz;qq z
Cq (z) = ĩq (z)eiθq z − i
dz


dz 2



2
ĩq (z) = i+ θprQq,q Cq (z)e−iθq z

(8)

q

where θq = ω/vz0 − (kzq + kw ) is the characteristic detuning parameter for a given mode. The coupling between
the e-beam with transverse density distribution functionf (r⊥ ) and the FEL radiation field is given by the parameter
FEL Theory

66

κ

q,q 

0
=
(kzq + kw )
8Pq

 

∗

2
f (r⊥ )Ẽpm,q ṽ w
⊥ · Ẽ ⊥q d r⊥ .

(9)
The radiation field and the undulator field are assumed to
be polarization matched. The axial ponderomotive field is∗Ẽpm,q (r⊥ ) = 12 [ṽ ⊥q × B̃ ⊥w + ṽ ∗⊥w × B̃ ⊥q ] · êz whereṽ⊥q is the transverse electron velocity due to the Lorentz
force of the q th mode of the signal field, B̃⊥w is the transverse magnetic field of the undulator, ṽ⊥w is the transverse
velocity due to the undulator field and B̃⊥q = μ0 H̃⊥q .
The term JJ = [J0 (α) − J1 (α)]2 can be included in
the coupling parameter κq,q for a strong planar undulator (JJ = 1 for a helical undulator geometry), whereJ0 and J1 are the first and second order Bessel functions
2and α = ωcK 2 /(8γ 2 vz0
kw ) where K = e|B̃⊥w |/mckw
is 
the undulator parameter. The relativistic factor is γ =γz 1 + K 2 /2 with γz2 = 1/(1 − βz2 ). The effect of
the longitudinal space-charge in the beam is represented
by the finite-width beam parameter θpr = r̄θp whereθp = ωp0 /vz0 is the longitudinal space-charge parameter(plasma wavenumber) of a uniformly distributed electron
beam profile used in a 1D model. The plasma reduction
factor satisfies |r̄| ≤ 1, and can be calculated numerically for a specific e-beam geometry[7]. In the limit thatλβz  r0 where r0 is the e-beam radius, one can make theapproximation r̄  1.
The first equation in Eqs (8) describes the excitation of
the mode amplitude Cq of a virtual dielectric waveguide
eigenmode due to the density perturbation and transverse
wiggling motion of the electrons throughout the FEL interaction. The second equation in (8) highlights the evolutionof the modal density bunching parameters through the ebeam coupling to the expansion modes.
The initial conditions for Eqs (8) specify the operating
characteristic of the FEL. For example, when operating asa single-pass amplifier (seeded FEL) there is no initial density and velocity modulation ĩq (0), dĩq (z)/dz|z=0 = 0 and
the initial seed field is non-zero Cq (0) = 0. Alternately,
for a self-amplified spontaneous emission FEL (SASE), theamplified shot noise can be related to the pre-bunching conditions ĩq (0) = 0, dĩq (z)/dz|z=0 = 0 and the input signal
field vanishes Cq (0) = 0.

SUPERMODE MATRIX SOLUTION

q

 d2

2
Qq,q = θp2 κq,q in Eq (8) where θp2 = e2 n0 /γγz2 0 me vz0
and the e-beam mode-coupling coefficient κq,q is

In the high-gain regime of an FEL the radiation field is
optically guided towards the beam axis. After a sufficiently
long interaction length, prior to the onset of saturation, abalance is reached between the natural diffraction effects of
the radiation and the focusing effects of the gain-guiding.
The FEL settles into a period of steady exponential growth,characterized by a radiation field profile that propagatesself-similarly which can be descried by a specific, fixed
combination of expansion modes called the supermode. In

Proceedings of FEL 2007, Novosibirsk, Russia

order to find the system supermodes, it is enough to findthe characteristic solutions to Eq (8). These are the combinations of expansion modes that propagate with a distinct
wavenumber kSM , and can be found by looking for a solution of the formẼ SM (r) =bq Ẽ q (r⊥ ) eikSM z(10)q

where the mode amplitude coefficients bq are constants andthe z-dependence is contained solely in the exponential
term. The excitation equations for this supermode expansion can be found by transforming the mode amplitude coefficents Cq (z) via:
Cq (z) = bq ei(kSM −kq )z .

(11)

Plugging this expression into the coupled excitation evolution equations (8), a single equation is obtained for thesupermode coefficients:
 


2
2
(θpr
−θSM
) (kSM −kzq )bq +κdq,q bq =Qq,q bq ,
q

q

(12)
where θSM = θ + k − kSM is the supermode detuning
parameter, and θ is the detuning parameter for a 1D model(kzq = k). Since we anticipate that the supermode propagates with a slightly modified axial wavenumber from thatof free-space, we define kSM = k + δk and Eq (12) can be
written in matrix form




2
2
d
(δk − θ) − θpr [Iδk + κ − Δk] + Q b = 0 (13)where Δk is diagonal with matrix elements given byΔkq = kzq − k.
Solutions to the determinant equation |[(δk − θ)2 −2θpr ][Iδk + κd − Δk] + Q| = 0 result in 3N solutions forδk, where N is the number of expansion modes. Each δk
can then be inserted in Eq (13) to find a non-trivial solution (if one exists) for the mode amplitude vector b, thecomponents of which are the expansion coefficients of asupermode of the FEL system. From Eq (10) and the definition of kSM it can be seen that the solution for δk withthe largest imaginary component drives the highest gain,
and dominates over the rest of the supermodes. This value,δkSM , used in solving Eq (13) will yield the coefficients ofthe dominant supermode.
We note that when Δk, κd = 0, as in the case of an expansion into a free-space mode basis, the matrix equationin (13) reduces to a generalized matrix form of the canonical FEL cubic equation. Further, in the limit of a largetransverse beam profile, Qq,q → Q and Eq (13) is the familiar 1D FEL cubic equation for the mode independent
beam coupling parameter Q.

LAGUERRE-GAUSSIAN MODE
EXPANSION
The choice of the refractive index in Eq (3) determines
the form of the basis expansion used in the excitation

MOPPH022

equations (8). For quadratic refractive index of the form
n2 (r⊥ ) = n20 [1 − 2Δ(r/a)2 ] with Δ  1, the constituent
VDE expansion basis consists of a complete, orthogonal setof either Hermite-Gaussian (HG)[9] or Laguerre-Gaussian(LG) functions[10]. Since both HG and LG modes also occur as solutions to the paraxial wave equation, this choicefor the refractive index identifies a connection between the
VDE method and a description of the FEL system using
paraxial, diffracting modes of free-space. The intrinsic advantage of the guided mode expansion formalism is theability to efficiently model the signal field during high-gain
over many Rayleigh lengths with only a few modes.
For geometries that are largely axisymmetric over the interaction length, LG modes provide a convenient working
basis to model the FEL radiation. They have the form2

−ilφẼ⊥;p,l (r, φ) ∝ e

− r2

e

w

0

√
r 2
w0

|l|

L|l|
p

2r2
w02

(14)

where Llp is an Associated Laguerre polynomial. The mode
index q takes on two values (p, l) corresponding to the radial and azimuthal mode numbers, respectively. The argument of the LG polynomials
contain the parameter defined√
as w02 ≡ 2a/kn0 2Δ which sets a characteristic waist sizein terms of the refractive index parameters.The field modes
in Eq (14) are thus identical to free-space LG fields that satisfy the paraxial wave equation, when the free-space modes
are evaluated at the waist. This waist definition specifies acharacteristic dielectric profile form for a quadratic dielectric, in which a free-space Laguerre-Gaussian mode withwaist size w0 will propagate as a guided eigenmode.
It is noted that the LG modes of Eqn (14), as well as
those of a free-space system, possess an axial field component for both the electric and magnetic fields for modes
with |l| > 0. The magnitude of the axial electric field component is on the order of λ/w0 by comparison to the principle transverse component, and can be neglected, validating
the approximation made in deriving the amplitude evolution equation (4)[11].
It is instructive to cast the associated Rayleigh range fora free-space paraxial wave in √terms of the dielectric parameters zR = kw02 /2 ≡ a/n0 2Δ, which yields a refractive index n2 (r) = n20 − (r/zR )2 . The axial wavenumber
kzq = kz;p,l is given by2
kz;p,l= k 2 n20 −4(2p + l + 1).
w02

(15)

The refractive index on axis can be taken as n20  1 and the
FEL signal field can be expanded into a sum of LG guided
modes given by Eq (14), each with wavenumber kz;p,l . The
expansion waist w0 is arbitrary, but can be chosen to beon the order of the e-beam size to facilitate efficiency inmodeling the beam evolution with a finite number of modes
included in the expansion[12].

FEL Theory

67

MOPPH022

Proceedings of FEL 2007, Novosibirsk, Russia

8.6

5.0

1.0
0.8
0.6
0.4
0.2
0.0

4.5
4.0

r/r 3.5
0

3.0

8.4
8.2

1 dP [m-1]
P dz
-3

-2

-1

2.5

0

r/r

1

2

8.0

3

0

7.8

2.0
0

1

2

z [m]

3

4

0

1

2

z [m]

3

4

Figure 1: Left: Numerically modeled evolution of the radiation spot size throughout undulator for VISA FEL at λ =1064nm for θ = 0 detuning. Three spot sizes (ws0 = 2r0 , 3r0 , and 4r0 ) for a P = 0.1μW gaussian seed are introduced22
at the undulator entrance with a r0 = 115μm gaussian e-beam f (r) = e−r /r0 . During the start-up period early on, theseed beam diffracts briefly until exponential gain develops. The self-focusing effects then guide the beam toward a fixed
spot size, characteristic of the FEL supermode. Inset: Normalized field intensity (solid) and phase (dashed) profiles ofsupermode. Right: Normalized differential radiation power evolution for each input seed. The power slope for each input
spot size evolves towards the same value after the supermode is established halfway through the 4 m VISA undulator.

SIMULATIONSResults generated by the VDE method that uses an LG
mode expansion basis to model the Visible to Infrared
SASE or Seeded Amplifier (VISA) FEL currently in operation at Brookhaven National Laboratory are shown in
Figure 1. The VISA FEL is ideal for investigations using
an LG expansion since it has generated both hollow andspiral transverse em intensity patterns that are suggestiveof single or multiply interfering LG modes[13]. The resultsin Figure 1 show the evolution of various injected radiation
fields towards the supermode, both in the transverse spot
sizes (left) and in the differential power curves (right) as afunction of the longitudinal coordinate. Both the inwardly
curved phase front (dashed line – inset) and the “pinchedgaussian” intensity profile (solid line – inset) of the radiation at the undulator exit (z=4 m) display the signature
characteristics of a gain-guided FEL supermode.

CONCLUSIONS
We have presented a description of the FEL electromagnetic signal field during high-gain through an expansion
into a complete set of eigenmodes of a virtual dielectric
waveguide. The FEL supermode can be found in the smallsignal limit by finding the eigenfunction solutions to thecoupled mode excitation equations derived from a cold ebeam fluid model. The choice of a quadratic index medium
for the virtual dielectric yields a set of guided HermiteGaussian or Laguerre-Gaussian modes that relate to paraxial modes of free-space. Future work will involve comparisons of the VDE formulation with 1) experiments at VISA,
where plans are underway to measure the phase and mode
content of the em radiation[14] and, 2) numerical simulaFEL Theory

68

tions using GENESIS 1.3 to verify and support the analytic
and experimental results. The coupling to higher-order radial and azimuthal modes will also be investigated.

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Communications 97, 272 (1993).
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Applied Optics 21, 141 (1982).
[11] W. L. Power, et al Phys. Rev. A 52, 479 (1995).
[12] E. Hemsing, A. Gover, and J. Rosenzweig, unpublished.
[13] G. Andonian, et al, Proceedings of FEL 2006 Conference,
443-446, Berlin, Germany.
[14] E. Hemsing, et al, Proceedings of PAC 2007 Conference,
1263-1265, Albuquerque, New Mexico, USA.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH023

ENHANCING FEL POWER WITH PHASE SHIFTERS∗
Daniel Ratner† , Stanford University, CA, 94305 USA
Alex Chao, Zhirong Huang, SLAC, Stanford, CA 94309 USA
Abstract
Tapering the undulator parameter is a well-known
method for maintaining the resonant condition past saturation, and increasing Free Electron Laser (FEL) efficiency.
In this paper, we demonstrate that shifting the electron
bunch phase relative to the radiation is equivalent to tapering the undulator parameter. Using discrete phase changes
derived from optimized undulator tapers for the Linac Coherent Light Source (LCLS) x-ray FEL, we show that appropriate phase shifts between undulator sections can reproduce the power enhancement of undulator tapers. Phase
shifters are relatively easy to implement and operate, andcould be used to aid or replace undulator tapers in optimizing FEL performance.

INTRODUCTION
Despite the projected six orders of magnitude increasein peak power for Self-Amplified Spontaneous Emission(SASE) x-ray FELs, some applications, including single
molecule imaging, may require still higher photon flux [1].
To increase the power in higher harmonics, it is possible toshift the FEL electron phase relative to the radiation, suppressing the power in the fundamental wavelength and prolonging growth of the harmonics [2]. We have studied therelated use of phase shifts to correct slippage at saturation
and boost the power output of the fundamental wavelength.
Similar methods have been mentioned in the past in connection with harmonic radiation [2] and numerical simulations [3]. Here we undertake a detailed analytical and numerical study of enhancing FEL power with phase shifters.
We explore the relation between phase shifts and undulator tapers to calculate optimal phase shifts for SASE FELs
in the saturation regime. The phase shift method, while
equivalent to tapering the undulator parameter, provide an
independent knob to maximize the FEL performance.

ONE-DIMENSIONAL ANALYSIS
The resonant condition
λ1 = λu

1 + K 2 /2
2γ02

(1)

sets the radiation wavelength, λ 1 for an FEL; after each
undulator period, λ u , the electron bunch slips behind theradiation by exactly λ 1 . It follows that when the resonantcondition holds, the phase, Ψ, between the electron bunchand radiation stays constant (up to 2π). Near saturation,∗ Work supported by Department of Energy contract DE–AC02–
76SF00515.
† dratner@slac.stanford.edu

the bunch loses significant energy to the radiation, and the
FEL resonant condition begins to fail. As γ 0 → γ < γ0 ,the resonant wavelength increases, and the electrons slip
more than one radiation wavelength during each undulator period. Introducing a phase shift (by means of a small
chicane) can correct for the increase in slippage by shifting the bunch backwards into the previous bucket. (If, overmany undulator periods, the bunch has accumulated extra
slippage of Δθ, then the chicane shifts the electrons an additional 2π − Δθ. There is no easy way to shift electrons
forward.) After the shift, the electron bunch is once againin phase with the radiation, preserving the resonant condition farther into saturation.
To show that compensating for the additional slippage
can optimize the radiation power in the undulator, we use a
simplified 1-D FEL model and neglect the effect of detuning. The slowly varying radiation field ã is given bydã= −e−iθj  .
dz̄

(2)

The phases, θ ≡ (k + ku )z − ωt + const, are the longitudinal positions of the electrons relative to the electron bunch
given in units of λ 1 /2π = 1/ku . The variable z̄ ≡ 2ku ρz,
is the scaled position along the undulator. Here ρ is the dimensionless FEL parameter [4]. Finally, the average in Eq.
(2) is taken over all electrons. Taking ã ≡ Ae iΨ , with Ψ
the phase of the radiation relative to the electron bunch, we
can separate out the magnitude and phase components of
the radiation field:


dã
dΨ
dA
= eiΨ
+ iA
.
(3)
dz̄
dz̄
dz̄
Inserting Eq. (3) into Eq. (2) and separating real and imaginary parts givesdA= − cos(θj + Ψ) ,dz̄
dΨ 1= sin(θj + Ψ) .
dz̄ A

(4)
(5)

Our strategy is to maximize A by introducing an arbitrary phase shift, φ between the radiation and electrons, andthen maximize dA
dz̄ with respect to φ at all points along theundulator. (A chicane delays all particles relative to the radiation, introducing an arbitrary change in relative phase of
the bunch.) Our goal, then, is to choose φ to maximize thequantity −cos(θj + Ψ + φ).
Adding the arbitrary phase, φ, givesdA= cos(θj + Ψ) cos(φ) − sin(θj + Ψ) sin(φ) (6)dz̄

FEL Theory

69

MOPPH023

Proceedings of FEL 2007, Novosibirsk, Russia

To find the optimal phase shift, we differentiate with respect to φ to findsin(θj + Ψ)
φmax (z̄) = arctan −.
(7)cos(θj + Ψ)
Carrying out the maximization then requires the calculationof φmax (z̄) at all points past saturation along the undulator.
(φ is a function of z̄, because θ j and Ψ are also functionsof z̄.)
Substituting the result from Eq. (7) into Eq. (6) we find,for cos(θj + Ψ) > 0,dA= cos(θj + Ψ)2 + sin(θj + Ψ)2 ≡ |b| ,dz̄ max(8)where b is the bunching factor of the electrons.
We originally motivated the phase shift by the need tomaintain a constant Ψ, the phase between the electron
bunch and the radiation. We would like to check that ourbest phase, φmax , optimized to increase the radiation amplitude, A, will simultaneously keep Ψ fixed. Returning to
Eq. (5), now with an arbitrary phase inserted, we havedΨ
∝ sin(θj + Ψ) cos φ + cos(θj + Ψ) sin φ . (9)dz̄Plugging in φmax from the optimization condition, Eq. (7),gives
sin(θj + Ψ)
dΨ∝sin(θj + Ψ) − cos(θj + Ψ)
dz̄
cos(θj + Ψ)
= 0.

(10)

We find that implementing the phase shifts, φ max , does indeed keep the phase, Ψ, fixed, consistent with our initial
goal of maintaining the correct slippage length.

EQUIVALENCY TO UNDULATOR TAPER
To find the optimal phases, Eq. (7), we can numerically evaluate sin(θj + Ψ) and cos(θj + Ψ) at eachdesired phase shifter location. This, of course, is not verypractical for an actual SASE FEL. However, we motivatedthis approach by the need to maintain the resonant condition (Eq.1). Tapering the undulator, an established method
for optimizing FELs, works through the same principle [5].
From the resonant condition, we see that shifting the phaseis equivalent to decreasing the undulator parameter. To express a phase shift in terms of a taper, we start with theponderomotive phase equationdθ[1 + K 2 /2]= ku − k1
.
dz̄
2γ 2

(11)

relating the change in phase, φ = Δθ, to the undulator parameter, K. An undulator taper is a small shift
K0 → K(z̄). Plugging into Eq. (11), dropping the second order term, and using the resonant condition, k u /k1 =FEL Theory70(1 + K02 /2)/(2γr2 ) givesγ2γ 2 K0 (K(z̄) − K0 )dθ= ku − ku r2 + ku r2
.
dz̄
γ
γ
1 + K02 /2(12)

Using the notation η = (γ − γ r )/γr , |η|  1 yields theusual FEL phase equation with a correction term of order
K0 − K(z̄):

K0 (K0 − K(z̄))
dθ= 2ku η −
.
(13)
dz̄
2 + K02
Thus we find a change, K 0 → K(z̄), results in a change,θ → θ + Δθ, with accumulated phase shift z̄
K0 (K0 − K(z̄  )) Δθ(z̄) = −2kudz̄
(14)
2 + K02z̄0
where K(z̄) is some arbitrary function (i.e. an optimized
taper) and the integral starts from the last phase shift at
position z̄0 .
The advantage of deriving phase shifts in this manner isthat SASE FEL undulator tapers are well understood, andthe optimal function K(z̄) can be calculated from the FEL
parameters, for instance by the GINGER self-taper algorithm [6]. With a predetermined taper function, we canplug into Eq. (14) and calculate the optimal phase shifts
for an arbitrary FEL.
We have shown that shifting the phase continuously is
identical to tapering the undulator parameter. However, thephase shift is most interesting if implemented discretely,with the taper from each undulator section replaced bya single shift. In this case, the exact equivalence breaks
down. The larger the shift, the more time the FEL spends
at a suboptimal phase, and for long undulators the accumulated difference K(z̄  ) − K0 might require large phaseshifts, Δθ(Lu ), near the end of the undulator (Eq. 14). To
determine the practicality of discrete shifts, we use FEL parameters similar to the LCLS at 1.5 Å [7] for numerical examples (Table 1). Although LCLS does not currently haveperiodic phase shifters, designs for similar projects such as
the European XFELs [8] have incorporated phase shifters
between undulator sections. Using Eq. (14), we find thetaper-equivalent shifts for LCLS have Δθ < 1, suggestingthat the method of phase shifts will match the performanceof an undulator taper.
Table 1: SASE Simulation Parameters
Radiation wavelength (λ 1 )1.5 Å
Bunch current
3.4 kA
Undulator period (λ u )3 cmUndulator parameter (K)3.5
Electron energy
13.6 GeV
Relative RMS energy spread
1x10 −4
Normalized transverse emittance
1.2 μmBeta function
25 mProceedings of FEL 2007, Novosibirsk, Russia

MOPPH023

Taper vs Phase Jump (3m), Seeded Case

NUMERICAL RESULTS
1-D Simulations

10

10

P (W)

To simulate phase shifts, we started with a 1-D FEL
code, including energy spread but not emittance effects.
We used four different types of optimization:

Fundamental, taper
3rd harmonic, taper
Fundamental, phase shift
3rd harmonic, phase shift

810

1. Phase scan,
610

2. Numerically optimized phase shifts,
3. Linear energy taper, and

020

4. Phase shifts derived from a linear taper.

60

80

Figure 2: Comparison of taper and equivalent phase shifts
every 3m for Seeded FEL, 1-D simulation.
Taper vs Phase Shift (3m), SASE case
1010Fundamental, taper
3rd harmonic, taper
Fundamental, phase shift
3rd harmonic, phase shift

P (W)First we used a brute force phase scan. To determine thenth phase shift at position z n , we optimized the power at
position zn+1 by trying 5 (or more) different phase shifts.
Then, picking the best phase for the n th position, we optimized position z n+1 .
Second, we used the results from Eq. (7) to calculate optimal phase shifts numerically. We calculate the phase for2 cases: shifts every 1m and every 3m. The 3m shifts areless effective than the phase scan because the shifts are infrequent, and Δθ > 1. The results for the first two methods
are given in Fig. 1.

40
z (m)

5

10

Phase Boost (Seeded Case)
0

11

P (W)

10

20

40
z (m)

60

80

Figure 3: Comparison of taper and equivalent phase shifts
every 3m for SASE FEL, 1-D simulation.

10

10

Numerical phase 3m
No shift
Numerical phase 1mPhase Scan 1m

9

10

45

50

55

60
65
z (m)

70

75

80

Figure 1: Fundamental radiation power from phase shifts.
Phases done 3 ways: Numerical optimization every 1m(dark green), Numerical optimization every 3m (lightgreen), Phase scan every 1m (red). The fourth plot (blue)
has no phase shifts.
Third, we used a linear taper to boost the fundamental
power. Fourth, we calculated the taper-equivalent phaseshifts (Eq. (14)), implemented every 1m. The final
two methods are computationally identical if the phase isshifted on each iteration. However, the results still matchfor less frequent phase shifts, so long as the shifts are small(Δθ < 1). Results for both seeded and SASE cases are
given in Figs. 2 and 3. Performance is worse for the third
harmonic (green), because the shifts are relatively larger
than in the case of the fundamental.

Finally, we compare phase shifts derived from the optimal linear taper to numerically optimized phase shifts(Eq. (7)), and the results from the phase scan. The phaseshifts are all well matched (Fig. 4), confirming the equivalence of the four optimization methods.

3-D Simulations
We repeated the same study using the FEL code GINGER. To find an optimal undulator taper, ΔK(z), we used
GINGER’s self-taper algorithm [6]. With η defined abovedη
1 dγr
eK[JJ]=−− 2
E sin(θ + Ψ)dz
γ0 dz
2γ0 mc2
When the energy change is small (in the exponentialrregime), we can ignore the dγ
dz term. However, at saturation, the energy loss is significant (of order ρ), and theresonant energy γ r changes. Following [5], we define a
synchronous phase Ψ r from−eK[JJ]
1 dγr≡ 2
E sin(Ψr ).
γ0 dz
2γ0 mc2

FEL Theory

71

MOPPH023

Proceedings of FEL 2007, Novosibirsk, Russia

Taper Phase Equivalent
Numerical Phase
Phase Scan

3

Power (watts)

Delta Theta (radians)

Taper vs. Phase shift: 3-D SASE

Phase Comparison

4

2
1
0
0

20
40
60
Undulator Position (meters)80

Z (meters)

Figure 4: Phases determined by phase scan, numerical optimization and taper equivalent (Seeded case).
rwith Ψr determined by both dγ
dz and K. Any particle withthe synchronous phase will then define the center of thebucket, with particles nearby in phase space performing a
synchrotron oscillation around the synchronous phase. (Bydefinition, the energy η is constant.) An optimal phase Ψ r
is determined by optimizing bucket size and dγ r /dz, which
together set the energy transferred from electrons to radiation. We can then find a function K(z) to maintain thephase Ψr as a constant throughout the saturation regime.
Alternatively, we can manipulate the phase directly throughperiodic phase jumps, as described in Eq. (14) above. If
the phase jumps are frequent enough so that Δθ < 1 (orequivalently, ΔΨ), the system will effectively maintain theresonant condition without resorting to altering K.
Using GINGER’s self-design taper function we createdan optimal taper and then found the equivalent phase shifts(Fig. 5). We confirm the 1-D results, showing an equivalence between a taper and phase shift for an LCLS-like
SASE FEL (Fig. 6, Table 1). The equivalence starts to failat the very end of the undulator, when Δθ > 1.

Undulator Value (aw0 = sqrt(2)*K)

Undulator K Value for Strong Self−Design Taper

CONCLUSION
We demonstrate the equivalence between phase shifts
and undulator tapers. If the required phase shifts are small(Δθ < 1), then the shifts can be implemented discretely
and still mimic the effect of an undulator taper. In particular, we simulate phase shifts placed between undulator sections for an x-ray FEL and find the results are equivalent tothose of an optimized taper. The phase shift method could
be useful as a replacement or enhancement of undulator
tapers when the use of tapers is constrained by technical issues. Even when the undulator parameter of each undulator
section can be individually adjusted, placing phase shifters
between the undulator sections provides independent control and fine tuning capability over the FEL power.

ACKNOWLEDGMENTS
We would like to thank W. Fawley, B. McNeil, and H.-D.
Nuhn for many helpful discussions.

REFERENCES[1] H. Chapman, S. P. Hau-Riege and J. Hajdu, Prepared for 28th
International Free Electron Laser Conference (FEL 2006),
Berlin, Germany, 27 Aug - 1 Sep 2006
[2] B. McNeil et al., Phys. Rev. Lett. 96, 084801 (2006).

2.475

2.47

[3] A.A. Varfolomeev et al., Nucl. Instr. and Meth. A 407, 296(1998).
[4] R. Bonifacio, C. Pellegrini and L. Narducci, Opt. Commun.
50, 6 (1985).

2.465[5] N. M. Kroll, P. L. Morton and M. N. Rosenbluth, IEEE J.
Quant. Electron. 17, 1436 (1981).
2.46
0

20

40
60
80
100
Undulator Position (meters)

120

Figure 5: Taper for Seeded and SASE cases. Simulation
using GINGER’s 3D code.
FEL Theory

72

Figure 6: Power for normal (black), tapered (red) andphase-shifted (blue) LCLS-like SASE FEL, 3-D simulation. 12 Phase shifts between undulator sections (3.8 m).

[6] W.M. Fawley et al., Nuclear Instruments and Methods inPhysics Research A 483 (2002) 537541[7] Linac Coherent Light Source Conceptual Design Report,
SLAC-R-593, UC-414 (2002).
[8] TESLA Technical Design Report, TESLA FEL 2002-09,
DESY, 2002.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH025

THREE-DIMENSIONAL THEORY OF THE CERENKOV
FREE-ELECTRON LASER
H. L. Andrews∗ and C. A. Brau
Department of Physics and Astronomy, Vanderbilt University, Nashville, Tennessee, 37235, USA
THEORY

Abstract
We present an analytical theory for the operation of a
Cerenkov free-electron laser which includes diffraction of
the optical mode in the direction transverse to the electron beam. Because the width of the optical mode depends
on gain, the usual cubic dispersion relation is replaced by
a 5/2-power dispersion relation, which allows two roots.
These roots both have positive real parts, indicating thatthey are slow waves. For a narrow electron beam, the optical mode is much wider than the beam, thus reducing thegain by an order of magnitude from that predicted by thetwo-dimensional theory. In the limit of a wide electron
beam, the two-dimensional theory is recovered.

INTRODUCTION
Compact narrow-band far-infrared, or terahertz (THz),
sources have potential applications in a large numberof fields including biology, chemistry, and materials
science[1, 2]. The current THz sources in existence either
produce short-pulsed broadband radiation, or require verylarge facilities. The exceptions to these are CO 2 pumped
FIR lasers and backward-wave oscillators (BWOs). FIR
lasers only have discreet lines, making them impractical forspectroscopy, and BWOs do not reach short enough wavelengths. Free-Electron Lasers (FELs) based on either theSmith-Purcell effect or Cerenkov radiation offer the possibility of a source capable of producing narrow-band THz
radiation.
In a Cerenkov FEL the electron beam interacts with theevanescent wave of a single-sided dielectric waveguide.
Since the wave has a forward group velocity, the instability
is convective and the device works as an amplifier. Oscillation is achieved by feedback from reflections at the endsof the structure. The most powerful CFELs use ampere
beams in cylindrical waveguides [3] but smaller devices
can be constructed using milliampere beams in planar geometries [4]. The theory of cylindrical devices has beendeveloped in detail, and the agreement with experimental
results is good [3]. The theory for planar geometries has
been worked out in two dimensions [5]. We extend this theory to three dimensions by including diffraction of the optical beam in the direction transverse to the electron beam,parallel to the surface of the dielectric [6]. We show thatthe gain is reduced by an order of magnitude and the fundamental nature of the conventional three-wave interactionis altered.
∗ heather.l.andrews@vanderbilt.edu

To model the CFEL in three-dimensions we let the electron beam pass above a dielectric slab, bounded below by aconductor, as shown in Figure 1. The electron beam travels
in ẑ, while x̂ extends above the slab and ŷ is the transverse
direction. We assume a beam of width W , and a dielectricslab of depth H.

xW
EvanescentwaveyElectronbeam

HDielectricz

Figure 1: Geometry used for the three-dimensional model.
The electron beam has a width W and is allowed to extend to infinity in x. The dielectric had a depth H andis wide compared to both the evanescent scale height andmode width.
To make the problem tractable, we start by making threeassumptions. First, we assume the electron beam is uniform and extends infinitely far in x̂. This introduces negligible errors to the theory because the electron beam heightis actually on the order of the evanescent scale height. The
assumption is corrected at the end of the calculation byusing a filling factor. Next, we assume the operating frequency of the device is much larger than the plasma frequency or ω  ω e . This is justified by considering theoperating parameters of the most recent CFEL experiments
at Dartmouth [4], shown in Table 1. For these parameters ω ≈ 1012 Hz and ωe ≈ 109 Hz. Finally, we assume
that the mode width, Δy, is much greater than the evanescent scale height, Δx. For the Dartmouth parameters
Δx = βγλ/4π ≈80μm, where βc is the electron beam
velocity, γ = 1/ 1 − β 2 and λ is the operating wavelength. Diffraction arguments suggest that the evanescentmode width is on the order of Δy =βλZg /2π ≈mm
where Zg is the gain length.
We find the fields within and above the dielectric bysolving Maxwell’s equations and requiring the solutions tomeet the appropriate boundary conditions. Only TM modes

FEL Theory

73

MOPPH025

Proceedings of FEL 2007, Novosibirsk, Russia

Table 1: Parameters used in the Dartmouth experiments
and all theoretical predictions [4]Dielectric thickness
Index of refraction
Beam energy
Beam thickness
Beam current

350 μm3.6
30 keV
70 μm
1 mA

=
=

(1)

are considered, where k is the wave vector in the ẑ direction. We find the fields above the dielectric by starting in the electron rest frame, where we can treat the electron beam as an isotropic dielectric. We then transform thefields into the laboratory frame. By setting the fields above
and within the dielectric equal at the boundary, we find thedispersion relation. When there is no beam present, we findthe two-dimensional dispersion relation,
D (ω, k, ky ) =(2)n 2 ω 2 − k 2 c2
κ (ky ) cot [κ (ky ) H] + α (ky )n 2 ω 2 − k 2 c2
where n is the index of refraction of the dielectric slab,
ky is the ŷ component of the wave vector, κ (k y ) is thex̂ component of the wave vector within the dielectric, andα (ky ) is the x̂ component of the wave vector above thedielectric. The dispersion relation is plotted in Figure 2.
2

Normalized frequency

Vacuum Light Line=∂D (ω, k, ky )∂ω(ω0 ,k0 ,0)Dy=∂D (ω, k, ky )∂ky2
(ω ,k ,0)Dispersion
Relation(4)0

and δω and δk are the shifts in frequency and wave vector from the synchronous point, β g is the group velocity, α0 = α (ω0 , k0 , ky = 0) and ky is a dummy variable.
Computations show that D ω > 0, Dy < 0 and βg > 0. In
general this equation must be solved numerically, but foreither a wide or narrow electron beam, analytical solutions
to the dispersion relation can be found.

Wide Electron Beam
When the electron beam is wide, W  Δy, the sincfunction behaves like a delta function, so we evaluate theintegral at ky = ky . We recover the two-dimensional cubic
dispersion relation,2(δω − βcδk) (δω − βg cδk) =ωe2 α0,γ 3 Dω

(5)

the roots of which are shown in Figure 3. As in the twodimensional case, one root corresponds to a fast wave, one
to a slow wave which gains energy from the electron beam,
and one to the structure wave, which decays. For steadystate amplifier operation we take δω = 0 and find that thegain in three dimensions with a wide beam,√3
μ3D−wide = −Im (δk) =2

Beam Line

1

Dω

0

E0 (x, y) ei(kz−ωt)
H0 (x, y) ei(kz−ωt)

1.5

(3)

where

of the formEz
Htdispersion relation about this point and find,(δω − βcδk) Dω (δω − βg cδk) + Dy ky2 Ē (ky ) =W ωe2 α0 ∞     W ky − ky
k
sinc
dk
Ē
y
y
3
2π γ
2
−∞

α0
ωe2
γ 3 β 2 βg c 3 D ω

1/3

(6)

is identical to the two-dimensional gain.

Synchronous Point
0.5

Im(δk)

Dielectric Light Line
0
0

1

2
3
4
Normalized wave number

5

Figure 2: The two-dimensional dispersion curve for the parameters used in experiments at Dartmouth (see Table 1).
Only the first order branch is shown.

Structure wave
Fast wave

Re(δk)
Slow wave

When the electron beam is present, we anticipate thatthe highest gain will be found in the vicinity of the synchronous point, shown in Fig. 2, where the electron-beamline intersects the dispersion curve or, ω 0 = βck0 . We also
assume that most waves are traveling parallel to the direction of beam travel so k y ≈ 0. We can then expand the
FEL Theory

74

Figure 3: Roots of the dispersion relation for a wide electron beam. These are the same as for the two-dimensional
result.

Proceedings of FEL 2007, Novosibirsk, Russia

Narrow Electron Beam
When the electron beam is narrow, W  Δy, we approximate sinc (x) ≈ 1. The integral becomes trivial, andwe are able to invert the Fourier transform of the field using
contour integration. The dispersion relation in this limit isW ωe2 α0 E0 (0, 0) eyΔky
2 γ 3 Dy (δω − βcδk)2 Δky

Δky2 =1Dω(δω − βg cδk)Dy

(8)and the sign of the root is chosen such that for positive y
Re (Δky ) < 0 and for negative y Re (Δk y ) > 0. Solving
this dispersion relation on axis for the steady-state amplifiercase, y = 0 and δω = 0, we find the roots areδkn = K 2/5 ei(4/5)nπ
where

Using the parameters in Table 1, we can compare the results of the two-dimensional theory with thethree-dimensional theory and experimental observations.
The vertical and transverse field profiles for the threedimensional theory using a narrow electron beam areshown in Figures 5 and 6, respectively. The transverse

z

where

(7)

DISCUSSION AND COMPARISON WITH
EXPERIMENT

Normalized E fieldE0 (0, y) =MOPPH025

(9)

0.8
0.6
0.4
0.2
Within dielectric
0
-0.4

W
α0
ωe2

.
K=
1/2
3
2
5/2
2 γ β βg c
Dω |Dy |

-0.3

-0.2

(10)

Figure 4 shows these five roots. Only two, n = 2 andAbove dielectric

-0.1
0
0.1
0.2
Vertical distance (mm)

0.3

0.4

Figure 5: Vertical profile of the electric field. The fieldheight is much smaller than the field width shown in Figure 6.

Im(δk)
1n=3
n=1
Normalized E field

0.8
z

n=0
Re(δk)
n=4
n=2

0.6
0.4

Figure 4: Roots of the dispersion relation for a narrow electron beam. Because of physical constraints, only n = 2 andn = 3 roots are true solutions. The n = 2 root has positivegain, while n = 3 has negative gain. Both modes have thesame width and are slow waves (Re (δk) > 0).
n = 3 are physically admissible solutions; for the others,
the fields diverge at y = ±∞. Of these the n = 2 root has
positive gain and the n = 3 root has negative gain where
the gain is given by
μ3D−narrow = −Im (δk2 ) = K 2/5 sin

2
π .
5

(11)

From Equation 7, we find the mode width at the 1/e point
to be
2
2
Dy
= 1/5
Re (Δky )βg cDωKzz

Im(E )z0.2
0-6

Δy = −

Re(E )

|E |

1/2

sec

π
5

. (12)-4-2
0
2
Transverse distance (mm)46Figure 6: Transverse profile of the electric field. The field
is much wider than the electron beam used in experiments.
It is also wide compared with the evanescent scale height.
field profile shows that the mode width, Δy ≈ 6 mm,
is large compared to both the width of the electron beamand the scale height of the evanescent wave, as initially assumed.
In computing the gain, we recognize that the electron
beam only extends above the dielectric a distance comparable to the scale height of the evanescent wave, rather thanwell beyond the wave. To correct for this we reduce theelectron density, or equivalently ω p2 , by a filling factor [7, 8]
Ff ill = 1 − e−W/Δx .

(13)

We find that the two-dimensional gain is μ 2D ≈ 50/m,
in good agreement with the theoretical prediction of 60/m

FEL Theory

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Proceedings of FEL 2007, Novosibirsk, Russia

by the Dartmouth group [4, 5]. The three-dimensional gain,
μ3D ≈ 10/m, is a factor of 5 smaller. This can be understood as diffraction diluting the effective current density
by spreading the optical mode over an area much larger
than the electron beam. The experimental value for gain reported by the Dartmouth group [4] is μ exp ≈ 250−450/m.
This is 5 − 9 times larger than the two dimensional theory
and 25 − 45 times larger than the three-dimensional theory.
The origin of this discrepancy is not understood.
Equally interesting are the structure of the dispersion relation in three dimensions and the location of the roots.
In place of the cubic dispersion relation characteristic of
two-dimensional geometries and axially symmetric structures, we obtain and 5/2-power dispersion relation. The
two roots which satisfy the dispersion relation are labeledn = 2 and n = 3 in Figure 4. The n = 2 root has gain
while the n = 3 root has loss. Both roots have the same
real part, corresponding to the same mode width and indicating that both are slow waves (Re (δk) > 0). This result
is surprising because it suggests that transverse diffraction
in a three-dimensional structures forbids fast waves. We
can understand this result physically by recognizing thatwhen waves are confined to the region near the electron
beam the situation is similar to waves guided by a dielectric
waveguide. Because its index of refraction exceeds unity,
the dielectric waveguide only supports slow waves, so optical modes supported by the CFEL can only be slow waves.

FEL Theory

76

ACKNOWLEDGEMENTS
The authors gratefully acknowledge helpful discussions
with J. H. Brownell, C. H. Boulware and J. D. Jarvis. This
work was supported by the Medical Free Electron Laser
Program and the Department of Defense under grant number F49620-01-1-0429.

REFERENCES[1] P. H. Siegel, IEEE Trans. Microwave Theory and Techniques
50, 910 (2002).
[2] S. P. Mickan and X.-C. Zhang, Int. J. High Speed Electron.
13, 601 (2003).
[3] I. de la Fuente, P. J. M. van der Slot and K. J. Boller, Proceedings of the 2004 FEL Conference, p. 314 (http://JACoW.org).
[4] I. J. Owens and J. H. Brownell, J. Appl. Phys. 97,104915(2005).
[5] I. J. Owens and J. H. Brownell, Phys. Rev. E. 67, 036611(2003).
[6] H. L. Andrews and C. A. Brau, J. Appl. Phys. 101, 104904(2007).
[7] H. L. Andrews, C. H. Boulware, C. A. Brau, J. T. Donohue,
J. Gardelle and J. D. Jarvis, New J. Phys. 8, 298 (2006).
[8] G. F. Mkrtchrian, Phys. Rev. ST-AB 10, 080701 (2007).

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH026

THREE-DIMENSIONAL THEORY OF THE SMITH-PURCELL
FREE-ELECTRON LASER
J. D. Jarvis and H. L. Andrews,
Department of Physics and Astronomy, Vanderbilt University, Nashville, TN 37235, U.S.A.
We present an analytic theory for the exponential-gain(growth) regime of a Smith-Purcell free-electron laser
amplifier (oscillator), which includes the effects oftransverse diffraction in the optical beam. The opticalmode is guided by the electron beam, having a mode
width that depends upon the gain length. For the case of awide electron beam, the dispersion relation converges
with that of the 2-D theory. When the electron beam isnarrow, the conventional cubic-dispersion relation is
replaced by a five-halves dispersion. The dispersive
properties of the grating divide device operation into four
distinct regions, two amplifier and two oscillator. The
number and location of physically allowed roots changes
depending on operating region. Additionally, in the
narrow-beam case, new challenges arise in satisfying theboundary conditions required for operation as an
oscillator

In this work, we include the effects of transverse
diffraction in the optical beam of an SPFEL. The
approach used is similar to that used for the 3-D theory of
the Cerenkov FEL [10]. As expected, three-dimensional
effects increase the gain length and oscillator start current
substantially. Furthermore, compared to the 2-D theory,
their dependence on the beam current increases due togain guiding. We find that diffraction of the optical beamin the periodic-grating structure subdivides device
operation into two amplifier regions and two oscillator
regions. For the amplifier and oscillator regions furthestfrom the Bragg point, we find the inclusion of a fast wave
in the physically allowed solutions.
This is very
surprising, considering the nature of a guided system. For
the oscillator region closest to the Bragg point there are
only two physically allowed solutions. It is not known
how the required boundary conditions on the electron andoptical beams can be satisfied in this region.

INTRODUCTIONDISPERSION

The wide range of potential applications for THz radiation
is currently driving interest in the development of intense,
compact, tunable THz sources. Such applications include:
resonant excitation and spectral analysis of chemical andbiological molecules and systems, medical and industrial
imaging, and investigations in materials science andnanostructures [1,2]. Electron-beam-based devices arevery promising sources of THz radiation. These include
synchrotrons, conventional FELs, and slow-wave devices,such as backward-wave oscillators. While synchrotronsand conventional FELs are large and expensive, slowwave devices can be compact, laboratory-scale
instruments.
Slow-wave structures support subluminal
electromagnetic modes, which may interact resonantlywith an electron beam passing in close proximity. This
resonant interaction causes bunching in the electron beam
and amplitude growth of an evanescent optical field. For
an open-grating structure, superradiant Smith-Purcell
radiation may be extracted at harmonics of the evanescentwave [3]. This configuration is known as a Smith-Purcell
free-electron laser (SPFEL). The SPFEL may be operated
as an amplifier (convective instability), or as an oscillator(absolute instability), depending on the sign of the laser
wave’s group velocity. The two-dimensional theory ofsuch a device has been examined in detail for the
exponential gain/growth regime [4,5,6,7], and is closely
supported by PIC simulations [6,8,9]. A two-dimensional
numerical treatment of device operation from startup to
saturation, with one-dimensional electron dynamics, hasalso been performed [7].

In an SPFEL, resonant energy exchange between
the electron beam and bound surface modes gives rise tospatial modulations in the beam density. These density
modulations lead to superradiant enhancement of theemitted SP radiation, and subsequent modification of its
angular distribution [3]. In the following analysis we
calculate the fields subject to the Maxwell equations andboundary conditions and solve for the dispersion relation.
We then introduce the electron beam as a perturbation andcalculate the resulting wavenumber and frequency shifts
for solutions to the dispersion relation.

Abstract

Table 1: Dartmouth grating and beam parameters

Grating period
Groove width
Groove depth
Grating length
E-beam width/heightE-beam current
E-beam height above
grating(measured from bottom ofbeam)

173 µm62 µm
100 µm
12.7mm
60 µm
1 mA
0 µm

For an electron beam energy of 150 kV and the grating
parameters of Table 1, the intensity scale height of theevanescent wave is Δx = βγλ / 4π ≈ 38 µm , whereβ ~ 0.43

isthenormalized

electronvelocity,

FEL Theory

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MOPPH026

Proceedings of FEL 2007, Novosibirsk, Russia

γ = 1/ 1 − β 2 , and λ ~ 10−3 m

is the free-space

1

⎤2
2 ⎡D
(δω − β cδ k ) ⎢ ω (δω − β g cδ k ) ⎥ = Δ (1)
⎣⎢ Dy
⎦⎥

wavelength. We anticipate from simple diffraction
arguments that the transverse mode width is of orderΔy ≈ βλ Z g / 2π(~millimeters),

where

Zg

(~centimeters) is the gain length. Schematics of the device
geometry with all pertinent dimensions are given in
Figures 1 and 2.

where β g is the evanescent wave’s goup velocity, δωand δ k are the complex frequency and wavenumber
shifts respectively, Dω and Dy are partial derivatives of

the no-beam dispersion function with respect to ω andk y 2 , andΔ=

β 3c 2W ωe 2⎛ω⎞tan ⎜ 0 H ⎟ ⎡⎣1 − cos ( k0 A ) ⎤⎦ . (2)22
ALDy γ ω0⎝ c⎠Calculations show that Dω is negative, irrespective of k ,Fig. 1 Geometry of grating structure, viewed from the side

but Dy changes such that Dy > 0 near the center of theBrillouin zone ( k / K = 1/ 2 ) and Dy < 0 towards theedges of the zone ( k = 0, K ) . This subdivides operationof the SPFEL into the four distinct regions pictured in
Figure 3 with the dispersion relation. Some roots are
eliminated in each region of operation because they do notallow the fields to vanish at y = ±∞ . A diagram
detailing this selection is given in Figure 4. We now
consider the amplifier and oscillator regimes of the
SPFEL.
Fig. 2 Geometry of evanescent wave and electron beam,
viewed from front
Because the fields vanish exponentially above the scaleheight, we simplify the theory by allowing the electron
beam to extend to infinity in the x direction. A filling
factor can be used to correct for errors introduced by thisapproximation [6,11]
To calculate the dispersion relation for thegrating, in the absence of the electron beam, we expand
the field above the grating in Floquet series and the fieldin the grooves as Fourier series. Invoking the Maxwell
equations and matching the fields at the grating surface,
we arrive at the empty grating dispersion function

Fig. 3 Dispersion relation with different regions ofoperation

D (ω , k , k y 2 ) , where ω is the frequency, k is thelongitudinal wavenumber, and k y is the wavenumber inthe y direction. We then expand the dispersion function
about the synchronous point ( ω0 = β ck0 ) in ω , k , andk y 2 , introducing the electron beam as a perturbation. In
the limit where the electron beam is infinitely wide thedispersion relation matches the 2-D theory [5]. For thecase of a very narrow beam the resulting dispersion
relation is
FEL Theory

78

Fig. 4 Diagram for selection of allowed rootsProceedings of FEL 2007, Novosibirsk, Russia

AMPLIFIER
When the device operates as a steady-state
amplifier, δω = 0 and β g is positive. In region II, the

MOPPH026

scaled down by a factor of three to appear on the samegraph.

roots of the dispersion relation are
2

4
i nπ

δ kn = Γ 5 e 5

(5)

where
1

Dy Δ 21.
Γ= 2 2β c Dω β g c(6)Similarly, in region I the roots are
2 i ⎛ 4 nπ + π ⎞
⎜
⎟
5⎠
5 ⎝5

δ kn = Γ eFig. 6 Computed gain for 2-D and 3-D theories as afunction of beam voltage.

(7)

In region II only two roots are physically allowed,
n = 2,3 . From Figure 5 we see that these are slow
waves, i.e. they have a phase velocity lower than that of
the no-beam-operating point.

The transverse profile of the electric field is given in
Figure 7, and the 1/ e mode width is found to beΔy ≈ 4.4mm . By examining the geometry of thismode, it is clear that the initial assumptions madeconcerning its dimensions are justified

Fig. 5 Roots for region II in the complex plane
Fig. 7 Transverse profile of the electric-field strength
In region I, however, there are three physicallyallowed roots including one fast wave solution. It issurprising that a fast wave is allowed in a gain-guided
system. In region II, the n = 3 root has loss and then = 2 root has gain. The gain for the n = 2 root isgiven by
2

⎛2 ⎞
⎝
⎠

μ3 D = − Im (δ k2 ) = Γ 5 sin ⎜ π ⎟5(8)

and has a corresponding 1/ e optical mode width of
−

1

⎛ D
⎞ 2 −1⎛π ⎞Δy = 2 ⎜ ω β g c ⎟ Γ 5 cos ⎜ ⎟ .
⎜ Dy
⎟
⎝5⎠
⎝
⎠

(9)

The relationship given in (9) is simply understood to be
the manifestation of gain guiding in the SPFEL. As an
example, we consider the grating and beam described inTable 1. The three-dimensional gain is plotted in Figure6, along with the two-dimensional gain, which has been

OSCILLATORIn regions III and IV the group velocity of the evanescentmode is negative. This allows information about thebunching of the electron beam at the grating exit to be
carried back upstream. This serves as an intrinsic form of
feedback and, provided that the beam current exceeds theso-called start current, allows the device to oscillate. Fora solution to exist in the oscillator case, three boundary
conditions must be satisfied in conjunction with thedispersion relation (1). The electron beam must be free of
density and velocity modulations at the upstream end of
the grating, and the input optical field at the downstream
end must vanish [5,6]. These boundary conditions are
satisfied by interference of the three waves that compose
the mode. Solutions to the inhomogeneous system canhave different transverse widths due to the presence ofgain guiding. Therefore, if only inhomogeneous solutions
are used, the boundary condition on the input field cannot
be satisfied for all y . For a general solution to thesystem, arbitrary amounts of the homogeneous solutions
may be added. In the following analysis we require that

FEL Theory

79

MOPPH026

Proceedings of FEL 2007, Novosibirsk, Russia

the boundary conditions be satisfied only on the beamaxis. We find that while region IV has three physicallyallowed roots, only two waves are admitted in region III.
It is not clear how all three boundary conditions may besatisfied without the presence of a third wave. We
therefore restrict our analysis of the oscillator regime toregion IV.
To form a mode of the oscillator, each wave must havethe same frequency shift δω . The boundary conditions
are defined bycharacterized by the number and location of physicallyallowed roots to the dispersion relation. Fast waves areincluded in some regions of operation despite the guided
nature of the interaction. In the present theory the mode
width vanishes mathematically at the boundaries of theseregions( D → 0 ) . These consequences are not fullyyunderstood at present.

1/ δ12 1/ δ 2 2 1/ δ 3 2
1/ δ1
eiξδ1

1/ δ 2eiξδ 2

1/ δ 3 = 0
eiξδ3

(10)

where δ j and ξ are dimensionless variables given by
2

1
1 5⎡ 2 52
⎤
2 ⎛
β
c
β
⎞
Dω 2 ⎥ ⎛⎞1⎢g
δj = ⎢δω ⎟ , (11)⎜⎜⎟⎟ ⎥ ⎜ δ k j −βc ⎠Δ⎝ Dy ⎠ ⎥ ⎝
⎢
⎣
⎦
2

1 ⎤5
⎡
⎛ Dy ⎞ 2 ⎥
Δ
⎢
ξ =⎢
Z.
(12)
⎟
5
1 ⎜
Dω ⎠ ⎥2 2⎝
2⎢ β c βg⎥⎣⎦
To find the start current we require Im ⎡⎣κ (ξ 0 ) ⎤⎦ = 0 ,

where
2

1
1 5
⎡ 2
⎤
2
2
β
β
⎛
⎞
D
1⎞
g
⎢
⎥ ⎛ 1
ω
+ ⎟ δω
κ = −⎢⎜⎜⎟⎟ ⎥ ⎜⎜ ββ ⎟⎠Δ ⎝ Dy ⎠⎢⎣⎥⎦ ⎝ g(13)

and solve the dispersion relation

δ j2 δ j − κ ±1 = 0(14)

subject to (10). The lowest dimensionless root found isξ0 = 1.194 , κ ( ξ0 ) = 1.802 . Both the 2-D and 3-Dstart currents are plotted as a function of operating voltage
in Figure 8.

CONCLUSIONS
We have presented a three-dimensional theory of SPFEL
oscillator (amplifier) operation for the exponential growth(gain) regime. We find that 3-D effects substantially
increase both gain length (amplifier) and start current(oscillator).
Unexpected consequences result from
inclusion of diffraction in the grating’s periodic structure.
Device operation is divided into four regions, which are
FEL Theory

80

Fig. 8 Oscillator start current as a function of electron
beam voltage

ACKNOWLEDGEMENTS
The authors gratefully acknowledge helpful
discussions with C. A. Brau and K.-J. Kim. This work
was supported by the Medical Free Electron Laser
Program of the Department of Defense under grant
number F49620-01-1-0429.

REFERENCES[1] S. P. Mickan and X.-C. Zhang, Int. J. High-Speed
Electron. and Sys. 13, 601 (2003).
[2] P. H. Siegel, IEEE Trans. Microwave Theory andTechniques 50, 910 (2002).
[3] H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D.
Jarvis, Phys. Rev. ST-AB 8, 110702 (2005).
[4] H. L. Andrews, C. A. Brau, Phys. Rev. ST-AB 7,070701 (2004).
[5] H. L. Andrews, C. H. Boulware, C. A. Brau, and J. D.
Jarvis, Phys. Rev. ST-AB 8, 050703 (2005).
[6] H. L. Andrews, C. H. Boulware, C. A. Brau, J. T.
Donohue, J. Gardelle, and J. D. Jarvis, New J. Phys. 8(2006) 289.
[7] V. Kumar and K. J. Kim, Phys. Rev. E 73, 026501(2006)[8] D. Li, Z. Yang, K. Imasaki, and Gun-Sik Park, Phys.
Rev. ST-AB 9, 040701 (2006).
[9] J. T. Donohue and J. Gardelle, Phys. Rev. ST_AB 8,060702 (2005).
[10] H. L. Andrews and C. A. Brau, J. Appl. Phys. 101,
104904 (2007)[11]G. F. Mkrtchian, Phys. Rev. ST-AB 10, 080701(2007)

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH028

ON NMR PROBING OF THE KINETICS OF A FREE-ELECTRONLASER-INDUCED CHEMICAL EXCHANGE
S.P. Babailov, IIC SB RAS, Novosibirsk, Russia
Abstract(PICE, in particular, molecular photoisomerization
Determination of the rate constants of chemical reactions) is an efficient application of NMR spectroscopy
exchange reactions (at dark conditions, Figure 1) and the [1,2].
quantum yields of photo-induced chemical exchange

0.02

2500

V
0.01

2000

1500

0
-200

1000

-100

1
k, 

s

0
500

n, Hz

100

200

Figure1: Calculated NMR line-shape for a two-site chemical exchange at dark condition (T1=T2=10 с, Δν=200 Гц, therate constant (k) changes from 38 to 2500 с-1).
We are proposed a combined approach for study the
kinetics of photo-induced chemical exchange (PICE)
hν1

⎯⎯→ B
A ←⎯⎯
hν 2

hν1
⎯⎯→
A + B ←⎯⎯
C
hν 2

(1)
(2)

Continuous and pulse irradiation of the chemicalsystem in the presence of PICE can be achieved using
FEL.

reactions (see (1), (2)), which involves a free-electron
laser (FEL) and NMR spectroscopy [3].

THEORETICAL
Based on the analytical equations derived in the work
we consider the time-dependent dynamics of variation of
the instant NMR line shape for two-site chemical
exchange.

FEL applications

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MOPPH028

Proceedings of FEL 2007, Novosibirsk, Russia
t

r

⎡

(

uur

r

)

⎤

−1 −Rt1(3)v(ν,t)=Im⎢e−(R2+Δi ω)tG0 −iω1∫e−(R2+Δi ω)(t−τ) e−Rt1 Mz0 −MR
0 1 (e −I)T1⋅ P dτ⎥

⎣

0

⎦

oscillations (on the NMR line shape) damped with time(see Figure 2, (3)).

If one induce an abrupt increase in the rate constant ofchemical exchange (for example, by quickly heating thesystem or PICE), then the NMR line shape will changewith time, ultimately reaching another new steady state.
Our calculations show that there are beats and0.01

V 0.005
0.02
0

-200
t, s
0.01

-100

0

n, Hz

100

200

0

Figure 2: Calculated time-dependent NMR line-shape for a two-site chemical exchange at photo-induced chemical
exchange condition (T1=T2=10 с, Δν=200 Гц, k changes from 100 to 2500 с-1 (at abrupt increase)).

CONCLUSION
The information about the time-dependent instant line
shapes provides possibility to predict the real kinetics of
PICE. Prospective objects are molecular conformers andspin isomers. So, FEL can be used in the setup for PICE
studies in combination with a NMR spectrometer.

REFERENCES[1] S.P. Babailov, E.M. Glebov, A.I. Kruppa, and V.F.
Plyusnin, “NMR in Photo-Induced chemical
Exchange Systems. Double-Resonance Inverse
Fractional Population Transfer Application for
Investigation of 1,2-(2,2’-Dipyridyl) Ethane
FEL applications

82

Photoisomerization Kinetics”, Concepts in Magnetic
Resonance, 2006, 8, P.571.
[2] S.P. Babailov, “Lanthanide Paramagnetic
Probes for NMR spectroscopic studies of
Molecular Conformational Dynamics in
Solution.
Applications
toMacrocyclic
molecules”, Progress in Nuclear Magnetic
Resonance
Spectroscopy,
2007,(doi:10.1016/j.pnmrs.2007.04.002 )http://dx.doi.org/10.1016/j.pnmrs.2007.04.002[3] S. P. Babailov, “Photo-induced chemical
exchange in solutions: NMR spectroscopic
detection of the kinetics”, Russ. Chem. Bull.,
Int.
Ed.,
2006,
10,
p.1631.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH030

TERAHERTZ IMAGING AND RADIOSCOPY WITH 160X120
MICROBOLOMETER 90 FPS CAMERA*
A.L. Aseev, D.G. Esaev, M.A. Dem’yanenko, I.V. Marchishin, Rzhanov Institute of Semiconductor
Physics SB RAS, 630090 Novosibirsk, Russia
B.A. Knyazev, G.N. Kulipanov, N.A. Vinokurov, Budker Institute of Nuclear Physics SB RAS,
630090 Novosibirsk, Russia.
Abstract
An uncooled micromolometer matrix camera has beendeveloped for IR and THz high-speed imaging. The
120x160 matrix consists of resistive vanadium oxide
elements on a silicon nitride bridge. The element size is
46x46 micron at the array period of 51 micron. We
describe device fabrication process and matrix operational
characteristics. Application of the camera in quasi-opticalsystems with Novosibirsk terahertz free electron laser as aradiation source is described. Recording rate up to 90
frames per second has been achieved.

two decades. Microbolometer FPAs, based onthermoresistance effect have got the greatest expansion.
Vanadium oxides (VOx) and amorphous silicon are
mainly used as thermoresistance material. In the lattercase process of microbolometer fabrication is carried out
completely within the framework of usual silicon
technology.

INTRODUCTION

Fig. 1: Scanning electronic microscope photograph of 160х120
microbolometer FPA fabricated on silicon readout circuit.
Line number
0

20

40

60

80

100

120

50

60

1000
800

US (arb.units)

TERAHERTZ imaging is critically important for many
applications. Appearance of high power terahertz sources,
such as free electron lasers, enables using “parallel”
recording techniques rather than recording images pointby-point with scanner. The last technique is routinely
used in the time domain spectroscopy (TDS) systems,
where recording an image takes minutes and hours.
Recently commissioned Novosibirsk terahertz freeelectron laser generates terahertz radiation at thefundamental mode in a range of 120 – 240 μm with theaverage power 100 – 200 W at the repetition rate 5.6MHz
and second and third harmonics with the average powerof about several Watts. A number of imaging techniques
employing the thermal effect of terahertz radiation weredeveloped during past two years for recording images on
the user stations [1 – 2]. These imaging techniques have
many advantages, but each of them has at the same timecertain drawbacks. One of them has a good spatial
resolution, but pure sensitivity. Other being sensitive has
no good spatial resolution. In this paper we describe theapplication of a microbolometer matrix to the recordingof images in the terahertz spectral region.

3

2

1

600
400
200
0
0

MATRIX DESCRIPTION
The expansion of application sphere of thermal imager
and others infrared (IR) devices along with increase of its
sensitivity demands of decrease of cost, power
consumption and weight, more convenience to use andhigh reliability. All these requirements are satisfied byuncooled focal plane array (FPA) actively developed last

10

20

30

40

t (ms)

Fig. 2. Time dependence of 160x120 microbolometer FPA
output signal normalized on sensitivity at pulse illumination. (1)the decay of FPA output signal after illumination: (2) the
increasing of the signal during illumination, (3) is anintermediate situation.

___________________________________________*This work was supported in part by SB RAS under Integration Grant
174/6, by grant RNP.2.1.1.3846 from the Russian Ministry for Educationand Science, and grant 07-02-13547 from Russian Foundation for Basic
Research

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MOPPH030

Proceedings of FEL 2007, Novosibirsk, Russia

The high performance of uncooled FPA mentioned
above is achieved the mainly due to development oftechnologies of thermosensitive layers preparation andmicrobridge structure fabrication. Since uncooled FPA are
fabricated in integrated-circuit form the basic requirement
to the technologies mentioned above is their compatibility
with fabrication technology of the silicon readout
integrated circuit (ROIC). The traditional methods ofthermosensitive vanadium oxides layers preparation reactive magnetron and ion-beam sputtering - are enoughcomplicated and require the complex expensive
equipment. For preparation of thermosensitive amorphoussilicon layers the technology of plasma enhanced
chemical vapor deposition (PECVD) from monosilane
with addition phosphine is used that creates additionaldifficulties.
Vanadium oxide 160×120 pixel matrix was designed
for the operation in the middle infrared spectral region (8– 14 μm). The fabrication technology and operational
characteristics of the matrix in this spectral region are
described in paper [3]. In this paper we describe theapplication of this matrix for the recording of themonochromatic radiation in the spectral range 130 –150 μm.

The matrix was used as a recorder in a number ofquasi-optical systems developed at Novosibirsk freeelectron laser. In the right upper corner in Fig.3 theinternal structure of a tablet pressed from Teflon powder
with addition of DNA is shown. The image was recordedby means of the radioscopy of the tablet with FEL as asource (see schematic in Fig. 2, ref. [5]).
Other application of the matrix was the radioscopy ofwrapped objects and substances. Two pictures in thelower row in Fig. 3 demonstrates the capability of thematrix for the examination of partially transparent toterahertz radiation substances for the inspection of illegal
objects and for the control of the box and container
contents in industry and stores by means of theradioscopy. Fig. 4 demonstrates a capability of the matrix
for imaging of the objects illuminated by terahertz
radiation (reflection/scattering mode).

TERAHERTZ IMAGING WITH VOX
MATRIX
Though the matrix was not optimal for terahertz
radiation, it approves itself as a very perspective tool forterahertz imaging. It appears to be more sensitive thanpreviously developed technique. It has a spatial resolution
close to the wavelength limit. We have demonstrated therecording of a moving object image with a rate up to 90
frames per second.

Fig. 4. Image of a wire spring with diameter of 2 mm.

CONCLUSION

No object, incident beam

A microbolometer matrix approves itself as a powerfultool for terahertz imaging both in transmission andreflection modes. Further development of the techniquewill be directed on the increasing matrix elements andInternal structure of a Teflon tablet
optimizing matrix design for the terahertz region.
with addition of DNA

REFERENCES

Image of a metallic circle witha semicircle opening wrappedin a piece of cotton fabric

Image of a plastic pen insidea paper envelope

Fig. 3. Imaging terahertz radioscopy, λ = 130 mm. Imager:
microbolometer matrix. Matrix size: 160x120 pixels, 16 bit,
8,2x6,2 mm, Recording rate: up to 90 frames per second.

The microbolometer matrix was applied for study offocusing terahertz radiation with a reflective kinoform(Fresnel) lens [4]. It was used for imaging radioscopy ofrat bones that is necessary for study of osteoporosis
development [5].
FEL applications

84[1] V.S. Cherkassky, B.A. Knyazev, V.V. Kubarev, etal.” Imaging techniques for a high-power THz freeelectron laser”, Nuclear Instruments and Methods inPhysics Research A, vol. 543, p. 102-109, 2005.
[2] V.S Cherkassky, V.V. Gerasimov, G.M. Ivanov, et al.
“Techniques for introscopy of condense matter interahertz spectral region”, Nuclear Instruments andMethods in Physics Research A 575, pp. 63-67, 2007.
[3] M.A. Dem’yanenko, V.N. Ovsyuk, V.V. Shashkin, etal. Uncooled 160х120 microbolometer IR FPA basedon sol-gel VOx, International congress on Optics andOptoelectronics, Proceedings of SPIE, 5957, 340(2005).

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH030[4] B.A. Knyazev, G.N. Kulipanov, I.A. Polskikh, et al.
““Diffraction optical elements and optical systems
with a high power monochromatic terahertz source”,
These Conferenc, Paper MOPPH033[5] M. Gonchar, V. V. Gerasimov, B. A. Knyazev,“Spectroscopy and spectrally resolved radioscopy of
biological substances using terahertz free electron
laser
radiation”,
These
Conference,Paper
MOPPH031

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SPECTROSCOPY AND SPECTRALLY RESOLVED RADIOSCOPY OF
BIOLOGICAL SUBSTANCES USING TERAHERTZ FREE ELECTRONLASER RADIATION*
A. M. Gonchar, Institute of Cytology and Genetics SB RAS, Novosibirsk
V. V. Gerasimov, Novosibirsk State University
N.G. Gavrilov, B. A. Knyazev, Budker Institute of Nuclear Physics, SB RAS, 630090, Russia
Abstract
Osteoporosis is a major cause of morbidity of older
people. Direct financial expenditure for the treatment of
osteoporosis fracture in the U.S. is estimated at $10-$15
billion per year. Though there are a number of methods
for diagnostics of osteoporosis, X-ray radioscopy, NMR,
element analysis, densitometry, etc., the development of
new methods, which are complementary to the existingones, is highly desirable. We have carried out firstexperiments on the examination of spectroscopic
characteristics of healthy and osteoporosis-affected bone
tissues in the terahertz spectral range. The samples wereprepared by pressing of grounded bone tissue obtained
from the intact rats Wistar and from the senescenceaccelerated rats OXYS. The OXYS rats suffered
hereditary osteoporosis developed early in life are,therefore, a useful model for examining osteoporosis. The
first experiments using a Fourier-spectrometer showed
considerable difference in the bone tissue absorbance fortwo strains, though statistic tests are still required.
Because the bone tissue is a highly-absorbing substance,
the attenuated total reflection spectroscopy seems to be
the most adequate method for detailed bone study.
Imaging radioscopy of bone samples using a matrix of
microbolometers as a sensor and the Novosibirsk freeelectron laser as a source of monochromatic terahertz
radiation is described.

complementary information about the bone tissue
characteristics that can be valued for diagnostic ofosteoporosis.
Recently, the capabilities of terahertz spectroscopy forbones research have been started to investigate. Until
now, a few researches of bones using the terahertz timedomain spectroscopy (TDS) have been done. This
technique allows obtaining information on the bonedensity and the complex refractive index. Bone A
technique for the computer tomography of bones based on
TDS had been demonstrated in the paper [2]. The
information about the optical properties of threedimensional (3D) structures of the investigated bone in
the far-infrared region was obtained. Newly developed
high-power terahertz sources, such as the Novosibirsk
free-electron laser, open up new possibilities for bone
radioscopy and imaging, including study of dynamical
processes [3].
The goal of this study was the investigation of capabilities
of osteoporoses diagnostics by comparison absorption
spectra of normal and osteoporosis bone tissue. As amodal for the investigation two genetic strains of rats werechosen, Wistar (intact rats) and OXYS (senescenceaccelerated rats with the early onset of osteoporosis). The
strain OXYS was founded at the experimental animallaboratory of Novosibirsk Institute of Cytology and

INTRODUCTION*This work is partially supported by Integration Grant 174/6 fromSB RAS, by grant RNP.2.1.1.3846 from the Russian Ministry for
Education and Science, and grant 07-02-13547 from RussianFoundation for Basic Research

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400
-1

Absorption coefficient (cm )Osteoporosis is a systemic skeletal disordercharacterized by low bone mass and micro architectural
deterioration of bone tissue, leading to enhanced bone
fragility and an increased tendency to fracture.
Osteoporosis has a long latent period and clinicallyreveals already in the presence of fractures when the bonemineral density is reduced significantly [1]. Thus, forpreventing and treatment this disease the early diagnosis isnecessary. Today there are several experimental
techniques in diagnostic of the osteoporosis such as dual
X-ray densitometry and computer tomography, NMR, etc.
In spite of high developing and routine of such techniquefor bone research, the using of terahertz radiation can give

Wistar, 2 months

350
300
250
200

OXYS, 2 months

150
OXYS, 2 years

100
50

Wistar, 2 years
0
50

100
150
200
Wavelength, μm

250

300

Figure 1: Absorbance vs. wavelength for the bone
samples of intact (Wistar) and senescence-accelerated(OXYS) rats of different ages.
Genetics. The animals of this strain have a particularly
short life span and accelerated development of age-Proceedings of FEL 2007, Novosibirsk, Russia
associated pathological phenotypes similar to several
geriatric disorders observed in humans.

MOPPH031

data. Measurements of bone spectra using the ATR
spectrometer are in progress.

Radioscopy with microbolometer matrix

METHODS AND RESULTS
Fourier-spectrometer measurements
The transmission spectra in the region of 30-300 μm forthe bones of two-month and two-year Wistar and OXYS
rats were recorded using a Fourier-spectrometer Bruker
IFS66v/S (Fig. 1). The samples were prepared by pressingof grounded bone tissue into 200-400 μm thick tablets.
Previously, bones from rats were lyophilized and reduced
to fragments into the powder in the agathic mortar. The
characteristic size of the powder particles was less thenwavelength of the THz radiation used in our experiments.
Measurements of the tablet spectra reveal significant
absorption of terahertz radiation. So high absorption canbe attributed to the absorption of liquid water, which ispresent in bone tissue in the free and bonded state. The
plots in Fig. 1 show clear difference between theextinction coefficients for two-month Wistar and OXYS
rats, as well as (may be not so clear) for the two-year
animals. Unfortunately the signal magnitude at the Fourier
spectrometer detector in these experiments was near the
FS noise. To increase the reliability of the measurements
we have started study of the extinction coefficient using
an attenuated total reflection (ATR) spectroscopy.

Spectrally resolved terahertz radioscopy of the bones is
a prospective technique for the examination of internalbone structure and detection of osteopathy location. We
applied a 120×160 pixel microbolometer matrix [5] forthe radioscopy of the rat bones. The experimental setup is
shown in Fig. 2 and two recorded images are presented inFig. 3. Intensity distributions along one of the matrix rows
are shown in the plot for the initial beam and for the beam
passed the bone.

Figure 2: Experimental scheme of radioscopy using MMB
with a polyethylene lens.

Attenuated total reflection technique
ATR is a one of the most adequate techniques for the
spectroscopy of highly absorbing substances. The
comparison of capabilities of spectrometers for terahertz
spectral range is shown in Table 1. Recently, a two-beam
ATR spectrometer meant for the operation with tunable
FEL was developed [4]. This system was tested using theTable 1: Comparison of capabilities of spectrometers
for terahertz spectral range
Spectrometer type
Capability
FS
AS
ATR
Measurement of highly
absorbing samples
Measurement of low
absorbing samples
No impact of reflection
No impact of scattering
Measurement of real andimaging parts of the refraction
index
Capability for 2D imaging
spectroscopy

m

m

+

+
−
−

+
−
−

m

+
+

−

−

+

−

+

+

samples with known optical constants (water, hexane, andbenzene) and are showed a good agreement with reference

Figure 3: Imaging of rat bones using the MMB: rate 90
frames per second at the bottom (from left to right):
reference beam, pass beam through the bone, the bone’s
photo; at the top: horizontal profile of intensity of thereference beam (dash line) and pass beam (solid line).

CONCLUSION
Thus, the first experiments on rat bone spectroscopy
revealed obvious correlation between the absorbance andthe strain of two month rats OXYS and Wistar andbetween of two-year OXYS and Wistar rats. The firstradioscopy experiments using MMB showed thecapability, in spite of high bone absorption, recording ofradioscopic images of bone tissue using terahertz FEL
radiation. Further investigations of the bone spectra using
ATR technique and radioscopy will give the answer whereor not the spectral differences between Wistar and OXYS
can be applied for pre-clinical screening analysis of theefficiency of pharmaceutical medicines for osteoporosis
treatment.

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REFERENCES[1] D. Faibish, “Mineral Changes in Osteoporosis
Review,” Clin Orthop Relat Res., vol. 443, pp. 28–
38, 2006.
[2] B. Ferguson, X.-C. Zhang, “T-ray computed
tomography,” Optics Letters, vol. 27, no. 15, 2002.
[3] V. S. Cherkassky, V. V. Gerasimov, G. M. Ivanov etal. “Techniques for introscopy of condense matter interahertz spectral region,” Nuclear Instruments inPhysics Research, no. 575. pp. 63-67, 2007.
[4] V. S. Cherkassky, N. G. Gavrilov, V. V. Gerasimov
et al. “Attenuated total reflection spectrometer withterahertz free electron laser as a source,” in Proc. ofInt. Conf., IRMMW-THz 2006 Shanghai, pp. 459.
[5] A.L. Aseev, D.G. Esaev, M.A. Dem’yanenko, et. al.
These Conference, Paper MOPPH030.

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MOPPH032

DEVELOPMENT OF METAL MESH BASED QUASI-OPTICAL
SELECTIVE COMPONENTS AND THEIR APPLICATION IN HIGHPOWER EXPERIMENTS AT NOVOSIBIRSK TERAHERTZ FEL*
S.A. Kuznetsov#, BINP SB RAS, Novosibirsk State University,
Novosibirsk, 630090, Russian Federation
V.V. Kubarev, P.V. Kalinin, B.G. Goldenberg, V.S. Eliseev, E.V. Petrova, N.A.Vinokurov
BINP SB RAS, Novosibirsk, 630090, Russian Federation
Abstract
In this paper we discuss main types of metal meshbased passive selective components of THz-quasi-optics
required for applications in experiments at Novosibirsk
terahertz free electron laser. The first experimental results
on development of thin-film metal mesh polarizing
beamsplitters and frequency filters by methods ofphotolithography and electroforming are presented. The
technological aspects of the promising LIGA-techniquebeing in progress in the Siberian synchrotron radiation
centre and destined for production of thick metal meshcomponents with thickness compared to radiation
wavelength are described.

INTRODUCTION
Successful realization of scientific programs of theSiberian Centre of Photochemical Research [1, 2]
operating on basis of Novosibisk terahertz free electron
laser (NovoFEL), which fundamental generation
harmonics overlaps a spectral range 1.3÷2.5 THz, requires
application in user experiments different types of passive
quasi-optical selective devices intended for spatial andfrequency gating of powerful beams of NovoFEL
radiation. The necessary instrumentation includes beamsplitters, attenuators, frequency filters and some elementsof focusing optics. Along with desired selective
characteristics such devices should be capable ofoperating over a long period of time under high-power
load conditions without noticeable degradation of theirproperties. It admits to employ in selective components
only low absorbing and thermostable materials, such as
high conductivity metals and special types of polymers.
The best solution is in use of metal mesh structures withspecially designed subwavelength topology of mesh cells.
For minimizing absorption the metal structures should be
wafer-free, however in case of non-self-bearing topology
or small metallization thickness structure fastness requirespresence of supporting thin-film polymeric substrates.
In this report we discuss selective properties of themain types of metal mesh structures required for
NovoFEL experiments and present first results ofdevelopment of metal mesh components by three different
manufacturing techniques: a) contact photolithography;b) electroforming; c) LIGA. Dealing with a minimal___________________________________________* This work is supported in part by the Russian Foundation for Basic
Research (project No. 07-02-01459-a).
#sakuzn@inp.nsk.su

topological size of the mesh pattern about a few microns,each of these techniques enables to produce meshcomponents within its own corresponding range ofmetallization thickness: a) ≤1 µ; b) ~10 µ; c) ~100 µ.
It should be elucidated that conventional
photolithography is considered to be the most adequate,
relatively cheap and well-proven technology for
manufacturing metal mesh quasi-optical components
traditionally used in low- and moderate-power THzapplications. In NovoFEL user experiments employmentof such “photolithographic” components is restricted due
to high average power of NovoFEL radiation, reaching
400 W nowadays and expected to be raised in the future.
Small thickness of metallization and presence of dielectriccarrier substrates in such components limit their surface
and volumetric thermal conductivity resulting in dangerof quick overheating and destruction under high-power
load conditions. The best “high-power” alternative to“photolithographic” components (in case of self-bearing
topology) are the components based on substrate-free
self-supporting thick metal mesh structures manufactured
by conventional electroforming and LIGA techniques. In
spite of higher technological costs such components areof great interest for NovoFEL applications since they aremuch more thermostable and mechanically firm and havea much higher radiation destruction threshold. Anotherinherent and important feature of thick metal structures ismuch stronger low-frequency attenuation due to a
waveguide cut-off effect that can be effectively used forsolving problems of harmonics filtration and THz-beams
intensity control discussed below.

THZ-COMPONENTS REQUIRED FOR
NOVOFEL APPLICATIONS
By fundamental practical purpose influencing on choiceof mesh pattern topology the metal mesh based selective
components should be divided into three main groups(see Fig.1): 1) beam-splitters (attenuators); 2) frequency
harmonics filters; 3) diffractive optical elements.

Figure 1: Fundamental types of metal mesh based
components required for NovoFEL experiments:a) polarizing beam-splitter; b) frequency filter;c) diffractive optical element (amplitude transparency).

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Wideband beam-splitters and attenuators

Harmonics filters

Urgency of these components is connected withnecessity of NovoFEL radiation distribution oversimultaneously operating different user stations, as well
as THz-beams multiplexing and beam intensity control invarious user experiments. Due to almost 100%polarization linearity of FEL’s radiation [3] the bestsolution is in use of polarizing grids or 1-D meshes (Fig.
1a) with a grid pitch g much less than operating
wavelength λ. Such grids reflect effectively the Epolarized component of the incident radiation andtransmit its H-polarized component that enables to control
intensity of transmitted or reflected radiation by choosing
an appropriate orientation angle of the grid. For
simultaneous operation of different user stations the
NovoFEL facility needs beam-splitters with clear aperture
diameter up to ~250 mm at minimally realized grid pitch
values.
It should be pointed out that for a fixed value of min(g),which is determined by technological limitations,operational efficiency of a polarizing beam-splitter can begreatly enhanced by increasing its metallization thickness
t. As t grows the grid slots begin to manifest waveguide
properties that results in exponential decrease of thespectral transmittance for the E-polarized incident wave
due to a waveguide cut-off effect (Fig. 2a). For Hpolarization there is no prohibition on waveguide mode
propagation but in contrast to the case t → 0 thetransmittance appears to be frequency modulated(Fig. 2b). The last effect is explained by excitation ofstanding waves inside waveguide slots due to partialreflection of the propagating wave from the input andoutput slot boundaries. The approximate spectral
positions of H-transmission minima and maxima can beobtained from the formulas of Fabry-Perot resonances:
λ min ≈ 2t /( m + 1 / 2) , λ max ≈ 2t / m , m ∈ Ν .
In practice, for eliminating the negative effect of Htransmission modulation it is recommended to mount apolarizing beam-splitter at the angle of incidence
ϕ = arcos (q), where q is relative width of grid slots. In
this case reflection of the H-polarized wave vanishes due
to Malyuzhinets effect.

Detailed spectral measurements of NovoFEL radiation
show that along with a fundamental generation harmonics(λ = 118−235 µ) the laser spectrum contains the second
and the third ones which relative power in optimized
regimes reaches relatively high values: 2 % and 0.6 %respectively [4]. A study of these short-wave spectral
components and their interaction with investigatedsamples is a subject of great interest.
For filtering the higher FEL’s harmonics atsimultaneous strong (≥40 dB) suppression of the 1st one
the following 2-D metal mesh structures can be applied:− Nonresonat “inductive” meshes with circular openings(Fig. 3a, 6). At thickness t compared to radiation
wavelength such meshes act as effective high-pass filters,
which efficiency of low-frequency attenuation below thepoint νcutt-off≈1.841⋅c/(πd) is enhanced by the factor~32⋅t/d (dB) in comparison with similar thin meshes due
to a waveguide cut-off effect.
− Resonant “inductive” meshes of crossed dipole slots(Fig. 3b, 5b) with resonant band-pass transmission at
wavelength close to doubled slot length L. For small metallization thickness (t~1 µ) such single meshes provide
not higher than ~20 dB out-of-band attenuation. It can beaugmented at low frequencies by increasing t.
− Resonant “capacitive” meshes. Such meshes comprisedby disjointed resonant conducting elements are effective
for rejecting undesirable spectrum frequencies. Mesheswith hexagonally packed ring elements (Fig. 4) arerecommended for proving a widest rejection band
(FWHM~100%) at the maximal theoretical attenuationlevel ~35-40 dB.

Figure 2: Numerical simulation of influence of
metallization thickness t on frequency response of acopper polarizing beam-splitter (normal incidence): а) Еpolarization (E || slots); b) H-polarization (H || slots).
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Figure 3: Frequency response of nonresonant high-pass(a) and resonant band-pass (b) copper single-layer meshfilters for different metallization thickness t.

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 4: Simulated band-stop properties of thin single
resonant meshes with hexagonally packed circular ringelements (t~0.45µ, Al) deposited on a 3µ-polyimide film.

MOPPH032

Figure 5: Spectral transmittance of experimental samples
of 0.45µ-Al-mesh structures deposited on 3.5µ-PI-films:
1) g=41.4µ, 2a=12µ, 2b=6µ; 2) g=28.5µ, 2a=10µ, 2b=5µ.

Diffractive optical elements (DOEs)
DOEs (Fig. 1c), conditionally called as “irregular 2-D
mesh structures”, are intended for focusing THz-radiation
into a spot of a desirable shape. Such a problem arises for
instance in scheduled THz-experiments on governingsupersonic gas flows by controlling radiation energy
deposition inside a specified volume [5]. In contrast to“non-diffractive” mesh structures considered above DOEs
operate in a high order diffraction mode that is provided
by the greater topological size of a “mesh” pattern(g > 2λ). Detailed consideration of DOEs is beyond thescope of our paper and can be found for instance in [6].

SAMPLE THZ-COMPONENTSPRODUCED BY PHOTOLITOGRAPHYAND ELECTROFORMING
In the framework of the THz-instrumentation
development task we have adapted and successfully tested
the technology of contact micro-photolithography for
manufacturing thin-film free standing terahertz polarizers(Fig. 1a) and resonant band-pass filters (Fig. 1b) at
minimal topological size of the mesh pattern 4−6 µ andclear aperture diameter ∅ 66 mm. The polyimide films
3.5 µ thick were used as bearing substrates for Al-meshstructures with metallization thickness 0.45 µ. The typical
FIR transmission spectra of manufactured samples
obtained at the “Bruker IFS 66v/s” Fourier-transform
spectrometer are presented in Fig. 5. Since a radiation
source used in the FT-spectrometer is originallynonpolarized an auxiliary polarizer was used for obtaininga reference signal during FIR characterization of 4x8µpolarizers. The manufactured samples were also tested in
50 W THz-beams of NovoFEL radiation that let us
measure directly transmittances of mesh samples in a
low-transmission region without using a cryogenic
technique. E.g. the transmittance of 4x8µ-polarizers for
E-polarization appeared to be ~3.2⋅10-3 at λ = 126 µ.
The choice of thin polyimide substrates is conditionedby their satisfactory optical characteristics, highFigure 6: High-pass properties of free standing substratefree nonresonant 9µ-Ni-meshes with hexagonally packed
circular openings.
mechanical fastness and thermostability enabling towithstand radiation heating up to 3500C. By now
polyimide-film based mesh structures were successfully
tested at radiation power flows ~2 kW/cm2.
Successive use of photolithographic and electroforming
techniques enables to increase mesh metallization
thickness resulting in elimination of supporting polymeric
substrate in case of self-bearing structures. We
successfully tested this technology for production a set ofdichroic high-pass filters based on electroformed Nimeshes 8÷10 µ thick (Fig. 6). As such thickness is close
to the upper technological limit the only alternative for its
further increase is use of the LIGA-technique.

PRODUCTION OF THICK THZCOMPONENTS BY LIGA-TECHNIQUE
In comparison with conventional photolithography the
LIGA-technique being developed at the Siberian
Synchrotron Radiation Centre (BINP SB RAS) is basedon deep X-ray lithography and destined for producing
microstructures in a wide range of their thicknesses: froma few units up to hundreds microns [7, 8]. Such anadvantage of the LIGA-technology over optical and UVtechniques is realized due to high penetrability of X-ray
radiation into X-ray-sensitive resists and negligible
effects of parasitic Fresnel diffraction that makes LIGA to

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Figure 6: Main stages of the LIGA-technique: a-d) Хmask production; e-h) Х-mask application for obtaining athick metal mesh structure.
be ideal for manufacturing thick metal mesh based THzcomponents with extremely high aspect ratios
unachievable by any other methods.
The principal stages of LIGA include production of an
X-ray contrast mask which topological pattern replicatesthe pattern of a desired mesh structure, deep X-ray
lithography via the prepared X-mask and subsequent
growing of an output thick mesh structure byelectroforming. At present, we master the LIGAtechnique for producing self-bearing copper 2-D meshfilters 50÷100 µ thick at the minimal topological size ofmesh pattern about 10 µ. The main steps of the usedtechnology are shown in Fig. 6.
We use a direct method of X-mask creation [8] basedon direct forming a latent image of the required
microstructure or its fragment in the 30 µ-layer of the Xray sensitive negative resist SU-8 deposited onto
roentgenoparent wafer by irradiation under a collimatedmicrobeam of synchrotron radiation (SR) with photon
energy 4÷30 keV (Fig 6a). SR provides uniform
irradiation of the SU-8 layer over its depth that result inverticality of walls in output microstructures. As
roentgenoparent wafers the polished plates of special
carbonic glass 500÷600 µ thick are used. After removal of
the unirradiated resist by wet etching technique (Fig 6b) athin 1÷3 µ copper sublayer and a subsequent 10÷20 µlayer of rhenium or gold are deposited onto the wafer byelectroforming (Fig 6c). The layer of rhenium (gold) acts
as a roentgenopaque material required for the X-mask,
whereas a copper sublayer provides better adhesion of Re(Au) to the wafer surface. After final removal of theresidual resist (Fig 6d) the finished X-mask with typicaloperating area 10x10 mm2 is ready for next applications.
The stage of production of the output metal meshstructure (Fig 6e-h) includes steps similar to theconsidered above. X-ray exposure of a thick SU-8 resist
deposited onto a carbonic glass wafer is realized via the
prepared X-mask with subsequent multiplication of the Xmask pattern over desired area (Fig 6e). Irradiated regionsof SU-8 material cross-linked after exposure and cleaned
from unirradiated resist (Fig 6f) form the mask with deep
vertical walls which is used for the following
electroforming of a thick metal structure (Fig 6g). The
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maximal metallization thickness of the output meshstructure corresponds to the thickness of the SU-8 resist
which is 50÷100 µ thick in our LIGA-experiments. The
main problem appearing at the final step of production isseparation of a copper structure from the carbonic glass
wafer after removing the residual resist by wet etching(Fig 6h). This problem is solved by galvanic deposition of
an auxiliary 1µ-Re-layer onto the carbonic glass wafer
before electroplating of copper. It leads to decreasing
copper adhesion due to passivation of Re-surface.

CONCLUSION
Rapid progress in terahertz researches connected withappearance of high-power FELs requires detailed
development, designing and optimization of selective
components of terahertz quasi-optics necessary for highpower applications. For future experiments at NovoFEL
user stations the THz-components produced byconventional thin-film based photolithography andelectroforming are considered as supplementary to thick
LIGA-components which are of primary importance. We
place the emphasis on development of the LIGAtechnique and expect to obtain first high-quality THzLIGA-structures in 2007-2008.

REFERENCES[1] V. P. Bolotin, N. A. Vinokurov, D. A. Kayran et al.,“Status of the Novosibirsk terahertz FEL”, Nuclear
Instrum. Methods, vol. A543, pp. 81-84, 2005.
[2] N. A. Vinokurov et al., “Status of Novosibirsk ERL
and FEL”, in these Proceedings.
[3] V. P. Bolotin, V. S. Cherkassky, E. N. Chesnokov etal., “Novosibirsk terahertz free electron laser: status
and survey of experimental results”, Proc. Joint
IRMMW-THz-2005 Conf., Williamsburg, USA,2005, p. 495.
[4] V. V. Kubarev, N. A. Vinokurov, V. V. Kotenkov etal., “Harmonic Generation in the Novosibirsk
Terahertz FEL”, in Proc. Joint IRMMW-THz-2006
Conf., Shanghai, China, 2006, p. 162.
[5] V. V. Yakovlev, V. M Fomin. “Possibilities of laser
radiation application for solving aerodynamic
problems”, in Proc. 1st Russian THz-Workshop“Generation and application of terahertz radiation”,
24-25 Nov., 2005, Ed. B.A. Knyazev, Novosibirsk,
Russia, pp. 123.
[6] I. A. Polskikh, A. Fanova, B. A. Knyazev et al,“Diffraction Optical Elements and Optical Systems
with High Power Monochromatic Terahertz Source”,
in these Proceedings.
[7] W. Ehrfeld and H.Lehr. "Deep X-ray lithography forthe production of three dimensional microstructuresfrom metals, polymers and ceramics". Radiat. Phys.
Chem., vol. 45, No. 3, pp. 349-365, 1995.
[8] E.V. Petrova, B.G. Goldenberg, V.I. Kondratiev etal., “Production of thick wafer based X-masks fordeep X-ray lithography”, J. Surface Investigation. XRay, Synchrotron and Neutron Tech., 2007 (in press).

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MOPPH033

DIFFRACTION OPTICAL ELEMENTS AND OPTICAL SYSTEMS WITH A
HIGH POWER MONOCHROMATIC TERAHERTZ SOURCE *V.S. Cherkassky, A. V. Fanova, L.A. Merzhievsky, S.A. Zhigach, NSU, Novosibirsk, Russia
Young Uk Jeong, Hyuk Jin Cha, B.A., Korean Atomic Energy Research Institute
N.G.Gavrilov, B.A. Knyazev#, G.N. Kulipanov, I.A. Polskikh, N.A. Vinokurov, S.A., BINP,
Novosibirsk, Russia.
Abstract
We have developed reflective diffraction opticalelements (DOE) for focusing radiation of terahertz freeelectron lasers (FEL). Metal-dielectric Fresnel zone plates
and metallic kinoform “lenses” were fabricated and tested
using FEL radiation. A microbolometer camera (see thepaper by Esaev et al. at this conference) sensitive to THz
radiation had been applied for recording both terahertz
beam caustic and terahertz images. Diffraction efficiency
of a kinoform lens appears to be about unity. Quality ofimages obtained with the kinoform lens was studied. The
lens was used as a key element for a Toepler opticalsystem, which were used for studying condense matter
non-uniformities and deformations. The experiments were
performed at Novosibirsk and KAERI FELs.

TERAHERTZ OPTICAL ELEMENTS AND
SYSTEMS
Fresnel zone plates
Three Fresnel zone plates (with zone numbers of 91,
46, and 30, respectively, and the first Fresnel zone radii of
5.2, 7.35 and 9.0 mm) had been designed and fabricatedfor focusing terahertz radiation with simultaneousreflection under the right angle. The elliptically shaped
plates with the minor semi-axis of 5 cm and the aspectratio of 1:1.41 were formed by etching a copper foil cladon a fiber-glass plastic. The central zone of each plate wasreflecting.

____________________________________________*Work supported by Integration grants 174/6 and 22/6 from Siberian
Branch of Russian Academy of Science, by grant RNP.2.1.1.3846 fromthe Russian Ministry for Education and Science, and grant 07-02-13547
from Russian Foundation for Basic Research.…
#knyazev@inp.nsk.su

a

b

50

50

45

45
Temperature (C)Imaging in the terahertz spectral region (1 – 10 THz) isa subject of special interest for many applications such as
biological researches, medical diagnostics, study ofmaterials, security systems and many other applications.
Each optical system consists of a source of radiation,
optical elements and an imager. In this paper we describe
optical elements and recorders developed for imaging
with free electron laser (FEL) as a source. Most of theexperiments were carried out at high power Novosibirsk
FEL. Some of them have been done at KAERI FEL.
Because the refractive optical elements can be damagedby high power terahertz radiation, we have developed anumber of reflective diffraction optical elements (DOE).
Large-scale reflection DOE are often used in the
microwave spectral region, and the application of DOE in
terahertz optical systems is, obviously, very prospective.
Previously [1 – 3] we have developed (or adapted)
three recorders for the visualization of intense terahertz
radiation: a near-IR thermograph, a thermal-sensitive
Fizeau interferometer, and a “thermal image plate”. In
this paper we first used as a terahertz imager [4] amicrobolometer matrix, initially developed for the MIR
range 0. The matrix has higher sensitivity and better
spatial resolution, than the imagers mentioned above.

Temperature (C)INTRODUCTION

40
35
30

35
30

25

25
0

20

40

60

80

PixelsNo THz beam

c

40

100

120

140

20

40

60

80

100

120

140

PixelsWith Thz beamdFigure 1: A thermographic image of a zone plate
recorded with no radiation (a) and with THz irradiation(b); plots – effective temperature distribution along the
major ellipse axis. Intensity distribution in the initial
THz beam (c) and in the zone plate focus (d) recordedwith the thermal image plate.
The images of a zone plate taken at 2.5 – 3.0 μm withthe thermograph (Fig.1) show growing the temperature of
the dielectric zones up to 55 C, nevertheless, the zone
plate focuses THz radiation well. The focal lengths for allzone plates exactly correspond to designed values. Since
the principle focal length of a zone-plate is inversely
proportional to the radiation wavelength, f1 = r12 /λ0 , it canbe used at arbitrary wavelength, but low diffractio
efficiency (~10%) constrains its application.

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Proceedings of FEL 2007, Novosibirsk, Russia

Reflecting kinoform lensMore effective in comparison with a zone plate is akinoform or Fresnel lens, in which each zone surface isparabolically profiled. First, we tested a simplified
kinoform lens with elliptical zones, similar to the above
described zone plates, and with the profile designed forfocusing radiation at λ0 = 130 μm with f = 250 mm.
The kinoform lens was manufactured by drilling on a NC
machine. Minor radius of the first Fresnel zone was equal
to 8.06 mm. Measured diffraction efficiency of the lensappears to be close to unity.

shape must be an emulation of the off-axis parabolic
mirror that is not easy to fabricate.
To obtain a good focal spot, we fabricatedaxisymmetric kinoform lens, and by inclining it under asmall angle, extracted the reflected terahertz radiation
onto a small plane mirror that enabled displacing the focal
spot out of the initial beam. 2D surface plot in Fig. 3
demonstrates high quality of the focal spot for theaxisymmetric kinoform lens.

Image plane

Toepler scheme
Edge

Scatterer
Polarizer
Object

мм

мм

250

225

Kinoform
lens

мм

260

280

мм

New lens focus

Figure 3: Distribution of terahertz beam intensity inthe elliptical kinoform lens caustic surface (2-D plots)
and in the focus of axisymmetric kinoform lens (thelast plot) recorded with the microbolometer focal planearray.
Figure 2: Toepler optical system and images obtained
for a polyethylene film as an object: undistorted film
(left picture) and stretched ones.

Optical systems with kinoform lenses
The kinoform lens was used as a focusing element in a
Toepler quasi-optical system (Fig.2) intended for the
study of loaded solid samples and stretched films bymeans of terahertz radioscopy. Experiments were
performed both at NovoFEL and KAERI FEL. Dynamic
range and linearity of Toepler system response criticallydepend on the focal spot quality. Using a 160 × 120 pixel,
51 μm period microbolometer focal plane array 0, werecorded the distribution of terahertz radiation intensity(Fig. 3) in the caustic surface of the elliptical kinoform
lens without scatterer, object and knife-shaped edge.
The kinoform lens has a relatively small focal spot sizein the vertical direction (at L = 250 mm), which enables
using the lens for the study of vertical optical path
gradients, but the horizontal spot size is too large and theintensity distribution is uneven, which does not enablemeasurement of horizontal nonuniformities. The origin of
the horizontal focal spot distortion lies, obviously, in thesimplified Fresnel zone and surface shapes. The correct

FEL applications

94

CONCLUSION
Focusing elements and detectors developed in thisstudy enable designing of quasi-optical systems forimaging and radioscopy with a high power terahertz freeelectron laser. Examples of optical path gradientsrecorded when THz beam passed through stretchedpolyethylene film are shown in the bottom Figure 2.

REFERENCES[1] V. S. Cherkassky, V. V. Gerasimov, G. M. Ivanov, etal. “Techniques for introscopy for a high-power THz
free electron laser”, Nucl. Instrum. Methods in Phys.
Res. vol. A 543, pp. 102-109, 2005.
[2] N. A. Vinokurov, B. A. Knyazev, G. N. Kulipanov,
et al. “Visualization of radiation from a high-power
terahertz free electron laser using a thermosensitive
interferometer”, Tech. Phys., vol. 52, no.7, pp. 911–
919, 2007.
[3] V. S. Cherkassky, B. A. Knyazev, V. V. Kubarev, etal. “Imaging techniques for introscopy of condense
matter in terahertz spectral region”. Nucl. Instrum.
Methods in Phys. Res. vol. A 575 pp. 63-67, 2007.
[4] Dem’yanenko M.A.,Ovsyuk V.N., Shashkin V.V., etal. “Uncooled 160х120 microbolometer IR FPA
based on sol-gel VOx”, in Proc. SPIE, vol. 5957,
340-347, (2005).

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH034

DIAGNOSTICS OF AN ELECTRON BEAM USING COHERENTCHERENKOV RADIATION*
R. Tikhoplav#, P. Musumecci, J. Rosenzweig, S. Tochitsky, UCLA, Los Angeles, CA 90095
G. Gatti INFN/LNF, 00044 Frascati (RM) Italy
Abstract
The use of coherent Cherenkov radiation as adiagnostic tool for longitudinal distribution of an electron
beam is studied in this paper. This method will be
employed for the 7th harmonic bunching experiment at
Neptune linear accelerator facility at UCLA. Coherent
Cherenkov radiation is produced in an aerogel with anindex of refraction close to unity.

THEORETICAL BACKGROUND
Radiation due to a relativistic electron beam traversing
a medium, such as transition radiation (TR), has proved
itself to be a powerful tool for beam diagnostics, e.g.,determining the transverse distribution and position of anelectron beam as in TR screen technique. Such radiation
could also be used for reconstruction of the longitudinal
profile of the electron beam if the coherent part of suchradiation is known [1].
Regardless of the source of radiation (Cherenkov (CR),
Synchrotron (SR), or TR), the spectral response of theelectron bunch can be represented as following [2],(T (λ ) = S (λ ) N + N ( N − 1) F3 D (λ )

2

)

(1)

where S (λ ) is the spectrum of a single particle, λ iswavelength, N is the number of particles in the bunch, F3D
is the 3-D Fourier transform of the bunch particle
distribution, called the form factor,
F3 D (λ ) = F (λ ) FT (λ )(2)where F and FT are longitudinal and transverse form
factors respectively. Coherent part of radiation is
proportional to the number of emitters squared, thus it
gives a much stronger signal than the incoherent part. It isalso a function of a form factor which depends on the
shape of the bunch. If a longitudinal modulation of acertain period λ0 (micro-bunching) is introduced to thebunch with longitudinal Gaussian distribution of rms sizeσ, such modulation would change the form factor
resulting in enhancement of a corresponding frequency ofradiation and its harmonics.

()⎛ ∑ h (λ ) ⎞⎟⎟⎝⎠F (λ ) = exp − 2π 2σ 2 / λ 2 ⎜⎜1 +

(

n

0

(3)

n

)

(

where hn = a n exp − 2n 2 π 2σ 2 / λ 20 cosh 4nπ 2σ 2 / λλ 0 is
the modulation factor, n and an are the harmonics number____________________________________________*Work supported by US Department of Energy#
rodion@ucla.edu)

and its weight respectively. Such radiation would beanalyzed and a temporal distribution of the electron beam
could be deducted.

Coherent Cherenkov Radiation in the Aerogel
Cherenkov radiation induced by a single particle can be
expressed in terms of number of photons per unit
frequency,
∂N Ch
ph
(4)
= Lαθ c2 δ (θ − θ c )∂k∂θhere α is the fine structure constant, θc is Cherenkov
angle, L is the length of the electron path in the medium.
In the case of a bunched electron beam, the total numberof photons for Coherent Cherenkov Radiation (CTR) canbe expressed as the following,2
N Ch
ph ≈ π LN

α 2 22a n θ c FT (λ )σ(5)We are particularly interested in using the aerogel as a
medium for CTR. Aerogel, or ‘frozen smoke’ is a lowdensity solid-state material made by high temperature andpressure-critical-point drying of a gel composed ofcolloidal silica structural units filled with solvents [3].
Table 1: Aerogel Parameters
Parameter

Value

Material

SiO2

Density

20 kg/m3

Refractive Index, n

1.008

Cherenkov Angle, θc

7.25O

Melting Point

1200OCIts low density provides nearly non-destructive tool forthe electron beam diagnostics (see Table 1) and its small
refractive index n=1+Δ gives a small Cherenkov angle
θ c ≈ 2Δ .
The form factor (and consequently, the enhancement ofcoherent radiation) depends on the transverse shape of theelectron beam as well. A Gaussian transverse distributionf ( ρ ) ∝ exp(ρ 2 / 2σ T2 ) leads to suppression of shorter
wavelengths (see Fig. 1), unless the transverse size σT is
infinitely small. The corresponding form factor is givenby the following:
FT (λ ) = exp − 2π 2θ c2σ T2 / λ2
(6)This could be overcome if other transverse shapes are
employed. For example, transverse hard-edge distribution()

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MOPPH034

Proceedings of FEL 2007, Novosibirsk, Russia

theoretically is challenging due to partial coherence
between different elementary waves emitted by different
parts of an electron path [6]; but its upper limit is easily
set to be the total length of the medium L, which is in ourcase is 2.5 mm. Hence, the lower limit for Δθ is 14 mrad.

EXPERIMANTAL SET-UP
The Neptune facility at UCLA consists of a 15 MeV
Photoinjector linac which can provide a charge of up to
0.5 nC and a CO2 laser with peak energy of up to 100 J[7]. Using a CO2 regenerative amplifier (10.6 um) with 510 MW of power, we expect the electron beam to be fully
Table2: Neptune Bunching Experiment Parameters

Fig. 3: Number of photons of the Cherenkov radiationinduced by 160 pC electron beam for Gaussian and hardedge transverse distributions.

Parameter

Value

Undulator Length

33 cm

f ( ρ ) ∝ rect σ ( ρ ) gives a stronger signal than the

Undulator Period, λ u

3.3 cmGaussian, see Fig. 1. The corresponding form factor is

Undulator Constant, Ku

1.8Electron Energy

12.4 MeVElectron Charge

100 pC

Normalized Emmitance

5 mm-mrad

Laser Energy

1 mJ

Angular Distribution of the Cherenkov
Radiation

Laser Pulse Length

200 psLaser Intensity, I

1 GW/cm2

The delta-function nature of the theoreticalrepresentation for the angular distribution of Cherenkov
radiation makes unrealistically strict requirements for thetransverse emittance of the electron beam. Indeed, spatial
coherence of radiation is not achievable unless all theelectrons trajectories in the medium are perfectly parallel.
To treat the problem properly, one needs to take into
account the fact that the speed of an electron decreases bya small jump every time a photon is emitted. Interestingly,
this process is analogues to a spectral line broadening due
to finite life of an excited state.
L.I. Schiff [5] treated this problem and got thefollowing distribution for intensity of Cherenkov
radiation as a function of an angle between the directionof the motion of an electron and direction of radiation:sin 2 y(8)
I (θ ) = I (θ c ) 2
y
where
l
(9)
y = 2π (cosθ c − cosθ )λLaser Beam rms Size

0.65 mmT

FT (λ ) =(J1 2π θ σ / λ
2π θ σ / λ
2

2 2
c T
2 2 2
c T

2

)

(7)

Hard edge distribution is not the only one that gives agood response in the high frequency range. Other
techniques such as putting a grid of wires across the beam
could be used [4].

l is the length of a free path. Distribution (8) has a certain
width. Let Δθ to be FWHM of (8), i.e.,
I (θ c + Δθ / 2) = I (θ c − Δθ / 2) = I (θ c ) / 2 or sin y = y / 2 , andy ≈ 1.4 ; therefore from (9) it follows thatΔθ ≈ 2.8 /(2πl(10)
sin θ c )λFinding the exact value for the length of the free path l
FEL applications

96

bunched after traversing a 10 period undulator tuned tothe 7th harmonic of the laser [8], see Table 2.

SUMMARY
A novel method for micro-bunching diagnostics of anelectron beam using aerogel has been analyzed and will
be tested at Neptune facility at UCLA. By measuring therelative intensities of different harmonicas the whole
longitudinal modulation can be reconstructed. The lower
limit for the angular width of the Coherent Cherenkov
Radiation was found to be 14 mrad which corresponds tothe beam parameters available at the Neptune facility.

REFERENCES[1] R. Tikhoplav, PhD Dissertation (2006).
[2] O. Grimm, et al., DESY April 24, 2006 Internalreport (2006).
[3] http://stardust.jpl.nasa.gov/tech/aerogel.html[4] G. Gatti, et al., Proc. of 2007 Part. Accel. Conf. 998(2007).
[5] L.I. Schiff, Quantum Mechanics (1949).
[6] J.V. Jelley, Physics-Uspekhi 58, 231 (1956).
[7] http://pbpl.physics.ucla.edu[8] P. Musumeci, et al., these proceedings.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH036

FIRST EXPERIENCES WITH THE FIR-FEL AT ELBE
U. Lehnert, P. Michel, W. Seidel, G. Staats, J. Teichert, R. Wünsch
Forschungszentrum Dresden-Rossendorf e.V., 01314 Dresden, Germany
Abstract
We show the design and the parameters of operation of
the long-wavelength (U100) FEL at ELBE. First lasing
has been shown in August, 2006. Since then, the laser has
undergone thorough commissioning and is available foruser experiments since fall, 2006. Besides in-house users
the IR beam is available to external users in the FELBE(FEL@ELBE) program witch is a part of the integrated
activity on synchrotron and free electron laser science inthe EU. At the beginning of 2007 lasing in the full
designed wavelength range from 20 µm to 200 µm wasdemonstrated. The laser power typically reaches several
Watts in cw operation but drops for very longwavelengths depending on the size of the used outcoupling hole. However, there exists a serious problem
with small gaps in the wavelength spectrum. We attribute
this behaviour to the transmission characteristics of theovermoded partial waveguide used from the undulator
entrance to the first mirror.

INTRUDUCTION
At Forschungszentrum Dresden-Rossendorf, Germany,
the radiation source ELBE (Electron Linac with highBrilliance and low Emittance) operates on the basis of asuperconducting linear accelerator for electron energies
up to 40 MeV with an average beam current of 1 mA in
quasi continuous wave (cw) mode. The electron linac
serves as a driver to generate several kinds of secondary
radiation and particle beams. Two free-electron lasers
generate radiation in the mid and far infrared for a verylarge field of applications reaching from semiconductor
physics to biology. In addition, MeV Bremsstrahlung for
nuclear (astro) physics, monochromatic hard-X-ray
channelling radiation for radiobiological experiments, andin near future also neutrons and positrons for studies innuclear reactor science and materials research areprovided. The quality and range of the provided beams
will be extended even further when the superconducting
photo-electron gun [1] which is tested at present will
become operational. The first FEL to become operational
at ELBE was the mid-IR FEL [2] using two undulatorswith 27.3 mm period. With the available beam energies it
covers a wavelength range from 3-24 µm. To extend thewavelength range into the far-IR a second FEL with a 100
mm period [3] undulator was installed. It now provides
laser light from 20-200 µm. After first lasing in August,2006 it is in routine user operation since fall, 2006. The
relevant user facilities comprise 6 optical laboratories.
Some of these are also used by in-house groups, mainly inthe areas of semiconductor physics, and radiochemistry,and experiments there will require a certain level ofcollaboration with the in-house researchers. In particular
noteworthy is the fact that a number of additional opticalsources from the visible to the THz frequency range areavailable, e.g. for two-colour pump-probe experiments.
These sources (Ti:sapphire laser and amplifier, OPO,
OPA, broad-band THz generator) are all based on
Ti:sapphire oscillators which are synchronized to the FEL
with an accuracy better than a ps. Two laboratories areintended to provide users with utmost flexibility for theirown experiments, also in scientific areas not covered byin-house groups (e.g., surface physics, molecularphysics).

U100-FEL SETUPThe FIR-FEL at ELBE (see Fig. 1) uses a hybrid
undulator with 100 mm period length. It consists of 38
periods equipped with SmCo magnets which were chosen
due to their better radiation resistance with respect to
NdFeB. With a minimum gap of 24 mm a maximum Krms
parameter of 2.7 is reached. The whole wavelength range
from 20-200 µm is covered with electron beam energies
from 20-35 MeV. To allow small undulator gaps awaveguide optical beam transport through the undulator isnecessary. The ELBE FIR-FEL uses a partial waveguidespanning from the undulator entrance to the downstream
mirror. The interior height was chosen to 10 mm. In
horizontal direction the waveguide is wide enough toallow essentially free propagation. Thus, an overmoded
parallel-plate waveguide is formed which shows low
losses for the principal mode. The downstream mirror wasplaced as a cylindrical mirror inside the waveguide. On
the upstream side the optical beam propagates freely
through the focusing quadrupoles and the dipole to a
toroidal mirror. To optimize the coupling between the
waveguide mode and the free propagation the horizontal
curvature of both mirrors was chosen to correspond to aRayleigh range of 180 cm. The vertical curvature of the
upstream mirror, however, equals its distance of 361 cm
from the waveguide entrance. Round-trip optical losses
inside the U100 resonator were computed using the
GLAD [4] code. The mode conversion between
waveguide and free propagation was approximated taking
only the fundamental waveguide mode into account. The
efficiency computed this way is above 94 % for all
wavelengths yielding a reasonably high Q of the opticalresonator. To allow for a near-optimum out-coupling over
the whole wavelength range the upstream mirror chamber
is equipped with three interchangeable mirrors ofidentical curvature but with 2.0, 4.0 and 7.0 mm outcoupling holes.

FEL operation

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MOPPH036

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 1: The setup of the FIR-FEL of ELBE. The electron beam enters from the right side through the blue bending
magnet and quadrupole triplet. The upstream mirror chamber contains three interchangeable mirrors with different
size out-coupling holes.

FEL OPERATION AND DIAGNOSTICS
Since the FEL gain is linearly proportional to the beam
peak current it is highly desirable to minimize the electron
bunch length in the vicinity of the undulator.
Accordingly, calculations of the laser gain yield an
optimum at minimum bunch length (see Fig. 2), eventhough this is bought at the expense of an increased
energy spread of the electron beam. When tuning theelectron beam the bunch length can be optimized by
maximizing the signal of coherent optical transition
radiation from a viewscreen. For the mid-IR FEL we havethis way reached a minimum 1.5 ps bunch length for an
optimized beam. It turns out, however, that for the startupof the FIR laser it is way more critical to minimize theenergy spread of the beam even though adjusting theaccelerator for energy spread drastically increases thebunch length at the undulator. The optical losses inside
the U100 resonator do not exceed 6 % per pass (see Fig.
3), even when only the lowest order hybrid waveguidemode is considered. When out-coupling is included thelosses rise by approximately twice the out-coupledfraction due to diffraction losses at the hole. These
calculations are in good agreement with a recently
measured value of 10 % loss per pass at 30 µm
wavelength with the 2 mm out-coupling hole. The
calculated average FEL output power reaches levels of 50
W for both maximum electron energy and undulator K
parameter. In practise about 12 W were measured anddelivered for user operation (see Fig. 4). To measure theenergy spectrum at the exit of the FEL has proven an
extremely versatile tool to start-up the lasing and to
optimize the FEL operation. In the mid-IR FEL one
typically can see the spontaneous emission and somespikes of increased intensity which one can use to
FEL operation

98

Figure 2: Computed small-signal gain in the low-gain
approximation.

Figure 3: Round-trip losses of the optical beam in
the U100 optical resonator. The black line shows themode conversion losses only. The coloured data
additionally include the out-coupling and diffraction
losses at different out-coupling hole sizes. At 30 µm
the 10 % loss per pass could be confirmed by cavity
ring down measurements.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH036

INACCESSIBLE WAVELENGTH

Figure 4: Typical output power of the FEL in CW
operation. The best measured values are higher for
most wavelengths but do not fully reach thepredictions. For small wavelengths the computations
show low power output due to high optical losses
which was not seen this significantly in theexperiment.

While the combination of a partial waveguide in theundulator up to the downstream mirror with free opticalpropagation between the undulator entrance and the
upstream mirror showed a reasonably high Q in theory
there seam to be problems in practice. We made theobservation that at some particular wavelengths it is
impossible to start the laser. In addition, the optical
spectra show well-defined suppressed wavelengths
distributed over the whole range of operation. One
example for this is shown in Fig. 6. At a fixed setting of
the electron beam, the emission wavelength of the FEL
was shifted by changing the undulator gap. For all
recorded spectra the emission is suppressed at 30.3 µm
wavelength with a marked drop in efficiency and output
power when the nominal lasing wavelength just meets thedropout. An absorption line in the optical beam path tothe diagnostic station can be excluded because thesuppression effect is seen in the energy spread of theelectron beam as well.

optimize the tuning until the laser starts. In the FIR-FEL
the detection efficiency of our normally used reference
detector is too low to see the spontaneous emission or
small spikes of lasing startup. One, however, immediately
notices the increase in energy spread on a viewscreen in
the dispersive section after the FEL as soon as the FEL
starts. It is even possible to use the energy spread as ameasure for the amplitude of the optical field inside theresonator. Fig. 5 shows the energy spectrum when tuning
the length of the optical resonator.

Figure 6: Optical spectra of the laser output shifting thenominal FEL wavelength over a wavelength gap at
30.3 µm.

Figure 5: Energy spectra of the electron beam after
passage through the FEL. The red trace shows the
spectrum for a negative optical cavity detuning where
the laser is off. Over green to blue the colours than
indicate an increasing detuning with laser action. For
minimum detuning (brown trace) the maximum power
is out-coupled from the electron beam with someelectrons loosing about 2 % of their initial energy.
One notes that a certain fraction of the beam does nottake part in the laser interaction and remains
unchanged in energy.

We presently try to explain this effect with aninterference of different optical waveguide modes. The
re-circulated optical beam mainly couples into thefundamental transverse waveguide mode essentiallyspread over the whole waveguide gap. The light createdby the laser interaction inside the undulator, however, isemitted in a localized area where the much smaller
electron beam overlaps with the optical beam andtherefore has a completely different mode structure. We
have tried, to compute the phase of the emitted radiation
with respect to the fundamental mode assuming a certain
combination of modes which yields an angular emission
pattern known for undulator radiation. This is propagatedthrough the waveguide to the downstream mirror andback to the exit of the waveguide and yields the phasetransfer function pictured in Fig. 7. It is obvious that forphase angles larger than π/2 the gain vanishes or evenbecomes negative due to destructive interference with thecirculating fundamental mode. Fig. 8 compares therelative gain computed in this strongly simplified modelto the wavelengths at which we have observed difficulties

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MOPPH036

Proceedings of FEL 2007, Novosibirsk, Russia

to start lasing or drop-outs in the measured wavelength
spectra. Obviously, the match is not perfect and further
detailed study of the phenomenon is required.

Activity on Synchrotron and Free Electron Laser Science(IA-SFS)'', which comprises most synchrotron and FEL
facilities in Europe and provides financial support to users
from EC and associated states. Instructions for beam time
applications are available on the FELBE website(www.fzd.de/FELBE). A world novelty is the possibility
to use the Elbe IR radiation for experiments in highmagnetic fields. The beams of both FELs can be delivered
into the new High Magnetic Field Lab Dresden (HLD)[5,6] which was built recently in immediate vicinity to the
ELBE building. First experiments have been run this year
and scientific results are soon to be expected.

REFERENCES

Figure 7: Transfer function of the waveguide for light
generated with a gaussian profile at the interaction
with the electron beam.

Figure 8: Computed relative FEL gain over the
wavelength range. The green lines denote wavelengths
at which the FEL was operated so far. The red stripes
underline areas in which we had problems to start thelasing and blue lines show wavelengths at which the
FEL showed prominent drop-outs in the optical
spectrum.

OUTLOOK
Since first lasing in August, 2006, the FIR-FEL at
ELBE was commissioned successfully and has since been
put into full user operation. The full wavelength range has
been demonstrated with the major beam parameters
meeting specifications. With this, ELBE is established asa radiation source for the whole IR range from 3 to 200µm. Both FELs are operated as a user facility, being open
to users worldwide, provided their scientific proposals
have been favourably evaluated by the panel responsiblefor distribution of beam time. Under the name ``FELBE''
the facility is member of the EC funded ``Integrating

FEL operation

100[1] C. A. Arnold, H. Büttig, D. Janssen, T. Kamps, G.
Klemz, W.D. Lehmann, U. Lehnert, D. Lipka, F.
Marhauser, P. Michel, K. Möller, P. Murcek, Ch.
Schneider, R. Schurig, F. Staufenbiel, J. Stephan, J.
Teichert, V. Volkov, I. Will and R. Xiang,
Development of a superconducting radio frequency
photoelectron injector, Nuclear Instruments andMethods in Physics Research A 577 (2007) 440-454[2] P. Michel, P. Evtushenko, U. Lehnert, T. Dekorsy, F.
Gabriel, E. Grosse, M. Helm, M. Krenz, W. Seidel,
D. Wohlfarth, A. Wolf, R. Wünsch, First Lasing at
the ELBE mid-IR FEL, 26th International Free
Electron Laser Conference FEL 2004, Trieste, Italy[3] E. Grosse, U. Lehnert, P. Michel, R. Schlenk, W.
Seidel, A. Wolf, U. Willkommen, U. D. Wohlfarth,
R. Wünsch, A Far-Infrared FEL for the Radiation
Source ELBE, 27th Free Electron Laser Conference
FEL 2005, Palo Alto, USA[4] GLAD, Applied Optics Research, Woodland, WA
98674, USA[5] F. Pobell, A.D. Bianchi, T. Herrmannsdörfer, H.
Krug, S. Zherlitsyn, S. Zvyagin, J. Wosnitza, The
New High Magnetic Field Laboratory at Dresden: aPulsed-Field Laboratory at an IR Free-Electron-Laser
Facility AIP Conference Proceedings 850 (2006)
1649[6] J. Wosnitza, A.D. Bianchi, J. Freudenberger, J.
Haase, T. Herrmannsdörfer, N. Kozlova, L. Schultz,
S. Zherlitsyn, S.A. Zvyagin, Dresden Pulsed
Magnetic Field Facility, J. Magn. Magn. Mat. 310(2007) 2728

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH040

A STUDY OF DETECTION SCHEMES IN ELECTRO-OPTIC SAMPLINGTECHNIQUE*
Y. W. Parc#, I. S. Ko, POSTECH, Pohang 790-784, Korea
J. Y. Huang, C. Kim, PAL, Pohang 790-784, Korea
Abstract
Electro-Optic Sampling (EOS) is the ingenious tool forthe measurement of the electron beam. There are two
traditional detection schemes: one is the crossed polarizer
scheme and another is balanced detection one. A newdetection scheme called ‘Near Crossed Polarizer’ (NCP)
scheme in the EOS technique is developed to increase thesignal to noise ratio (SNR) in the experiment. The newdetection scheme is studied in detail and the 3D scanning
result with electron beam in FLASH is compared with thedetection scheme.

INTRODUCTION
The detection schemes for EOS measurement arestudied in theoretically and experimentally also. Two
traditional detection schemes are the crossed polarizer andthe balanced detection scheme. Those have each difficulty
to be applied in real diagnostic in the EOS measurementof the electron beam. To overcome those difficulties, newdetection scheme called ‘Near Crossed Polarizer’ scheme
is developed. In this letter, the detail study of the NCP
scheme is shown with 3D scanning result of the EOS
measurement.

THEORYEO crystals such as ZnTe and GaP have a character ofbirefringence materials when the electric field is applied
to the crystal. The refractive index of the crystal can becalculated from the constant energy surface in the electric
displacement vector space and the impermeable tensor
that is linear to the electric field strength. The refractive
index can be found from the refractive index ellipsoidequation by a principal-axis transformation [1, 2]. The
two main refractive indices n1, n2 of the crystal along theprincipal axes are given by

n03r41 E
23
nr E
n2 = n0 − 0 41
2n1 = n0 +(1)

where n0 is the initial refractive index, r41 is the electrooptic constant, and E is the electric field applied to the
crystal. The difference of the propagation speeds of eachlaser component, which is due to the different refractive
indices, changes the polarization of the incident laser
pulse. This brings the relative phase shift, Г, between thehorizontal component of the laser pulse and the verticalone, which is given by

πd 3
(2)
n0 r41 Ec
λ0
where d is the crystal thickness, ω0 is the mean angularfrequency of the laser pulse, c is the speed of light, λ0 is
the mean wavelength of the laser pulse, and E is theelectric field applied to the crystal.
Γ=

ω0 d

( n1 − n2 ) =Detection schemes
There are two traditional methods to detect thepolarization change; the crossed polarizer scheme andbalanced detection one. In the crossed polarizer scheme,
the laser intensity is measured by a polarizer and a
detector. The analytic expression of the intensity
difference ΔI in the case of the crossed polarizer scheme
is given by [1, 2]

ΔI = I 0 sin 2 ( Γ / 2 )(3)where Γ is the relative phase shift between the twopolarized parts of the laser field and the I0 is the initialintensity of the laser pulse. There is another method todetect the polarization change called balanced detection
scheme. In the balanced detection scheme, the laser
intensity is measured by a quarter-wave plate, a polarizer
and two detectors. The quarter-wave plate enhances therelative phase shift by a quarter of one wave length. The
analytic expression of the intensity difference ΔI in thecase of balanced detection scheme is given by [1, 2]

ΔI ≡ I h − I v = E h − E v = I 0 sin ( Γ )
2

2

(4)

where all parameters are same with above Eqs., h and v
represent ‘horizontal’ and ‘vertical’ each. When therelative phase change Γ is 7o in the crossed polarizer
scheme, the change of the initial laser intensity is merely
0.37% from Eq. (3). This signal change is too low to be
detected in real diagnostics setup. However, in thebalanced detection scheme, there is 12% change of theinitial laser intensity from Eq. (4) for the same Γ. The
signal level is high enough to detect, but the balanced
method is difficult to apply in real diagnostic setup. To
overcome those difficulties, a new method called Near
Crossed Polarizer (NCP) scheme is developed. In the newdetection scheme, the laser intensity is measured by aquarter wave plate, a half wave plate, a polarizer, and a
detector. The intensity with NCP scheme is calculated by
the multiplication of the Jones matrices of the each wave
plate [3]. The calculated intensity is given by

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Proceedings of FEL 2007, Novosibirsk, Russia

I (θ , ϕ , Γ )= ⎣⎡1 + cos ( Γ + 2ϕ − 4θ ) sin 2 ϕ − cos ( Γ − 2ϕ + 4θ ) cos 2 ϕ ⎦⎤ / 2= ⎡⎣1 − cos ( Γ ) cos ( 4θ − 2ϕ ) cos ( 2ϕ ) + sin ( Γ ) sin ( 4θ − 2ϕ ) ⎤⎦ / 2……………………………………………….(4)where the θ is angle of the half wave plate, φ is angle ofthe quarter wave plate and the I0 is the initial laser
intensity incident to the EO crystal. The signal level andbackground also are changed according to the angles of
the half and quarter wave plates. In Fig. 1, theexperimental layout with the NCP scheme is shown.

Fig. 3. The intensity with ‘crossed polarizer scheme’
when Г is 2 degree. θ is the angle of half wave plate forcompensation and φ is the angle of quarter wave plate.
Note that y axis is normalized by the initial laser intensity.
FIG. 1. Layout of the electro-optic sampling.

In Fig. 4, the measurement result of the theoreticalprediction shown in Fig. 3 is plotted.

In Fig. 2, there is a measurement result of the electron
beam with the NCP scheme in FLASH [4].

Fig. 2. The typical measurement of the electron beam in
FLASH. In this measurement, the quarter wave plate is
set as -4 degree and the half wave plate is set as -2 degree.
The GaP crystal thickness used in this measurement is
180 μm. The distance between the electron beam and the
crystal is 1.5 mm on average. The electron beam energy is
800 MeV and the total electron beam charge is 0.8 nC.

3D view of the signal in NCP scheme
In Fig.3, the theoretical intensity change of EO signal
by half and quarter wave plate is shown with 3D plotwhen Г is 2 degree. The background intensity change
which means Г is 0 degree is not shown in this paper,
however the behaviour of the two graphs is similar.

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102

Fig. 4. The intensity with ‘crossed polarizer scheme’measured in FLASH. θ is the angle of half wave plate forcompensation and φ is the angle of quarter wave plate.
Note that y axis is not normalized by the initial laser
intensity. The unit is same with the Fig. 2 i.e. the ICCDunit.

SCANNING RESULT IN TEO SETUP IN
FLASH
The half and quarter wave plates are scanned to find thebest condition to measure the electron beam. In Fig. 5, thetheoretical prediction of the SNR function in 3D view isProceedings of FEL 2007, Novosibirsk, Russia
shown, in which the peak position is where the θ = 0 and
φ = 0 because the theoretical background is 0.

MOPPH040

In Fig. 6, the peak position is not at θ = 0 and φ = 0 pointdue to the leakage of the laser due to the imperfection of
the polarizer. The background is not 0 even at θ = 0 and φ= 0, so the denominator of the SNR function is not 0. Thatmakes the shift of the maximum position of SNR. With θ= 0 and φ = 0, the NCP scheme is same with the CP
scheme, that means the level of signal is quite low to be
detected in some situation. In the real diagnostics
experiment, the maximum SNR point should be searchedin each diagnostics setup to make balance between the
SNR and the absolute signal level to be detected withgood resolution.

ACKNOWLEDGMENT
Fig. 5. Theoretical prediction of SNR. θ is the angle ofhalf wave plate for compensation and φ is the angle ofquarter wave plate.
There is a region lower than 1 which means the signal islower than the background. This can be occurred atcertain angles of the half and quarter wave plate, because
the changed polarization of the laser pulse with the angles
is decreased by the modulation of EO crystal.
In Fig. 6, the experimental result of the SNR function
in 3D view is shown.

This work was supported by Grant No. R01-2006-00011309-0 from the Basic Research Program of the Korea
Science & Engineering Foundation and the Center forHigh Energy Physics (CHEP) at the Kyungpook National
University. One of authors (Y. W. Parc) extends his thanks
to DESY for the hospitality during his stay (2006.11 ~2007.04).

REFERENCES[1] M. Bruken et al., TESLA Report 2003-11 (2003).
[2] S. Casalbuoni et al., TESLA Report 2005-01 (2005).
[3] B. Steffen, “Electro-Optic Methods for Longi-tudinal
Bunch Diagnostics at FLASH” Thesis, The
University of Hamburg (2007).
[4] private communication with A. Azima in DESY.

Fig. 6. SNR measured in FLASH. θ is the angle of halfwave plate and φ is the angle of quarter wave plate.

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COMPARATIVE STUDY OF ELECTRO-OPTIC EFFECT BETWEENSIMULATION AND MEASUREMENT *Y. W. Parc#, I. S. Ko, POSTECH, Pohang 790-784, Korea
J. Y. Huang, C. Kim, PAL, Pohang 790-784, Korea
Abstract
Electro-Optic Sampling (EOS) is a promising method
to measure various properties of the electron beam nondestructively. In this Letter, a rigorous analysis procedureof the electro-optic (EO) measurement is introduced. The
measured data of electron beam by electro-optic
technique is analyzed in terms of the relative phase shift
between the horizontal and the vertical components of thelaser. A simulation study is done with the pulse
propagation method, which utilizes Fourier transform toinvestigate the evolution of an electromagnetic pulse
inside the EO crystal. The analysis result of the EO
measurement expressed in terms of the relative phaseshift is compared with the simulation, and they show agood agreement.

INTRODUCTION
Non-destructive measurement of the electron bunch
length with femtosecond resolution is one of essential
issues to operate XFEL facilities successfully [1]. During
last several years, the EOS method has been successfully
implemented to measure femtosecond electron bunches
and arrival time at FELIX, SPPS, and FLASH facilities[2-8].

where d is the crystal thickness, ω0 is the mean angularfrequency of the laser pulse, c is the speed of light, λ0 is
the mean wavelength of the laser pulse, and E is theelectric field applied to the crystal.

Detection scheme
A new method called Near Crossed Polarizer (NCP)
scheme is developed. In the new detection scheme, thelaser intensity is measured by a quarter wave plate, a halfwave plate, a polarizer, and a detector. The intensity with
NCP scheme is calculated by the multiplication of theJones matrices of the each wave plate [11]. The calculated
intensity is given by

I (θ, ϕ, Γ) / I0
= ⎣⎡1−cos( Γ) cos( 4θ −2ϕ) cos( 2ϕ) +sin( Γ) sin( 4θ −2ϕ) ⎦⎤ /2(3)

where θ is angle of the half wave plate, φ is angle of thequarter wave plate, and I0 is the initial laser intensity
incident on the EO crystal. The signal level and thebackground are also changed according to the angles of
the half and the quarter wave plates. The signal to noise
ratio can be increased by the control of the angle of theplates [12].

THEORYEO crystals such as ZnTe and GaP have a character ofbirefringence materials when the electric field is applied
to the crystal. The refractive index of the crystal can becalculated from the constant energy surface in the electric
displacement vector space and the impermeable tensor
that is linear to the electric field strength. The refractive
index can be found from the refractive index ellipsoidequation by a principal-axis transformation [9, 10]. The
two main refractive indices n1, n2 of the crystal along theprincipal axes are given by
n03 r41 E
(1)
2
3
nr E
n2 = n0 − 0 41
2where n0 is the initial refractive index, r41 is the electrooptic constant, and E is the electric field applied to the
crystal. The difference in the propagation speeds, which isdue to the different refractive indices, changes thepolarization of the incident laser pulse. This brings therelative phase shift, Г, between the horizontal componentof the laser pulse and the vertical one, which is given by
ωd
πd 3
(2)
Γ = 0 ( n1 − n2 ) =nr Ecλ0 0 41

EXPERIMENTAt the FLASH facility in DESY, there is an EO
diagnostic section called Timing Electro-Optic (TEO)
setup to measure the electron beam properties. The TEO
setup is used to measure the bunch length and the timing
jitter of the electron beam by the spatial decoding methodwith GaP crystal as shown in Fig. 1 [8].

n1 = n0 +FEL operation

104

Figure 1. Layout of the electro-optic sampling.
In the spatial decoding method, the laser pulse ispropagated through the EO crystal with 45o angle, and thetiming information of the electron beam is converted tothe spatial information of the image measured by the
ICCD camera [5, 8].

Proceedings of FEL 2007, Novosibirsk, Russia
In order to study the electro-optic effect induced by theelectron beam, it is necessary to know the initial intensityof the laser as shown in Eq. (3). Normally, the initialintensity of the laser for the EO diagnostic is so high to bemeasured by ICCD camera directly without damaging
ICCD itself. Thus, the initial intensity of the laser is
extrapolated from the measured data with several anglesof the half wave plate using Eq. (3), where ICCD candetect the intensity of the laser passing through the EO
crystal and polarizer safely. If the angle of the quarterwave plate is fixed, the laser intensity at the ICCD iscontrolled by the half wave plate in front of the polarizer
as shown in Fig. 1. The extrapolated initial intensity of thelaser is 4466 which will be shown elsewhere.
A measurement result is shown in Fig. 2 which shows asignal with 47.6 unit of the ICCD at 12.6 ps position in
the measurement window.

MOPPH041

I (θ = 0o , ϕ = −2o , Γ ) = 47.6

4466 ⎡⎢1 − cos ( Γ ) cos ( −2 × ( −2 ) ) cos ( 2 × ( −2 ) ) ⎤⎥=2 ⎢ + sin ( Γ ) sin ( −2 × (−2o ) )
⎥
o

⎣

o

(4)

⎦

From the solution of Eq. (4), we can get the relative
phase shift Γ = 7.13o which represents that the laser
passing through the EO crystal is elliptically polarized.

SIMULATIONIn the simulation, the electric field inside the crystal iscalculated from the longitudinal profile of the electron
beam. The pulse propagation method, which utilizes
Fourier transform of the electric field to investigate theevolution of the electric field inside the EO crystal, isused in this simulation.
An electron beam with Gaussian charge distribution is
generated to simulate the measurement. The beam charge
Q is set as 0.06 nC and the rms pulse width σt of theelectron beam is set as 40 fs which corresponds to thebunch length of the electron beam 12 μm. The thicknessof GaP is the same 180 μm as the experimental condition.
Simulation results for different distances between theelectron beam and the crystal are shown in Fig. 3, and thepeak values for different distances are shown in Fig. 4.

Figure 2. Electron beam measurement by TEO setup at
FLASH. The GaP crystal thickness is 180 μm. The
distance between the electron beam and the laser at the
crystal is 2 mm on average. The half wave plate angle is
0o. The quarter wave plate angle is –2o.
There is a small peak at 16 ps position, which is
generated by the reflection of THz radiation at the backsurface of the EO crystal [10]. The time duration between
the main peak and the small one is determined by the
thickness of the EO crystal and the speed of THz
radiation in the EO crystal. The GaP crystal thickness
used in this experiment is 180 μm. It makes the travel
distance of THz radiation 360 μm which corresponds to
3.4 ps travel time. The radial distance from the electron
beam and the EO crystal can be controlled by a remotecontrol system. The radial distance between the electron
beam and the crystal in the measurement is 2 mm on the
average which can be known from the radiation detection
by glass optic fibers in FLASH [13].
The maximum relative phase shift Г of the measured
pulse can be calculated from Eq. (5) with the peak valueof the measured data in Fig. 2. In the measurement, theangle θ of the half wave plate is set to 0o and the angle φof the quarter wave plate is set to –2o. Analysis of thepeak in Fig. 2 with the initial laser intensity I0 = 4466 isshown asFigure 3. Simulation results: (a) The relative phase shift
Γ, and (b) the intensities from NCP scheme are shown.
The dash-dot line (top) represents the result of the
distance between laser and the EO crystal R = 1 mm, thedotted line (middle) represents the result of the R = 3 mm,
and the dashed line (bottom) represents the result of the R= 5 mm. The charge of the electron beam is 0.06 nC andthe rms pulse width is 40 fs. The half wave plate angle θis 0o and the quarter wave plate angle φ is –2o.

Figure 4. Simulation result for different distance R. (a)Maximum points of Fig. 6 (a) are plotted along R. The
data is fitted by Eq. (10) shown as a solid line. (b)Maximum points of Fig. 6 (b) are plotted along R. The
curve is the fitting result with Eq. (11).

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Proceedings of FEL 2007, Novosibirsk, Russia

SUMMARY
This Letter introduces a rigorous procedure to analyse
the EO technique to measure the electron beam nondestructively. The initial intensity of incident laser isobtained by the extrapolation of the data measured atlower intensity. Accurate relative phase shift obtained by
precisely estimated incident laser intensity and NCP
scheme provides EOS as a tangible technique for nondestructive measurement of electron beams. Simulation
results with the pulse propagation method are wellmatched with the analysis result of the measurement.

ACKNOWLEDGMENT
This work was supported by Grant No. R01-2006-00011309-0 from the Basic Research Program of the Korea
Science & Engineering Foundation and the Center forHigh Energy Physics (CHEP) at the Kyungpook National
University. One of authors (Y. W. Parc) extends his thanks
to DESY for the hospitality during his stay (2006.11 ~2007.04).

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106

REFERENCES[1] PAL/POSTECH, “4-th Generation Light Source
Conceptual Design Report,” November 2004.
[2] X. Yan et al., Phys. Rev. Lett., 85, p. 3404 (2000).
[3] I. Wilke et al., Phys. Rev. Lett., 88, p. 124801 (2002).
[4] G. Berden et al., Phys. Rev. Lett., 93, p. 114802(2004).
[5] A. L. Cavalieri et al., Phys. Rev. Lett., 94, p. 114801(2005).
[6] J. Rossbach et al., Eur. Phys. J. D, 37, p. 297 (2006).
[7] B. Berden et al., Proceedings of European Particle
Accelerator Conference 2006, Edinburg, Scotland, p.
1055 (2006).
[8] A. Azima et al., Proceedings of European Particle
Accelerator Conference 2006, Edinburg, Scotland, p.
1049 (2006).
[9] M. Bruken et al., TESLA Report 2003-11 (2003).
[10] S. Casalbuoni et al., TESLA Report 2005-01 (2005).
[11] E. Hecht, Optics, 4th ed., Addison-Wesley, Inc.,
2002, p. 377[12] private communication with B. Steffen in DESY
[13] private communication with A. Azima in DESY
[14] H. J. Bakker et al., J. Opt. Soc. Am. B, 15, p. 1795
(1998).

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH042

LOSSES IN OPTICAL RESONATOR OF NOVOSIBIRSK TERAHERTZFEL: THEORY AND EXPERIMENT
V.V. Kubarev#, BINP, Novosibirsk, Russia
Abstract
A direct comparison of the simple universal analyticaltheory used earlier to design an optical resonator for the
Novosibirsk terahertz free electron laser (NovoFEL) andnumerous subsequent experiments is presented. A good
agreement of the theory with the experiments is shown. A
possibility of future optimization of the optical resonator
is described.

INRODUCTION
Round trip losses are the main parameter of most laser
resonators. There are many different numerical methods
to calculate losses of resonators with given geometries.
However, an optimal geometry is not known when a newresonator is being created. A simple search for different
geometries is ineffective. In this case we need someanalytical theory. In [1], the author of this paper proposeda simple universal analytical method to calculate small
losses in stable open laser resonators. A comparison of themethod with well-known papers in which numerical [2, 3]
and cumbersome analytical [4] methods were used only
for certain types of losses and geometries shows a good
agreement.
On the other hand, the free electron laser gives us aunique possibility of direct experimental measurement ofsuch losses, which is practically impossible inconventional lasers due to the inertia of their active
media. First measurements of this type on NovoFEL withthe start optical resonator were published in [5]; theyshown a good agreement of the theory and experiment. In
this paper, a nominal optical resonator with larger output
coupling was investigated in a wider spectral range.

THEORY
Diffraction losses сi caused by different small
perturbations at the center of a Gaussian mode (openings)
and at its periphery (mirror apertures, diaphragms,
scrapers) are equal, according to [1], to double"geometrical" losses сi= 1 – (1 - cg)2 ≈ 2сg. Geometricallosses сg are a part of the mode cross-section overlapped(cut) by a perturbation. The total resonator losses can beevaluated as:cΣ = 1 − ∏ (1 − ci ) ≈ ∑ ci
i

(1)

i

This property of additivity for losses at the openings
and outer apertures of mirrors is shown in paper [1]. For
one-type aperture losses at the periphery of a beam(mirrors, diaphragms, scrapers), the additivity condition issatisfied if the elements with losses are divided by adistance exceeding the length La= d⋅δ/λ, where d and δ
are typical sizes of the mode and perturbation, and λ is the
wavelength. The mode fills the cutoff part of its peripheryat this distance. This condition is satisfied for the main
components of our resonator losses. The losses in othersections of the resonator can be ignored because of the
exponential sensitivity of the Gaussian beam to narrower
diaphragms.
The calculation model of our optical resonator aftersome optimization of diaphragm diameters and theirpositions is shown in Fig.1. Values of the diameters andaxial distances between the resonator center and thediaphragms are presented in Table 1. We assume that thediaphragms are full absorbing because many of them havea special absorbing ceramic coating [5] and the crosssection of vacuum pipes of our resonator is sufficiently
large.
Thus, the resonator losses per round trip (for removed
scrapers and symmetrical positions of all diaphragms to
the resonator center) are:cΣ = 1 − (1 − cmo ) 2 (1 − cmd ) 4 (1 − cmh1 ) 2 (1 − cmh 2 ) 2 ×× (1 − cd 1 )8 (1 − cd 2 )8 (1 − cd 3 )8 ,(2)
where cmo and cmd are the ohmic and outer aperture
losses of mirrors; cmh1 and cmh2 are the losses on openings
in the mirrors; cd1, cd2 and cd3 are diaphragm losses (pickup sensor aperture, banding magnet camera aperture, andundulator aperture, respectively). For simplicity, we use
one-index numeration of the losses in Fig.1, Table 1, andFig.6, according to equations (1) and (2).
From the well-known experimental data for opticalproperties of solid gold, we can obtain the ohmic losses ofour mirrors with gold coating: cmo=10-2(0.71-1.2λ [mm] ).
For losses of the Gaussian TEM00 - mode with theradial field distribution E ∼ exp(-r2/r02); r0 = {λLf /π [1+(z/Lf )2]}1/2, where Lf is the Rayleigh length, one canobtain the following formulas:
сdk,md = exp{-π dk Lf /[2λ(Lf + zdk,md )]}(3)

cmh = πdmh2/{2λLf[1+(L0/2Lf )2]},

(4)

2

2

2

where k =1, 2, 3 ; d is the diameter of the losses
component, and L0 = 26.589 m is the resonator length.
The dependences of total losses as functions ofwavelength for different Rayleigh lengths are shown in
Fig.2. The value Lf = 5 m and mirror radiuses R =L0[1+(2Lf /L0)2]/2 = 15 m were chosen as optimal in the

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Proceedings of FEL 2007, Novosibirsk, Russia

wavelength range from 100 to 300 µm. Different losses
components for this Rayleigh length are shown in Fig.6.
2

5

1
z

6

7

7

3

5

6

2
1
4

0

Though we checked many times the detector linearity inthe measurement of CW submillimeter power, we also
investigated the parameter for pulsed measurement. It iseasy to see in Fig.3 that our detector is also linear in this
case.
120

Schottky diode signal (mV)

100

Figure 1: Calculation model of the optical resonator.
Numbers at elements are i indexes according to equations(1) and (2).
Table 1: Diameters and positions of losses elements
Index i

Diameter d[mm]Position z
[mm]

2

190

13294.53913294.54

3.513294.5

5

105

7500

6

101

6300

7

78

4500

Losses (%)

100

10

80

60

40

20

0
0

20

40

60

80

100

Transmittance of attenuator (%)

Figure 3: Signal of the Schottky diode detector versus
transmission of the attenuator for working conditions of
the detector.
We measured the losses of the nominal opticalresonator just after its assemblage (in 2004) and recently(in June 2007) for a wider spectral range. The lastexperiment is shown in Fig. 4. Electron pulses of
NovoFEL were switched off at the time marked byarrows. After this time, light pulses decayed exponentiallyfor the wavelength range from 120 to 200 µm. The losses
were calculated as c = 1 – T/τ, where T = 177.4 ns is therepetition period of pulses, τ is the decay time of the best
exponential asymptotic. When the losses constituted about
twenty percent, we did not find an exponential power
decay. The losses for different periods averaged over four
oscillograms are shown in Fig.5. In this case, we assume
that the losses of the first decay period are more close toreal losses of the NovoFEL optical resonator in thestationary regime. Thus, it is this value that is used in acomparison with the theory in the next section.
0,02

1
0.1

0.15

0.2

0.25

0

Wavelength (mm)
-0,02
-0,04
Signal (V)Figure 2: Total losses per round trip of NovoFEL versus
wavelength for different Rayleigh lengths: Lf = 3 m(dotted line), Lf = 4 m (dashed line), Lf = 5 m (thick solidline), Lf = 6 m (dash-dotted line), Lf = 7 m (thin solidline).

a)

-0,06
-0,08
-0,1
-0,12
-0,14

EXPERIMENT
As before [5], we used in the experiments a detector on
the basis of the Schottky diode matrix with a travelingwave antenna in the corner cube reflector [6]. We
specially used a not the fastest Schottky detector to have asufficient number of measured points on one light pulse.
FEL operation

108-3,50E-06-1,50E-06

5,00E-07

2,50E-06

4,50E-06

6,50E-06

Time (s)Figure 4: Time evolution of NovoFEL light pulses afterswitch-off of electron pulses for radiation at awavelengths 129.8 µm (a). Switch-off time is shown byarrows.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH042

COMPARISON OF THE THEORY AND
THE EXPERIMENT

0,02
0

Signal (V)

-0,02
-0,04

b)
-0,06
-0,08
-0,1
-0,12
-3,50E-06-1,50E-06

5,00E-07

2,50E-06

4,50E-06

6,50E-06

Time (s)0,02Signal (V)

0

-0,02

c)
-0,04

-0,06

-0,08
-1,50E-06-5,00E-07

5,00E-07

1,50E-06

2,50E-06

Time (s)

0,04
0,02
0
Signal (V)

-0,02
-0,04

d)

-0,06
-0,08
-0,1

A comparison of the theory and the experiment ispresented in Fig.6. Different lines in the figure show
various components of losses and total round trip losses
according to the scheme of Fig.1 and expressions (1)-(4).
We can see that the main components of losses for shortwavelengths are hole losses whereas in the longwavelengths range these are diaphragm losses. Two setsof experimental points were measured in 2004 and 2007.
We can see that there is a good agreement of the theory
and the experiment within the accuracy of the calculationand measurement (≈ 10 %).
Nevertheless, we can assume that experimental losses
somewhat exceed theoretical values. A first probableexplanation of this can be some depreciation of theoreticalohmic losses in the mirrors, especially in the shortwavelengths range. These losses were calculated for an
ideal optical solid gold surface. The real surface of ourmirrors is a diamond machined copper surface of opticalquality with a gold coating.
Most out-of-order experimental point for λ =152.5 µm
was measured in regime with modulation sideband
instability, which probably has a small influence on themode intensity distribution. We plan to repeat theexperiment with damped sideband instability.
Another possible correction of the long-wavelengths
losses is connected with inexact axial position of theabsorption diaphragms (Fig.1). Geodetic measurements
give such transversal displacements of the diaphragms,
which increase the total losses for λ = 200 µm by 1 %.
100

-0,12
-0,14
-2,00E-06-1,00E-06

0,00E+00

1,00E-06

Time (s)60

Losses (%)

50

10

Losses (%)

Figure 4: Time evolution of NovoFEL light pulses afterswitch-off of electron pulses for radiation with different
wavelengths: 152.5 µm (b), 197.3 µm (c), and 229.4 µm(d). Switch-off time is shown by arrows.

1

40
30
20

0.1
0.1

10

0.12

0.14

0.16

0.18

0.2

0.22

0.24

0.26

0.28

0.3

Wavelength (mm)

0
1

2

3

4

5

6

7

Period number

Figure 5: Losses averaged over four oscillograms versus
the number of periods after switch-off for λ = 229.4 µm.

Figure 6: Theoretical (curves) and experimental (points)
losses of nominal NovoFEL resonator. Theoretical curves
fit the following notation in Fig.1: dotted line (1), dashedlines (3, 4), light gray line (2), gray line (6), dash-dottedline (5), and thin solid line (7); thick solid line is totalround trip losses. Experimental points: circles (2007
experiment), triangles (2004experiment).

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Proceedings of FEL 2007, Novosibirsk, Russia

PROBABLE OPTIMIZATION OF THE
OPTICAL RESONATOR
A probable optimization of the optical resonator is inincreasing of the useful part of optical resonator losses,
which is output power of NovoFEL. Now the power is
output through circular openings at the centers of mirrors.
According to the presented theory, additional diffraction
losses at the openings are equal to useful losses. Thus, if
we use some uniform output coupling system not
perturbing the mode intensity distribution, the NovoFEL
output power can be increased at least two times. A
Michelson interferometer with a CVD-diamond film
beam-splitter can be such a system. If the beam-splitter
thickness is 53 µm and the electric field vector of laser
radiation is perpendicular to the incident plane of thebeam-splitter, it can overlap optimally the entire operating
NovoFEL range. An additional possibility of the system istuning of optimal output coupling for different regimes
and wavelengths. The maximal value of output coupling
as a function of wavelength is shown in Fig.7. The output
coupling can be tuned from zero to this value. In the
figure, the present fixed useful output coupling is given
for comparison. Measured optical properties of CVDdiamond in terahertz range are presented in [7]. They
allow an installation of the material into optical resonator.
Thus, in the future the NovoFEL output power can beincreased more than two times with such sufficiently large
CVD-diamond film.
1
0.9
0.8

Output coupling

0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.12

0.13

0.14

0.15

0.16

0.17

0.18

0.19

0.2

0.21

0.22

0.23

0.24

Wavelength (mm)Figure 7: Maximal output coupling of tunable CVDdiamond Michelson output coupling system (solid line)
and present fixed output coupling through openings(dashed line).

CONCLUSION
Losses in the NovoFEL optical resonator were
measured in its operating range. There is a good
agreement between the measurements and a theory which
was used for design of the optical resonator. On basis of
the theory, upgrade the optical resonator is proposed. The
uniform tunable CVD-diamond output coupling system
can increase the NovoFEL output power more than twotimes.
FEL operation

110

REFERENCES[1] V.V. Kubarev, “Babinet principle and diffraction
losses in laser resonators”, Quantum Electronics 30(2000) 824-826.
[2] T. Li, “Diffraction losses and selection of modes inmaser resonators with circular mirrors“, Bell Syst.
Techn. J. 44 (1965) 917-932.
[3] D.E. McCumber “Eigenmodes of a symmetriccylindrical confocal laser resonator and theirperturbation by output-coupling apertures”, Bell Syst.
Techn. J. 44 (1965) 333-363.
[4] V.V.Lyubimov, I.B. Orlova “Approximate calculationof oscillations in resonators with concave mirrors”,
Opt. Spectrosk. 29 (1970) 29.
[5] V.V. Kubarev, B.Z. Persov, N.A. Vinokurov, A.V.
Davidov, “Optical resonator of powerful free-electron
laser”, Nucl. Instr. & Meth. A 528 (2004) 199-202.
[6] V.V. Kubarev, G.M. Kazakevich, Y.U. Jeong, B.J.
Lee, “Quasi-optical highly sensitive Schottky-barrier
detector for a wide-band FIR FEL”, Nucl. Inst.&
Meth. A 507 (2003) 523-526.
[7] V.V. Kubarev, “Optical Properties of CVD- diamondin Terahertz Range and Its Applications on the
NovoFEL”, Proc. of conf. IRMMW-THz 2007,
Cardiff, Great Britain, September 2-7, 2007.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH043

CONTROL AND DIAGNOSTIC SYSTEM FOR NOVOSIBIRSK FELRADIATION
V.V.Kubarev, E.V.Makashov, K.S.Palagin, S.S.Serednyakov. Budker Institute of Nuclear Physics,
630090, Novosibirsk, Russia.
1.

Abstract
The architecture and main capabilities of the control
and diagnostic system for the Novosibirsk FEL coherent
radiation are described. The software managing thissystem employs a client-server model. The softwaredeveloped is able to work both in client and server modes.
It can also control various equipment – from the FEL
optical cavity mirrors to the local equipment of user
stations. The mode of control program operation andcontrolled equipment are determined by external
configuration files. Some results of the system operation
are also presented.

INTRODUCTION
The first stage of the free electron laser (FEL) based onenergy recovery linac is now working at Budker Instituteof Nuclear Physics [1]. Generation of coherent radiationin the wavelength range of 120 to 200 microns has beenachieved. This radiation is applied in a number of userand diagnostic experiments. To apply the radiation
successfully, it is necessary both to know its main
parameters and to transmit them to the user stations and
FEL control panel. In addition, it is necessary to control
some radiation parameters (wavelength) and to set up thesystem.
To solve these and some other tasks, a control system
has been developed. It performs the following:

Measurement and diagnostics of the main radiation
parameters, i.e. wavelength, power and transversal
shape of radiation beam.
2. Control over some FEL components (optical cavity)
as well as over the radiation wavelength.
3. Real-time transmission of the main radiation
parameters to the computers of user stations.
Operation of this system is considered in more details
below.

SYSTEM ARCHITECTURE
This system consists of a certain set of equipment(ADCs and controllers of step motors) and a program to
manage this equipment. Besides, the program uses aremote control interface for a set of parameters of theenergy recovery linac as well as reading some parameters
necessary for users. Figure 1 presents a scheme of theentire system. The program can work in client and servermodes. The program mode and configuration ofequipment to control (step motor controllers, numbers of
ADC channels, etc.) are set in external configuration files.
Thus, applying various configuration files, the program
can work in various modes and control different
equipment.

Figure 1: Scheme of the system
FEL operation

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Proceedings of FEL 2007, Novosibirsk, Russia

The server program runs only on one computer, which
is linked with two local networks – a FEL control
network and a network of user computers (see Fig.1). The
server captures required parameters of FEL operation,transforms them, calculates needed values and yields
them to both networks. The server also has means tocontrol the radiation wavelength and the FEL opticalcavity. These means are inaccessible for the client part ofthe program.
The client programs work both the computers
controlling the FEL and those at the user stations. The
client programs have a number of sub-programs tomeasure radiation characteristics that are inaccessible inthe server part of the program.

CONTROL OVER THE PARAMETERS OF
THE OPTICAL SYSTEM AND FELRADIATION
FEL operation is frequently linked with the necessity ofsetting up separate components of the optical system. For
instance, it is necessary to periodically adjust the positionof the mirrors of the optical cavity as to the maximum of
extracted radiation with the help of step motors.
Sometimes it is also necessary to measure radiation power
in a cavity with the help of calorimeters. Since theseparameters are linked with the FEL as a whole, the system
has been developed in such way that they could becontrolled only from one computer, the server program isrunning on, and they would be inaccessible for otherclient programs. The configuration files of the server
program contain information about the step motors
connected to the mirrors of cavity and scrappers as wellas information about the ADC channels intended forradiation measurement in several places – immediately at
the cavity output (see Fig.1) and at the accelerator hall
output. Control over all these parameters makes it
possible to set up different operational modes of the FEL
optical system and work with them.
As is known, the main merit of FEL is the possibility of
rapid re-tuning of radiation wavelength. That is why
scanning over the radiation wavelength is anotherradiation control function of the server. The FEL radiation
wavelength dependence is expressed by the following
formula:

λ =

2

⎛
k
⎜1 +
2 ⎜
2γ ⎝
2

d

⎞
⎟
⎟
⎠

,

where
λ is the radiation wavelength;d is the period of undulator;
γ is the electrons’ relativistic factor;

k is the undulator parameter, k = k 0 ⋅ I ,where I is the current in the windings of the undulator
and k0 is the coefficient of proportionality.
FEL operation

112

The best way to rapidly re-tune radiation wavelength isthrough varying undulator current. Undulator current ismanaged from the control program for the magnetic
system, so current value variation has to be realized via
the option of magnetic system remote control with theEpics Channel Access protocol [2]. A scheme of scanning
cycle is presented in Fig.2. The server organizes a cycleof sequential variation of undulator current within set
limits and with a given step. The program sends client
requests for undulator current adjustment to the server ofthe control program for the magnetic system, waits for 3
seconds (for the field to reach the steady state) and thenreads the indications of radiation sensors. In addition, inorder to compensate the possible influence of undulator
field variation on the beam path, requests for adjustmentof some other elements of the magnetic system are sent
(see Fig.2). The total (incident) power of radiation andpower of radiation absorbed in a sample or transmitted
radiation are measured in the course of retuning cycle.
The desired spectrum is obtained after normalization of
the obtained dependence of the second value on theundulator current as to the first value (the total power),since the total power can vary a little during themeasurement cycle. By now, the maximal range ofcontinuous scanning is 120 to 150 microns, while the total
range of radiation wavelength is 120 to 230 microns.

Figure 2: Cycle of scanning over the radiation
wavelength.

MEASUREMENT OF MAIN
PARAMETERS OF RADIATION
For experiments with FEL radiation it is necessary toknow its main parameters, i.e. the radiation wavelength,radiation beam shape and its power. Since theseparameters can vary with time, it is necessary to measurethem periodically. Most of these measurements are done
at a specially-created diagnostic station. In the systembeing described, these functions are realized as a set ofsub-programs, which are only accessible in the client partof program. The following have been done by now:
1. Radiation wavelength measurement with the help of
Fabri-Perot interferometer.
2. Radiation power measurement with the help ofsapphire calorimeter.
3. Measurement of the transversal distribution ofradiation beam power via two-coordinate scanning.
Radiation wavelength has been measured via a cycle ofscanning over the angles of rotation of Fabri-Perot etalon[3] relative to the incident radiation beam. In the course ofProceedings of FEL 2007, Novosibirsk, Russia
this cycle, the program displays a graph of radiation
intensity vs. this angle. A typical plot is shown in fig.3

Figure 3: Radiation wavelength measurement with thehelp of Fabri-Perot interferometer
The radiation wavelength is calculated from thepositions of maximums in the graph, by the following
formula:λ=2d(cos θ 1 − cosθ n )nwhere:λ is the radiation wavelength to measure;d is the distance between the lattices;θ1 and θn are the rotation angles corresponding to the 1st
and nth maximums.
It can be seen from the formula that the accuracy ofradiation wavelength determination is in proportion to then, the number of the last maximum, or to the maximal
rotation angle. That is why the cycle is organized over a
maximal possible range of angles.
Transversal beam distribution was measured with thehelp of a two-row array of piroelectric radiation detectors,
installed in the path of the incident FEL radiation. The
array is connected with a shifter, which moves in a
direction normal to the line of detectors. In the course ofmeasurement the program organizes a cycle over thecoordinate of line shift. All detectors in the line areinquired between the steps of this cycle. As a result,radiation power on a rectangular area of scanning getsmeasured. This area covers the entire radiation beam andamounts to about 15х20 cm. The spatial measurement
resolution equals the distance between adjacent detectors
and is less than 1 cm in one coordinate and about 4 mm in
the other. Fig. 4 presents a graph of the picked-up
distribution of radiation power.

MOPPH043

TRANSMISSION OF MAIN
PARAMETERS OF RADIATION TO THE
USERS
For experimental work with radiation, a user stationneeds real-time information on radiation parameters –wavelength and power – as well as on the main
parameters of the accelerator – frequency and energy ofthe beam and current of the undulator. In this system, thisinformation is transmitted from the program working inthe server configuration to programs running in the client
mode. The Epics Channel Access protocol is used as thecommunications protocol. A scheme of this interaction isshown in Fig.1. The server program gets main parametersof FEL operation from other control systems of the FEL.
Then the program computes a theoretical wavelength ofradiation from these parameters. Then the Channel
Access Server specifies this wavelength and some otherof main FEL parameters under other names, making themaccessible for reading by clients. Besides, the computer
the server is running on is connected to an ADC on whichmeasurements of radiation are terminated. These values
are also specified by the server and are accessible for all
client programs.
As it is shown in the fig. 1, the computer the server isrunning on is connected to two local networks – a control
network for the FEL and a network of user computers. As
a result, all information yielded by the server program isaccessible both on control computers and on the user
stations. In any of its configurations (server or client), theprogram has means for displaying these values in realtime. Besides, it is able to write the history of allparameter values for the last working session on a harddisc, which can be useful at long-term experiments sinceradiation power can vary during FEL operation.

CONCLUSION
This system is now used in FEL operation. Capabilitiesof the system allow one both to control FEL radiation andcarry out experiments on measurement of its
characteristics. Different configurations of program work
make it possible both to transmit and receive main
parameters of system operation as well as to control
different devices, e.g. the mirrors of the optical cavity andequipment at the user stations.

REFERENCES[1] N.G. Gavrilov, B.A. Knyazev, E.I. Kolobanov, et al.
Status of Novosibirsk high-power terahertz FEL.
NIM 2007, Vol. A575, p 54-57.
[2] Philip Stanley EPICS R3.13, Channel Access Portable
Server,http://lansce.lanl.gov/organization/EPICSdata/ca/castut/server-1.html

Figure 4: Transversal distirbution of power in theradaition beam.

[3] M. Born, E. Wolf Principles of optics, Nauka, 1973
(in Russian)

FEL operation

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Proceedings of FEL 2007, Novosibirsk, Russia

OPERATION OF NEAR-INFRARED FEL AT NIHON UNIVERSITY*
K. Hayakawa#, Y. Hayakawa, K. Nakao, K. Nogami, T. Tanaka, LEBRA, Funabashi, Japan
A. Enomoto, S. Fukuda, K. Furukawa, S. Michizono, S. Ohsawa, KEK, Ibaraki, Japan
M. Inagaki, T. Kuwada, T. Sakai, I. Sato, Nihon University, Tokyo, Japan
Abstract
The near-infrared FEL at Laboratory for Electron BeamResearch and Application (LEBRA) in Nihon University
has been operated for a variety of scientific applications
since 2003. The stability of the FEL power was improved
appreciably by the advanced stability of the 125MeV
electron linac. Currently fundamental FEL wavelength
ranges from 1 to 6 microns, which is restricted by theelectron energy and the optical devices. The higher
harmonics in the visible region is also available [1]. The
maximum macropulse output energy of 60mJ/pulse has
been obtained at a wavelength of 1725 nm. The short FEL
resonator length at LEBRA results in relatively highoptical energy density on the surface of the resonatormirrors; present copper-based Ag mirrors in use at
LEBRA are not durable enough for long-term operation.
Generation of intense harmonics by means of nonlinear
crystals has been tested. The preliminary results havedemonstrated the conversion efficiencies of 3 to 9% for
the second harmonic generation by the fundamental FEL
in the wavelength region from 1400 to 1800nm.

The FEL beam line and the optical resonator systemhave been installed to provide the near-infrared FEL forvarious studies [2]. To increase the FEL gain, magnetic
bunch compression has been performed in the 90-degree
bending system [3].
Table 1: Main parameters of the LEBRA linac.
Accelerating rf frequency

2856

MHz

Klystron peak output rf Power

30

MW

Number of klystrons

2Electron energy

30~125

MeV

Energy spread (FWHM)

0.5~1

%

Macropulse beam current

200

mA

Macropulse duration

20

μsec

Repetition rate

12.5

Hz

Table 2: LEBRA undulator parameters.

INTRODUCTION

Resonator length, L

6.718

m

The electron linac at LEBRA has a conventional
configuration. It consists of the DC electron gun with adispenser cathode, the prebuncher which is a 7-celltravelling wave structure, the buncher which is a 21-celltravelling wave structure and three 4-m long regularaccelerating sections. The specifications of the electron
linac are listed in Table 1. Schematic layout of theaccelerating structures, the RF system and the beam lines
for FEL and parametric X-ray (PXR) generations areshown in Fig. 1.

Undulator period

48mm

Undulator length

2.4m

Number of periods

50

Maximum K (rms)
1.35
To generate a monochromatic and spatially coherent
X-ray beam, the PXR beam line has been installed next to
the FEL beam line.

Signal generator
RF amp.

FC

Klystron
Attenuator
Phase
shifterMagnetic lensElectron
Gun Prebuncher

FEL
Beam Line

PXR
Beam Line
Coil

Buncher

Steering coil

Q triplet

4-m Acc Section 4-m Acc Section 4-m Acc Section

Analyzer

FC

Figure 1: Schematic layout of the accelerating structures, RF system and the FEL and the PXR beam lines___________________________________________*"Academic Frontier" Project for Private Universities: matching fund subsidy from MEXT, Japan, 2005-2007#
hayakawa@lebra.nihon-u.ac.jp

FEL operation114

Proceedings of FEL 2007, Novosibirsk, Russia

The undulator consists of a planar Halbach-type
permanent magnet, where the electron beam is wiggled in
the vertical plane. The specifications of the FEL system
are listed in Table 2. The optical beam is extracted
through the small coupling hole made in the mirror center.
The light beam extracted from the optical resonator iscollimated using the beam expander that consists of anellipsoidal mirror and a parabolic mirror, and thentransported to the experimental rooms through thevacuum ducts.
In this paper, the wavelength dependence of the FEL
intensity, the time structure of the FEL pulse and the
problem of the resonator mirror damage are reported.
Also, the results of the experiments for generating theharmonics by means of nonlinear optical crystals (NLO)
are discussed.

CHARACTERISTICS OF FEL LIGHT
Correlation between the oscillating wavelengthand the optical energy per macropulse
The FEL output power is very sensitive to the changeof the orbit and the focusing of the electron beam, and it
also depends on the adjustment of the optical resonatorand the extent of damage of the resonator mirrors. Hence,
the reproducibility of the FEL power level is not very
good even at the same electron energy and the same
undulator gap width. However, there is a roughcorrelation between the oscillating wavelength and theoptical energy per macropulse. The dependences of theoutput FEL energy on the wavelength have been obtainedfor various electron energies in the wavelength region
from 1160 to 6130nm as shown in Fig. 2.
In the short wavelength region the saturation level isrelatively high, though the gain is small and the loss islarge. The FEL macropulse duration becomes short near
the oscillation limit at the short wavelength end where thesaturation is not achieved stably. In the long wavelength
region the macropulse duration is relatively long and thesaturation is stable. However, due to the relatively low
saturation level and small output coupling, the energy of
the FEL extracted from the optical resonator decreases
Output energy per macro pulse

55(Mev)

energy per pulse (a.u.)

60
80

65

60

70
80

40

90

20

100

0
0

2000

4000

6000

8000

wavelength (nm)Figure 2: Wavelength dependence of the output
energy per macropulse.

MOPPH046

gradually with increased wavelength.
In the LEBRA FEL, the output energy per macropulse
has the maximum at the wavelengths around 2000 nm.
The maximum record of 60mJ/pulse has been achieved at
the wavelength of 1725nm.

Pulse structure
To increase the peak electron beam current, the electron
bunch has been compressed by using the 90–degree
bending magnet system placed just upstream of the FEL
system. The analysis of the energy spectra of 100-MeV
electron beam obtained by the acceleration in different RFphases suggests that the bunch length of approximately
3ps (FWHM) at the exit of the linac has been compressed
to 1ps (FWHM) or less at the entrance of the FEL system.
This implies that we can expect a very short FEL pulse.
Since the FEL pulse is a coherent wave packet, theapproximate pulse length can be deduced from themeasurement of autocorrelation width. A typical shape of
the autocorrelation traces measured at a wavelength of1500 nm by using a Michelson interferometer is shown in

Figure 3: Autocorrelation trace at the wavelength of
1500nm.
Fig. 3. In this figure the horizontal axis expresses the
position of the movable mirror measured along the opticalaxis in the interferometer, in units of micron, and thevertical axis expresses the relative intensity of the lightdetected by means of an InGaAs photo diode. The FEL
pulse width of approximately 60 μm in spatial domain or
200 fs in time domain has been deduced from this trace.
By using the same method, the pulse width of thesecond and the third harmonics have been deduced
approximately to be a half and two third the width of thefundamental FEL, respectively. The intensities of theseharmonics have been measured by means of a Si photo
diode.

Mirror damage
To oscillate FEL over the wide region of wavelengths,
protected silver-coated copper mirrors have been used forthe optical resonator. In fact, this type of mirror has anextremely high reflectance at the wavelength region
longer than 0.4 μm, and has demonstrated the highest
durability ever experienced at LEBRA as a FEL resonatormirror. Use of protected silver-coated silicon mirrors was
attempted. The mirrors suffered serious damage soon

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Proceedings of FEL 2007, Novosibirsk, Russia

after the FEL oscillation started. A photograph of thedamaged silicon mirror and its expanded image aroundthe coupling hole are shown in Fig. 4. In this figure, it
looks that the coated silver was melted and the silicon
substrate was excavated. On the contrary, the copper
mirrors were usable at least several months, although the
FEL power level decreased gradually and the mirrors
eventually had to be replaced.

extremely high energy density caused by very short FEL
pulses in the optical resonator. Under the present situation,
the resonator mirrors have to be replaced every three orfour months.
The FEL beam radius on the resonator mirror can beenlarged by shortening the Rayleigh range. Then theenergy density may be reduced sufficiently so that mirror
damages can be avoided. When the Rayleigh range isshortened, the resonator mirrors have to be adjusted very
precisely so as to keep the confocal condition. Since there
has been found no other efficient solutions, mirrors withsmaller curvature radii will be tested if the lifetime of themirror can be increased.

HARMONIC GENERATION USING NLO

Figure 4: Damages on the surface of the Ag coatedsilicon. Entire mirror (25mm in diameter) and close up
around the coupling hole.

Figure 5: Damages and discoloration on the surface of
the Ag-coated copper mirror. Entire mirror (25mm indiameter) and close up around the coupling hole.
A demounted mirror and its expanded image aroundthe coupling hole are shown in Fig. 5. Different from thecase of the silicon mirror, the surface over the wide area
near the center of the mirror has discolored. The coatedsilver around the coupling hole has been lost; the copper
substrate is visible and it looks melted. Degradation of theresonator mirrors by the damage on the surface is aserious problem in generating a high power FEL. As
mentioned previously, the micropulse width of the
LEBRA infrared FEL has been estimated to be as short as
200 fs. Therefore, damage to the mirrors could be due to
FEL operation

116

Preliminary experiments for generating harmonics [4]of the FEL by using NLO devices have been performed.
The KTiOPO4 (KTP) crystals have been used for second
harmonic generation (SHG) and third harmonic
generation (THG). The cutting angle and theantireflective coating of the crystal for SHG were
optimized for the fundamental wavelength of 1500 nm
and the second harmonic of 750 nm. Similarly the crystal
for THG was optimized for corresponding wavelengths.
The conversion efficiencies of SHG obtained with theTable 3: Fundamental and second harmonic
wavelengths, energies per macropulse and conversion
efficiencies.
2nd nm
1st mJ
2nd mJ
efficiency %1st nm
1400
700
~3
~0.15
~5
1500
750
~4.5
~0.4
~9
1600
800
~6
~0.45
~7.5
1700
850
~7.5
~0.6
~8
1800
900
~9
~0.3
~3
NLO have been 3 to 9% for the fundamental wavelengths
from 1400 to 1800nm as listed in table 3. Typicalmacropulse waveforms of fundamental FEL, nonlinear
second harmonic and SHG are shown in Fig. 6. The SHG
waveform is similar to the fundamental one. The THG
waveform was also observed, however the conversion
efficiency was far smaller than 1%.
A KTP crystal works under Type-II phase matching(a)(b)
Figure 6: Macropulse waveforms of fundamental andsecond harmonic: (a) fundamental (lower trace) andnonlinear harmonic (upper trace), (b) fundamental andSHG.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH046

condition. Hence the second harmonic is generated fromtwo fundamentals with their polarization planes at rightangles to each other. Due to the group velocity mismatch
between the two components of fundamental light, theconversion phenomenon occurs only within about 1 mm
in depth from the surface of the crystal, which restricts theconversion efficiency. If it is necessary to increase theconversion efficiency, other kinds of crystal should be
used.

REFERENCES[1] Y.Hayakawa, et al, “Characteristics of thefundamental and the higher harmonic generation at
LEBRA”, Nucl. Inst. and Meth. A 507 (2003) 404408.
[2] K.Hayakawa, et al, “The LEBRA 125 MeV electron
linac for FEL and PXR generation”, Proc.
LINAC2004, Luebec, Aug. 2004, p 90.
[3] K.Yokoyama, et al. “Bunch length measurements at
LEBRA”, Proc. LINAC2004, Luebec, Aug. 2004, p
411.
[4] P.A.Franken, A.E.Hill, C.W.Peters, and G.Weinreich.
“Generation of Optical Harmonics”, Phys. Rev. Lett.
7, 118-119 (1961).

FEL operation

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Proceedings of FEL 2007, Novosibirsk, Russia

ARC-EN-CIEL project electron beam dynamics
C. Bruni ∗ , A. Loulergue, M. E. Couprie, Synchrotron SOLEIL, Saint-Aubin, France

ARC-EN-CIEL Phase 1

Abstract
ARC-EN-CIEL project is based on the development offourth generation tunable light source of high brilliance inthe VUV to soft X-ray wavelength domain. The projectwill evolved into three phases : first and second phases arein single pass configuration, while third phase comports
recirculation loops. For delivering a high brilliance lightsource with high peak power short pulses, the high charge
electron beam should have subpicoseconde duration withlow emittance and energy spread. In order to keep optimal
slice characteristics for light production, phase space nonlinearities due to optics aberrations and collective effects
should be minimized. In ERL configuration, the accelerator scheme and focusing should be optimized to take into
account collective effects as Beam Break Up instability.

INTRODUCTION
This project is based on the development of a fourth
generation subpicosecond light source, with a high brilliance and tunable in the VUV to soft X-ray wavelengthdomain[1]. ARC-EN-CIEL views two simultaneous modesof operation :• A high charge, low emittance electron beam for
HGHG (High Gain Harmonic Generation) operation: a 1 nC electron bunch charge compressed by two
chicanes, with 1 to 10 kHz repetition rate and 1 to 10µA average current,• A high average current electron beam for synchrotron
radiation operation : a 0.2 to 1 nC electron bunchcharge, with 1 to 100 MHz repetition rate and 1 to
100 mA average current.
The HGHG based FEL sets requirements on the beam :high charge, sub-picosecond duration, and low emittance.
Optics aberration or collective effects, which are accentuated by high charge, are able to generate non linearities,
which damage beam characteristics [2, 3].
Adding recirculation loops allows high average current
operation and the energy to be increased by keeping highdensities subpicosecond bunch. However, collective effects as Beam Break up instability, form a feedback loop
between electron beams and RF cavities. Then, hereafter a threshold current, the oscillation amplitude of thebeam transverse position exponentially grows leading to
the beam loss [4].
∗ christelle.bruni@synchrotron-soleil.fr

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118

LINAC 1 HC

BC 1

LINAC 2

ARC-EN-CIEL Phase 2
LINAC 1 HC

BC 1

LINAC 2

BC 2

LINAC 3

ARC-EN-CIEL Phase 3
2 GeV
1 GeV
LINAC 1 HC

BC 1

LINAC 2

BC 2

LINAC 3Figure 1: Representation of the ARC-EN-CIEL accelerator
for the different phases. LINAC : Linear accelerator composed of cryomodules, HC : third harmonic cavity, BC :bunch compressor. To view all components, the representation is not scaled. Phase 1 is 70 m long, phase 2 : 200m, phase 3 : 200 m with a radius of the arcs of 15 and 30
meters.
This paper presents the electron beam dynamics for the
ARC-EN-CIEL project in single pass and ERL configuration, especially on the conditions for minimizing non linearities and Beam Break Up instability.

SINGLE PASS CONFIGURATION
ARC-EN-CIEL phase 1 and 2 (see fig. 1) aim at providing a 220 MeV and 1 GeV electron beam. The technology employed is a RF gun [5] followed by superconducting TESLA type [6] cryomodules. Chicanes are used
to compress the beam duration. In this section, simulations realized for both single pass cases of ARC-EN-CIEL
are presented by pointing out the optimisation for the light
production.
The RF gun and the cavity modules have been simulatedusing ASTRA [7]. The laser, which lights the photocathodeis 20 ps long (2.1 mm rms) with a cylindrical uniform distribution. To take into account the Coherent Synchrotron
Radiation (CSR) in the chicane, the CSRTrack code [8] hasbeen employed to model the compression scheme.

ARC-EN-CIEL phase 1
The RF gun produces a 1.1 π mm mrad total emittance with a total charge of 1 nC. Then a first cryomodule(LINAC1) leads to an energy of 120 M eV . A third harmonic cavity (HC) tuned in order to suppress non linearities(RF and magnetic) is placed before the chicane [9]. FigureProceedings of FEL 2007, Novosibirsk, Russia

-0.2

ith
ou
t

-0.4
-0.6

W

pz (MeV/c)the CSR effect in the chicane. In spite of this non linearities, the slice emittance along the bunch remains almost
constant with a low value around 1 π mm mrad (see figure 4b). The peak current at the center of the bunch attains
0.9 kA.

With

0.0

-0.8
-1.0

-2

0

2

4

s (mm)

Figure 2: Comparison of the longitudinal phase space ofthe electron bunch before the chicane without or with a harmonic cavity in the case of ARC-EN-CIEL phase 1. Charge
1 nC, energy 110 MeV.

a)

∆E/E (%)

0.4
-4

0.2

0.0

-0.4

-0.2

0.0

0.2

0.4

s(mm)
2.0

ε (π mm mrad)

2 illustrates the effect of the harmonic cavity after the firstcryomodule, which highly distorts the beam. However the
distortion in the edges of the distribution remains due tothe space charge force, which could be linearized by an ellipsoidal shaping of the laser at the cathode [10, 2]. The
compression, from 7 to 500 f s rms long is realized thanks
to a magnetic chicane (BC1). A compromise between asmaller energy beam chirp and a reduced effect of CSR
leads to a ten meters long chicane with a R56 coefficient
set at 0.2 m. The compression increases the total emittancefrom 1.1 to 2 π mm mrad (see figure 3). Whereas with anadequate optics [11], the slice emittances along the bunchremain almost unchanged (ranging from 1 to 1.5) with asmall mismatch from slice to slice. The compressor creates a correlated emittance that reaches 0.2 π mm mrad,
which denotes a spread of the slices in the transverse phasespace. Although weak, it is the main contributor to the total
emittance increase by strong mismatching.

ε (π mm mrad)

MOPPH048

b)

1.5
1.0
0.5
0.0
10

20

30

40

NsliceFigure 4: Electron bunch simulations for ARC-EN-CIEL
phase 1. a) Longitudinal phase space representation, b)
slice emittance along the bunch at the end of the linear accelerator. Charge 1 nC, Energy 220 MeV, bunch duration
500 fs

ARC-EN-CIEL phase 2

2.0

total

1.5

slice

1.0
0.5

correlated

0.0
0

2

4

6

8

10

12

schicane(m)Figure 3: Evolution of the total, central slice and correlated emittance along the chicane at 110 MeV in thecase of ARC-EN-CIEL phase 1. Charge 1 nC, energy
110 MeV, compression from 7 ps to 500 fs, R56 = 0.2 m,
Lchicane =10m.
Then, the second linac, formed by two cryomodules witha phase adjusted to obtain a minimized energy spread at theend of the accelerator, increases the energy from 110 M eV
to 220 M eV . The slice energy spread remains low and of
the order of 0.05 %.
Figure 4a illustrates the longitudinal phase space representation of the electron beam at the end of the accelerator.
It presents distorsions due to the space charge force andFor this case, the compression uses a second chicane
placed at an energy around 500 MeV. The compression isrelaxed in the first chicane from 7 ps to 800 fs comparedto ARC-EN-CIEL phase 1. This leads to a conserved slice
and total emittance whereas a correlated emittance is created in the chicane. Then, a second linac composed byfour cryomodules increases the energy from 110 M eV to550 M eV and enables adjusting the energy spread chirp
for a second chicane (R56 = 0.05 m), which compresses
the beam from 800 fs to 250 fs with very small degradation of the total and slice emittances. A third linac (fivecryomodules) tuned to redress the energy spread brings theenergy to 1 GeV. The electron beam slice energy spreadand emittance are represented in figure 5. They remain
small along the bunch around 0.04% of central slice energy
spread, 1.2 π mm mrad of slice emittance, and a peak current of 3 kA.

ERL CONFIGURATION
ARC-EN-CIEL phase 3 consists in adding two recirculation loops. The electrons beam is first accelerated during
a first pass in the accelerating cavities, and decelerated with

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MOPPH048

Proceedings of FEL 2007, Novosibirsk, Russia

0.2

25
Optics function (m)∆E/E (%)

a)
0.1
0.0

-0.1
-0.2

-0.2

-0.1

0.1

0.2

βy

βx

10
5
0

10

20

0.3

s (mm)

2.0

1.5

0.0

ηx

15

0
-0.3

ε ( π mm mrad)

20

30
s (m)

40

50

Figure 6: Optics functions versus the position along the arc
at 1 GeV. βx : vertical beta function, βx : horizontal beta
function, ηx : dispersion function.

b)

0.0
10

20

30

40

NsliceFigure 5: Electron bunch simulations for ARC-ENCIEL@1 GeV. a) Longitudinal phase space representation,b) slice emittance along the bunch at the end of the linear
accelerator. Simulations parameters are : charge=1 nC, Energy=1 GeV, bunch duration =250 fs

1000

a)

500

0
60

βx (m)

b)

β (m)

0.5

E (MeV)1.0

βy (m)

40
20
0

an opposite phase during a second pass, while restoring theenergy to the high frequency structures. By way of limited
numbers of turns, the electron bunch duration can stay inthe picosecond order contrarily to storage rings. For Energy Recovery Linac (ERL) mode, higher average current
can be obtained. A high current operation requires a separate cw gun based on a DC photoinjector (Jlab type), which
provide a 1 to 100 MHz pulsed electrons beam at 0.2 to 1
nC charge. A SRF gun will be employed depending on
their development [13].

Arcs optics
Two recirculating loops at 1 and 2 GeV are added to
ARC-EN-CIEL phase 2. There lattices are based on the
Double Bend Achromat of SOLEIL storage ring withoutstraight sections. Each arc are respectively 50 and 100
m long for 1 end 2 GeV. The optics is design in order
to control globally and locally the first and second order isochronism (R56 and R566 ) to prevent over compression or lengthening of the bunches. The chromaticities arealso tunable. The optical functions of the 1 GeV arc aresketched on figure 6.

Beam Break up and linac focusing
ARC-EN-CIEL design should takes into account the required conditions, particularly on the transverse focusing,to minimize the Beam Break Up current threshold. Studies of this instability for ARC-EN-CIEL is realized thanks
to BI code [12]. From a collective point of view, instaFEL projects

120

40

80

120

s (m)

160

480

520

560

s (m)

Figure 7: a) Energy and b) beta functions versus the position along the accelerator. Parameters are : drift between the quadrupoles and between the cryomodule and thequadrupole is set at 0.3 m and the length of the quadrupoles
at 0.3 m, focusing strength of 2.5 m−2 and threshold current of 30 mA for 1 MHz repetition rate.

bilities become more critical as the case of linear accelerator. Instabilities lead to beam loss at a threshold current,
which depends on optics, number of recirculations and cavity quality factor. Transverse beam break up appears to be
the limiting factor for ERL [4]. To simulate the transverse
transport of the ERL configuration, a code has been developed under Matlab. It allows the parameters of the accelerator and the optical function to be adjusted. Simultaneously the transfer matrix calculated for each element iswritten in the lattice file BI code input. The matlab codescans the optical functions and optimizes the threshold current for a given accelerator configuration. The quadrupoles
are approximated by thin lenses surrounded by two straightsections. The straight length is half the quadrupoles ones
Lqp . The arc is not yet relevant and is just considered as anellipse transport with imposed conditions at the entrance
and at the exit. The phase advance of the arc is adjusted
to maximize the threshold current. The β functions are thesame at the entrance and at the exist of the arc, and the αfunctions are of opposed sign to keep the symmetry.

Proceedings of FEL 2007, Novosibirsk, Russia

the two recirculations needed for 2 GeV is predicted to bearound 20 mA.

100

I th (mA)

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CONCLUSION
50

100 MHz

1 MHz

0
0.5

1.0

1.5

-2

2.0

2.5

k (m )
Figure 8: Intensity threshold as a function of the focusing
strength of the quadrupoles. Drift between the quadrupoles
and between the cryomodule and the quadrupole is set at
0.3 m and the length of the quadrupoles at 0.3 m.

ARC-EN-CIEL single pass accelerator has been designed in order to maximize the electron beam brillianceand to optimize parameters as the energy spread for the
production of HGHG light. ERL loops could provide in
addition synchrotron radiation from undulators and FEL
oscillation in the UV-X wavelength domain. BBU instabilities does not limit a high average current operation. But
further investigations have to be realized to obtain a highaverage current with two recirculation loops.

ACKNOWLEDGMENT
The simulations presented here consider a gradedgradient transverse focusing scheme [14] with triplet
quadrupoles with a focusing strength arrangement(−k/2, k, − k/2). In order to keep the symmetry of
the optical functions, there are quadrupoles sets between
each cryomodules, at the beginning and at the end of thelinear accelerator section. Preliminary simulations with asimplified design considering a 1 GeV linear accelerator,
have been done with one recirculation. The focusing
strength is choose to be constant in the first half of thelinear accelerator, when the electrons increase their energy.
As a consequence, it results from the simulations an evolution of the current threshold as a function of the focusing
strength. Figure 7 illustrates the energy variation along therecirculations loops and the optical function. The focusing
scheme enables to adapt the optical function to the caseof lower energy of the electrons : in the first half of theaccelerator, when the energy increases and in the second
half one when the energy decreases. The optical function
presented (see Figure 7b) are symmetric compared to thecenter of the arc. They are comprise between 2 and 55 m.
With a maximum charge in ERL configuration of 1 nC,
the average current is 1 mA (resp. 100 mA) for 1 MHz(resp. 100 MHz) repetition rate. As a consequence, theBeam Break Up threshold current should be larger than 1
mA for 1 MHz and 100 mA for 100 MHz. The dashedcurve of figure 8 shows that whatever the focusing strength
the threshold current of the beam break up instability ishigher than 1 mA. So the Beam break up instability does
not limit the current of the ERL operation at 1 MHz repetition rate. On the other hand, an operation at 100 mA canbe done only for few focusing strength. In fact, the Beam
Break up instability is more critical at 100 MHz repetition
rate and will need a careful design of the optics.
In a next step, simulations have to be done versus different parameters acting on the transfer matrix from turnto turn and from element to element. For the case of
Nr recirculation loops, the Beam Break Up instability becomes critical as the threshold current is smaller of a factorNr (2Nr − 1). As a consequence, the maximum current for

The support given by EUROFEL contract No 011935 is
acknowledged.

REFERENCES[1]

M.E Couprie (these proceedings).

[2]

C. Limborg-Deprey and P. R. Bolton, Nucl. Instrum. Methods A 557, 106 (2006).

[3]

S. Heifets, G. Stupakov, and S. Krinsky, Phys. Rev. ST Accel. Beams 5, 064401 (2002).

[4]

G. H. Hoffstaetter and I. V. Bazarov, Phys. Rev. ST Accel.
Beams 7, 054401 (2004).

[5]

Y.kim, F. Lohl, S. Schreiber, and K. Flottmann, proceedingsof LINAC http://accelconf.web.cern.ch, 391 (2006).

[6]

B. Aune, R. Bandelmann, D. Bloess, B. Bonin, A. Bosotti,
M. Champion, C. Crawford, G. Deppe, B. Dwersteg, D. A.
Edwards, et al., Phys. Rev. ST Accel. Beams 3, 092001(2000).

[7]

K. Flottman, ASTRA, a space charge tracking algorithm,
http://www.desy.de/ mpyflo.

[8]M.
DohlusandT.
Limberg,
CSRTrack,
http://www.desy.de/xfel-beam/csrtrack/index.html.

[9]D. Dowell, T. D. Hayward, and A. Vetter, proceedingsofParticle
Accelerator
Conference
http://accelconf.web.cern.ch, 992 (1995).

[10] F. Sacherer, IEEE Trans. Nucl. Sci. NS 18, 1105 (1971).
[11] M. Dohlus and T. Limberg, proceedings of Particle Accelerator Conference http://accelconf.web.cern.ch, 1015
(2005).
[12] I. Bazarov, BI, http://www.lns.cornell.edu/ ib38/bbucode/src/.
[13] A. Todd, Nucl. Instrum. Methods A 557, 36 (2006).
[14] D. Douglas, Report JLAB-TN-00-027 (2000).

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MOPPH050

Proceedings of FEL 2007, Novosibirsk, Russia

STATUS OF THE UNDULATOR SYSTEM OF THE
SEEDED HGHG-FEL TEST BENCH AT MAX-LAB*
J. Bahrdt, W. Frentrup, A. Gaupp, K. Goldammer, K. Holldack, M. Scheer,
BESSY, Berlin, Germany
M. Brandin, F. Lindau, D. Pugachov, S. Thorin, S. Werin, Lund University, Lund, Sweden,
J. Kuhnhenn, Fraunhofer INT, Euskirchen, Germany
Abstract
Within the EUROFEL Design Study a seeded HGHGFEL will be set up at the 450 MeV linac at MAX-lab.
The undulators and the dispersive section have been
installed. Two different glass fiber based radiation dosemonitors have been integrated. We report on theperformance of these components. The impact ofelectron losses on undulator magnets and the Cherenkov
fibers have been simulated. The THz radiation as
produced by the bunched electron beam in the dump
magnet can be used as a measure of the longitudinal andtransverse overlap of the electron beam and the laser
beam which has been concluded from simulations.

INTRODUCTION
Within the European FEL Design Study a single stage
seeded HGHG FEL [1] test bench is currently set up at
MAX-lab [2]. The electrons will be accelerated in theinjection linac of the MAX-I-III rings. The FEL
experiment is located inside the MAX-II storage ringand the electron beam will be available between theinjections into the MAX-lab rings. A new low emittancephotocathode gun [3] will be installed at the end of
2007. The commissioning of the complete setup will
start in September 2007 using an existing gun which
provides a bunch charge of 0.08nC.
BESSY has built and installed the two permanent
magnet undulators (modulator and radiator) and theelectromagnetic chicane. Permanent magnets are
sensitive to radiation damage and the deposited doses
have to be monitored. For this purpose two glass fiber
systems have been implemented: i) A Cherenkov systemdelivers fast signals which will be used for a laserinterlock system in case of an electron beam missteering.
ii) Absolute dose measurements are done with apowermeter system which is based on another type ofglass fiber. A detailed study and comparison of bothmeasurements systems in combination with numericalsimulations will be very helpful for the design of future
FEL sources.
The alignment of the electron beam with respect tothe laser beam is crucial for a reliable operation of theseeded FEL and a robust diagnostic is required.
*This work has been partially supported by the EU
Commission in the Sixth Framework Program, Contract
No. 011935 – EUROFEL.
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122

Simulations show that the spectral distribution of theTHz radiation as produced by the electron bunch in the
dump magnet changes significantly if the seed laserinteracts with the electron beam. Thus, the THz will be
helpful in the commissioning phase and also later during
normal operation as an input for feedback systems.

THE UNDULATORSThe parameters of the undulators and the chicane havebeen described in [4]. The electron beam height at the
FEL location of 520mm requires a horizontal operationof the two undulators. The undulators have beenmeasured and shimmed in the vertical position at the
BESSY field measurement bench. After shimming thedevices have been rotated by 90° and mounted onto
three columns each. Fig. 1 shows the radiator inoperating position at MAX-lab. In the final position thefield integrals will be checked with a pulsed wire system
and air coils at the undulator ends will be used tocompensate residual field errors.

Figure 1: Radiator of the APPLE II type in operating
position without vacuum chamber. Four power meter
sensors (see below) at each undulator end (orange cable)
are installed.

THE CHICANE
The chicane consists of four electromagnets (Fig. 2).
Each magnet is made of two low carbon steel pieces (C< 0.01%) which are bolted together. The poles have been
wire cut. The number of windings per coil is 432. The
measured field integrals per Ampere for the four
magnets are: 10.9, 10.9, 10.6, 10.7 Tmm / A.
The magnetic hysteresis of the four magnets asmeasured with a moving wire is ±0.25 Tmm (Fig. 3).

Proceedings of FEL 2007, Novosibirsk, Russia
Hall probe measurements show a reproducibility of the
field setting below 5e-4 after two cycles (Fig. 3).

MOPPH050

Cherenkov photons. The experiences gained with thesesystems will be valuable for the BESSY Soft X-Ray
FEL [11].

Cherenkov System

0.5
0.4
0.3
0.2
0.1
0
-0.1
-0.2
-0.3
-0.4
-0.5

reproducibility (dB/B)

residual field integral (Tmm)

Figure 2: Electromagnetic Chicane.

-2

0

2

current (A)

0.005
0.004
0.003
0.002
0.001
0
-0.001-0.002-0.003-0.004-0.005-202current (A)Figure 3: Left: Hysteresis of field integrals of the four
magnets. The measurement noise is due to the presenceof up to 30Tmm field integrals. Right: Reproducibilityof field settings within a sequence of several current
cycles of the magnets.

A Cherenkov fiber system [12] is fast and the signal
can be used to switch off the electron beam in case of
intolerable beam losses. During the commissioning
phase the relative intensities of the individual fibers canbe used to align the electron beam properly.
The system installed at the MAX-lab FEL consists offour radiation insensitive glass fibers (core: 300μm,
cladding: 300 μm) mounted directly onto the circularundulator vacuum chamber which has a diameter of
10mm (Fig. 4). Thus, the fibers will provide detailed
spatial information even for large undulator gaps. The
sensitivity of the fibers is small as compared to large
luminescence detectors. The small size, however,
permits an installation close to the electron beam overmany meters.
The GEANT [13] simulations are based on a 1nC
bunch hitting the vacuum chamber wall of the modulator
under zenith angles of 0.1 and 1mrad and azimuthal
angles of 0, 45 and 90°, respectively. Four Cherenkov
fibers and one Thermo Luminescence Detector (TLD)
are included in the model (Fig. 4). The evaluatedradiation doses induced in the TLD and the magnets andthe produced Cherenkov photons are summarized in(Tab. 1). The given number of photons is the number
detected by the photomultiplier (applying a numericalaperture of 0.22 inside the fiber and including thespectral characteristics of the multiplier).

RADIATION PROTECTION
OF THE MAGNETS
Significant demagnetization of undulator permanent
magnets in storage rings have been reported in theliterature [5-7]. The risk of demagnetization is evenhigher in single pass devices like linac based FELs.
Extensive studies have been performed to get aquantitative understanding of demagnetization effects [8,9]. Collimation systems have to be designed such thatthe radiation dose deposited into the magnets remains
below an acceptable limit [10].
In the MAX-lab FEL a stainless steel capillary(length: 100mm, diameter 3mm, wall thickness:
12.5mm) is located in front of the modulator preventing
the electron beam from hitting the circular beam pipe incase of a failure of the two vertical deflecting dipole
magnets at the laser beam port (vertical beamdisplacement due to the dipole magnets: 20mm).
The electron losses will be monitored with two
different systems, a Cherenkov system for fast beam loss
detection and a powermeter system for absolute dose
measurements. GEANT simulations have been
performed to estimate the radiation doses in the magnets
and to evaluate the corresponding number of produced

Figure 4: Cross section of the modulator including thepermanent magnets (red), vacuum chamber (blue),
Cherenkov monitors (black) and TLD monitor (green).
Table 1: Results from GEANT simulations.
anglesmrad / °TLD
mGy / nC

0.1 / 00.1 / 45
0.1 / 90
1.0 / 01.0 / 45
1.0 / 90

1207
131
77
2730
412
279

max. dosein magnetmGy / nC
57
205
287
188
487
588

Cherenkov photons/nC
forwardbackward
direction direction
6.7e7
1.1e7
9.7e7
1.5e7
7.2e7
1.2e7
1.2e8
2.1e7
1.6e8
2.7e7
1.3e8
2.3e7

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123Proceedings of FEL 2007, Novosibirsk, Russia

Maximum doses of 0.59 Gy/nC are detected for the
1mrad case (Fig. 5). It has been shown [14] that amaximum reduced dose (electron energy > 20MeV) of
70kGy can be tolerated in case of the BESSY Soft XRay FEL which represents a rather conservative number
for the short MAX-lab FEL. Thus, the number ofgenerated Cherenkov photons is sufficiently high todetect even small electron beam losses long before themagnets are damaged. The exact detection limit of theCherenkov fibers will be subject to future combined
numerical and experimental studies at the FEL.
1 mrad beam

0.1 mrad beam

5

10NP070002A
λ = 658 nm
P = 7 µW
T = 27°C
t = 7200 s

4

10Induced Loss [dB/km]

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3

10

2

10

1

10

A=51⋅D±15%
1.312 Gy/s
0.0624 Gy/s
0.0064 Gy/s
0.00054 Gy/s

0

10

-2

10

-1

10

0

10

1

10

2

10

3

10

4

10

Dose [Gy(SiO2)]

Figure 6: Calibration of the selected fiber.
70

dose[mGy/nC]

175
150
125
100
75

60
50
40
30
20

50

10

r[m

15

10

5

0

0

1000
25

r[m

20

m]

500
15

]

]

20

m]

0
30

500

m

25

m

30

m

1000

10

5

0

0

m

0

z[

25

z[

dose[mGy/nC]

200

Figure 5: Radiation doses inside the magnets induced by
a 1nC electron bunch hitting the vacuum chamber. The
data are averaged over the 0°, 45° and 90° scenarios.

Powermeter System
Absolute radiation dose measurements can be donewith calibrated glass fibers [15]. The fibers can beinstalled along the region of interest (e.g. the complete
undulator system) providing spatial information of thebeam losses (Optical Time Domain Reflectometer,
OTDR). Another approach is a system of several local
sensors which are multiplexed. The spatial resolution of
the latter system is slightly lower (depending on thenumber of channels) but the complete dynamic range isavailable for each channel whereas in the OTDR system
the dynamic range is available only for the wholesystem. A system with 16 local sensors has been
installed at the MAX-lab FEL.
Glass fibers for telecommunication applications are
not optimized for radiation dosimetry. Usually, theoptical parameters which are relevant for dose
measurements can vary by orders of magnitude. Thisrequires a careful selection of the fibers. Four
germanium and phosphorous doped polyimid coated50/125/145 µm graded index fibers from different
suppliers have been tested by the Fraunhofer INT,
Euskirchen, Germany. A fiber fabricated by J-Fiber,Jena, Germany, has been selected for the MAX-lab FEL.
The calibration of this fiber as determined with a Co-60
source is plotted in figure 6.
The figure of merit for the fiber selection is acombination of various parameters: i) high dynamic
range; ii) radiation sensitivity; iii) annealing after
irradiation; iv) linear response on total radiation dose; v)
low sensitivity on dose per time.
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The chosen fiber has the following performance (Fig.
6): i) in combination with the currently installed lightsource and the power meter the dynamic range is 30-40
dB ii) the attenuation is described by: (dB / km) = dose(Gy) * 51. For comparison: the sensitivity of
conventional germanium doped 50/125/250 µm gradedindex fibers as used to connect the sensor modules to thelight source and the analyzer is two orders of magnitude
lower. iii) 24h after irradiation less than 10%. iv) The
deviation from a linear curve within the range from 0.011000Gy is smaller than ±15%. v) A linear response has
been demonstrated for dose rates between 0.0005 Gy/s
up to 1.3 Gy/s.
The MAX-lab system consists of sixteen channels.
One channel serves as a reference. The read out time forall 16 channels is less than 60s. The light source consistsof an LED (658 nm) powered by a stable constantcurrent power supply. 10% of the output power ismeasured directly (excluding the optical coupler, theoptical switches and all fibers) with a power meter. In atemperature stabilized environment the source drifts are
only 0.01dB / day. The influence of typical source drifts
in a rough environment of 0.02-0.05dB / day can easily
be compensated.
The reference fiber has no sensor module attached but
is shortcut at the FEL location. It can be used tocompensate for drifts of the support fibers.
The sensor fibers are wound to rectangular flat coils(50x50mm**2) and the radiation exposed length of one
fiber is approximately 2m. The coils are mounted onto
the magnet girders close to the upstream anddownstream ends of the undulators. At smallest gap the
distance to the electron beam is 7mm for the modulatorand 28mm for the radiator. Radiation sensitive fibers areused only for the coils. The distance of 40m between the
FEL and the electrical cabinet is bridged with radiation
insensitive fibers.
The system has been installed in March 2007 and thedrifts have been monitored since that time. The opticaltransparency of the 15 fibers has been corrected forfluctuations of the light source. The signals show a longterm drift of ±0.03dB per day and a periodic structure
superimposed to it (Fig.7, left). The drifts are dominatedby temperature fluctuations which is concluded from acorrelation diagram (Fig. 7, right). The various fibers
show individual temperature dependencies. The data can

Proceedings of FEL 2007, Novosibirsk, Russia

relative optical power (dB)relative optical power (dB)be corrected using a specific temperature coefficient foreach fiber. Two temperature sensors are installed at each
undulator end. After correction the residual drifts arewell below ±0.01dB for a period of several days. Thisguarantees a long term system sensitivity of better than
0.2Gy. The remaining differences between the fibers are
due to the individual characteristics of the cascaded
optical coupler behind the light source.
In case the fibers have reached the upper limit of thelinear regime of 1000Gy they can be thermally annealed
at a temperature of up to 350°C in order to recover thefull transmission.
0.04
0.02
0
-0.02
-0.04
-0.06
-0.08

-0.12

25

30

35

The THz power spectral density emitted there is ~N(N+1)f, where f is the square of the Fouriertransformation of the longitudinal electron density and
N=0.6x10^9 (0.1 nC) is the number of electrons.
The calculated form factor f for the two cases (Fig. 8,
right) demonstrates that the coherent far infraredemission in the range between 1 and 10 THz can be
employed to detect the overlap between seed laser andbunch in the modulator. By setting an appropriate highpass filter the signal from a THz detector will almost
completely drop to zero for a successful energy
modulation of the electrons.

0.02

REFERENCES

0.01
0
-0.01
-0.02
-0.03
-0.04
-0.05

-0.1

MOPPH050

-0.06
22

24

26

time (days)

28

30

time (days)

Figure 7: Left: Long term stability of the system
consisting of 15 fibers. Right: The day by day
fluctuations (blue) are closely correlated to thetemperature variations (black).

THZ DIAGNOSTICS
The diagnostics of the FEL resonance in themodulator will be performed using a strong difference incoherent THZ emission [16,17] from the seeded andunseeded bunch after propagating through an additional
bending magnet (dump magnet) behind the radiator.
Since the electrons are gathering path length differences
controlled by R56 along the magnet, the bunch shape intime domain is different for the seeded and unseededcase. This is caused by the change in energy spread dueto the FEL resonance (Fig. 8 left).

Figure 8: Left: Projection of the seeded and unseeded
electron density in the bunch according to start-to-end
simulations [2] after passing an R56 of 0.05 m. Right:
Expected envelopes of THz spectra (formfactor) emitted
by theses bunches for the seeded and unseeded case.

[1] L. H. Yu, J. Wu, Nucl. Instr. and Meth. in Nucl. Res.
A 483 (2002) 493.
[2] S. Werin, al., these proceedings.
[3] S. Werin et al., Proceedings of the EPAC 2006,
Edinburgh, Scotland, 2006, pp 130-132.
[4] J. Bahrdt et al., Proceedings of the EPAC 2006,
Edinburgh, Scotland, 2006, pp 59-61.
[5] P. Colomp, T. Oddolaye, P. Elleaume, “Partial
Demagnetization of ID6 and Dose Measurements on
Certain Ids”, Machine Technical Note 1-1996/ID,
1996.
[6] M. Petra et al., Nucl. Instr. and Meth. in Phys. Res.
A, 507 (2003) pp. 422-425.
[7] P. Colomp, T. Oddolaye, P. Elleaume,“Demagnetization of Permanent Magnets to 180
MeVElectron
Beam”,
Technical
Report
ESRF/MARCH-ID/93-09, European Synchrotron
Radiation Facility, ESRF March 1993.
[8] T. Bizen, T. Tanaka, Y. Asano, D.E. Kim, J.S. Bak,
H.S. Lee, H. Kitamaru, Nucl. Instr. and Meth. in
Phys. Res. A 467-468 (2001) 185-189.
[9] M. Marechal, T. Shintake, SRI2003, Conference
Proceedings, AIP 705, (2004) pp 282-285.
[10] H. Schlarb, “Collimation System for the VUV FreeElectron-Laser at the TESLA Test Facility”, Thesis
Work, Universität Hamburg, DESY-THESIS-2001055, Nov. 2001.
[11] “The BESSY Soft X-Ray FEL”, Technical design
Report, D. Kraemer et al., Berlin, 2004.
[12] M. Körfer, W. Göttmann, F. Wulf, J. Kuhnhenn,Proceedings of DIPAC 2005, Lyon, France, 2005,p301.
[13] GEANT 3.21, Detector Description and Simulation
Tool, Computing and Networks Division, CERN,
Geneva, Switzerland.
[14] J. Bahrdt et al., Proceedings of the FEL Conference
2006, Berlin, Germany, 2006, pp521-528.
[15] H. Henschel, M. Körfer, J. Kuhnhenn, U. Weinand,
F. Wulf , Nucl. Instr. and Meth. in Phys. Res. A 526(2004) pp. 537-550.
[16] Holldack et al. PRL 96, 054801 (2006).
[17] A. A. Zholents and K. Holldack, Proceedings FEL
Conference 2006, Berlin, Germany, 2006, pp725727.

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NONLINEAR HARMONIC GENERATION IN THE BESSY SOFT X-RAY
FEL∗
K. Goldammer, BESSY, Berlin, Germany.
Abstract

INTRODUCTION
The BESSY High-Energy (HE-) FEL uses a cascade offour HGHG stages to convert a seed laser of 297.5 nm
down to 1.24 nm. Each stage consists of a modulator, dispersive chicane and radiator. Analytic studies [3] predictthat the signal-to-noise ratio (SNR) in HGHG FELs decreases by the square of the harmonic nbumber used during
conversion. As the total conversion factor in the BESSY
HE-FEL is 225, degradation of the radiation due to noise isa critical issue. In order to conserve the excellent temporal coherence of the seeded FEL radiation, a new design is
proposed that uses harmonic radiation to reduce the number of HGHG-stages. Its prospects are investigated in thispaper.
Harmonic radiation is intrinsically produced during the
FEL process in planar undulators and leads to coherent
emission at higher harmonics of the FEL resonance [4]. It
becomes significant in the high gain regime of an FEL andtypically provides for power levels in the range of 1% or
0.1% of the fundamental depending on the harmonic number.
The new design uses harmonic radiation from the first stage
radiator. Its fifth harmonic has a wavelength of 11 nm andcould hence be applied directly as a seed for the third stage
modulator. Figure 3 illustrates the idea.

HARMONIC CONTENT OF FIRST STAGE
The BESSY High Energy FEL first radiator is a planar
undulator with the period length of λu =92 mm and a∗ Work supported by the Bundesministerium für Bildung und
Forschung, the State of Berlin and the Zukunftsfonds Berlin

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126

Figure 1: Schematic picture of new proposal for BESSYHigh Energy FEL: harmonic radiation from first stage radiator could be used to the seed third stage. The second stage
could be omitted. Stages 1 to 3 depicted.

total length of 3.69 m. The radiator has to be prolonged
significantly to yield sufficient fifth harmonic power forseeding the third stage. The harmonic power in the firstradiator then evolves as depicted in Fig. 2.

2

10Peak Power [GW]Free Electron Lasers (FELs) do not only radiate at thefundamental frequency, they may also radiate coherently
at higher harmonics. This process is referred to as nonlinear harmonic generation or NHG. NHG is of high interest,
because it extends the output wavelength of FELs to several harmonics of the FEL resonant frequency. In cascaded
High Gain Harmonic Generation (HGHG) FELs, harmonic
radiation may be used to improve frequency-conversion
and reduce the number of HGHG-stages. BESSY proposes
to build a cascaded HGHG FEL with three FEL lines [1].
They cover a wavelength range of 51 nm (Low-Energy
FEL) to 1.2 nm (High-Energy FEL) and consist of up to
four HGHG-stages. In this paper, we present studies of
the BESSY High-Energy FEL harmonic content performed
with the upgraded version of the simulation code Genesis 1.3 [2].

0

10

−2

10

−4

h1: 55.9 nm
h3: 18.6 nm
h5: 11.2 nm

10

−6

10

0

5

10
15
Undulator Length [m]20

Figure 2: Simulation of BESSY High-Energy FEL radiation power along first radiator. From top to bottom: fundamental, third and fifth harmonic radiation. Simulation
performed with new version of Genesis 1.3 [2].
It can be observed that the harmonics start later than thefundamental and enter their exponential gain regime after
approximately 5 to 7 m. After that they rapidly reacha significant output power because they have a shorter
gain length (higher gain) than the fundamental. This
corresponds well to analytic predictions [5].

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH051

Figure 3: Schematic view of new design BESSY High Energy FEL with table of undulator properties.

Radiator 1

RESULTS
Maintaining the nominal undulator configurations for thethird and fourth stage, the power at the end of the third andfourth radiator evolves as depicted in Fig. 5. The power
1.2

Radiator 3

1

1
0.8
Intensity [a.u.]

The choice of λu and K plays an important role in FEL
performance. In order to find the optimal undulator settings for the first radiator with respect to a short gain lengthand high output power, a range of FEL configurations werestudied. The combination of K=6 and λu =61.2 mm is agood compromise that reduces the fundamental gain lengthby about one fourth [6]. With the assumption of a 10 mm
undulator gap, this corresponds to a peak flux of 1.6 T in
the undulator magnets which is technically feasible [7].
A schematic view of the new design is given in Fig. 3. The
radiator length is fixed at 9.4 m (153 periods) where thefifth harmonic power is in the range of 230 MW. Simulation studies of the fresh bunch parts show that this keeps
the increase of energy spread at a tolarable level.
The temporal and spectral power distribution of the fifth
harmonic at the end of the radiator then evolve as depicted
in Fig. 4. However, the fifth harmonic power at the end

lator and radiator and the fresh bunch chicane after the firstradiator. In order to maintain sufficient energy modulationin the third stage modulator, it has to be extended from 30
to 100 periods, equal to about 5 m of undulator. However,
the extension of the first and the third stage does not exceed
the original length reserved for the second stage.

Power [GW]

NEW DESIGN

0.8
0.6

1

0.4

0.8

0.2

0.6
0.4

0.15

0.1

0.05

0.4
0.2

50

60
70
Time [fs]

80

90

0

50

60
70
Time [fs]

80

0

90

Radiator 4

0.5

11.1

11.2 11.3 11.4
Wavelength [nm]11.5

Figure 4: Temporal and spectral power distribution of fifth
harmonic radiation of first radiator at 9.4 m. Undulator period 61.2 mm, K=5.98.
of the prolonged radiator is about a factor eight lower thanthe original seed power for the third stage. This requires
a careful readjustment of the undulator lengths in all subsequent stages. The total length of the first stage is now
15.5 m including the dispersive section in between modu-

3.72
3.74
Wavelength [nm]

3.76

0.8

0.3
0.2

0.6
0.4
0.2

0.1
0
40

3.7

1

0.4
Power [GW]

0
40

0
40

0.6

0.2

Intensity [a.u.]

Intensity [a.u.]

Power [GW]

0.2

50

60
70
Time [fs]

80

90

0

1.23 1.235 1.24 1.245 1.25
Wavelength [nm]Figure 5: Simulation of temporal and spectral power distribution at end of third radiator, top, and fourth radiator,bottom, in scheme 1.

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MOPPH051

Proceedings of FEL 2007, Novosibirsk, Russia

levels compare well to the output power in the original design. When using the radiation from the fourth radiator
to seed the final amplifier, it reaches an output power of
2.5 GW. This slightly exceeds the nominal output powerof 1.8 GW. The temporal and spectral power distribution at
the end of the final amplifier are depicted in Fig. 6. The
Original Design
1
New Design010Intensity [a.u.]

Power [GW]

0.8
−1

10

−2

icantly longer than in the first radiator (LG1D =1.8 m as
opposed to 1 m). This means that the radiator has to be
prolonged significantly to yield sufficient fundamental gain
for the harmonic power to become noticeable. As a consequence, the total undulator length in this case would exceed
the nominal HE-FEL length, which is certainly a drawback.
The long undulators also provoke a significant SASE background from the unseeded buch parts. Figure 7 depicts the
temporal and spectral profile of the third harmonic at 23 m
along the third radiator. The peak power is about a factor of

0.6

0.03

0.4

0.025

1
0.8

10

40

50

60
70
Time [fs]

80

90

0

1.238 1.24 1.242 1.244 1.246
Wavelength [nm]

0.015
0.01

0
10

0.6
0.4
0.2

0.005

Figure 6: Simulation of temporal and spectral power distribution at end of final amplifier.

15
20
Bunch Length [µm]0251.23 1.235 1.24 1.245 1.25
Wavelength [nm]Figure 7: Temporal and spectral power distribution of third
harmonic radiation of third radiator at 23 m.
six lower than the output of the fourth radiator in the nominal design. As a result of the degradation of electron beam
quality in the long undulator, the spectrum shows several
spikes and sidebands.
When using the harmonic radiation from the third radiator to seed the final amplifier, the HE-FEL line yields the
temporal and spectral power depicted in Figure 8. The fi0.14

10.12Power [GW]

output power of the final amplifier in the new design compares well to the output power of the original HE-FEL design. The pulses have become shorter, which is due to thefact that the harmonic pulses at the end of the first radiator
are significantly shorter than the fundamental pulses. Radiation from unseeded bunch parts, the background in Fig. 6,
left, is also greatly reduced. This can be attributed to the
reduced number of HGHG stages. Figure 6, right, shows
the improvement of the final amplifier spectrum. The new
design results in fewer temporal spikes and the output radiation is concentrated in a smaller bandwidth (30% net
reduction), thus showing improved temporal coherence.
However, there are still two peaks visible in the spectrum.
The shorter wavelength spike is a sideband which is amplified because it lies within the FEL bandwidth1 . It alreadyappears in the output of the fourth radiator, see Fig. 5, bottom, which has been used to seed the final amplifier. It
probably results from the bunching distribution of the electrons in the radiator. Ref. [1] explains that the electrons
can get overbunched, meaning that they move too far in thepotential bucket, and generate a modulation of the emitted radiation frequency. This could be avoided by readjusting R56 in the dispersive chicanes at the expense of output
power.

Intensity [a.u.]

−3

0.02

0.8

0.1

Intensity [a.u.]

0.2Power [GW]

10

0.08
0.06

0.6
0.4

0.04
0.2

0.02
0
10

15
20
Bunch Length [µm]2501.23 1.235 1.24 1.245 1.25
Wavelength [nm]Figure 8: Temporal and spectral power distribution at endof final amplifier when using third harmonic radiation fromstage three.

HARMONIC CONTENT OF THIRD STAGE
Harmonic radiation might be used again for an additionalchange in the design. The third harmonic radiation of thethird radiator has a wavelength of 1.24 nm and can be used
to directly seed the final amplifier.
However, this idea is more of a theoretical than a practical option. The gain length in the third radiator is signif1 The relative FEL bandwidth of the order of the FEL parameter ρwhich is about 1e-3 in the final amplifier.

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128

nal amplifier spectrum is dominated by a spiky SASE spectrum and does not convey the advantages of High Gain Harmonic Generation any more.

CONCLUSION
The use of harmonic radiation from the first stage forseeding the third stage is a promising option for the BESSYHigh Energy FEL. The simulation studies performed with

Proceedings of FEL 2007, Novosibirsk, Russia

the new version of Genesis [2] show that it is a feasible
option and yields an output power and spectral bandwidthcomparing well to the original design. Moreover, the newscheme that uses harmonic radiation has a number of benefits:
1. The complexity of multi-stage cascading is reduced
as the number of HGHG stages decreases from fourto three. This can be expected to greatly improve
the practicability of the proposed machine both during commissioning as well as during operation.
2. The constraints on the electron beam are relaxed. The
BESSY Soft X-Ray FEL implements the serial use of
the fresh-bunch technique in each HGHG stage [8].
As a consequence, a long electron bunch with a highcurrent region in the range of several hundreds of femtoseconds is required2 . In order to reach a peak current of 1.75 kA current along the entire bunch, an initial bunch charge of 2.5 nC needs to be generated in
the injector. Saving one HGHG-stage reduces the required bunch length by a few hundred femtoseconds.
The bunch charge could be lowered to 1.5 to 2 nC suchthat the effects of space charge could be reduced. As
a consequence, the beam emittance decreases and the
FEL efficiency is enhanced.

MOPPH051[3] E. Saldin, E. Schneidmiller, M. Yurkov, “Study of a noise
degradation of amplification process in a multistage HGHG
FEL,” Opt. Comm. 202 (2002) pp. 169-187.
[4] Z. Huang and K.-J. Kim, ”Nonlinear harmonic generation ofcoherent amplification and self-amplified spontaneous emission”, Nuclear Instruments and Methods in Physics Research
A 475 (2001), pp. 112-117.
[5] Z. Huang and K.-J. Kim, ”Three-dimensional analysis of harmonic generation in high-gain free-electron lasers”, Phys.
Rev. E 62, 7295 (2000)[6] K. Goldammer, ”Studies of Harmonic Generation in Free
Electron Lasers”, PhD Thesis, Humboldt-Universität Berlin,
2007[7] Johannes Bahrdt, private communication, 2007.
[8] Li-Hua Yu and I. Ben-Zvi, ”High-gain harmonic generationof soft X-rays with the fresh bunch technique”, Nuclear Instruments and Methods in Physics Research A 393 (1997),
pp. 96-99.

3. The total undulator length decreases. This is beneficial due to two reasons: a) the FEL pulses are lessprolonged by slippage in the undulators. This resultsin shorter output pulses. b) The fresh parts of the electron beam are less degraded in energy-spread before
they come to use in their corresponding stages. This
improves the quality of the electron beam and the FEL
performance.
However, it has to be noted the experimental experience
with harmonic emission in the soft X-ray regime is still
small. FEL theory also shows that harmonic radiation is
critically dependant on strong FEL gain on the fundamental. If a only a few of the relevant electron beam parameters (e.g. peak current or energy-spread) do not meet the
expectations, the first radiator might saturate significantly
later and not yield high intensity harmonic emission as predicted. Experiments with harmonic emission from HGHG
FELs should hence be conducted to further investigate thisissue.

REFERENCES[1] D. Krämer, E. Jaeschke, W. Eberhardt (Editors), The Bessy
Soft X-Ray Free Electron Laser, ISBN 3-9809534-0-8, 2004
[2] S. Reiche, K. Goldammer, P. Musumeci, “Recent Upgrade to
the Free-electron Laser Code Genesis 1.3,” To be PublishedIn the Proceedings of Particle Accelerator Conference (PAC
2007).
2 The length was chosen to allow for seeding five consecutive bunchparts, accounts for slippage of FEL radiation in the radiators and includes
a safety margin for timing difficulties.

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Proceedings of FEL 2007, Novosibirsk, Russia


OUTPUT PERFORMANCE OF THE STARS HGHG DEMONSTRATORAT BESSY*

B. Kuske Ý , K. Goldammer, A. Meseck, BESSY, Berlin, Germany
Abstract
BESSY is planning to construct a free-electron laser
facility, STARS - Super conducting Test-Accelerator for
Radiation by Seeding, to demonstrate cascaded high-gain
harmonic generation (HGHG) FELs. A 325MeV superconducting linear accelerator will drive two HGHG-stages,
where the second stage is seeded by the radiation from thefirst stage. Such a cascading of the HGHG scheme allows for a reduction of the STARS output wavelength down
to the few 10nm range. This paper describes the layout
and the expected performance of the facility, the achievable wavelength range, the harmonic content of the radiation, the potential of super-radiant pulses and first tolerance
studies for bunch parameter mismatch.

INTRODUCTION
In 2004, BESSY presented the Technical Design Report for a 2.25GeV linac driven Free-Electron Laser (FEL)
user facility, covering the VUV to soft X-ray spectral range[1]. The facility utilizes the high-gain harmonic generation principle (HGHG), first demonstrated at Brookhaven
National Labratory, USA, in 2000 [2]. In order to reachthe short wavelength range, several cascaded HGHG stages
are foreseen. In 2006, the German Science Council recommended the construction of a demonstrator to investigate the possibility of cascading HGHG stages. A Conceptual Design Report for this demonstrator, ’STARS’- Super
conducting Test-Accelerator for Radiation by Seeding, hasbeen published in 2006 [3]. STARS will consist of a normal conducting RF gun, a superconducting 325MeV linac,
a collimation and diagnosis section and a 27.5m undulator section [4]. It will produce pulses in the spectral range
from 18eV to 31eV. For further details see [5]. This paper
details the layout of the undulator section and presents theperformance of STARS at different wavelengths and operational modes. A few preliminary calculations concerning
the stability of the machine are shown.

MECHANICAL LAYOUT OF THE
UNDULATOR SECTION
The undulator section will consist of two HGHG stages
separated by a fresh bunch chicane, that delays the electron bunch so that the radiation of the first stage seeds a
preceeding, fresh part of the beam. Each stage starts witha short undulator to modulate the energy of the electron£ Funded by the Bundesministerium für Bildung und Forschung(BMBF), the State of Berlin and the Zukunftsfond BerlinÝ Bettina.Kuske@bessy.de

FEL projects

130bunch (modulator). It is followed by the dispersive section
consisting of four identical dipoles. The adjacent undulator, called radiator, consists of two respectively three separated segments tunable to the harmonics of the modulators’
resonant frequency. Table 1 lists the important parameters
for all four undulators.
Table 1: Characterization of the STARS undulators (Modulators: M1, M2, Radiators R1, R2.)Type
Period [m]No. Periods
Aper. [mm]Max.
[T]Max. B [T]Length [m]Res.  [nm]M1
planar
0.05
10
10
1.1
0.5
800

R1
planar
0.05
2*40
20
1.1
2* 2.0160/200

M2
planar
0.05
30
20
1.1
1.5
160/200

R2
Apple III
0.022
3*150
7
0.839
0.621
3*3.3
40/50/66

The fresh bunch chicane is mechanically identical tothe dispersive sections. In order to control the electron
beam size along the length of almost 30m, a total of 9
quadrupoles are distributed, one before and after each chicane and one in between undulator segments. The matching into the section will be handled in the preceding collimator. The total length of the chicanes is 2.5m; the distance
between undulator segments is 1.0m. The chicanes will
also host all necessary diagnostics, as well as all vacuum
components, which shall not be incorporated into the undulators. Phase shifters and further diagnostics are placed
between undulators segments. The correctors necessary tocontrol the trajectory of the bunch are incorporated into thequadrupoles.

OPERATIONAL MODES
A tunable 800nm Ti-Saphir laser will be used to seed thefirst modulator. There will be a small chicane right in frontof the modulator as a port for the beam. The 4th or 5th harmonic of the beam modulation can be amplified in the following radiator by tuning the dispersive section and driving
the undulator gap. After the radiator the electron bunch isdelayed by 100 fs in the fresh bunch chicane. Thus, in thesecond modulator, the preceding, unused part of the bunchis seeded by radiation 160nm and 200nm. The second radiator can be tuned to the 4th or 3rd harmonic of the resonant
frequency of the second modulator, so that the final output

Proceedings of FEL 2007, Novosibirsk, Russia

200

0.6
0.4

100

spectral power [a.u.]1

0.8
power [MW]spectral power [a.u.]

power [MW]

10

300

0.2
0.1

10

20

30 40
s [μm]

50

60

0

1

1

0.8

0.8

spectral power [a.u.]

1

100

MOPPH052

0.6
0.4
0.2

39.6 39.8 40 40.2 40.4
wavelength λ [nm]020 30 40 50 60
s [μm]

0

0.6
0.4
0.2

49.5 50 50.5
λ [nm]

066 66.5 67
λ [nm]

Figure 1: The temporal and the spectral power, at 40nm
and helical polarization, when optimizing the output of thefirst radiator segment (black) and the second segment (red).

Figure 2: Temporal and spectral power at 50nm (black)and 66nm (red) for planar radiation, optimized for the firstradiator segment.

ranges from 40nm to 66nm. Despite changing the combination of the harmonics, the tunability of the seed laser frequency allows for delivering any intermediate frequency.
The second radiator consists of three undulator segments.
Depending on the final bunch parameters and the chosen
wavelength, the saturation length varies, and the gaps of
one or two segments might be opened for certain operating
conditions. The second radiator will be an APPLE III typeundulator [7], so that the polarization is variable. Due to thesegmented layout of the radiators and the tunability of thedispersive sections, a wide range of operational modes arefeasible. By increasing the fields in the chicanes, the FEL
process can be pushed to saturate at the end of the first segment of Radiator 2, with a very good signal to noise ratioof 10 . The saturation point moves towards the end of thesecond segment of Radiator 2, when the chicane strength isrelaxed. Higher temporal as well as a much higher spectral
power can be reached, at the expense of a smaller signal tonoise ratio, see Fig 1.
Furthermore, the tolerance of STARS to bunch parameter deviations, like the finally achievable emittance or theenergy spread is largely increased. Best results for a bunch
emittance of 1.0  mm mrad e.g. are reached by using only
one segment of Radiator 1. In this sense, the following
performance characteristics are only examples of what isachievable.

stage, to include any possible spontaneous radiation effects.
The bunches are seeded at 800nm by a 275MW, 30fs Gaussian shaped seed pulse. The average sliced emittance extracted from the start-to-end simulation is 1.0  mm mrad,a value much smaller than measured so far in state-of-theart normal conducting guns for 1nC bunch charge. On
this account, the sliced emittance of the bunches has beenraised to 1.5  mm mrad. The averaged bunch parameters
are listed in Table 2.

PERFORMANCE
All calculations presented have been performed using
GENESIS1.3 [6]. As the performance strongly depends on
the bunch parameters, only start-to-end bunches, i.e. resultsfrom particle tracking studies in the gun, linac and collimator were used as input for the performance calculations.
The dispersive chicanes were modeled using the transfer
matrix feature of GENESIS and the bunch part used in thesecond stage has also been tracked through the first HGHG

Table 2: The main average bunch parameters vary slightly
for the two bunch parts used in the two stages

Gamma
Emittance [ mm mrad]
Rel. energy spread
Beam size [m]current [A]total bunch charge [nC]

part 1
part 2
639.6
638.5
1.44
1.50
3.3 10  3.1 10 
126, 118 130, 134
508
512
1.0

The calculations do not include any magnetic errors or
trajectory offsets, except for those inherent to the bunch, or
any bunch-to-bunch fluctuations.
Fig. 2 shows the temporal and spectral power for 50nm
and for 66nm and planar polarization taken behind the firstradiator segment. In order to switch from 50nm to 66nm
only the second radiator has to be re-tuned to the third harmonics of 200nm. Due to the increased undulator K-value
the power increases. For the longer wavelengths it becomesincreasingly difficult to suppress the background radiation
and avoid the onset of super-radiance to maintain a pure
spectrum when optimizing the output of the second radiator segment.
Table 3 displays the three main operational modes and

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131Proceedings of FEL 2007, Novosibirsk, Russia

their performance parameters optimized for clean spectra
and maximal power. Any intermediate wavelength can beachieved by varying the seed laser wavelength and adjusting the undulator gaps.

Wavelength
Polarization
No. segments
Power [MW]Pulse energy [J]
Pulse width [fs]% of pulse energy
in 0.1 % bandwidth
background energy /pulse energy [%]

40nm
P
H
2
2
120 163
2.8 3.8
18
19
53
53

50nm
P
H
1
1
275 336
6.1 7.4
16
16
41
41

66nm
P
1
328
9.2
24
23

6.6

6.6

2.3

5.9

7.1

The FEL power can be increased beyond saturation byslightly detuning the undulator. This leads to the onset ofthe super-radiant regime, [8]. The coherence length, i.e.
the slippage within one gain length, becomes comparable
to or larger than the pulse length. When the radiation poweris high enough, bunching occurs instantly in a small fraction right ahead of the pulse, the power is further increased
and the electrons immediately debunch again. As a result,much higher peak powers at very short pulse lengths can beachieved, at the expense of a deteriorated spectral purity.
Fig. 3 displays the results achievable at 40nm planar polarization and an emittance of 1.0  mm mrad taken behind
the third undulator segment, when the undulator K-value isreduced by 1.7%. The peak power is 1.4GW, the pulse energy is 43J. Despite the deteriorated spectrum, still 40%of the energy is located within 0.1% of the spectral bandwidth. The FWHM pulse length is 14fs.

SENSITIVITY TO BUNCH PARAMETERS
In preliminary tolerance studies, the sensitivity of the
STARS performance to large changes of single bunch parameters has been studied for the most sensitive case at
40nm and planar polarization. These calculations model
basic parameter deviations, e.g. when the calculated energy
spread or the emittance differ from the predictions. In thiscase, the undulator section can be adjusted to achieve thebest performance under the given conditions. To achieve
the following results, the structural flexibility of STARS as
explained above has been exploited. In order to preserve
the typical variation of the parameters over the bunch, theparameters have been scaled for each slice. Please notethat the expected shot to shot parameter variations are muchsmaller than the given offsets. Shot to shot fluctuations can
not be counteracted and have to be studied separately. The
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1

1.2

power [GW]

Table 3: Main STARS performance parameters for planar(P) and helical (H) polarization.

1.4

spectral power [a.u.]

MOPPH052

1
0.8
0.6
0.4

0.6
0.4
0.2

0.2
0

0.8

0

10 20 30 40 50 60
s [μm]

0

39
40
39.5
wavelength λ [nm]Figure 3: Temporal and spectral power of the super-radiantpulse at the end of the third radiator segment. Still 40% of
the power are located within 0.1% bandwidth. The FWHM
pulse length is 14fs.

most critical parameters for the performance are the emittance, the energy spread and the current. Their values andthe maximum output power are listed in Table 4.
Table 4: Maximal achievable power, in case major bunch
parameters should not match the predictions. The reference
values are indicated by italic letters. By using the second
radiator segment, even the 68MW reached for an emittanceof 2.0  mm mrad could be improved.
Parameter

Value

Segment

Emittance
mm mrad]

1.0
1.5
2.0
3e-5
1e-4
450
500
550

1
1
1
1
2
2
1
2

Rel. energy spreadcurrent [A]Peak power
[MW]
145
120
68
120
127
100
120
156

HARMONIC CONTENT
Recently, an upgrade of GENESIS has been developedthat allows for the computation of harmonics in the FEL
output for planar undulators [9]. This program has beenused to investigate the STARS output at 13.3nm. Fig. 4
shows the results for two radiator segments. To increase theharmonic content of the radiation, a longer duration of the
FEL process, i.e. using two radiator segments is profitable.
20% higher peak power and a much cleaner spectrum canbe found after the second segment.

Proceedings of FEL 2007, Novosibirsk, Russia
0.7
1

0.6
spectral power [a.u.]

power [MW]

0.5
0.4
0.3
0.2

0

0.6
0.4
0.2

0.1
0

0.8

10 20 30 40 50 60
s [μm]

013.1 13.2 13.3 13.4 13.5
wavelength λ [nm]Figure 4: Temporal and spectral power of the 3rd harmonicin the second radiator segment when tuned to 40nm planar
radiation.

CONCLUSION

MOPPH052[4] M. Abo-Bakr et al., ”STARS — A Two-Stage High-Gain
Harmonic Generation Demonstrator”, Proc.of thr Particle Accelerator Conference (PAC 2007), Albuquerque, New Mexico.
[5] J. Knobloch et al., ”STARS — An FEL to demonstrate Cascaded High Gain Harmonic Generation”, FEL’07, this proc.
[6] S. Reiche, ”GENESIS 1.3: A Full 3D Time Dependent FEL
Simulation Code”, Nuclear Instruments and Methods A429
(1999) p. 243.
[7] J. Bahrdt, W. Frentrup, A. Gaupp, B. Kuske, M. Meseck, M.
Scheer, ”Undulators for the BESSY Soft X-ray Free Electron
Laser”, Proc. of the 26th International Free Electron Laser
Conference (FEL 2004) Trieste, Italy.
[8] L. Giannessi, S. Spampinati and P. Musumeci, ”Non Linear Pulse Evolution in Seeded and Cascaded FELs”, Proc. ofthe 27th International Free Electron Laser Conference (FEL2005), Stanford, California, USA.
[9] S. Reiche, K. Goldammer, P. Musumeci, “Recent Upgrade to
the Free-electron Laser Code Genesis 1.3,”, Proc.of thr Particle Accelerator Conference (PAC 2007), Albuquerque, New
Mexico.

BESSY proposes the construction of a demonstrator,
STARS, to investigate the possibility of cascading HGHG
stages in order to provide reproducible fs pulses in awavelength range much shorter than provided by available
lasers. The general layout of the undulator section of themachine has been presented, and simulation results of the
expected performance of different operational modes havebeen shown. The proposed layout proved to be flexible
enough to cope with a wide range of bunch parameters,
due to the modular construction of the radiators and theflexibility provided by the dispersive sections. Calculation
with an emittance of 1.5  mm mrad and an energy spreadof 1.010  predict almost the same peak power as calculations for an emittance of 1.0  mm mrad and an energy
spread of 3.310 , when the undulator section is properly
optimized and the second radiator segment is used.
It is known that the synchronization between the bunch
and the seeding radiation is one of the critical aspects of
HGHG FELs. The effects of timing jitters is expected to belarge, but has yet to be studied. The influence of magnetic
errors, trajectory offsets and undulator errors will be studied in the near future, but their influence is expected to be
far less critical.

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] A. Doyuran et al., ”Characterization of a High-Gain
Harmonic-Generation Free-Electron Laser at Saturation”, Phys. Rev. Lett. 86, 5902 (2001). URL:
http://link.aps.org/abstract/PRL/v86/p5902.
[3] The STARS Design Group, ”STARS - Proposal for the Construction of a Cascaded HGHG FEL”, BESSY Internal Report, Berlin, October 2006.
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Proceedings of FEL 2007, Novosibirsk, Russia

SMALL-APERTURE VACUUM-CHAMBER DESIGN FOR STARS*
J. Bahrdt, V. Dürr, A. Meseck† , M. Scheer, G. Wüstefeld
BESSY GmbH, Berlin, Germany
Abstract
To demonstrate and investigate the cascaded high-gain
harmonic generation (HGHG) scheme proposed for the
BESSY Soft X-ray FEL, BESSY plans to build a testfacility called STARS consisting of two HGHG stages. The
radiator in the second stage is planned as an APPLE III device which provides the highest field for a circular beam
pipe. It’s minimum Gap of 7 mm translates into a 5 mm
inner diameter of the vacuum chamber, which leads to ahigher pressure and an increase of the wakefields. An analysis of the impact of the wakefields and the expected vacuum profile is thus required. Results of this analysis andvacuum calculations and measurements are presented.

INTRODUCTION
To provide radiation with high power, short pulse lengthand full coherence in the VUV and soft X-ray regime,
BESSY plans to build a seeded FEL facility based on thehigh-gain harmonic generation scheme [1, 2]. The technical design report of the BESSY Soft X-ray FEL facility[3] was evaluated in 2006 by the German Science Council and recommended for funding subject to the condition
that its key technology, the cascaded HGHG scheme, bedemonstrated beforehand. To address this issue, BESSY is
proposing the proof-of-principle facility STARS [5] for a
two-stage HGHG cascade which will serve as a user facility even after the commissioning of the BESSY FEL. The
STARS is seeded by a tunable laser covering the spectral
range of 700 nm to 900 nm. The target wavelength ranges
from 70 nm to 40 nm with peak powers up to a few hundred
MWs and pulse lengths less than 20 fs (rms). The polarization of the fully coherent radiation is variable. For efficient lasing a 325 MeV driver linac is required. It consistsof a normal-conducting gun, superconducting TESLA-type
modules modified for CW operation and a bunch compressor, for more details see please [4, 5, 6].
The STARS comprises a cascade of two HGHG stages
each consisting of an undulator (acting as modulator) /dispersive chicane / undulator (acting as radiator) section.
The two modulators and the first radiator of the STARS
are planned as planar devices. The second (final) radiatorneeds to be helical to provide full polarization control of theoutput radiation. This radiator consists of three undulator
modules and will be realized as an APPLE III [7] device.
The period lengths and the minimum gaps, i.e. free aperture between the magnet rows, of the undulators are cho∗ Worksupported by the Bundesministerium für Bildung und
Forschung and the Land Berlin† meseck@bessy.de

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sen such that the desired wavelength range can be covered
for an electron beam energy of 325 MeV. The planar devices have a period length of 50 mm and a minimum gapof 20 mm and 10 mm respectively. The period length of
the final radiator amounts to 22 mm and the minimum gap
is 7 mm. This small gap translates into 2.5 mm for thevacuum chamber inner radius.
Generally, the small conductance caused by such a small
aperture leads to a higher pressure, which has to be counteracted by a suitable vacuum pumping scheme as far as
possible. An other impact of the small aperture is the enhancement of the wakefields. In spite of the moderate peakcurrent of 500 A predicted for STARS, an increase of theundulator wakefields can be expected.
The degradation of the electron beam quality due to thehigher pressure and the change in the electron energy by the
wakefields decline the FEL output radiaton. We present a
analysis of their impact on the FEL performance.

CIRCULAR BEAM PIPE AND APPLE III
TYPE RADIATOR

Figure 1: A sketch of the magnetic structure of an APPLE III device.
The second radiator will be realized as an APPLE III
device providing full polarization control of the radiation.
This APPLE type requires a round beam pipe to allow for
more magnetic material located close to the electron beam,
see Figure 1. For the second radiator of STARS, the freeaperture between the magnets is 7 mm and the smallest vertical distance amounts to 4.4 mm which provides enoughspace for Hall probe measurements as well as for a fixture
to support the vacuum chamber. An APPLE III type structure has been chosen for a number of reasons:Proceedings of FEL 2007, Novosibirsk, Russia• For the same minimum aperture (7mm in this case)
the APPLE III device provides a factor of 1.35 higher
fields when compared to the APPLE II design. Notethat the minimum aperture of 7 mm is limited by theacceptable aperture of the electron collimation systemand the alignment concept.
• The natural focusing of an APPLE III design issmaller than that of an APPLE II. The natural focusing
depends on the transverse field profiles which changes
with gap and row phase of the variably polarizing Radiator. The focusing strength has an impact on theelectron beam size and has to be compensated by asuperposed external quadrupole lattice.
• The APPLE III design provides space for the installation of glass fiber radiation monitors (to detect beamloss) close to the electron beam without sacrificing
gap (the diameter of Cherenkov glass fibers is 0.7mm)[8, 9].

MOPPH054

Figure 2: The calculated vacuum profile of the second radiator with a module length of 3 m.
Scattering of 300-MeV-Electrons on N2-Gas

2006/10/19 11.56[ dNe/ Ω]
10 6

However, the needed circular beam pipe with the small
inner radius of 2.5 mm reduces the vacuum conductance,even more than an elliptical beam pipe with a short axis of
2.5 mm. Therefore a suitable pumping scheme has been
designed.

10 5
Geant3

10 4Geant410 3elast. scat. f. nucl.

10 2
10
1
10

VACUUM SYSTEM
A carefully designed pumping system for the second
radiator requires 3 m long modules with 1 m long sections between them. The intersections will comprise thepump,focussing quadrupoles, phase shifter and diagnostic. Figure 2 shows the calculated vacuum profile forthis scheme. The peak value is in the 10 −6 mbar range.
Measurements with a commercially available copper tubing (with a inner radius of 2 mm) have yielded a value of
5 × 10−7 mbar. After several weeks of measurement thepressure fell to 2×10 −8 mbar. Therefor pressures less than1 × 10−7 mbar can be expected for the final radiator.
Gas pressures in this range are not expected to produce
significant radiation damage in the undulators or impact
the photon flux. The question, whether the elastic scattering on nuclei, which provides the major contribution to
the scattering process for 300 MeV electrons, can cause a
noticeable angle error, has been investigated by analyticalmodels [10, 11, 12] and Monte-Carlo simulations. The results of the calculation and simulations with GEANT3 and
GEANT4 [13, 14] are summarized in Figure 3. Depicted
is the number of scattered electrons per solid angle versus
the scattering angle (for 300 MeV electrons). The electrons
are scattered on N 2 in a target length of 4 m with a pressure of 10−5 mbar. Most electrons are scattered in a verysmall angle, less than 0.01% have a scattering angle larger
than 10 μrad. Therefore, for a vacuum pressure less than
10−5 mbar the scattering on rest gas can be neglected.

-1

0

50

100

150

200

250

300

350

400

450
500
angle [μrad]

Figure 3: The number of scattered electrons per solid angle versus the scattering angle for 300 MeV electrons scattered on N2 in a target length of 4 m with a pressure of
10−5 mbar.

WAKEFIELDS
Due to the small aperture of the second radiator, measurable wakefields are expected in spite of the low peak current of 500 A. The change of the electron energy by thesewakefields could perturb the FEL interaction by pushing
the electrons off-resonance. An analysis of the wakefields
was performed to estimate their impact on the FEL performance.
Figure 4 shows the temporal profile of the wakefields,
where the black line is the resistive wake, the blue lineis the geometrical wake, the red line is the sum of themand the green line is the current profile. Two examples areshown for different inner radii (r) of a copper pipe. The
aperture for the diagnostic box (gap) is 20 mm. The temporal profile of the wakefields for different aperture of diagnostic box are depicted in Figure 5, also an example withaluminum pipe is shown.
The dominant sources were found to be the resistive wall
wakes and the effect of geometry at the diagnostic ports,
each contributing about 50% to the total wakefield. Max-

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Proceedings of FEL 2007, Novosibirsk, Russia

imum calculated values were of order 5 kV/m for a pipe
inner radius of 2.5 mm.

Figure 4: Temporal profile of the wakefields, where theblack line is the resistive wake, the blue line is the geometrical wake, the red line is the sum of them and the green
line is the current profile in [a.u.].Two examples are shownfor different inner radii (r).
Compared with published LCLS wakefield calculations[15, 16] the peak current in STARS is more than 20 times
smaller and in turn much weaker wakefields are expected.
There is no advantage of the use of aluminum pipe for thesecond radiator of STARS, see Figure 5. Note that for
STARS the AC component of the resistive wall wakefields
can be neglected, as the STARS bunch (500μm rms [6]) ismuch longer than the LCLS bunch (20μm rms [15]).
The energy loss due to the wakefields (5 keV/m) was included in the calculation of the FEL radiation using GENESIS [17]. Figure 6 compares the FEL performance with andwithout the energy loss. The temporal and spectral profilesof the FEL output are shown for the shortest target wavelength of STARS. For a beam pipe with a inner radius of
2.5 mm and the expected beam properties of STARS, theimpact of the wakefields is negligible.

CONCLUSION
A small-aperture vacuum-chamber with an inner radiusof 2.5 mm is planned for the second radiator of STARS.
Generally, such a small aperture leads to a higher pressure
and an increase of the wakefields. Thus it causes a degradation of the FEL output.
The expected pressure and its impact on the electron
beam has been calculated for the second radiator. Additionally, the pressure was measured in a test setup. The
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Figure 5: Temporal profile of the wakefields, where theblack line is the resistive wake, the blue line is the geometrical wake, the red line is the sum of them and the green lineis the current profilein [a.u.]. Three examples are shown fordifferent aperture of diagnostic box (gap) and materials.

increase of the pressure seems to be very moderate. Thus
the electron beam will not be disturbed.
Due to the wakefields, an energy loss of 5 keV/m is expected for the second radiator. Including this in the FEL
simulations, almost no impact could be observed. We conclude that the small-aperture beam-pipe of the second radiator causes almost no degradation of the FEL performance.

REFERENCES[1] L. Yu,“Theory of high gain harmonic generation: an analytical estimate ,” NIM A 483 (2002) 493.
[2] L. Yu, “High-gain harmonic generation of soft X-ray withthe “fresh bunch” technique,” NIM A 393 (1997) 96.
[3] “The BESSY Soft X-ray Free Electron Laser, Technical De-

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH054[11] W. A. McKinley, “The Coulomb Scattering of Relativistic
Electrons by Nuclei”, Phys.REV.74 (1948) 1759.
[12] J. Le Duff, “Current and Current Density Limitations in Existing Electron Storage Rings,” NIM A 239 (1985) 83.
[13] S. Agostinellia et al.,“GEANT4 - A Simulation Toolkit”,
NIM A506 (2003), 250-303R. Brun et al.
[14] “GEANT Detector Description and Simulation Tool”, v.
3.21, CERN Program Library CERN (1993).
[15] K. L. F. Bane, G. Stupakov, “Resistive Wall Wakefield in the
LCLS Undulator”, proceedings PAC05.
[16] S. Reiche et al., “Optimization of the LCLS X-ray FEL output performance in the presence of strong undulator wakefields”, proceedings PAC05.
[17] S. Reiche, “GENESIS 1.3”, NIM A 429(1999) 243.

Figure 6: Temporal (top) and spectral (bottom) profiles of
the FEL output are shown for the shortest wavelength (i.e.
40 nm) aimed at STARS with (black line) and without (reddiamond) the energy loss due to the wakefield.

sign Report”, March 2004, eds.: D. Krämer, E. Jaeschke, W.
Eberhardt, ISBN 3-9809534-08, BESSY, Berlin (2004).
[4] B. Kuske, K. Goldammer, A. Meseck, “Output Performanceof the STARS HGHG Demonstrator at BESSY”, this conference.
[5] “STARS - Proposal for the Construction of a Cascaded
HGHG FEL”, eds.: J. Knobloch, E. Jaeschke, W. Eberhardt,
BESSY, Berlin (2006).
[6] T. Kamps et al., “STARS - A Two-Stage High-Gain Harmonic Generation FEL Demonstrator”, proceedings PAC07.
[7] J. Bahrdt, W. Frentrup, A. Gaupp, B. Kuske, A. Meseck, M.
Scheer, “UNDULATORS FOR THE BESSY SOFT-X-RAY
FEL”, proceedings FEL 2004, Trieste, Italy.
[8] J. Bahrdt,“APPLE UNDULATORS FOR
FELS”,proceedings FEL 2006, Berlin, Germany.

HGHG-[9] J. Bahrdt,“ Status of the Undulator System of the Seeded
HGHG-FEL Test bench at MAX-Lab”, this Conference[10] J.D. Jackson,(1975).

“Classical Electrodynamics”,

2.Edition

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Proceedings of FEL 2007, Novosibirsk, Russia

MEASUREMENT OF THE PROJECTED NORMALIZED TRANSVERSEEMITTANCE AT PITZ∗
L.Staykov† , J. Bähr, C. Boulware, H. J. Grabosch, L. Hakobyan, M. Hänel, S. Khodyachykh,
S. Korepanov, M. Krasilnikov, S. Lederer, A. Oppelt‡ , B. Petrosyan, S. Rimjaem, A. Shapovalov§ ,F. Stephan, DESY, Zeuthen, Germany
J. Rönsch, Hamburg University, Hamburg, Germany
D. Richter, BESSY, Berlin, Germany
K. Flöttmann, DESY, Hamburg, Germany
G. Asova, K.Boyanov, I.Tsakov, INRNE-BAS, Sofia, Bulgaria
Abstract
In this paper we present results from the emittance meaThe main objective of the Photo Injector Test facility
at DESY in Zeuthen (PITZ) is the production of electron
beams with minimum transverse emittance at 1 nC bunchcharge. PITZ consists of a photo cathode RF gun, solenoids
for compensation of the space charge induced emittance
growth and a booster cavity. In order to study the emittance evolution along the beam line three Emittance Measurement SYstems (EMSY’s) were installed downstreamof the booster cavity [1]. In a first operation period in October 2006 the emittance was measured for gun gradientsof about 40 MV/m. A new gun cavity is presently installedat PITZ and conditioning up to a gradient of 60 MV/m isongoing. In this work we present recent results from measurements of the normalized projected transverse emittanceof the electron beam. The emittance is measured using
the so called single slit scan technique. Measurements arepresented for different gun and booster gradients, solenoid
strengths and initial beam size at the photocathode.

INTRODUCTION
Major goal of PITZ is the development and optimizationof electron sources that fulfill the requirements for SASE
FEL’s such as FLASH and XFEL. The optimization process is conducted by extended numerical simulations using
ASTRA [2], and closely followed by research and development of appropriate instruments for electron and laser
beam characterization (see [3, 4]).
A simplified scheme of PITZ is shown on Figure 1. It
consists (right-to-left) of a 1.5 cell L-band RF gun equippedwith a Cs2 T e cathode, pair of solenoids for space charge
compensation, low energy beam diagnostics, a booster cavity, high energy diagnostics including three EMSY’s (installed at 4.3, 6.6 and 9.9 m downstream the cathode) anda beam dump. A photocathode laser system provides carefully shaped laser pulses with variable transverse diameterand flat hat longitudinal distribution (see [4, 5]).
∗ This work has partly been supported by the European Community,
Contract Number RII3-CT-2004-506008, and by the ’Impuls- und Vernetzungsfonds’ of the Helmholtz Association, contract number VH-FZ-005.
† Presenting author, e-mail: lazaraza@ifh.de‡ now at PSI, Vilingen§ on leave from MEPHI, Moscow

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surements made in October 2006 and summer 2007 using
two different gun cavities:• prototype 3.1 conditioned in summer 2006 and optimized in October 2006 up to the maximum requirements for FLASH with a peak power of 3.5 MW resulting in gun gradient of about 40 MV/m [6];• prototype 3.2 which was conditioned and optimized
this summer with a peak power of up to 6.9 MW resulting in a gun gradient of ∼60 MV/m [7].
For gun prototype 3.1 the emittance was measured using the three existing EMSY’s as a function of the mainsolenoid focusing current for various booster phases. For
prototype 3.2 the emittance was measured only at the first
EMSY (distance from the cathode 4.3 m) for various beam
sizes at the cathode and different energy gain from thebooster. In addition the optimized settings for gun 3.1 wereapplied to gun 3.2 and the emittance was measured, the results are compared and discussed.

EMITTANCE MEASUREMENT SETUP
The transverse emittance at PITZ is measured using theso called single slit scan technique. A schematic representation of the technique is shown on Fig. 2. For thistechnique the uncorrelated local divergence is estimated by
cutting the electron beam into thin slices and measuring
their size on a screen after propagation in a drift space. The
so called sheared normalized RMS emittance is then calculated using the following definition [8]:pεn = βγ · hx2 i · hx′2 i.

(1)Here hx2 i and hx′2 i are the second central moments ofthe distribution of the electrons in the so called trace phasespace where x′ = px /pz represents the angle of a single
electron trajectory with respect to the whole beam trajectory1 . The RMS beam size is measured on an additional
OTR or YAG screen at the position of the slits. The uncorrelated divergence is obtained by analyzing the profiles of
1 valid for small momentum spread within the bunch, otherwise more
precise definition should be used (i.e. [9]).

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH055

Figure 1: Layout of PITZ.
the beamlets produced from the slits which drift some distance Ld downstream. There the spatial distribution of thebeamlets corresponds to the local uncorrelated divergence,hx′2 ilocal which can be derived from the size of the beamlet
using:
pphx′2 ilocal =hx2b i.
Ld(2)p
Here hx2b i is the RMS size of the beamlet on the screen
after distance Ld . The total uncorrelated divergence of thebeam is estimated by a weighted average of several measurements of the local divergence taken from different locations across the beam:′2

hx i =

NX

wi · hx′2 ii .

EMITTANCE MEASUREMENTS
On Fig. 3 the evolution of the beam emittance as simulated with ASTRA2 is shown for the two different accelerating gradients, 40 and 60 MV/m, used for the measurements. The simulation parameters are set close to PITZ
machine parameters, shown in Table 1. The curves lookdifferent since for 40 MV/m the goal of the optimization
was to have the slowest rise of the emittance along thebeam axis in order to resemble the conditions for emittanceconservation. At 60 MV/m the goal was to have the minimum emittance at 4.3 m downstream the cathode (locationof EMSY1).

(3)

i=1

The Lorentz factors βγ is measured using a dispersive
section downstream of EMSY.

Figure 3: Emittance evolution along the beamline for two
different gun gradients.

40 MV/m accelerating gradient at the cathodeFigure 2: Schematic representation of the single slit scan
technique.
The measurement system was optimized to measureemittance as low as 1 mm.mrad for 1 nC charge per bunchwith precision better than 10 % (see [10]). The slits aremounted on two orthogonal actuators which host also the
YAG and OTR screens for transverse beam distribution
measurements. Single slit masks with slit opening of 10
and 50 µm and thickness of 1 mm. Rotating and goniometric stages are providing precise angular adjustment of theactuators for improved angular acceptance of the system.

The characterization of gun 3.1 was done with maximum
input power of 3.5 MW. Therefore, all the emittance measurements were made with a maximum accelerating gradient of about 40 MV/m which resulted in a maximum
mean beam momentum right after the gun of up to about 5
MeV/c. In addition, at solenoid currents below 280 A, thefull beam size at z=1.0 m was approaching 12 mm whichis the size of the vacuum chamber at the low energy dispersive arm located at this position (see Fig. 1). This was afurther limitation to our available optimization range.
2 all the RF phases are relative to the phase of maximum mean momentum gain in ASTRAFEL projects

139Proceedings of FEL 2007, Novosibirsk, Russia

Table 1: Machine parameters for emittance measurements.
par.
gun 3.1
gun 3.2
Units
Eacc
43
∼60
MV/m
φgun
-2
0
deg
Imain
274-290365-376
A
Pmean
12.85
11 to 14.8
MeV/c
φbooster
0 to -20
0
deg
XYini
0.51
0.33 to 0.55mm
rt /ft6-8
6-8ps
F W HM∼18∼20
psεn, [mm.mrad]

MOPPH055

ASTRA fit, gun 3.1
εx , gun 3.1
εy , gun 3.1
εx , gun 3.2
εy , gun 3.2

5

4.5
4

3.5
3

2.5
2
1.5
1
0.5
0278 280 282 284 286 288 290 292 294 296 298

Imain, [A]εn, [mm.mrad]

On Fig. 4 the dependence of the projected normalized
transverse emittance on the current in the main solenoid
at three different locations along the beamline is shown.
All other injector parameters are fixed as shown in the Table 1, φbooster = φref -10 deg. A minimum is visible for
EMSY1 around Imain = 282 A. For the other two stations
the minimum of the emittance could not be characterized
because of the above mentioned limitations in the optimization range. Another notable fact is the large disagreement
between the results at EMSY3, Imain = 284 A, and thesimulations shown on Fig. 3. This can be explained by alarge error of the beam size measurements due to the factthat the beam at EMSY3 is of a size comparable with thescreen. Also the narrow dipole chamber in the low energy
section could cause a dilution of the phase space.

98

EMSY1, 4.3 m
EMSY2, 6.6 m
EMSY3, 9.9 m

7
6
5
4
3
2

Figure 5: Comparison of the measurement with gun 3.1 andgun 3.2 as well as with ASTRA simulations for the gun 3.1
case. The machine was set to have the same mean momentum at about 40 MV/m, booster phase with respect to the
maximum acceleration phase is -5 deg, initial beamsize is
0.5 mm.
position with respect to Imain of about 8 A. This large discrepancy is still to be understood.

60 MV/m accelerating gradient at the cathodeFor the gun 3.2 the RF power in the cavity was increased
up to the limit of our RF system (∼ 7 MW in the gun). This
corresponds to an accelerating gradient of about 60 MV/mor mean beam momentum after the gun up to 6.5 MeV/c
However the problem with the aperture at the low energy
dispersive arm remained therefore we decided to use only
the first EMSY (z=4.3 m) and to optimize for lowest emittance at this location. One of the optimization parame-.
ters was initial beam size (laser spot size at the cathode)
The main solenoid current (Imain ) was scanned around thebeam waist at EMSY1. The energy gain from the booster
cavity was varied such that the final beam momentum wastuned to 9.5, 11.0, 13.0 and 14.5 MeV/c.
.

Imain, [A]εn, [mm.mrad]

1
0
272 274 276 278 280 282 284 286 288 290 292

εx, n
εy, n
εx εy

2.4
2.2

Figure 4: Emittance as a function of the current in the mainsolenoid. Gun at 40 MV/m and booster phase with respect
to the maximum acceleration phase is -10 deg.

2

1.8
1.6

On Fig. 5 a comparison between gun 3.1 and 3.2 isshown, the machine settings were set such to reproduce theconditions during the measurements with gun 3.1, namely
the mean momentum from the gun (4.95 MeV/c), final momentum after the booster (12.85 MeV/c) and the laser spot
size on the cathode (initial beam size ∼ 0.51 mm). Altoughthere is agreement within the error bars between the minimum values, εn,3.1 = 1.37 ± 0.14, εn,3.2 = 1.54 ± 0.15,
there is obvious large discrepancy between the minimum
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140

1.4
1.2
1
366

368

370

372

374

376

Imain, [A]Figure 6: Emittance as a function of the main solenoid
focusing strength. Gun 3.2, mean momentum after thebooster 14.45 MeV/c.

εn, [mm.mrad]

On Fig. 6 one sees the dependence of the projected emittance on the focusing strength of the main solenoid. The
geometrical average minimum of the measured emittanceis 1.26 ± 0.18 mm mrad. Analog scans have been performed at different momentum gain from the booster. For
fixed laser parameters, gun gradient and phase, as well as
booster phase the minimum emittance obtained from a scanof Imain is shown in Fig. 7 as a function of the momentum
gain in the booster.
εx, n
εy, n
εx εy

2.2

X’, [mrad]

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH055

1

80000
70000

0.5

60000
50000

0

40000
30000

-0.5

20000
10000

2

1.8

-1

-0.4

-0.2

0

0.2

0.4

0

X , [mm]1.6
1.4

Figure 8: Phase space distribution at P = 14.45 MeV/c,
Imain = 373 A, on crest phases of gun and booster.

1.2
4.5

5

5.5

6

6.5

7

7.5

8

∆P, [MeV/c]

Figure 7: Minimum of the emittance as a function of the
momentum gain in the booster.
The beam emittance has been re-measured in details forthe best machine parameters: P = 14.45 MeV/c, Imain =373 A, XYini = 0.33 mm. A very good reproducibilityof about 2-3% has been demonstrated. Furthermore we dida very detailed scan with the slit technique, using as small
as 25 µm separation between the individual slit positions.
The phase space distribution is shown on Fig. 8. To theauthors knowledge this image has unprecedent resolution
in the trace space for such beam parameters. The ultimate
resolution of our current system is estimated to be 36 µm
x 15.4 µrad.

CONCLUSIONS[4] M.Hänel et al., “Photocathode Laser Pulse Diagnostics at
PITZ”, Proceedings of the FEL’07[5] J.Bähr et al., “Upgrades of the Laser Beam-line at PITZ”,
Proceedings of the FEL’05[6] A.Oppelt et al., “Tuning, Conditioning and Dark Current
Measurements of a New Gun Cavity at PITZ”, Proceedingsof the FEL’06[7] S.Rimjaem et al., “Status and Perspectives of the PITZ facility upgrade”, Proceedings of the FEL’07[8] V.Miltchev, “Investigations on the transverse phase space ata photo injector for minimized emittance”, PhD thesis, Humboldt University Berlin[9] K. Flöttmann, Some basic features of the beam. emittance,
Phys. Rev. ST Accel. Beams 6[10] L.Staykov et al., “Design Optimization of an Emittance
Measurement System at PITZ”, Proceedings of the DIPAC’05.

Gun 3.1 was conditioned up to 40 MV/m and characterized resulting in normalized beam emittance of 1.37 ± 0.14
mm mrad.
Corresponding machine parameters were applied to gun
3.2 at 40 MV/m yielding 1.54 ± 0.15 mm mrad.
Gun 3.2 was conditioned up to 60 MV/m and delivered
minimum transverse normalized emittance of 1.26 ± 0.18
mm.mrad.

REFERENCES[1] L.Staykov et al., “Commissioning of a New Emittance Measurement System at PITZ”, FEL’06.
[2] K.Flötmann, ASTRA, http://www.desy.de/˜mpyflo[3] S.Khodyachykh et al., “New beam diagnostic developments
at PITZ”, Proceedings of the PAC’07
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Proceedings of FEL 2007, Novosibirsk, Russia

STATUS OF THE SPARX FEL PROJECT*
C.Vaccarezza, D.Alesini, M.Bellaveglia, S.Bertolucci, M.E Biagini, R.Boni, M.Boscolo,
M.Castellano, A.Clozza, L.Cultrera, G.Di Pirro, A.Drago, A.Esposito, M.Ferrario, D.Filippetto,
V.Fusco, A.Gallo, A.Ghigo, S.Guiducci, M.Migliorati, L.Palumbo, L.Pellegrino, M.Preger,
C.Sanelli, M.Serio, F.Sgamma, B.Spataro, A.Stella, F.Tazzioli, M.Vescovi, C.Vicario, INFN
Frascati, Italy
F. Ciocci, G.Dattoli, A.Doria, F.Flora, G.Gallerano, L.Giannessi, E.Giovenale, G.Messina, P.L.
Ottaviani, G.Parisi, L.Picardi, M.Quattromini, A.Renieri, C. Ronsivalle ,ENEA C.R. Frascati, Italy
S.Cialdi, C.Maroli, V.Petrillo, M. Rome, L.Serafini, INFN-Milano, Italy
L.Catani, E.Chiadroni, A. Cianchi, C.Schaerf, INFN-Roma II, Roma, Italy
P.Musumeci, M.Petrarca, INFN Roma, Italy
F.Alessandria, A.Bacci, F.Broggi, C.De Martinis, D.Giove, M.Mauri, INFN/LASA, Segrate, Italy
L.Ficcadenti, M.Mattioli, A.Mostacci, University La Sapienza, Roma, Italy
P.Emma, SLAC, Menlo Park, CA, U.S.A.
S.Reiche, J. Rosenzweig, UCLA, Los Angeles, CA, U.S.A
Abstract
The SPARX project consists in an X-ray-FEL facility
jointly supported by MIUR (Research Department of
Italian Government), Regione Lazio, CNR, ENEA, INFN
and Rome University Tor Vergata. It is the naturalextension of the ongoing activities of the SPARC
collaboration. The aim is the generation of electron beams
characterized by ultra-high peak brightness at the energyof 1 and 2 GeV, for the first and the second phaserespectively. The beam is expected to drive a single pass
FEL experiment in the range of 13.5-6 nm and 6-1.5 nm,
at 1 GeV and 2 GeV respectively, both in SASE and
SEEDED FEL configurations. A hybrid scheme of RF
and magnetic compression will be adopted, based on theexpertise achieved at the SPARC high brightness
photoinjector presently under commissioning at Frascati
INFN-LNF
Laboratories[1,2].
Theuseofsuperconducting and exotic undulator sections will bealso exploited. In this paper we report the progress of thecollaboration together with start to end simulation results
based on a combined scheme of RF compression
techniques.

THE SPARX LAYOUT
A spectral range from 13 nm to 1 nm has been considered
for the radiation. SASE-FEL’s in this wavelength range
require high brightness beam at the undulator entrance. In
Table 1 the electron beam parameter list is reported forsuch a source, while in Fig. 1 the schematic layout of theaccelerator is shown. A 150 MeV SPARC-likephotoinjector [1] is meant to provide a 300-500 A beam,adopting the velocity bunching compression scheme. A
first linac section L1 rises the beam energy up to 300
MeV, where a first magnetic chicane is foreseen mainly
for comparing the overall efficiency between the twocompression methods at low energy. After a second linac
section L2, i.e. at the energy around 0.6 GeV, the main
magnetic compressor BC2 is located rising the beam peakcurrent up to Ipk≈1 kA, according to a ‘hybrid”

Table 1: Electron beam parameters

Beam Energy

1÷2

GeV

Peak current

1-2.5

kA

Emittance (average)2

mm-mradEmittance (slice)1

mm-mradEnergy spread (correlated)

0.1%

Repetition Rate

50

Hzcompression scheme consisting in one RF compression
stage at low energy, plus one magnetic chicane at 0.6
GeV. A third accelerating section L3 brings the beamenergy up to E≈1GeV and a first extraction dogleg DL1
drives the beam through a diagnostic section and to thefirst undulator where both SASE and seeding experimentsin the radiation wavelength range of λr≈ 13 ÷5 nm areforeseen. This is what is meant for the first phase of the
SPARX project. For the Phase II another linac section
will bring the beam energy up to 1.5 GeV where a third
magnetic chicane BC3 is foreseen to compress the beamand reach peak currents of the order of Ipk≈2÷2.5 kA. The
last linac L4 brings the final energy up to E=2GeV. A
second extraction dogleg DL2 provides the beamdiagnostics and delivery to the second undulator for the
wavelength range λr≈ 5÷1.5 nm

Fig. 1:: SPARX Linac schematic layout____________________________________________*Work partially supported by MIUR for the realization of “Grande Infrastruttura Laser ultrabrillante per raggi X multiscopo”

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142Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH058

The RF Photoinjector
The injector design is based on the SPARC highbrightness photoinjector presently under commissioningat Frascati Laboratories [1,2]. It considers a 1.1 nC bunch
10 ps long (flat top) with 1.1 mm radius, generated inside
a 1.6-cell S-band RF gun of the same type of the BNLSLAC-UCLA one [3] operating at 120 MV/m peak fieldequipped with an emittance compensating solenoid. Threestandard SLAC type 3-m TW structures each one
embedded in a solenoid boost the beam up to 150 MeV.
According to the simulation results the beam compression
at low energy (<150 MeV), still in the space charge
dominated regime, turns out to be feasible provided that aproper emittance compensation technique is adopted [4],Moreover the propagation of a short bunch in thefollowing accelerating sections reduces the potential
emittance degradation caused by transverse wake fields,
while a proper phasing of the linac can control thelongitudinal wake fields. A systematic study based on
PARMELA code simulations has been done in order to
optimize the parameters that influence the compression[5], the results of computations show that peak currents
up to kA level are achievable at the injector exit with agood control of the transverse and longitudinal emittanceby means of a short SW section operating at 11424 MHz[6] placed before the first accelerating section. On theother side the results obtained without the IV harmoniccorrection prior the RF compressor, show that is anyway
possible to reach good compression factors but paying fora heavy deformation of the longitudinal bunch
distribution, a strong sensitivity to RF compressor phase,and a highly non linear longitudinal phase space. In Table
2 a summary is reported of the RF compression studies
results. A medium RF compression factor has been chosen
and presented here as the first referring case for the
SPARX beam dynamics studies, it gives an average peakcurrent Ipk≈400 A at the exit of the photoinjector, as
highlighted in Table 2 and shown in Fig. 2.

The Linac
In the present configuration the SPARX accelerator(PHASE I and II) is composed of four separate S-band
linac sections L1, L2, L3, L4, with E= 25 MV/m
accelerating field, located downstream a SPARC-likephotoinjector (see Fig. 1). At the entrance of each of thethree magnetic chicanes an X-band section is provided tolinearize the beam longitudinal phase space prior themagnetic compression. For the 1 GeV channel of Phase I,
both L1 and L2 sections are meant to work off crest, toprovide the required energy chirp to compress the beam in
BC2, while the on crest L3 section rises the beam energy
up to E=1 GeV and contributes to the energy spread
reduction. For the magnetic compression in BC3, theproper off-crest acceleration is applied also to the L3
section, while L4 contributes to the energy spreadcancellation and brings the beam energy up to E=2GeV.

Table 2: RF compressor parameterRFphase range

B1,B2,B3(gauss)Current(A)

Emittance(μm)-60°/-75°

1200,0,0117-1510.7-75°/-83°

1200,1400,0151-2490.8-83°/-87°

1200,1400,0249-458

1.3-87°/-91°

1200÷1800

458-1180

2.8

Fig. 2: Average current, transverse emittance andenvelope, axial magnetic field vs. z for a final 450 A
electron beam., tracked with PARMELA [7].
The invariant envelope matching condition will beapplied to the lattice as proposed by Ferrario et al [8].

The Bunch Compression
To increase the beam current up to the kA ordermagnitude a magnetic compression stage is foreseen in
the BC2 chicane for the beam with final energy E=1GeV,
Ipk≈1 kA (Phase I), and in the BC3 chicane for the beamwith final energy E=2 GeV, Ipk≈2.5 kA (Phase II). With
the previously described setting for the RF photoinjector,
a further compression factor of 2 in the BC2 chicane
produces an average peak current Ipk≈1 kA, able to reach
SASE saturation in the wavelength range of λr≈ 10÷6 nm
at the energy of 1GeV. The parameters of the BC2compressor for this case are shortly listed in Table 3. The
photoinjector incoming beam has been generated withPARMELA, considering a thermal emittance value of
εx≈0.6 μm, the downstream tracking in the chicane has
been performed with ELEGANT [9]. The tracking in theBC2 chicane has also been checked with PARMELA and
CSRtrack [10] codes in order to clarify the role played by
the space charge effect in the transverse emittance
dilution [11]. The three codes outputs show substantiallythat for a peak current around Ipk≈1 kA the space charge
effect doesn’t heavily contribute to dilution of thetransverse emittance.

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Proceedings of FEL 2007, Novosibirsk, Russia

Table 3: BC2 compressor parameters .
Beam Energy
Initial rms bunch length
Final rms bunch length
Incoming energy spread
Momentum compaction
2nd order mom. compaction

E
σzi
σzf
σδi
R56
T566

GeV
mm
mm
%
mm
mm

intensive study is ongoing to explore the most suitableconfigurations according to the user community needs.
0.5
210
90
.45
-27
+42

A hybrid compression scheme with velocity bunching andBC2 only is nevertheless foreseen and RF compression
tests will be performed at the SPARC facility in thesecond half of 2007. After the BC2 compressor theenergy of the beam is raised up to 1 GeV and the first
dogleg DL1 delivers the beam to the 1 GeV undulator
system, where both SASE and seeded radiation schemes
are foreseen for a radiation length in the range ofλr ≈ 13 ÷ 5 nm. After the 1 GeV DL1 dogleg insertion
another linac section brings the beam energy up to 1.5

Figure 4: Radiation Spectrum of the fifth harmonic
for a possible seeded scheme at 2.3 GeV.
Table 4: Preliminary Parameter list
Experiment example at 2.3 GeV. (Fig. 7)
Periods
Sections
Period(cm)K

Undulator 1
21
9
5.4
4.299

of

Seeding

Undulator 2
42
10
2.7
2.51

CONCLUSIONS

Figure 3: Slice analysis of the horizontal beamemittance after BC2 compressor as obtained with
Elegant and Parmela code simulation.
GeV where the third magnetic compressor BC3 is located,in order to reach a peak current of the order of Ipk ≈ 2.5
kA. After the last linac, at around 2 GeV, a second
dogleg DL2 brings the beam to the second undulator
system for radiation length in the range of λr ≈ 1.5 ÷ 5
nm. A special attention is devoted to the space charge
effect relevance in both the BC2 and BC3 compressors: inFig. 3 the simulation results for the transverse beamemittance are reported as obtained with the Elegant andParmela codes. A projected emittance dilution of the 30%
is obtained so far; the compressor optimization is still inprogress in order to further reduce the transverse dilution
due to the space charge effect.

The undulator and FEL
Both SASE and seeded radiation modes are foreseen ateach of the two energy steps of the SPARX channel. As
an example in Table 4 the very preliminary parameter list
is reported for the two undulators of a possible seeding
experiment at 2.3 GeV. In Fig. 4 the radiation spectrum
is shown for the fifth harmonic of the λ=13 nm seed. An
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144

The SPARX project aim is the generation of electron
beams characterized by ultra-high peak brightness at theenergy of 1 and 2 GeV, (Phase I and II), for SASE and
SEEDED FEL experiments in the range of λr≈ 13.5÷1.5
nm. It is jointly supported by the Italian Government andRegione Lazio with a five years schedule for the firstphase. The critical components such as the RFcompression scheme, magnetic chicane, etc. will be tested
during the phase II of the SPARC project. A first generallayout for SPARX has been proposed and first start to end
simulations for the 1 GeV channel of Phase I, have beenpresented using a “hybrid” scheme of bunch compression
with RF and magnetic compression techniques involved
together.

REFERENCES[1] http://www.lnf.infn.it/conference/sparx05/Giornate diStudio SPARX e Applicazioni[2] A. Cianchi, et al., Proc. of DIPAC07, Venice, Italy[3] M. Ferrario, et al., “Experimental results with the
SPARC emittance-meter”, Proc. of PAC07,
Albuquerque, New Mexico, USA.
[4] C.Vicario, et al., “Laser and RF Synchronization
Measurements at SPARC”, Proc. of PAC07,
Albuquerque, New Mexico, USA.
[5] C. Ronsivalle et al. "Comparison Between SPARC
E-Meter Meas. and Simulations", Proc. of PAC07,
Albuquerque, New Mexico, USA.
[6]
http://www.lnf.infn.it/acceleratori/sparc/SPARC
Technical Design ReportProceedings of FEL 2007, Novosibirsk, Russia

MOPPH058[7] B. Spataro, et al, “A Bi-periodic X-band RF cavity
for SPARC”, Proc. of EPAC06, Edinburgh, Scotland[8] L. Ficcadenti, et al, “RF measurements results of the
final brazed SPARC RF deflector”, Proc. of PAC07,
Albuquerque, New Mexico, USA.
[9] L. Giannessi, et al, “Future Seeding Experiment at
SPARC”, Proc. of FEL 2006, Berlin, Germany.
[10] M.D. Dohlus, T. Limberg, “CSRtrack: Faster
Calculation of 3-D CSR Effects, FEL04, Trieste.
[11]C.Vaccarezza, et al, “Status of SPARX FEL project”,
Proc. of EPAC06, Edinburgh, Scotland.

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Proceedings of FEL 2007, Novosibirsk, Russia

THE DRIVE LASER SYSTEM FOR CFEL
Li Weihua,Chen Yanan
Institute of Applied Electronics,CAEP,China
Abstract
A reliable and compact drive system is one of the key
components for the stable operation of FEL.We havedeveloped a solid-state drive laser system to meet therequirements of the CFEL(CAEP FEL) research.The
system consisted of a passive mode-locked oscillator witha timing stabilizer,a regenerative amplifier and afrequency conversion part.After the 4-th harmonics,theduration of 15 picoseconds Gaussian pulses withwavelength 266nm at a repetition rate 54.17MHz wereobtained.These micropulses were contained within amacropulses envelope as long as 1 to 6μs,which wasemitted from the drive laser at a repetition rate at
3Hz,6Hz or 12Hz,one single micropulse energy as large
as 4μJ was achieved.The design specifications,configuration and diode-pumped amplifier of the drive
laser system are also described.

INTRODUCTION
A reliable and compact drive laser system is one of the
key components for the stable operation of FEL.It willstrongly affect the performance of the FEL,such as the
specifications as following:the micropulse duration ofelectron beam,the micropulse current of electron beam,thejitter of micropulse-peak-current,and so on[1].We havedeveloped a all-state-solid drive laser system to meet therequirements of the CFEL research,as shown in table
1.The laser stablility,e.g.,energy stability,timing stability
and the pointing stability,was also requested stringently
during the course of the research[2].

DRIVE LASER SYSTEM
The drive laser system,which was shown in Fig.1,was
consisted of a passive mode-locked oscillator with atiming stabilizer,a regenerative amplifier and a frequency
conversion part.

Oscillator
The seeding laser GE-100-XHP,is a passive modelocked laser with a semiconductor absorber mirror(SESAM),developed by Time-Bandwidth Products Ltd,
Switzerland[3].Its repetition rate is 54.167 MHz,equal to
1/24 of 1300MHz L-band radio frequency, which wasused for the photocathode RF gun.The timing stabilizer
measured the phase and the frequency offset between thelaser pulses and the reference RF signal,and adjusted thecavity length to synchronize the two signals[4].

Regenerative Amplifier
It was composed of one-double-pass and two-singlepass stages.A Pockels Cell captured a “maropulse” from
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146

the continuous pulses output to increase the pulse
energy.Every “macropulse” contains 50 to 300 micropulses,as long as 1us to 6us.

Harmonics Generator
This component coverted the fundamental output to the
4-th harmonics,which would illuminate the photocathodeCs2Te.The net conversion efficiency was close to 20%
from the fundamental to the 4-th harmonics.The UVenergy was obtained up to 1.2mJ per “macropulse”,4uJ
per micropulse.

LASER PERFORMANCE
Amplitude Uniformity
The amplitude uniformity from micropulse to
micropulse in the same macropulse was quested stringently for the CFEL research.We have measured it at the portof regenerative amplifier,2-th harmonics and 4-th harmonics,as shown in Fig.2,Fig.3,Fig.4.The variation of
amplitude uniformity from micropulse to micropulse was
3% rms or less.

Energy Stability
UV energy stability was measured for 300 shots by apower meter.The statistical results showed that theEnergy fluctuation was 2.8%rms or less.The curve ofenergy deviation from the mean value was shown in
Fig.5,which were 84 data from the 300 shots.

Timing Jitter
The timing jitter of the laser oscillator was estimatedfrom the output of the phase detector in the feedback
loop.A phase detector measured the phase difference
between the fast photodiode signals of laser pulses andthe reference RF signal,and generated an “error
signal”.This phase difference was related to the timing
jitter between the laser phase and the reference RFphase.The timing jitter of the oscillator was estimated as
0.4ps rms.

Pointing Stability
The pointing stability of 266nm output pulses wasmeasured by a CCD camera.Beam profiles were
measured on a screen plate at 30 meters away form thelaser output port.Pointing stability of the beam centroid
was estimated to be 0.1mrad rms in Y direction,and
0.01mrad rms in X direction,as showed in Fig.6 andFig.7.The scale between the pixel to actual dimension was
13.7 pixels to 1mm.Fig.8 was the beam profile.
Other specifications and the laser performance werelisted on Table 2.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH060

CONCLUSION
The all-solid-state drive laser system has beendeveloped on the basis of the laser diode pumping,thepassive mode-locked oscillator with SESAM and thefeedback timing stabilizer.The drive laser was
reliable,compact and satisfying to meet the requirementsof the CFEL research.

REFERENCES[1] Li Zhenghong,Hu Kesong,Yang Maorong etc.The RF
Photoinjector Research,High Power Laser and Particle Beams,2000,12(3):366[2] F.Sakai,M.Yorozu,Y.Okada etc.All-Solid-State Picosecond Laser System for Photocathode RF Gun.
[3] High Power Mode-locked Diode-Pumped Picosecond
Laser,User Mannual,Time-Bandwidth Ltd,Switzerland.
[4] Timing Stabilizer Feedback System Accessory,User
Mannual,Time-Bandwidth Ltd,Switzerland.
[5] A.R.Fry,M.J.Fitch etc.Laser System for The TTF
Photoinjector at FERMILAB.IEEE,1998[6] J.Early,J.Barton etc.The Los Alamos FEL Photoinjector drive laser,Nuclear Instruments and Methods
in Physics Research ,A318(1992)381-388
Tab.1 The Parameters of CFEL
1

Electron Energy/MeV

35-40

2

Beam Pulse Current/A>30

3Beam Pulse Duration/ps

3-5

4

Pulse Repetition Rate/MHz

54.17

5

Maropulse Duration/μs

1-66Maropulse Rep. Rate/Hz

3-6-12

7

Pulse Timing Jitter/ps<2

8

Micropulse Amplitude Jitter/rms<3%

9Energy Spread<1%

Fig.2 The amplitude uniformity at the port of amplifierFig.3 The amplitude uniformity at the port of2-th harmonics

Fig.4 The amplitude uniformity at the port of
4-th harmonics

CLX-1100

RF Signal

GE-100-XHPP
1#Amplifier2#3#Amplifie
output2ω

4ω

Fig.1 Layout of the Drive Laser System for CFEL

)% 8
(e
ul 6
av
na 4
em
2
mo
rf 0
ec
ne -2
re
ff -4
iD
-6
0

20
40
60
80
Number of events(times)

100

Fig.5 The UV energy fluctuation from mean value

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Proceedings of FEL 2007, Novosibirsk, Russia

Tab.2 The performance of the drive laser system

The Position of Beam Centroid245)l
ex 240
ip
(s
ix
A 235
X

230

1

6

11

61

12 62 13
Times

63

14

64

1

Wavelength/nm

266

2

Pulse width/ps

10-15

3

Frequency/MHz

54.17

4

Pulse Energy/μJ

3-55Maropulse duration/μs

1-66Maropulse repetition. rate/Hz

3-6-127

Micropulse timing jitter/ps<2

8

Amplitude jitter/rms

3%

9

Pointing stability/mrad

0.11

Fig.6 The pointing stability at X direction
The Position of Beam Centroid
250
240
230
）
le 220xi 210p200（
si 190
xA
180
Y
170
160
150

1

6

11

61

12 62 13
Times

63

14

64

Fig.7 The pointing stability at Y direction

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Fig.8 The profile of UV pulse spotProceedings of FEL 2007, Novosibirsk, Russia

MOPPH061

DESIGN OF THE PAL TEST FEL MACHINE
Mungyung Kim*, Jinhyuk Choi, Jung Yun Huang, Heung-Sik Kang, In Soo Ko, Tae-Yeon Lee,
Jong-Seok Oh, Sung Ju Park, PAL, Pohang, South Korea
Chang-Mook Yim, POSTECH, Pohang, South Korea
Abstract

In order to the PAL-XFEL, the 1st stage will be to build
a test machine, whose design parameters are presented
here. It will be a 200 MeV machine that has the target
wavelength of visible range. The design details andsimulation results are shown in this paper.

INTRODUCTION
The Pohang Accelerator Laboratory (PAL) is going tobuild a new X-ray free electron laser (XFEL) machine
based on the self-amplified spontaneous emission (SASE)
scheme [1]. For the first step of the project, a test machineisconsidered to build. But it means extra time andbudget is required. Fortunately, we have found sufficientarea in the linac building. Usually PAL linac is operated
as an injector for the 2.5 GeV storage ring. So anotherlinac, test linac, beside of the preinjector area in the linac
building, is operated for low energy experiments with 60~ 100 MeV. Furthermore RF cathode gun system isinstalled to test as an injector of the PAL FEL in theassembly room of the building. The injector consists of
two accelerator columns with about 80 MeV. If we
combine with two machines, the test linac and the injector,
we need only one acceleration column and one chicane tohave a 200 MeV linac for the test machine of PAL FEL
project. It means we can save time and budget toconstruct a building of the test machine. So the test
machine is designed to install in the area. Fig 1 shows the
structure of the PAL preinjector area and schematic layoutof the test machine. In this paper, the simulation results
and detail designs of the machine will be reported.

Figure 1: Drawing with preinjector area in the linac building and schematic layout of the test machine. The test machineis designed to install in the dashed block.

BEAM DYNAMICS DESIGN
The test machine consists of a 78 MeV injection part,
linear accelerator with a chicane, beam transport line,
SASE radiation area with three undulators and experimentarea as shown in Fig. 1.
The injection part consists of a photo-cathode RF gun
and two accelerating columns. The beam charge from the
RF gun is 0.5 nC with 10 ps pulse length 60 Hz repetition___________________________________________*mungyung@postech.ac.kr

rate in maximum, and the final energy of the injector is 78
MeV. After the injector, the beam pulse length is 777 μm,
peak current is 60 A, energy spead is 0.3 % and rms
normalized eimttances are 0.9 μmrad both direction withhorizontal and vertical. PARMELA is used to simulate theinjection part.
The linear accelerator is composed of two parts, bunch
compressing and accelerating. The bunch compressing
part consists of one accelerating column, L1, and one
chicane bunch compressor BC1. At the exit of theinjection part the electrons enter the L1 where they are

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Proceedings of FEL 2007, Novosibirsk, Russia

accelerated to ~ 120 MeV. Acceleration occurs off-set
crest to provide correlated energy spread along the bunchthat will compress it in the compressor BC1 shown in
Fig.1. The momentum spread for bunch compressing
depends on RF phase (off-set crest) and power. The
accelerating column is limited to accelerate up to ~ 50
MeV. And there is only one accelerating column in the L1.
Because it limits the RF power, we have small variation
about RF phase. The other component for bunch
compressing is momentum compaction factor (R56) ofBC1.
BC1 is located at that point of 110 MeV, andcompresses the beam pulse length from 773 μm to around
228 μm to have peak current above 300 A. Because of the
RF power limitation, momentum compaction factor (R56)
of BC1 is also limited. RF phase affects on energy spreadof the beam, and R56 affects significantly on emittance ofthe electron beam. We choose lower emittance, we gethigher energy spread, and vice versa. For example, figure
2 shows the slice beam pulse shapes with the same peakcurrent 390 A in the case R56 is varying. When R56 is 31.8 mm, the RF power of L1 is 16.7 MV/m and RF
phase of L1 is –49.8o. When R56 is -63.1 mm, the RF
power of L1 is 15.0 MV/m and the RF phase of L1 is –28.8o.

The beam transport line from L2 to undulator is very
short because of the space problem. So we have no dogleg structure [2]. It consists of two quadrupole doublets toadjust beta function of the beam at the entrance undulator.
At this point the beta-x is 6.22 m, alpha-x is –1.48, beta-yis 6.67 m and alpha-y is 1.44.
At the entrance of undulator, in this test machine, above
300-A peak current, below 1.5 μmrad emittance andbelow 0.2% energy spread are required for visible
wavelength FEL. In this design, the simulation results
using ELEGANT code satisfies the demands. At theentrance of undulator, the peak current is about 390 A,
normalized slice emittance is 1.2 μmrad and energy
spread is about 0.012 %.

Figure 3: Layout of test machine for PAL XFELThe figure 3 shows layout of the test machine and various
beam dynamic simulation results. The figure 4 shows beta
functions and eta functions along beamline, and figure 5
shows beam profiles in dE/E-dz plane. Table 1 summarize
parameters of the test machine.
Table 1: Parameters of the Test Machine

Figure 2: Slice beam pulse shapes at the entrance of theundulator. In the simulation particle number is 200,000
and slice number is 300. It shows current profiles (left), xaxis emittance profiles (Right) and energy spread (down).
From the tedious calculations with elegant code, wechoose R56 is -31.8 mm. In the case, beam energy is 110
MeV, projected RMS energy spread is about 1.25 % at
BC1. The bending angle of the BC1 is 7.2o, drift length
between two dipole magnets is 1.2 m, and the length ofeach of four dipole magnets is 0.3 m.
2nd accelerating part (L2) consists of two acceleratingcolumns with 15.4 MV/m RF power. Because L2 is also
used in low energy experiment like as test machine in thesame time, the structure is almost fixed. For the low
energy experiments, another thermionic electron gun will
be connected to the branch of the L2 at entrance.
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Parameter

Value

Unit

Nominal electron energy

200

MeV

Peak current

390

A

Final bunch length

228

μm

RMS slice energy spread

0.012

%

Normalized slice emittance

1.2

μmrad

Radiation wavelength

visibleFull undulator Length

10m

Saturation undulator length

6~7mProceedings of FEL 2007, Novosibirsk, Russia

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Figure 4: Beta and Eta functions along beamline of thetest machine.

Figure 5: 200,000 particle profiles in dE/E-dZ plane at
injector (left) and at entrance of the undulator (Right).

SUMMARY
The test machine with visible FEL using SASE forcompletion of 3.7 GeV PAL X-FEL is designed to satisfy
demands of time and budget to construct. The simulation
results are acceptable. We need more study about beamdiagnosis system in the machine.

REFERENCES[1] T. Y. Lee, Y. S. Bae, J. Choi, J. Y. Hunag, H. S.
Kang, M. G. Kim, D. H. Kuk, J. S. Oh, Y. W. Parc, J.
H. Park, S. J. Park and I. S. Ko, “Design and PhysicalIssues of the PAL-XFEL” Journal of the Korean
Physical Society, Vol. 48, No. 4, April 2006, pp. 791~ 795.
[2] Linac Coherent Light Source (LCLS) Conceptual
Design Report, SLAC-R_593, April 2002, UC-414.

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FEATURES OF THE PAL-XFEL DESIGN∗
T.-Y. Lee† , J. Choi, and H. S. Kang
Pohang Accelerator Laboratory, San 31, Hyoja-dong, Pohang, Kyungbuk 790-784, KOREA

Abstract
PAL-XFEL, the new XFEL project of Pohang Accelerator Laboratory, aim to emit hard X-ray of 1 − 1.5 Å, although its beam energy is only 3.7 GeV. To achieve thegoal, coherent third harmonic radiation will be utilized.
This paper discusses schemes of hard X-ray generation
with 3.7 GeV electron beam and concludes that use of thethird harmonic is the only possible way.

INTRODUCTION
The storage ring based third generation light source has
spread all over the world in the last twenty years and is
now a useful and common facility for scientific research.
However, even more advanced X-ray source, the XFEL facility, is not likely to be so. Apparently, the X-ray FEL(XFEL) is achievable only by a high energy electron beam.
To make 1 − 1.5 Å hard X-ray FEL, the electron energy
has been chosen 14.35 GeV for the Linac Coherent Light
Source (LCLS) in SLAC [1] that is under construction and17.5 GeV for the European XFEL in DESY [2] that is approved. Not only the linear accelerator but also the undulator in XFEL is long; the LCLS undulator is 112 m long andthe European XFEL undulator is even longer, 260 m. We
may have to conclude that hard X-ray FEL is too expensive
to be available in most countries. Is it possible to reducethe machine size? The SPring-8 Compact SASE Source(SCSS) project in Japan tries to reduce the whole facility
size by using an in-vacuum undulator and the new technology of C-band linear accelerator [3]. It is going to need
only 8 GeV electron beam to generate hard X-ray. However, building and maintaining an 8 GeV electron machine
still costs a lot even with the new technology. A natural
question is how compact an XFEL facility can be.
PAL-XFEL, the new XFEL project of Pohang Accelerator Laboratory (PAL) [4], tries to achieve the goal by utilizing the third harmonic SASE radiation. It will uses 3.7
GeV electron beam. Below it will be shown that 1 − 1.5
Å hard X-ray FEL can not be achieved by 3.7 GeV electron energy, if we insist to use only the fundamental SASE
radiation. Therefore, PAL-XFEL may be the lowest energy hard X-ray FEL machine. The only defect is that thetransverse coherence of the PAL-XFEL third harmonic radiation would be far from perfect. Basic parameters of the
PAL-XFEL are listed in Table 1 for unfamiliar readers.
∗ Work supported by Korean Ministry of Science and Technology† tylee@postech.ac.kr

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Table 1: Parameters of PAL-XFEL
Beam Parameters
Value
Unit
Electron energy
3.7
GeV
Peak current
3
kA
Normalized slice emittance1
mm mrad
RMS slice energy spread
0.01 %
Full bunch length
270
fs
Undulator Parameters
Undulator period
1.5cm
Segment length
4.5m
Full undulator length
80mPeak undulator field
1.19
T
Undulator parameter, K
1.49
Undulator gap
4mm
Average β-function
10m
FEL ParametersÅ
Radiation wavelength3
FEL parameter, ρ
5.7 × 10−4
1Peak brightness
5 × 1031
Peak coherent power
1
GW
Pulse repetition rate (Max.)60
Hz
1D gain length
1.2m
Saturation length, Lsat
45m
1 photon/(sec mm2 mrad2 0.1%BW)

BEAM ENERGY DEPENDENCE OF XFELFACILITY SIZE
To find the possibility of using low electron beam energy
for an hard X-ray FEL, we need to know its beam energy
dependence. To find out the beam energy dependence of an
hard X-ray FEL, recall that the resonant wavelength of an
undulator is given by


K2
λu
,
(1)
λr = 2 1 +2γ
2where λr is the resonant wavelength, λu the undulator period, γ the Lorentz factor, and K the undulator parameter.
K is defined by
K = 0.934B0 [Tesla]λu [cm],(2)where B0 , the undulator peak magnetic field, depends not
only on the undulator gap and period but also on the magnet
material. If we consider a hybrid undulator with vanadium
permendur, it is given by 2 
gg(3)+ 1.520
B0 = 3.694 exp −5.068λu
λu

Proceedings of FEL 2007, Novosibirsk, Russia
with g denoting the gap. In LCLS, for λr = 1.5 Å, thebeam energy is 14.35 GeV, λu = 3 cm, and g = 0.65 cm.
If we want to use lower beam energy, we have to use shorterλu and smaller K that depends on λu and B0 . Since B0 depends on g/λu , we have two parameters (λu and g/λu ) tobe controlled to compensate for the decreasing beam energy. Hence, we fix g/λu (and thus B0 ) and use only λu .
Solving Eq. (1) for λu while keeping the LCLS value of theratio g/λu = 0.217, we can determine λu that gives 1.5 Å
hard X-ray at a lower electron energy. First, arranging Eq.
(1) for λu , we obtain a cubic equation
2

2
4λr γ
λu =
,
(4)
a2
a2
where a = 0.934B0 . Solving this cubic equation, we obtain λu as a function of γ or E, the electron energy. The
graph of λu versus E is shown in Fig. 1. As E decreases
from the LCLS energy, λu decreases almost linearly. Sinceg/λu is fixed, g = 0.217λu also decreases making invacuum undulator an inevitable choice at lower electron energies. Figure 1 may imply that hard X-ray FEL is achievable by using very low energy electrons if the undulator period is properly short. However, the undulator gap g should
also be very small, which causes serious problems. Hence,both λu and g can not be arbitrarily small and electron energy can not be very low.
λ3u +

3.5

Undulator Period (cm)

3

2.5

2

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Note that ρ roughly defines the upper bound of the electronenergy spread σE /E in a slice. The SASE process begins
only when σE /E < ρ and it stops (saturates) when σE /E
grows and reaches ρ. Hence, ρ should not be too small for
successful power growth.
The fundamental length scale to determine the saturation
length is the one-dimensional gain length defined byλu.
L1D = √
4 3πρ(7)

In general, a large ρ is preferred not only for high gain,
but also for a short gain length. In Eq. (5), note that σx2 =βn /γ where n is the normalized emittance and β is thebetatron function. The currently achievable value for n isaround 1.2 μ-rad and β is free to choose. The optimal βthat gives the shortest saturation length is given by [5] 1/2 3/2 1/2
IA
n λu
.
(8)
βopt = 11.2
I
λr K[JJ]
Using βopt in Eq. (5), we obtain1/2 
1/3
1
I λu
λr
ρ = K[JJ].
2IA n89.6π 2 n γ 2(9)Using the LCLS value I = 3.4 kA, the dependence of ρ
on E as λu moves on the line of Fig. 1 is shown in Fig. 2.
Note that ρ also decreases as E decreases. The requirement
σE /E < ρ gives a severe restriction for a compact XFEL
source. The LCLS value of σE /E is approximately 0.01%,
which means σE ≈ 1.4 MeV. As the electron energy E islowered, the relative energy spread σE /E increases whileρ decreases. At around E = 4.5 GeV, σE /E is comparable
to ρ. Hence E = 4.5 GeV seems the lowest possible energy
for 1.5 Å XFEL.
−4

6

x 10

1.5
5.5

1

2

4

6

8

10

12

14

16

Electron Energy (GeV)

Figure 1: Graph of λu that gives 1.5 Å radiation as a function of E. The ratio g/λu is fixed to 0.217, the LCLS value.
To build a compact XFEL, we also have to reduce theundulator length. To estimate the SASE saturation length,
Lsat , and find its energy dependence, a key parameter isthe FEL parameter ρ defined by1/3
1 I λ2u K 2 [JJ]2,(5)ρ=2γ IA 8π 2 σx2
where IA = 17045 A is the Alfen current, I is the beam
peak current, σx is the cross sectional beam size, and [JJ]
is defined by




K2
K2
− J1
.
(6)
[JJ] = J0
4 + 2K 2
4 + 2K 2

FEL Parameter (ρ)

0.5

5

4.5

4

3.5

3

2.5

2

1.5

2

4

6

8

10

12

14

16

Eelctron Energy (GeV)

Figure 2: Graph of ρ as a function of E.
The three dimensional parameter L3D is usually described as(10)
L3D = L1D (1 + η),
where η measures the deviation from the one dimensional
theory due to diffraction, emittance, and energy spread.

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153Proceedings of FEL 2007, Novosibirsk, Russia

Lsat and Psat , the saturated peak radiation power, are approximately given by
2

L1D Iγmc2,
Psat = 1.6ρ
L3D
e


Psat λr.
(11)
Lsat = L3D ln
2ρ2 EcCertainly, Lsat is an important factor to determine thewhole machine size. Using Eqs. (5) and (10) in Eq. (11),the E-dependence of Lsat is revealed and shown in Fig. 3.
Lsat also decreases as E decreases from the LCLS energy
and reaches the minimum at around E = 5 − 6 GeV. In
Fig. 3, the part below E = 4.5 GeV is meaningless, because the energy spread exceeds ρ and there is no SASE
process. The abnormal abrupt increase of the saturation
length indicates the meaninglessness. Psat is depicted inFig. 4 on the logarithmic scale. Note that Psat decreases
slowly as E decreases from the LCLS energy to E ∼ 4.5
GeV and drops rapidly outside of it. Psat is still above 1
GW. Therefore, a compact XFEL does not sacrifice the radiation power. Overall, the shortest XFEL for 1.5 Å can bebuilt at around E = 4.5 GeV.

10

Radiation Power (GW)

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1

0.1

0.01

2

4

6

8

10

12

14

16

Electron Energy (GeV)

Figure 4: Graph of Psat as a function of E.
of transverse coherence of LCLS is approximately 0.83. At
a lower energy and shorter undulator period, the transverse
coherence would be worse. Therefore, we conclude that
hard X-ray FEL is achievable at a lower electron energy
but its transverse coherence may not be perfect.

240
1
220
0.9

Degree of Transverse Coherence

Saturation Length (m)

200
180
160
140
120
100

0.8

0.7

0.6

0.5

0.4

80
0.3
60

2

4

6

8

10

12

14

16

Electron Energy (GeV)

Figure 3: Graph of Lsat as a function of E.

0.2

5

10

15

20

Electron Energy (GeV)

Figure 5: Degree of transverse coherence for 1.5 Å XFEL
as a function of E.

TRANSVERSE COHERENCE
The condition for the transverse coherence is roughly
given by
λr
n
∼
.
(12)
γ
4π
This rough condition claims that the beam energy has tobe high enough to secure the transverse coherence for avery small λr (hard X-ray). Since Eq. (12) is an order ofmagnitude relation, accurate estimate of transverse coherence needs a computer. Especially, the degree of transverse
coherence at the saturation was obtained as a function ofˆ = 2πn /(λr γ) [5]. Converting this result to our purpose,
we obtain Fig. 5, which shows clearly that the degree oftransverse coherence for 1.5 Å hard X-ray decreases as theelectron energy decreases. According to Fig. 5, the degree
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CHOICE OF PAL-XFEL
Although hard X-ray FEL is possible by using E = 4.5
GeV, note from Fig. 1 that the undulator period and thus theundulator gap is very small at the energy. The gap is around
only 2.5 mm. This may not be an unreasonably small number. However, it causes not only beam handling difficulty
but also severe wakefield effect that reduces the radiative
power. If we try to choose a safer gap (maybe larger than
3 mm), the beam energy should be at least 6 GeV, which is
not compact at all. Therefore, it may be concluded that hard
X-ray FEL is not achievable by a compact XFEL machineof beam energy lower than 4 GeV. That is why PAL-XFEL
chose to use the third harmonic radiation [8, 9, 10]. Then

Proceedings of FEL 2007, Novosibirsk, Russia
even smaller hard X-ray FEL facility is possible. If we generate 3 Å fundamental radiation at a even lower energy of
3.7 GeV, its 1 Å third harmonic radiation is usable. Since
the needed undulator is shorter than using the fundamental
radiation, the whole facility size is really compact.
The only problem is the output power. The output powerof the third harmonic is much lower than that of the fundamental mode. The ratio of the third harmonic power to thefundamental power is given by [11])P3= 0.094 ×
P1



K3
K1

2
.

(13)

K1 and K3 , coupling factor of the fundamental and third
harmonic respectively, are special cases of Kh defined by(h−1)/2

Kh = K(−1)[J(h−1)/2 (Q) − J(h+1)/2 (Q)], (14)where Q = hK 2 /(4 + 2K 2 ). It is straightforward to compute (K3 /K1 )2 as a function of K. As shown in Fig. 6, it
increases from zero and becomes almost flat after K > 2.5
saturating to (K3 /K1 )2 = 0.22, which gives the asymptotic value P3 /P1 ≈ 0.02. Hence, P3 can not exceed 2%
of P1 . With K = 1.49, the PAL-XFEL value, P3 is approximately 1% of P1 . Parameters of the two harmonics
are listed in Table 2. The peak power and peak brightnessof the third harmonic radiation is still very high. Finallythe degree of transverse coherence of the third harmonic
radiation, obtained at this low energy, is also low.

MOPPH062

SUMMARY
We have seen, in this paper, that it is possible to generate
1.5 Å hard X-ray FEL with lower electron energy (down to
4.5 GeV) and shorter undulator at the expense of reduced
degree of transverse coherence. However, the facility size
can be reduced even further by utilizing the third harmonic
radiation whose power is less than 2% of the fundamental
one and transverse coherence is also poor. PAL-XFEL is
one such example. We can not build a compact hard X-ray
FEL that has all three special properties. However, XFEL
with incomplete transverse coherence is still very useful,because the majority of experiments do not need the transverse coherence.

REFERENCES[1] J. Arthur et al., Linac Coherent Light Source Conceptual
Design Report, Stanford, SLAC (2002).
[2] A. Aghababyan et al., The European XFEL Technical Design Report, Hamburg, DESY (2006).
[3] SCSS XFEL R&D Group, SCSS XFEL Conceptual Design
Report, RIKEN/SPring-8 (2005).
[4] T.-Y. Lee, Y. S. Bae, J. Choi, J. Y. Huang, H. S. Kang, C. B.
Kim, D. E. Kim, M. G. Kim, Y. J. Kim, I. S. Ko, J. S. Oh,
Y. W. Parc, and J. H. Park, Proceedings of FEL 2006, Bessy,
Berlin, Germany, (2006) 210.
[5] E. L. Saldin, E. Schneidmiller, and M. Yurkov, Proceedingsof FEL 2006, Bessy, Berlin, Germany, (2006) 206.
[6] K. L. F. Bane and G. Stupakov, SLAC-PUB-10707, LCLSTN-04-11, (2004).

0.25[7] P. Emma, Z. Huang, C. Limborg-Deprey, J. Wu, W. Fawley,
M. Zolotorev, and S. Reiche, Proceedings of 2005 Particle
Accelerator Conference, Knoxville, USA, (2005) 344.

0.2

[8] W. Colson, IEEE J. Quantum Electron. 17, (1981) 1417.
[9] R. Bonifacio, C. Pellegrini, and L. Narducci, Opt. Commun.
50, (1984) 373.

3

1

(K /K )2

0.15

[10] Z. Huang, and K.-J. Kim, Phys. Rev. E 62, (2000) 7295.

0.1[11] E. L. Saldin, E. Schneidmiller, and Yurkov, Proceedings of
FEL 2005, SLAC, Stanford, USA, (2005) 51.
0.05

0

0

0.5

1

1.5

2

2.5

3

3.5

4

K

Figure 6: Graph of (K3 /K1 )2 as a function of K.

Table 2: Parameters of the two harmonics
Parameters
Fundamental Third harmonic
Wavelength (Å)
3
1
Peak power (GW)10.01
Peak brightness 2
1 × 1032
3 × 102911
Photons/pulse
5 × 10
1.5 × 1092
photon/(sec mm2 mrad2 0.1%BW)

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Proceedings of FEL 2007, Novosibirsk, Russia

POTENTIALITIES OF ELMI DEVICE FOR SUBMILLIMETER
GENERATION BY STIMULATED INTERCAVITY SCATTERINGIN PLANAR FEM *A. V. Arzhannikov*, V. T. Astrelin, A. S. Kuznetsov, S. A. Kuznetsov, P. V. Kalinin, S. L. Sinitsky,
V. D. Stepanov, BINP, Novosibirsk, Russia
N. S. Ginzburg, N. Yu. Peskov, A. S. Sergeev, V. Yu. Zaslavsky, I. V. Zotova,
IAP, N-Novgorod, Russia
Abstract
Paper describes main features of a project on two-stage
generation of submillimeter radiation at the ELMI device.
This novel variant of a two-stage scheme is based on
stimulated intercavity scattering. In accordance with thescheme, at the first stage a sheet electron beam drives
a 2D Bragg free electron maser (FEM) of planar geometry
to generate 4-mm pump wave. At the second stage thiswave undergoes stimulated scattering at the
supplementary electron beam to produce submillimeterradiation. In the paper we describe results of theoreticaland experimental investigations of various aspects of thetwo-stage scheme and some testing experiments on units
for realization of this scheme at the ELMI device.

of upstream 2D and downstream 1D Bragg reflectors
provides spatial coherence of radiation in a FEL driven bya large-size sheet e-beam [5], [6]. In the ELMIexperiments generated radiation has wavelength
λ0 = 4 mm with pulse duration up to 0.5 µs. The existenceof regimes with high level of the mm-radiation spectral
density near the frequency close to one of hybrid Bragg
resonator eigen modes during all the pulse has beenregistered.
One of the typical shots shown in the Fig. 1
demonstrates the FEM operation on the mode withfrequency 75.3 GHz. The single mode generation lasts
330 ns.

INTRODUCTION
In recent experiments at the ELMI-device the single
frequency operation of 4-mm planar FEM with
2D distributed feedback has been demonstrated [1].
These results created a basis for development of a twostage generator for the sub-mm band. A key feature of
the scheme proposed earlier in [2], is the use of two sheet
beams with a few kAmps currents that transported in twoparallel slit channels with a guiding longitudinal magnetic
field, which are connected by a special waveguide.
At the first stage one of the sheet beams passing in a slit
channel with static undulator magnetic field drives
2D Bragg FEM of planar geometry to generate 4-mm
pump wave as well as in the recent ELMI experiments.
This intensive 4-mm radiation accumulated in the FEM
resonator is transported through the special waveguideto the second slit channel where it is used as an
EM-undulator for the secondary stage of sub-mm FEL.
The special waveguide connection will be realized
in similar way as it was suggested earlier in the project ofmultibeam FEM with 2D distributed feedback where it
was used for synchronization of radiation generated
in different channels [3], [4]. Production of the two sheet
beams by one accelerator diode with two cathodes is alsosimilar to the process of operation of the multibeam diodedescribed in Ref. [4].

SCHEMATIC OF PROPOSEDEXPERIMENTS
At the first stage we plan to use a FEM with hybrid
Bragg resonator which was developed in the recent
experiments [1]. Hybrid two-mirror resonator consisting___________________________________________*arzhannikov@inp.nsk.su

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Fig. 1 Single frequency operation of 4-mm FEM:a) diode voltage (Udiode), beam current (Ibeam) and
mm-wave power; b) intercarrier frequency signal
from heterodyne mixer (heterodyne frequency
fdrive=75.43 GHz); c) mm-wave power spectrum.

Proceedings of FEL 2007, Novosibirsk, Russia
In a two-stage scheme such mm-radiation as an incident
wave should be scattered by the electrons with energy~1 MeV at the second stage of generation. Using theformula for the double Doppler effect the wavelength of
scattered radiation λ will be the following:

λ = λ0(1 − β cos θ ),(1 − β cos θ )s

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along e-beam velocity and 2D Bragg reflector).
The 2D Bragg resonator is optimized such a way toincrease amplitude of transverse propagating energy
fluxes B. These fluxes by connecting waveguides aretransported in the channel #2 for pumping electrontransverse oscillations.

(1)iwhere β = ν / c is the electron velocity, θi and θs —angles of incident and scattered waves with respect todirection of the electron velocity (Fig. 2).
For two cases of back-scattering and 90º-scattering

(1)

gives

λ ≈ λ0 / 4γ

respectively,where

γ = 1/ 1 − β 2formula2andλ ≈ λ0 / 2γ

2is an electron

relativistic factor. The expected wavelengths of thescattered radiation at output of the two-stage scheme arepresented in Fig. 2. As it is seen the radiation in the bandof 0.1–0.3 mm can be obtained in case of back-scatteringof 4-mm radiation whereas 90º-scattering provides
radiation wavelength in the band of ~0.2–0.5 mm for γ
in the range 2–3.4.

Fig. 3 Scheme of two-stage generation for the band of
0.2–0.5 mm: 1 — sheet REB for driving the planar
FEM-oscillator; 2 — sheet REB for mm-wave scattering;3 — 2D Bragg reflector; 4 — 1D Bragg reflector;
5 — special waveguide; 6 — area of 4-mm radiation
scattering on e-beam.
For the first experiments we plan to observe scatteredsignal amplification in the SASE (self-amplified
spontaneous emission) [7] regime in the absence of theresonator (mirrors) for sub-mm radiation. The spatial
growth rate for scattered short-wave radiation is given by
the expression [8], [9]:1/ 3

⎛ jb [kA/cm] ⎞ ao2 / 3
Γ[cm ] = 6.8 ⋅ ⎜⎟ ⋅ γ ,
⎝ λ0 [mm] ⋅ b[mm] ⎠−1(2)

where jb is the linear current density in the second beam,
a0 = 2.3·10-8λ0[mm]Ei[V/cm] is the pump wave strengthparameter, Ei is the pump wave amplitude and b is the gap
between the channel plates. For the pump radiation with
Fig. 2 Conversed wavelength due to scattering of 4-mm
radiation on beam electrons as the function of the beamγ -factor
Schematic drawings of experimental realization of
sub-mm generator based on two different scattering
schemes are presented in Fig. 3 and Fig. 5. For bothvariants we suppose to use sheet beams with 3–4 mm
thickness and 10–20 cm width and a current density morethan 1 kA/cm. The e-beams pass the slit channels atpresence of longitudinal guiding magnetic field with thestrength ~1 T. In the channel #1 of both variants theelectrons oscillate in undulator magnetic field andgenerate 4 mm pump wave. Theoretical studies of planar
FEM at ELMI accelerator demonstrates that the electricfield strength of 4-mm radiation inside the FEM resonatorcan amount to 105–106 V/cm. In Fig. 4 results ofsimulation of interactivity fields are presented for
configuration shown in Fig. 3 (z coordinate is measured

Fig. 4 Results of simulation of 4-mm generation in the 2D
Bragg FEM: profile of transverse (B) and longitudinal (A)propagating partial waves inside 2D Bragg structure.

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Proceedings of FEL 2007, Novosibirsk, Russia

Fig. 5 Scheme of two-stage generation for the band of 0.1–0.3 mm

λ0=4 mm and Ei =1 MV/cm this parameter is estimatedon the level a0 ~ 0.05–0.1. Thus, for the relativistic factor
γ = 3, jb = 1 kA/cm and b = 10 mm the spatial growth rateof sub-mm radiation is estimated as Γ∼ 0.1 cm-1.
Expression for the gain (2) is valid for a “cold” beamwith rather small velocity spreadδνc<< λ ⋅ Γ ≈ 0.04 .

(3)

The required value of the velocity spread can be obtainedby an accurate choice of geometry of magnetic field
configuration in accelerator diode and an appropriate
strength of guiding magnetic field. Analysis of thisproblem has shown that for experimental conditions of
the ELMI-accelerator in order to satisfy (3) we should
increase the guiding magnetic field up to 2.5–3 T.
In addition to these changes some reconstructions in theaccelerator diode and vacuum slit channels should
provide appropriate parameters for the first step of twostage experiments on production of sub-mm radiation in
SASE regime. After that it will be possible to use either
quasi-optical or some modifications of Bragg resonators
to obtain generation regime with corresponding
narrowing the radiation spectrum.
One of the problems related with observation of SASE
regime in the overmoded waveguide is suppression ofinteraction with low frequency modes. Such a problem
can be solved by using waveguide with variable gap
between plates. According to the results of KARAT
simulation of 200 GHz SASE (see [2]) the waveguidetapering provides possibility for suppression of low
frequency amplification. This result is explained thatvariation of the waveguide parameters affects morestrongly near cut-off modes with the large Brillouinangles.

TWO BEAMS PRODUCTION
As a first step for implementing the two-stage
generation scheme we have provided passing of two
similar sheet e-beams through the parallel slit channels
with the guide magnetic field 1.75 T. The scheme of thisexperiment was just like one shown in Fig. 5 only that the
Bragg resonator has been replaced with the regular planar
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waveguide. The result of this experiment is shown in Fig.
where beams currents measured on the collectors arepresented together with accelerator diode voltage.
As one can see the traces of beams currents are practicallythe same. Minor difference can be minimized by varying
the cathodes positions in the accelerator diode if required.

Fig. 6 Production of two sheet e-beams in a common
diode with two cathodes and transportation of thesebeams through the parallel slit channels: Udiode —accelerating voltage; Ibeam1,2 — currents of the beams.

CONCLUSION
Basing on the results of the experiments on generationof 4-mm radiation in a planar FEM together with theresults of theoretical investigations and computer
simulations, we proposed the submillimeter radiation
generator based on stimulated scattering of pumping
mm-wave on a high-current sheet REB with electronenergy ~1 MeV. Power level up to 1 MW of 100 μm
wavelength radiation with 0.1–1 μs pulse duration can bereached by constructing this generator on basis of alreadyoperating planar FEM with appropriate technicalupgrading at low financial costs. Thus technicalimplementation of such solution seems to be highly
prospective.

Proceedings of FEL 2007, Novosibirsk, Russia

ACKNOWLEDGMENT
The work was partially supported by CRDF
(grant NO-008-X1) and RFBR (grants 04-02-17118
and 05-02-17036) and is supported now by RFBR
(grant 06-08-01506) and Scientific Program “Problemsof Radiophysics” of RAS.

REFERENCES[1] A. V. Arzhannikov, N. S. Ginzburg, V. G. Ivanenko
et al. “Investigation of Mode Structure for mm-wave
Radiation Pulses Generated by Planar FEM at 2-D
Distributed Feedback”, Abstracts of 16th Int. Conf. on
High-Power Particle BEAMS, BEAMS'2006,
Oxford, UK, 2006, No. 19, p. 54.
[2] A. V. Arzhannikov, N. S. Ginzburg, P. V. Kalinin
et al. “Intercavity Scattering Scheme for Two-stage
Generation of Submillimeter Radiation on the Baseof Planar 2D Bragg FEM”, in Proc. VI Int. Workshop

MOPPH063“Strong Microwaves in Plasmas”, N. Novgorod,
Russia, 2006, vol. 1, p. 228.
[3] N. S. Ginzburg, N. Yu. Peskov, A. S. Sergeev et al,
Nucl Instrum Meth Phys Res A, 475 (2001) 173.
[4] A. V. Arzhannikov, V. T. Astrelin, V. B. Bobylev
et al, Nucl. Instrum. Meth. Phys. Res. A, 507 (2003)
129.
[5] N. S. Ginzburg, N. Yu. Peskov, A. S. Sergeev et al.
Thech. Phys. J, 26 #16 (2000) 8 (in Russian).
[6] N. S. Ginzburg, V. Yu. Zaslavsky, N. Yu. Peskov
et al. Thech. Phys. J, 76 n. 12 (2006) 80 (in Russian).
[7] R. Bontfacio, C. Pellegrini, L. M. Narducci, Optic.
Comm, 50 iss. 6 (1984) 373.
[8] V. L. Bratman, N. S. Ginzburg, M. I. Petelin, J. Exp.
Theor. Phys, 76 (1979) 930.
[9] P. Sprangle, C. M. Tang, W. M. Manheimer, Phys.
Rev. A, 21 (1980) 302.

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Proceedings of FEL 2007, Novosibirsk, Russia

A PROJECT OF SC ERL AT KAERI
A.V.Bondarenko, S.V.Miginsky, Budker Institute of Nuclear Physics, Novosibirsk, Russia
B.C.Lee, S.H.Park, Y.U.Jeong, Y.H.Han, Korea Atomic Energy Research Institute, Daejeon, Korea
Injection

32°
2m

Quadrupole Dump
32°
Undulator

160°

SC cavities

12°

Compton BS

160°

Sextupole
12°32°

22.4 mFigure 1. The layout of the ERL.
A project of an ERL at Korea Atomic Energy ResearchInstitute is described. The ERL will be connected to theexisting machine without any modification. It consists of
two 180° bents and two straight sections: one is for an
FEL, another for a Compton X-ray source. One canchoose the regime controlling the lenses. The total ERL is
isochronous to avoid any problem with longitudinal beam
instability. It will be possible to control both Sx and Sy
transformation matrix elements independently to suppress
longitudinal beam instability and allow the increase ofbeam current. Sextupoles will be installed in bents tosuppress chromatic aberration. This design provides
operation in FEL regime with high electron efficiency inthe range of electron energies 12–22 MeV.

INTRODUCTION
At present time, a superconductive linear accelerator
successfully operates at KAERI. It consists of an injector
with injection energy 2 MeV, injection beamline,
cryogenic accelerating module, which contains twocavities. Electron beam parameters are following:• bunch duration:
100 ps;• number of electrons per bunch:
1010;• electron energy (full):
10 MeV;• repetition rate:
5.6 MHz;• emittance:
2π mm·mrad;• energy spread (relative):6•10-3.
A future ERL based on this linac will be build at
KAERI. An FEL and a Compton source will be driven by
it. A project of the ERL should meet the following
requirements:• Accelerator should have two regimes, one for the
FEL and the other for the Compton source. The
regimes will be switched with magnets.
• The machine should operate in a wide energy range
in order to provide broad band FEL retuning. The
ERL will operate at the energy from 12 MeV up to
22 MeV.
• The possibility to control both Sx and Sy transport
matrix elements independently and total isochronismof the ERL is necessary to suppress longitudinal andregenerative transverse beam instability. Thispossibility permits to increase the beam current andthe FEL power.
• Low beam emittance degradation in the beamline isnecessary for successful FEL operation and beam

32°

0.5 m

Abstract

12°
2.5 m

Quadrupole
Sextupole
160°

8m
Figure 2. The layout of the first bent.

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160Proceedings of FEL 2007, Novosibirsk, Russia

Q u a d ru p o leβ x -fu n ctio n
75 m

S e x tu p o le
η -fu n ctio n

MOPPH064

D ip o leβ y -fu n c tio n

60 m
0 .5 m

F ig u re 3 . T he lattice fu n ctio n s in the first be nt.
Figure 3. The lattice functions in the first bent.
energy recovery. Therefore we should use sextupoles
to suppress chromatism which is the main reason ofemittance dilution.
• Large energy aperture of the dump and the beamline
after the undulator is necessary to obtain high FEL
efficiency, as the energy spread after the FEL is
proportional to its electron efficiency.
The machine will consist of two isochronous nearachromatic bents (their small chromatism compensatesv < c), and two straight beamlines separated by a dogleg.
The FEL and the Compton source will be installed onthese straight parts. The layout of accelerator optics isshown in figure 1.

FIRST BENT
Consider the first bent. It is necessary to control thelongitudinal dispersion from 7 up to 17 cm to compensate
that of the whole machine due to v < c. Emittancedegradation in the bent should be low to keep FEL
radiation quality. The dump is installed inside the first
dipole of the bent. This design allows to avoid anextraction chicane. It also has a big energy aperture(> 1 MeV in the whole energy range) to collect the whole

Quadrupole

Sextupole

β x-function

η-function

Dipoleβy-function

0.5 m
30 m
17 m

Figure 4. The lattice function in the beamline after the undulator in the FEL regime.
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waste beam without loss. The accelerated beam moves
through the common track together with the decelerated
beam. Due to that, the capability to control the common
track optics is very limited. Also the beam state at theentrance of the accelerating module is known only
approximately. So the bent should operate successfully inthe following range of the entrance lattice functions:⎧β from 25 m to 80 m⎪⎪ z
⎨β x from 35 m to 140 m⎪⎪⎩ α x , z ≤ 3
The layout of the first bent is shown in figure 2.
It consists of three bending dipoles for 12°, 32° and
160°, the first dipole bends beam to the right while thetwo others to the left. It allows setting large negative ηfunction in the second dipole to compensate thelongitudinal dispersion which gains in the mirror. The
lattice functions in the bent in the FEL mode are shown infigure 3. Controlling η-function in the second dipole
modifies the longitudinal dispersion in the whole bent
within the necessary range. Sextupoles are installed in thebent in places with big η-function and small β-function to
suppress chromatic aberration. The strengths of
sextupoles are selected to zero ∂η / ∂p and ∂η′ / ∂p ,and to decrease ∂α xy / ∂p and ∂β xy / ∂p to the level
where emittanse dilution due to chromatic aberration isequal to one due to nonlinear focusing in the sextupoles.
This optimization leads to comparably small emittance
dilution through the whole bent

Δε 2 / ε ≤ 0.75 .

BEAMLINE AFTER UNDULATOR
The beamline after the undulator consists of a dogleg(two 32° dipoles), a strait beamline for the Compton
source, the second bent similar to the first one, and an
injection chicane. The main feature of the beamline after
the undulator is big energy spread of the beam in the FEL
regime. It leads to high emittance degradation as a resultof chromatic aberration. Also large beam size due tononzero η and high energy spread leads to significant

FEL projects

162edge aberration in quadrupoles. Chromatic aberration canbe suppressed by sextupoles while edge aberration
prevents to conduct a beam with relative energy spreadgreater than 0.06. Suppression of chromatic aberration ismade similar to the first bent. The only difference is thebeamline needs more sextupoles as their strengths arelimited by emittance degradation. This method of
suppression of chromatism provides a possibility to
conduct a beam with relative energy dispersion 0.05
through the beamline with emittanse degradation

Δε 2 / ε ≈ 1 . The lattice functions in the beamline after
the undulator in the FEL mode are shown in figure 4.
The beamline was simulated with OPTI code based on
the linear transverse single-particle dynamics model. Thismodel neglects space charge effect, so can't be used forthe extraction beamline. In that case it is necessary to takespace charge effect into account due to small beam energy
in this part of the accelerator. It was made by code I&Eps[1]. In this simulation, focusing of the cavity wasconsidered as concentrated at the edges of the cavity.

CONCLUSION
This design provides operation with high electron
efficiency in the range of electron energies from 12 up to
22 MeV. It also allows suppressing longitudinal andregenerative transverse beam instability to increase beam
current. The output power of a future FEL will be a few
kW in the wavelength range from 35 to 70 μm.
The most desirable upgrade is one more pair of SC
cavities. In this case the maximum beam energy of the
ERL exceeds 40 MeV. It provide possibility to make an
FEL in the near-IR region. Of course, a new beamline isto be designed in this case.

REFERENCES[1] S.V.Miginsky An optimizer for high-current
beamlines, NIM A 558 (2006) 127-130.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH068

THE NIJMEGEN FEL, A FEL OSCILLATOR WITH HIGH SLIPPAGE
P.J.M. van der Slot∗ , E. van Geijn, K.J. Boller
Mesa , Department of Applied Technology, University of Twente, Enschede, NL
J. Jalink, W.J. van der Zande, IMM, Radboud University Nijmegen, Nijmegen, NL+

Abstract
The Nijmegen Free-Electron Laser (FEL) aims at producing narrow bandwidth radiation for high resolution
spectroscopy in the THz regime. To this end, the radio frequency accelerator based FEL will produce a train of phaselocked optical pulses. We use the Medusa1D code to simulate the performance of this system at various wavelengths
and undulator lengths and estimate the power available in asingle line of the phase locked spectrum.

INTRODUCTION
The High Field Magnetic Laboratory at the Radboud
University Nijmegen, and other such laboratories worldwide, have made it possible to study molecules in materials
in fields with strengths approaching 40 Tesla. All elementary excitation energies increase proportionally. As a consequence strong (> 100 W) and coherent radiation sources
are needed from 100 μm to 1.5 mm, the so-called THz gap.
Narrow bandwidth radiation is best suited for coherent, saturation, and pulse-echo studies. Pulsed intense radiation isbest suited for non-linear and time-resolved studies. The
parameters of the Nijmegen Free-Electron Laser (NijFEL)
have been chosen to provide such a radiation source. An RF
accelerator based electron source will provide short electron bunches creating a train of intense micropulses of picosecond duration. A narrow bandwidth, (Δλ/λ  10−5 ),equals the generation of bandwidth limited pulses (BWL)of hundreds of nanosecond duration. This is achieved byensuring that the micropulses in the macropulse are fully
coherent, either using spontaneous coherence or forcing
coherence using an intra-cavity interferometer. It is expected that spontaneous coherence is helped by using electron pulses with lengths comparable to the wavelength tobe generated. This implies the design of a FEL oscillator
with high slippage.
The zero design parameters to achieve this performancewith NijFEL are shown in table 1, and fig. 1 shows theresonant wavelength of NijFEL as a function of the undulator parameter K for different values of the electron beamenergy Eb . The ratio of the electron bunch length le tothe slippage distance Δzs (= Nu λ at resonance) varies
approximately from 0.015 to 0.3 depending on the actual
number of undulator periods and wavelength used. The
performance of the NijFEL system is therefore highly dominated by short pulse effects [1]. Because of the long wavelengths (see fig. 1), NijFEL will use a half open resonator

Figure 1: FEL resonant wavelength λr as a function of theundulator K parameter for different values of the electron
beam energy Eb .
that provides waveguiding between the poles of the undulator.
To determine the performance for various undulator
lengths and wavelengths, we use the Medusa1d code. This
code retains, in the 1d approximation, all the features of
the 3D Medusa code [2, 3]. It includes a simple oscillator model where the the radiation output at the undulator’s

Table 1: Zero design values for NijFEL. Lu = Nu λu is theundulator length
Accelerator
RF frequencye
Bunch charge
micro pulse duration
Beam energy
Emittance (norm.)
Energy spread (rms)
Duration macropulse
Rep. rate macropulses
Undulator
PeriodK (rms)Number of periods
Oscillator & radiation
Wavelength
Final rel. bandwidthPower (after filtering)
Total roundtrip loss
Waveguide heigth
Length

fRF
Qb
tp
Eb
n
Δγ/γ
Tm
frep

3
300
3
10-14
50
0.25
10-12
≤5

GHz
pC
ps rmsMeV
mm mrad
%
μs
Hz

λu
K
Nu

110
0.7-3.3
30-40

mm

λ
Δλ/λ
Pu
αL
h
Lr

0.1-1.5
10−5
>100
5-20
10
Lu +2

mm
W
%
mm
m

∗ p.j.m.vanderslot@tnw.utwente.nl

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Figure 2: Ep versus Eb after np = 100 passes for Nu = 30
(circles) and 40 (squares).
exit is multiplied by 1 − αL , αL being the total single passcavity loss, and, after appropriate shifting in the time tocompensate for slippage Δzs and cavity detuning δLc , isused as input for the next pass. Furthermore, Medusa1dincorporates some 3D effects through Xie’s fitting formula[4] which results in an increase of the energy spread of theelectrons and a filling factor that includes both diffraction
and guiding effects.

1D SIMULATION RESULTS
Medusa1d is not able to model the hybrid resonator thatis planned for NijFEL. A geometric filling factor can beused to model overlap between electrons and optical field.
However, this does not include possible guiding effects dueto the FEL interaction [5, 6]. We therefore compared thefilling factor for the hybrid waveguide and the one derived
from Ming Xie’s fitting formula for an open resonator. The
latter is found to be larger than the filling factor for the
hybrid waveguide. Apparently, guiding effects in NijFEL
are sufficiently strong to influence the filling factor. We
therefore consider an open resonator in the remaining partof the paper and use Xie’s fitting formula to calculate thefilling factor.
Furthermore, an up- and down taper of 2 periods is usedat the entrance respectively exit of the undulator to allow
proper injection and extraction of the electron beam. Values for parameters are taken from Table 1 unless otherwise
specified.

Performance at λ = 100 μm
In order to produce a narrow bandwidth, the train of coherent optical pulses within the macropulse must be as longas possible. We want to minimize transient effects at the
beginning of the macropulse. We therefore evaluate theperformance of NijFEL at λ = 100 μm for both maximum
gain and maximum efficiency settings of the electron beamenergy. For an electron beam energy of 14 MeV and a peakundulator field of Bu = 0.0941 T we find a maximum single
pass, small signal gain for λ = 101 μm. Figure 2 shows theintracavity optical pulse energy Ep after np = 100 passes
as a function of Eb . The cavity detuning is δLc = −0.5λwith respect to a synchronous cavity that is defined by theroundtrip time of an optical pulse in an empty cavity being
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164

Figure 3: Ep after np = 150 passes versus δLc for Nu =30 (circles) and 40 (squares) at maximum single pass, small
signal gain (A) and maximum efficiency (B).
a multiple of the time separating two consecutive electron
bunches 1 . Fig. 2 shows that maximum efficiency is foundat slightly higher value for Eb compared to the one required
for maximum gain. We therefore have determined the detuning curve for both Eb = 14 MeV and 14.1 MeV. The results are shown in fig. 3. Fig. 3A shows that for maximum
gain, Ep is about the same for the short and long undulatorfor −2λ < δLc < 0 and the longer undulator has a higher
pulse energy for smaller cavity lengths. Also the longer
undulator shows considerable output energy for δLc > 0,
where the shorter undulator fails to lase. At maximum efficiency, we find the short undulator having higher opticalenergies over most of the detuning range investigated, except for cavity lengths larger than the synchronous length
where the gain for Nu = 40 results in a sharp increase of
Ep . We observe that Ep for maximum efficiency setting isabout a factor of 2.5 larger than for maximum gain setting.
The number of roundtrips nb required to reach maximum
Ep is shown in fig. 4. This figure shows that indeed for thecase of maximum gain significantly fewer roundtrips are
required for the optical field to build up to saturation inside
the resonator. At this wavelength, a minimum of about 50
roundtrips is required at maximum gain for negative cavity
detuning and Nu = 40. It increases sharply for positive
detuning. The shorter undulator requires at least 50 moreroundtrips (∼ 1.5μs) to saturate. Also for maximum efficiency we find that the reduced gain results in a larger valueof nb .
The repetition rate of the optical micropulses will be
frep = 3 GHz. As a consequence, if all the optical pulses
are fully coherent, the resulting frequency spectrum of the
train of optical pulses will consist of very narrow lines(linewidth of the order of 10 MHz) separated by the 3 GHz.
Filtering of one of the narrow lines does not require a high
1 δL < 0 means a shorter cavity lengthcProceedings of FEL 2007, Novosibirsk, Russia

Figure 4: nb versus δLc for Nu = 30 (circles) and 40(squares) at maximum single pass, small signal gain (A)and maximum efficiency (B).

MOPPH068

Figure 6: Ep versus δLc for Nu = 30 (circles) and 40(squares) at maximum gain and 100 passes (A) and maximum efficiency and 150 passes (B).
ever this is more than compensated by the increase in pulse
length and hence a narrower spectrum, at least when the
detuning is not too large. As a result, the figure of merit
increase more rapidly for increasing positive detuning thenfor decreasing negative detuning. For Nu = 30, the behaviour is very similar, albeit that the gain becomes too low
for positive detuning values and hence both Ep and E3GHz
drop quickly to zero (at least when we limit ourselves to at
most 150 roundtrips). Fig. 5A also shows that, for large
negative detuning, the figure of merit drops as the increasein pulse duration can not compensate the drop in energy
any more.

Performance at λ = 300 μm
Figure 5: E3GHz versus δLc for Nu = 30 (circles) and 40(squares) at maximum gain (A) and maximum efficiency(B).
quality etalon as a consequence of the large 3 GHz line
spacing. To estimate the energy available after filtering, wehave also determined the intracavity optical energy E3GHz
of a single optical micropulse in a bandwidth of 3 GHz
around the central wavelength. This is an important figure of merit for narrow bandwidth operation of the NijFEL
system, as this energy may be concentrated in a line with awidth of 10 MHz. This figure of merit is shown in fig. 5 forboth the case of maximum gain and maximum efficiency,
and again for the two undulator lengths. As expected, we
find for Nu = 40 that E3GHz increases away from zero detuning [7]. For positive detuning this is due to both a higher
pulse energy and an increasingly longer optical pulse. For
negative detuning the micropulse energy decreases, how-

Similar simulations as in the previous section have been
done at a wavelength near λ = 300 μm as well, using
the same beam energy of 14 MeV. Using Bu = 0.255 T,
we find that the maximum single pass, small signal gainis found for λ = 307.5 μm. Using this wavelength,and varying the beam energy again around the value of
14 MeV, we find, that the maximum efficiency is now near
Eb = 14.24 MeV. Because we expect a higher gain thanfor λ = 101 μm, we have taken a maximum of 100 and
150 passes for the high gain respectively maximum efficiency setting. The same results as for λ = 101 μm but
now for λ = 307.5 μm are shown in figs. 6 to 8. Muchof the features found for λ = 101 μm are also present forthe 307.5 μm wavelength. However, for the case of highgain, the figure of merit is higher for the 30 period undulator than for the 40 period one, except for the longest resonator lengths investigated. Also, the higher gain at thiswavelength results in an extension of the detuning curve topositive detuning values for the 30 period undulator. For
the maximum efficiency setting, and moderate cavity de-

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Proceedings of FEL 2007, Novosibirsk, Russia
tor it is the other way around: at maximum gain, the figureof merit is about a factor of 2 larger for the wavelength
λ = 307.5 μm, and for maximum efficiency it is about thesame for the two wavelengths.

DISCUSSION AND CONCLUSION

Figure 7: nb versus δLc for Nu = 30 (circles) and 40(squares) at maximum gain (A) and maximum efficiency(B).

In the simulation, the NijFEL system can either be set
to produce maximum gain or maximum efficiency. For the
first setting, the buildup time is smallest and we would expect the smallest bandwidth after filtering provided that thewhole train of micropulses is fully coherent. The optical
micro pulse energy is however significantly lower than canbe obtain for the maximum efficiency settings. As a consequence, the figure of merit is also significantly higher forthe maximum efficiency setting. Note that since Medusa1d
is set up to use one frequency, it only calculates the opticalenergy in a finite bandwidth around this frequency. Thus,
the resulting bandwidth may be smaller than the gain bandwidth of the laser. Hence, Medusa1d will under estimate
the optical energy that can be produced by NijFEL.
The range of values for the figure of merit available
through tuning the length of the cavity is the same forboth undulator lengths at the longer wavelength, while for
λ = 101 μm the range is larger for Nu = 40.
For the parameters investigated, the minimum figure of
merit is 2 μJ. Assuming that half of αL is due to outcoupling of the radiation, and using the 3 GHz repetition rate of
the micropulses, we expect at least 300 W to be available inthe strongest spectral line of a fully coherent macropulse.
By optimising the detuning, the figure of merit can be atleast a factor of 3 to 5 larger, hence, it seems that the design goals for narrow bandwidth operation of NijFEL canbe realised with either undulator length. The performance
has to be evaluated at other wavelengths as well before theoptimum undulator length can be determined.

ACKNOWLEDGEMENT
Figure 8: E3GHz versus δLc for Nu = 30 (circles) and 40(squares) at maximum gain and 100 passes (A) and maximum efficiency and 150 passes (B).

We would like to thank Lex van der Meer of the FOM
Institute for Plasma Physics Rijnhuizen for the useful discussions.

REFERENCES
tuning, the 40 period undulator has a slightly higher figureof merit, while for large negative detuning, the 30 period
undulator has the higher figure of merit. This may be dueto the fact that we used the same Eb for both undulator
lengths while the actual value for optimum energy extraction may differ slightly (see fig. 2). Note, that for Nu = 40
and δLc > −300 μm, Ep is limited by the maximum number of roundtrips used in the simulation. Comparing thetwo wavelength, we find that for Nu = 40 the minimum
figure of merit is about the same for both wavelengths at
maximum gain setting, while for maximum efficiency andat slightly negative detuning values the figure of merit is afactor of two higher at 307.5 μm. For the shorter undulaFEL projects

166[1] W.B. Colson, in “Free-Electron Laser Handbook”, eds. W.B.
Colson, C. Pellegrini and A. Renieri (Elsevier, Amsterdam,
1990), Chap. 5.
[2] H.P. Freund, S.G. Biedron, and S.V. Milton. IEEE J. Quantum
Electron. 36, 275 (2000).
[3] H.P. Freund. Phys. Rev. STAB, 8, 110701 (2005).
[4] M. Xie. Nucl. Instrum. Methods Phys. Res., A445, 59 (2000).
[5] E.T. Scharlemann, A.M. Sessler, J.S. Wurtele. Phys. Rev.
Lett. 54, 1925 (1985).
[6] G.T. Moore. Nucl. Instrum. Methods Phys. Res., A250, 381(1986).
[7] A.M. Macleod, et.al., Phys. Rev. E 62, 4215 (2000).

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH069

3D MODELLING OF THE ERLP IR-FEL
D.J. Dunning, N.R. Thompson and J.A. Clarke, ASTeC, STFC Daresbury Laboratory, UK.
B.W.J. McNeil, SUPA, Department of Physics, University of Strathclyde, Glasgow, UK.
Abstract
The Energy Recovery Linac Prototype (ERLP) facility
is currently being commissioned at Daresbury Laboratory.
It serves as a testbed for technologies to be used in the
proposed 4th Generation Light Source (4GLS) facility. As
part of the ERLP facility, an infra-red oscillator FEL isdue to be commissioned early in 2008. In this paper we
present full three dimensional, time-dependent modellingof the ERLP IR-FEL using Genesis 1.3 in combination
with a paraxial optical propagation code (OPC). We also
discuss how this work will be used to inform
commissioning of the FEL.

INTRODUCTION
The full details of the design for the ERLP IR-FEL arepresented in [1] and summarised in Table 1 and a plan of
the FEL is shown in Figure 1. Commissioning of the FEL
is scheduled to begin early in 2008, and in preparation for
this, full three dimensional modelling of the FEL has been
carried out using Genesis 1.3 [2] in combination with aparaxial optical propagation code (OPC [3]). Both steadystate and time-dependent simulations have been
performed for three different modes of operation of the
FEL. The results detailed in this paper will serve as a
guide to the expected performance of the FEL during thecommissioning period and will allow a comparison withexperimental results so as to better inform FEL modelling
for the 4GLS project.
Table 1: ERLP IR-FEL design parameters.

Parameter

Value

Wiggler period
Gap (fixed)
Number of periods
Wiggler length
Deflection parameter, K
Nominal electron beam energy
Bunch charge
Bunch length (rms)Normalised emittance
Energy spread (rms)
Optical cavity length
Radiation wavelength (at 35
MeV beam energy)

0.027 m12 mm
40
1.08 m1.0
35 MeV80 pC<0.6 ps
10 mm-mrad
0.1 %
9.22438 m
4.394 µm

Figure 1: Plan of the FEL.

Operating Modes
The three proposed operating modes of the FEL are as
follows: normal mode, commissioning mode, andtransmissive outcoupling mode. A summary of theparameters for the different operating modes is given in
Table 2. In transmissive outcoupling mode the electron
bunch length is doubled, apart from this, the differences
between different modes are in the mirror radii ofcurvature (ROC) and outcoupling method.

NORMAL MODE
The normal operating mode is designed to havemaximum gain [4] and optimum output power. Details of
this optimisation are included in the next section. The
cavity is of a symmetric near-concentric design, of length
D = 9.22438 m, with mirror ROC R = 4.75 m. The mirror
angular alignment tolerance is ≪ 76 µrad. Outcoupling is
via a 1.5 mm radius hole in the downstream mirror,
giving a 12 % outcoupling fraction (chosen to maximise
the output power).
The optical mode radius at the centre of the wiggler is
w0 = 1.04 mm. At this location the matched electron beamradii are σx = 0.24 mm and σy = 0.30 mm. The electron
beam jitter (in transverse position) is expected to be no
more than 10 % of the beam radius. This means that thejitter in electron beam position is no greater than 3 % of
the optical mode size and ensures the coupling between
electrons and radiation is near-optimal. The optical mode
radius on the mirror surface, assuming the fundamental
transverse mode TEM00 is wmirror = 6.15 mm compared toa mirror aperture radius of a = 19 mm. The ratioa/wm ≈ 3:1: this is large enough to ensure that diffraction
losses from the fundamental mode are minimal. All
higher order transverse modes are wider, and will
therefore suffer more diffraction loss - this isadvantageous because it encourages lasing at thefundamental mode. In effect the limited mirror apertureacts as a crude method of transverse mode control.

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Table 2: A summary of parameters for the different operating modes (the abbreviations “US” and “DS” refer to
upstream and downstream respectively). The parameters: stability, angular alignment tolerance, mode size, cavity loss
and single pass gain are calculated using standard design formulae.

Mode
Mirror Material
Reflectivity
ROC (m)Mirror aperture radius (mm)Hole radius (mm)Outcoupling type (location)
Stability g2
Angular alignment tolerance θm (µrad)
Mode at waist w0 (mm)Mode at mirror wmirror (mm)Total cavity loss (%)
Single pass gain (%)
Electron bunch length σt (ps)NormalCommissioning

Transmissive

DS mirror
Cu/Au
>98%
>98%
4.75
4.75
19
19
No hole1.5
Hole (DS)0.88

US mirror DS mirror
Cu/Au
Cu/Au
>98%
>98%
4.75
4.75
19
19
0.75
0.75
Holes (DS + US)
0.88

US mirror DS mirror
Dielectric
Cu/Au
3% trans.
>98%
5.0
5.0
19
19
No holeNo holeTransmissive (US)
0.71

≪ 76
1.04
6.15
16
72
0.6

≪ 76
1.04
6.15
10
72
0.6

≪ 157
1.36
4.61
5
25
1.2

US mirror
Cu/Au

Cavity optimisation
The cavity geometry has been varied around the
proposed working point by changing the ROC of themirrors simultaneously such that the waist position of thelowest order cold-cavity mode is kept constant. Figure 2
shows the effect of varying the radius of the outcouplinghole and the ROC of the cavity mirrors on the output
power after 100 passes (by which time the FEL output isstable for almost all parameter sets used). This work has
been carried out using Genesis 1.3 and OPC in steadystate mode. The results show that the proposed working
point for normal mode operation (hole radius = 1.5 mm,
mirror ROC = 4.75 m) is near optimum in terms of output
power (~7.5 MW). The reduced output power around
ROC = 4.8 m can be explained by considering the shapeof the power profile at the downstream mirror (see Figure4); the intensity cross-section peaks off-axis, hence theon-axis power outcoupled through the hole is lower.

For the proposed working point, the normalised
intensity cross sections at saturation are shown in Figure 3
at different points within the optical cavity.

Figure 3: The normalised intensity cross sections atsaturation, for different points within the optical cavity.
Mirror radii of curvature = 4.75 m. The extent of the
figure in the x-direction is equal to the mirror size (radius= 19 mm).

Figure 2: Output power (W) as a function of hole radiusand mirror radii of curvature (i.e. keeping waist position
constant). For normal operation, the hole radius is 1.5 mm
and mirror ROC is 4.75 m.
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Figure 4: The normalised intensity cross section at thedownstream mirror, at saturation, for mirror radii ofcurvature = 4.8 m.

Proceedings of FEL 2007, Novosibirsk, Russia

Time-dependent simulations
Using Genesis 1.3 in time-dependent mode allows us tomodel the effects of cavity detuning, we are however,limited to detune the cavity only to half-integer multiplesof the wavelength. Figure 5 show the cavity detuning
curve for simulations of the FEL operating in normal
mode. Higher peak output power (~16 MW at a cavity
detuning of 2.2 µm) is seen compared to the steady state
result (~7.5 MW).
Shown as a comparison is the corresponding cavity
detuning curve for simulations performed using the onedimensional code FELO [5]. There is a fairly good
agreement between the two codes, particularly at smaller
detuning values. Shown in Figure 6 is a comparison of theresults from Genesis/OPC and FELO for a cavity
detuning value of 4.4 µm (where the output power
agreement between the two codes is closest); thelongitudinal profile of the output radiation at saturation isplotted. There is a good agreement between the two codes
for the longitudinal profiles of the FEL output atsaturation.
output power (MW)30

MOPPH069

of 2.2 µm; the width of the pulse is seen to be narrower
than for the detuning value of 13.2 µm shown in Figure 8.

Figure 7: Variation of longitudinal profile of the output
radiation with cavity roundtrip number for cavity
detuning = 2.2 µm.

Genesis & OPC
FELO

25
20
15
10
5
0
0

5

10

15

20

25

cavity detuning (µm)

Figure 5: Output power at saturation against cavity
detuning value for simulations of the FEL operating innormal mode, using Genesis 1.3/OPC and FELO.
12

Genesis & OPC
FELO

output power (MW)

10
8
6
4
2
0

0

500

1000

1500

2000

2500

3000

distance (µm)

Figure 6: Longitudinal profile of the FEL output atsaturation for a cavity detuning of 4.4 µm. Comparison
between Genesis/OPC and FELO.
Shown in Figures 7 and 8 is the variation of
longitudinal profile of the output radiation with cavity
roundtrip number for two different cavity detuning
values. Figure 7 shows the results with a cavity detuning

Figure 8: Variation of longitudinal profile of the output
radiation with cavity roundtrip number for cavity
detuning = 13.2 µm.

COMMISSIONING MODE
The commissioning mode of operation is designed forachieving first lasing; the cavity geometry is the same as
for normal mode but outcoupling is via both mirrors.
During commissioning we plan to monitor the FEL output
directly at the upstream mirror while simultaneously
monitoring the output from the downstream mirror in the
diagnostics room. We therefore decouple the two
problems of correctly steering the cavity to achieve lasing
and correctly steering the output radiation down the
beampipe to the diagnostics room.
Since outcoupling in this mode of operation is fromboth mirrors, smaller holes (0.75 mm radius) will be used,compared to the single hole used in normal mode
operation. It is anticipated that this will reduce transverse
mode distortion. Figure 9 shows the normalised intensity
cross sections at saturation, at different points within the
optical cavity. From the undulator entrance cross section
it is evident that there is some higher order mode content
in the radiation field.

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TRANSMISSIVE OUTCOUPLING MODE

Figure 9: The normalised intensity cross sections atsaturation for the FEL operating in commissioning mode,for different points within the optical cavity.
Time dependent simulations using Genesis 1.3 andOPC have been performed for the FEL operating incommissioning mode. Figure 10 shows the variation of
output power with cavity detuning value. Figure 11 shows
the variation of longitudinal profile of the output radiationfrom the downstream hole with cavity roundtrip number,for a cavity detuning of 2.2 µm.
output power (MW)6

The transmissive outcoupling mode of operation isdesigned to give us experience of using the transmissive
outcoupling method and to increase the tolerances toelectron beam transverse and longitudinal jitter and mirror
angular alignment. The mirror cavity is designed to befurther from concentric; increasing the mirror ROC to
5.0 m increases the optical waist to w0 = 1.36 mm,
reduces the cavity stability parameter g2 to 0.71 andrelaxes the angular alignment tolerance to ≪ 157 µrad.
The electron bunch length is doubled to σt = 1.2 ps which
halves the peak current but the calculated single pass gain
is still 25 %, sufficient to lase easily with the outcoupling
fraction reduced to 3 %.
The potential problem of mode distortion caused byhole outcoupling is removed by outcoupling using apartially transmitting (3 %) dielectric mirror. Because thecavity is further from concentric (compared to normalmode), the mode sizes shown in Figure 12 are wider at
the waist and narrower at the mirrors compared to Figure
3. Time dependent simulations using Genesis 1.3 andOPC have been performed for the FEL operating in thismode and output powers of up to 12 MW are seen.

Downstream output
Upstream output

5
4
3
2

Figure 12: The normalised intensity cross sections atsaturation for the FEL in transmissive outcoupling mode,
at different points within the optical cavity.

1
0
0

5

10

15

20

cavity detuning (µm)

Figure 10: Output power at saturation against cavity
detuning value for the simulations of the FEL operating incommissioning mode, using Genesis 1.3/OPC and FELO.

CONCLUSION
Full three dimensional modelling of the ERLP IR-FEL
has been carried out for the three different modes ofoperation of the FEL. For normal mode operation, theproposed cavity geometry and outcoupling hole radius
have been shown to be near optimum in terms of output
power. Time dependent simulations indicate a peak output
power of ~16 MW at a cavity detuning of 2.2 µm.

REFERENCES

Figure 11: Variation of longitudinal profile of the output
radiation from the downstream mirror with cavity
roundtrip number for cavity detuning = 2.2 µm.
FEL projects

170[1] N. Thompson, ERL Prototype FEL, internal report,
erlp-ofel-rpt-0001, 2003.
[2] S. Reiche, Nucl. Inst. Meth. Phys. Res. A, 429, 243,
(1999).
[3] J. G. Karssenberg et al, FEL-Oscillator Simulations
with Genesis 1.3, FEL Conf 2006, 407.
[4] N. Thompson, ERL Prototype FEL: Electron Beam
Matching, internal report, erlp-ofel-rpt-0006, 2004.
[5] B.W.J. McNeil et al, FELO, a one dimensional timedependent FEL oscillator code, FEL Conf. 2006, 59.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH072

THE IR-BEAM TRANSPORT SYSTEM FROM THE ELBE-FELs TO THE
USER LABS
W. Seidel, E. Grosse, M. Justus, K.-W. Leege, D. Proehl, R. Schlenk, A. Winter,
D. Wohlfarth, R. Wuensch
Forschungszentrum Dresden-Rossendorf, Dresden, Germany
Abstract
In the Forschungszentrum Dresden-Rossendorf, two
free-electron lasers (FELs) have been put into operation.
They produce laser light in the medium and the far infrared
wavelength range (4-150 µm). The IR ligh is transported toseveral laboratories in the same building and to the adjacentbuilding of the High Magnetic Field Laboratory as well,where the experimental setups are up to 70 m away from the
FELs. Constructional peculiarities, the large wavelength
range, the high average power in cw regime, and the beam
property requirements of the users pose a challenge to thebeam line design. The transport system includes vacuum
pipes, diagnostic elements, plane and toroidal gold-covered
copper mirrors, and exit windows. The designed transportsystem produces a beam waist at selected spots in each laboratory representing a magnified image of the outcouplinghole. Spot size and position are independent of the wavelength.

Field Laboratory (HLD, [3]) as well, where the experimental setups are up to 70 m away from the FELs.
The beam arriving at the user laboratories should be sufficiently narrow (a few millimeters). Its Rayleigh range
should be long enough (10 cm at minimum). The profile
should be circular with a Gaussian shape. It should notvary to much with the wavelength, with the size of the outcoupling hole and the used FEL. Linear polarization in horizontal or vertical direction should be conserved.

INTRODUCTION
The Radiation Source ELBE [1] at the Forschungszentrum Dresden-Rossendorf is centered around a superconducting Electron Linear accelerator of high Brilliance andlow Emittance (ELBE), constructed to produce cw electron
beams up to 1 mA beam current at 12-34 MeV. The electron beam is used to generate various kinds of secondary
radiation, mainly to drive two free-electron lasers in the infrared region (4-150 µm). Starting in the summer 2005,
beam time is offered to external users in the frame of the
EC funded ”Integrating Activity on Synchrotron and Free
Electron Laser Science” (FELBE project [2]).
The IR radiation is produced in one of the two hybrid magnet undulators U27 and U100. Changing the undulator gap
or the electron energy the wavelength of the produced IR
beam can be varied from 4 to 22 µm (U27) and from 20 to150 µm (U100). Additionally, a 633 nm beam from a HeNelaser used for mirror alignment has to be transported by thebeam line.
The outcoupled laser power to be transported by the beamline depends strongly on the parameters of the electron
beam and of the FEL undulator and resonator. Till now amaximum average cw power of 25 W has been obtained.
Theoretical estimates predict a maximum cw power ofabout 35 W.
The IR light is transported to several laboratories in thesame building and to the adjacent building (through a tunnel which is 27 m long) of the Dresden High Magnetic

Figure 2: Top view of the beam line from the U100 and
U27 FEL in the ELBE building to the user station in the
HLD building via diagnostic table and tunnel.

DESCRIPTION OF THE BEAM LINEThe designed beam line is able to transport IR light in
the wavelength range between 4 and 200 µm without noticeable diffraction and absorption losses. The HeNe adjustment beam is visible in the whole transport system. To
avoid the absorption of IR light in the ambient air the beamis guided in pipes which are either evacuated or purged with

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Figure 1: Top view of the beam line (red line) from the outcoupling holes of U27 and U100 through the diagnostic station
to the optical tables in the various user laboratories.
dry nitrogen gas. The mirrors are mounted along the wallsof the laboratories on supports 105 cm above floor, in general. Because of the large wavelength range we use reflective optics with metal mirrors [4] (gold-coated copper andstainless steel). Their reflectivity is 98.8% [4], the surface roughness is below 0.2 µm. In many cases the mirrors
are used simultaneously to deflect and to refocus the beam.
The distance between refocusing mirrors must be considerably smaller for the far infrared than for visible light.
Altogether 16 flat and 27 focusing mirrors are used in thetransport system (all are fixed in gimbal mounts). They
deflect the beam by 90 degrees. We use bifocal toroidal
mirrors to have the same focal length in the meridional andin the saggital plane. In this way we reduce the number ofmirrors to a minimum. To keep spherical aberration small
the radii of curvature must be larger than the beam radius
is. In general, the distance between two focusing mirrors is
short enough to keep the beam narrow enough for a 10 cm
beam pipe. In the tunnel to the HLD, a long straight distance has to be covered without any corner. Here we chosea 20 cm pipe to avoid refocusing within a straight sectionof the beam line. Farther, in the magnetic laboratories thebeam pipe can be reduced to 16 cm. The effective diameter of the mirrors (viewed in beam direction) is 10, 20 and
16 cm accordingly. The path of the IR beam from the FELs
to the experimental tables in the user laboratories is displayed in Fig. 1.
The beamline starts in the FEL cave at the outcouplingholes in one of the resonator mirrors of the U27- or U100FEL (left side of Fig. 1). There is a diamond windowroughly 4 cm behind the outcoupling holes. It separates theultra-high vacuum in the resonator from the beam line. The
window is mounted under the Brewster angle of 67 degrees
to let pass horizontally polarized light without reflecting
it. The window aperture has a diameter of 8 mm (U27)
and 12 mm (U100), respectively. To sustain the static anddynamic pressure difference the diamond slab is 350 µm(U27) and 570 µm thick. Further windows are placed on
FEL operation172

the diagnostic table (Diamond) and at the ends of each particular beam line (ZnSe, KRS-5, TPX, Quartz, Diamond,
respectively the beam properties). From the outcouplinghole the beam is transported to a diagnostic table in theneighboring room where the beam parameters can be measured. Some of them (average power, repetition rate) can
also be modified [5].
The FEL cave is separated from the user laboratories by
a radiation protection wall which is 2.6 m thick (see Fig. 1).
This wall has to be by-passed by the laser beam. A straightconnection between these rooms would allow γ-quanta andfree neutrons produced by the high-energy electron beam in
the FEL cave to enter the diagnostic laboratory.
Behind the diagnostic table the beam is transported into
6 laboratories in the ELBE building and additionally into
the High Magnetic Field Laboratory in a separate building.
The latter is connected with the ELBE building by a tunnel
which is 27 m long. The branch guiding the beam to the
HLD is shown in Fig. 2.
To evaluate the beam propagation theoretically we used
the method of the equivalent Gaussian beam [6]. The
beam passing the outcoupling hole is described as a circular Gaussian beam with a waist at the hole. The slightcurvature of the wave front at the outcoupling hole can beneglected. The waist size w0 in the hole is determined by
the diameter Dh of the hole according to w0 = 0.7 ∗ Dh /2.
The same relation is used to assign a nominal diameter
Db = 2∗w/ 0.7 to the Gaussian beam at any place in the
beam line. The description as a Gaussian beam is considered an approximation which allows analytically to evaluate the propagation of the outcoupled beam. We have tested
this approximation in several cases by means of the wave
optical code GLAD [7]. The diameter of apertures in the
beam line should be larger than the beam diameter Db , toavoid power losses and diffraction ripples in the beam profile. Fig. 3 shows the beam diameter Db along the beamline from the outcoupling hole to the diagnostic table forboth FELs. On its path, the beam is sufficiently slight toProceedings of FEL 2007, Novosibirsk, Russia

MOPPH072

Figure 3: Diameter Db of the IR beam calculated along the beam line from the outcoupling hole to the waist on the
diagnostic table (z=0) for various wavelengths and outcoupling holes with diameter Dh . Focusing (Mik) and flat mirrors
are indicated by vertical solid and broken lines, respectively. The position of the diagnostic waist is indicated by themagenta line. Left panel: U27-FEL, right panel: U100-FEL.

Figure 4: The same as in Fig. 3 for the beam line from the waist on the diagnostic table (z=0) to the HLD.
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fit into a 10 cm beam pipe. On the other hand, it is broad
enough not to damage the mirror surfaces by a big power
density. The waist on the diagnostic table (z = 0 in Fig. 3)
is common to the beams from each outcoupling hole in either FEL and to all wavelengths as well. Only the waist
size is proportional to the diameter of the outcoupling hole.
The narrow beam in the vicinity of the waist is used forbeam measurements and modifications.
The beam line to the HLD is a particular branch of the general line delivering the laser light from the IR FELs to several user laboratories. It branches off from the general line
behind mirror M43 by inserting the flat mirror MH1 (seeFig. 1) into the beam line. It bents the beam down to a specific line guiding the beam via mirrors MH2 - MH4 into atunnel on basement level which connects the ELBE building with the HLD. Arriving the tunnel the beam is refocused (MH4) to a nearly parallel beam. However, diffraction increases the IR-beam size much stronger than in therange of visible light. Towards the end of the tunnel the
beam is too thick for a 10 cm pipe and the pipe diameterhas to be increased to 20 cm. The beam size calculated
along the beam line is shown in Fig. 4.
In order to test the validity of the approximation by a Gaussian beam, the beam profile behind the outcoupling holeand on several positions in the beam line has been measured. These profiles are in conformity with the corresponding Gaussian profile. The power transmission of thebeam line depends strongly from the used windows, thewavelength and the length of the beam line and was measured to be 15-90 %.

REFERENCES[1] P. Michel et al., Proceedings of the 2004 FEL Conference, p.
8-13, Trieste, Italy[2] www.fz-rossendorf.de/felbe[3] J. Wosnitza et al., J. Phys.: Conf. Ser. 51, 619 (2006)[4] LT Ultra-Precision, www.lt-ultra.com[5] W. Seidel et al., Proceedings of the 2006 FEL Conference, p.
341-344, Berlin, Germany[6] H. Kogelnik, Appl. Opt. 4 (1965) 1562-1569[7] GLAD, Applied Optics Research, Woodland, WA 98674,
USA

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MOPPH073

THERMAL AND NON-THERMAL LASER CUTTING UTILIZINGADVANCED INDUSTRIAL LASERS AND ERL-FELS *Eisuke J. Minehara,
JAEA, 2-4 Shirakata-shirane, Tokai, Naka, Ibaraki 319-1195, JAPAN.
Abstract
The JAEA and JLAB energy-recovery IR free-electron
lasers (ERL-FEL) have successfully demonstrated theircapabilities of a sub ps pulse, high efficiency, GW highpeak power, kW average power, and wide tunability.
Utilizing the high power FEL and ERL technologies, we
could realize a more powerful and more efficient FEL
than 20kW and 25%, respectively, for nuclear industry,
pharmacy, medical, defense, shipbuilding, semiconductor
industry, chemical industries, environmental sciences,
space-debris cleaning, power beaming and so on very
near future. We have performed their thermal and nonthermal cutting experiments using advanced industrial
lasers like fiber, and water-jet guided ones and the ERLFELs, and have characterized them according to theirresultant effects.

INTRODUCTION
Two nuclear power plants of the 166MW Tokai power
station and 165MW Fugen power stations have been
prepared and partially started to decommission in Japan
recently. The Tokai power station is the first nuclear
power plant for commerce in Japan and decommissioningof the Tokai power station is the first project of thenuclear power plant for commerce in Japan. The Fugen is
the advanced thermal reactor prototype using heavy watermoderator, light water cooling, and dense piping structurein the core. Feasibility studies of laser cutting are
discussed here to compare a few kinds of commerciallyavailable advanced industrial lasers and ERL-FELs witheach other.
The currently-available CW lasers like CO2, YAG, andfiber lasers are widely used to cut, to drill and to peel-off
the material sheet, rod, and pipes of stainless steel,zirconium alloy, and others in the power plants, factories
and laboratories. Cutting mechanisms of all the lasers
listed above to machine the materials are blown off orburn out the melted one by feeding the assisting gases ofhighly-pressurized inert gases and oxidation gases like
N2, O2 and others. Therefore, we can easily expect that
there are some intrinsic difficulties to cut, to drill and topeel-off the materials wherever and whenever we cannot
feed either one of the laser power and pressurized gases tothe machining point. We can cut the stainless steel sheet
at the speed of 10 meter per minute or even the higher one
whenever we can feed enough amounts of the laser powerand gas at the cutting point. Double-layered, and multilayered sheets, and rod and pipe bundles are intrinsicallydifficult to cut completely using the mechanism discussed

here and all the lasers being commercially-available in theworld. Therefore, we have to give up cutting the layered
sheets and bundles at once simply using the mechanism
and all the lasers. We can only cut the layered sheets
layer by layer, and bundles step by step after removal of
the cut layer, cut rod, and cut pipe as long as we will use
all the commercially-available lasers. The layer by layerand step by step cutting with all the lasers is not so quick
enough to decommission the power station facilities.
There is no commercially-available sub-ps or a few ps
ultra-fast, GW peak power, kW average power freeelectron lasers [1] to cut the multi-layered and bundled
structures at once. As they have been under development
over last 10 years, they will be commercially available
next 10 years.

ADVANCED INDUSTRIAL LASERS
The figures 1 and 2 show the fiber laser device and cut
sample as one of the typical industrial laser examples.

Figure 1: 1 to 50kW CW Ytterbium fiber lasers are
manufactured by IPG Photonics. A typical example of thecommercially-available advanced industrial CW lasers.

___________________________________________*Work supported by in part by Grants-in-Aid for Scientific Research(A19206103).
#
minehara.eisuke@jaea.go.jp

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or even faster, we can directly cut them into the small
pieces from the inside to outside using a small andspecially -designed laser nozzle one by one.

Figure 2: A Stainless-steel plate of 4mm thick and 40mm
wide and 80mm long was successfully and quickly cut
using 20 bar compressed and focused N2 gas flow and
IPG made 2 kW CW Ytterbium fiber laser. The 2kW fiber
laser system usually has a capability of thick metal plate
cutting from a few mm up to ten and several mm.
The fiber lasers have been often used to produce the
CW power output ranging from several hundred W to 100
kW. In decommissioning the Fugen power station, we
can expect about 4000 tons of radioisotope-contaminatedwaste and 370000 tons of dismantled materials.
Especially, we can easily apply the currently andcommercially available lasers like fiber lasers to cut andto dismantle the dense piping structure and the thick tankin the Fugen power station.

Figure 3a: A Fugen Zirconium alloy pressurized tube ofabout 4.3mm thick and 117.8mm inner diameter was
successfully and quickly cut with 6m per a minute using
20 bar compressed and focused N2 gas flow and IPG 5kW
fiber laser.
The pressurized tube and Carandoria tube of Zirconium
alloy were originally tried to cut at the same instant in the
Fugen station. As it is very difficult for currently andcommercially available industrial lasers to cut at the same
instance, here we tried to cut them one by one by the fiber
lasers shown in Figs.3a and 3b. Because the speed of thelaser cutting is very fast and reliable in 5-6 m per minute
FEL applications

176

Figure 3b: The Zirconium alloy tube was cut with very
high speed of 6m per a minute, and cut-width was as
narrow as 0.25mm more or less. Surface condition of the
cutting edges is very beautiful and very smooth andslightly narrower than the Stainless steel cases.

Figure 4: Water jet-guided laser named LMJ(Laser MicroJet ) driven by 100-200W pulsed YAG laser manufactured
by Synova S.A., Switzerland is another typical exampleof the new, commercially-available, and advanced
industrial lasers.
A so-called water jet-guided laser named Laser MicroJet(LMJ) shown in Fig.4 is the newest laser manufacturing tool and applicable to decommissioning of
nuclear power plants. The LMJ was recently-invented by
the researchers in the early nineties at the Federal Instituteof Technology in Lausanne, Switzerland. We alreadyhave tried to cut, to drill and to peel-off non-radioactive
metal samples. We hope to increase the available laser
power in LMJ system from 100W to one kW, and we caneasily estimate that the needed duty factor is not so large
to be several % more or less.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH073

ERL-FELS
Figure 5 shows the JAEA free-electron laser that we
can convert them from quasi-CW machine to full CW or
higher duty ones to cut the multi-layered and bundledmaterials at once. After the conversion, we can sharply
cut the very thick tank wall with a very small gap width,
drill and peel-off without producing a large amount ofradioisotope (RI)-contaminated dusts during thedecommissioning operation.

High Power FELs 0.5GHzUHF
12MeV(FIR)/ 24MeV(MIR)/48MeV(NIR)
Decellerator
Beam Dump

1m
Optical Resonator
Outcoupler
MirrorMirror
6
FEL Output
7
5

HVPS Compressor RFPS
8

1
InjectorGun

2

3

4 Reflextron

Control Compressor

Eacc=4MV/m-8MV/m, 0.5GHz

6-12MeV(FIR) 1.5ｍ(Acceleration length)/5Cell
12-24MeV(MIR)

3m /10Cell

24-48MeV(NIR)

6m /20Cell

Figure 6: Three industrial FEL models for lasing in the
FIR, MIR, and NIR wavelength regions with thereflextron geometry. All of them use the 500MHz UHFband cavities of 5, 10 and 20 cells, respectively.

Figure 5: The JAEA energy recovery super-conducting
linac-based free-electron laser(ERL-FEL) at Tokai.
Very good cutting performances of ERL-FELs are
expected for Stainless-steel and Zirconium alloys becauseof millions times larger peak power, the same kW highaverage one, and very good laser divergence.
Three industrial FEL models having the reflextron[2] orsimilar geometry are illustrated in Fig. 6. Three of them
are infrared FELs, and the fourth ultraviolet or visible
FEL. As shown in Fig.6, the far-infrared FEL (FIR FEL)
ranging from 200 to 50micron wavelengths uses the
500MHz UHF band cavity of 5-10MeV electron energy
with the reflextron energy recovery geometry.
A mid-infrared FEL (MIR FEL) ranging from 50 to 8
micron wavelengths will use the 500MHz UHF band
cavity of 12-24MeV electron energy with the reflextron
geometry. Possible and typical applications are expected
to be large-scaled photochemical processing, medical,
pharmacy, rare-material separation, radio isotope
separation in nuclear decommissioning and so on. A nearinfrared FEL (NIR FEL) ranging from 12 to 2 micron
uses the same 500MHz cavity of 24-48MeV electron
beam energy with the reflextron.
As shown in Fig.7, 1.3micron high peak power andhigh average power JLAB FEL light could instantly cut
the 316L stainless-steel bar sample like boiling water
reactor components and stainless-steel thick bar withouthigh pressurized blow-off gas. All conventional laser
cutters must need a focused and very high pressurized gas
flow to blow off narrow part of the laser-heated andmelted metal material.

Figure 7: High peak power and high average power JLABFEL light could instantly cut the 316L stainless-steel bar
sample like boiling water reactor components andstainless-steel thick bar without high pressurized blow-offgas.
A 10 or 20kW industrial FEL which can lase at arounda fiber-transmittable wavelength of 1.3 micron and ataround water transmittable wavelength centered around
0.5 micron will be very useful to transmit their power to apin-pointed position in a distant area from the FEL. The
FEL will be widely used in the many factories like ashipyard, automobile factory, civil engineering, nuclear
power plant and so on.
A few FEL application examples will cover theapplication of non-thermal peeling, cutting, and drilling todecommission the nuclear power plants, and to prevent
stress-corrosion cracking in the nuclear decommissioning
industry. As a very thin cutting width has been thought torealize a so-called RI contamination freedecommissioning, we plan to use a water-jet guiding of
FEL light for non-thermal peeling, cutting, and drilling indecommissioning the nuclear power plants. And we also

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177

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Proceedings of FEL 2007, Novosibirsk, Russia

have demonstrated to prevent cold worked stresscorrosion cracking of the vital components like pressure
vessel shroud and recirculation pump piping in the
nuclear power plant. The cold worked stress-corrosion
cracking sample like BWR shroud is shown in Fig. 8.
A preliminary characterization of the 316L stainlesssteel samples shows that the KW CW fiber laser cutting
resulted molten zone, high residual tensile stressed area,and high Vickers number hardened layer in the surface,on the other hands, the water jet-guided and JLAB ERLFEL lasers no molten one, almost no residual tensilestressed one, and the low Vickers number one as the samewith the material deep inside.

Relatively low efficiency converted from the electron
beam to FEL power can be overcome, and increased torecover the remained beam power after the lasing by the
ERL. The ERL technology can be usable to make the
FEL efficient drastically, and to realize the industrial
FELs for many major industry fields including the nuclear
power ones soon. The reflextron like geometry can beapplied to make the industrial FELs compact, powerful,and efficient because an absolute value of the velocity
difference is very small between the acceleration anddeceleration along the accelerator cavity at the same
position, and we can recover very efficiently the beam
power at a few MeV or less electron energy.
We can also add that the preliminary characterization of
the 316L stainless-steel samples using ERL-FELs andwater jet-guided laser show very clear and promising
results for their non-thermal machining capabilities.

ACKNOWLEDGMENTS

Figure 8: A large number of typical cold worked stresscorrosion cracking(CWSCC) are found in the 316L
stainless-steel sample which have often been used in theboiling light water reactor (BWR) shroud and otherreactor internal components after the JIS(Japan Industry
Standard) defined MgCl2 SCC test of 20 hours.

CONCLUSIONSThe FELs driven by the superconducting RF linac have
intrinsically very high average power capability because
the linac driver is highly efficient and powerful.

FEL applications

178

The author gratefully express his thanks to Drs. G. Neil,
M. Shin, S. Benson, G. Williams, J. Kevin, J. Gubeli andmany other colleagues in JLAB FEL facility and all
members of JAEA ERL-FEL one for their valuable andkind suggestions and helps on the FEL machining trials,
and Profs. H. Horike and T. Fukuda of Osaka University
for his continuous encouragement. This work has been
supported in part by Grants-in-Aid for Scientific Research(A19206103).

REFERENCES[1] Minehara, E.J., et al., ‘‘Development and operation of
the JAERI superconducting energy recovery linacs’’ ,Nucl. Instr. and Meth. in Physics Research Section A,
Vol. 557, Issue 1, 1 Feb. 2006, pp 16-22.
[2] E. A. Heighway, “Magnetic Beam Defection System”.
Canadian Patent 993124, issued 1976.

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH074

PRELIMINARY DESIGN OF THE PROPOSED IR-FEL IN INDIA
Srinivas Krishnagopal∗ , Vinit Kumar
RRCAT, Indore, M.P. 452013, India
Abstract
We discuss preliminary design studies of an infrared (IR)free-electron laser (FEL) proposed to be built at the Raja
Ramanna Centre for Advanced Technology (RRCAT). The
design calculations and optimisations have been performed
using the three-dimensional time-dependent oscillator code
GINGER [1].

INTRODUCTION
A terahertz free electron laser, the CUTE-FEL, designed
to lase around a wavelength of 80 μm using a 10 MeV linac
is in an advanced stage of construction at RRCAT [2]. In
the next step in our FEL activities, we have proposed tobuild an IR-FEL. In this context, we have performed design
studies of an IR FEL to lase between 12-50 μm, which will
use a 15-25 MeV linac. In this paper, we focus mainly on
30 μm simulations and briefly discuss the results at 12.5
μm and 50 μm also. The high power, short pulse andwidely tunable coherent radiation from this IR-FEL can beused for performing a wide range of interesting research
applications that include experiments on direct as well as
indirect band-gap semiconductors, IR microscopy of biological samples, multi-photon dissociation experiments,
isotope separation, reaction dynamics studies, etc.
In the next section, we discuss the basic design considerations and then in the following section, we discuss design
simulation results. We finally conclude in the last section.

DESIGN CONSIDERATIONS
After preliminary consultaions with users, we found thata wavelength range of 12-50 μm is interesting for a wide
range of many interesting experiments. Using a 15-25 MeV
electron beam from an electron linac, and an undulator having period (λ u ) of 40 mm and undulator parameter K in therange 1-2, it should be possible to cover this wavelength
range, as can be seen from the following formula:
λR =

λu
K2
),
(1 +
2
2γ
2

(1)

where λR is the radiation wavelength, γ is the electron energy in units of its rest mass energy and K =eBu λu /2πmc, Bu is the peak undulator field, m is the rest
mass of electron and c is the speed of light. Note that wehave chosen maximum value of K = 2 such that we get awavelength tunability up to a factor of two by varying K
in the range 1-2. We will use a Halbach configuration of∗ skrishna@cat.ernet.in

pure permanent magnets for the undulator, where the dependence of peak magnetic field on the gap g between thejaws of the undulator is given by[3]Bu = 1.43Br exp(−πg/λu ).

(2)Here Br is the remanent field of the permanent magnet
used in the undulator. Using B r = 1.2 T for NdFeB magnets, we obtain the gap to be 15 mm for K = 2. We therefore will need to use an undulator vacuum pipe having innerdiameter (ID) of 11 mm.
The number of undulator periods N u is chosen to be 60
on the basis of gain considerations. The 2.4 m long undulator will be immersed in a 4.1 m long optical cavity. The
undulator will be asymmetrically placed in the optical cavity such that we have 1.05 m of space available for beamtransport and diagnostic on the upsteam side and 0.65 mof space available on the downstream side. Assuming a
Rayleigh range of 0.8 m, which is one third of the undulator length, the rms optical beam size at the waist is 1.4
mm. We therefore chose the rms electron beam horizontal
size σx at the waist to be around 1 mm for good overlap
with the optical beam. The rms electron beam size σ y in
the vertical direction is taken to be the matched beam sizein the undulator given by [3]n λuσy = √,(3)2πK
where n is the normalized rms electron beam emittance.
We choose n = 30 mm-mrad for our design calculation.
For the electron beam, we will use a micropulse charge
in the range 0.2-0.5 nC. The electron beam rms pulse widthis taken to be 4 ps and the relative rms energy spread istaken to be 0.5%. These parameters are easily acheivable.
In the next section, we present the results of design simulations.

DESIGN CALCULATIONS
For performing the design simulations, we have used
the FEL code GINGER [1], a multidimensional [full 3D
for macroparticles and 2D (r − z) for radiation], timedependent code to simulate the FEL interaction in singlepass amplifier as well as oscillator configurations. GINGER
utilizes the KMR [4] wiggle-period-averaged electronradiation interaction equations and the slowly-varying envelope approximation (SVEA) in both time and space forradiation propagation. For propagation outside the undulator for oscillator problems, the code uses a Huygens integral method. Shot noise is modeled by giving a controlled amount of randomness to the initial longitudinal

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179Proceedings of FEL 2007, Novosibirsk, Russia

phases of macroparticles; the algorithm [5] generates thestatistically-correct shot noise at the fundamental as well
as at harmonics.
The design parameters of the IR-FEL are given in Table 1. For the 30 μm simulations reported here, we haveused γ = 45.25. We first performed the time-independent
simulation using the code TDAOSC [6] which is an oscillator version of the code TDA [7]. For the parameters mentioned in Table 1, we obtained the single pass, small-signal
gain of 135%, saturated cavity power of 9.8 MW and holeout-coupled power of 2.0 MW. The resonator parameters
were optimized using TDAOSC and we obtained optimum
performance for the Rayleigh range of 0.8 m and the location of the waist in the middle of the optical cavity. The
optical mode profile at both the mirrors and the entrance of
the undulator is shown in Fig. 1. We find the modes arenearly Gaussian.

8

2x10

Radiation Intensity (arb. unit)

MOPPH074

entrance to the undulator

downstream mirror

8

1x10

upstream mirror

0
0

3

6

9

12

15

radius (mm)Figure 1: Mode profile of the radiation beam at different
locations as indicated in the figure.

Table 1: Design parameters used in the simulation
22.6 MeV
20 A
0.5%
30 mm-mrad
1.2 mm36.62 MHz.
0.37 mm, 1.00 mm
8 μs
40 mm
2.0
2.4 m
15 mm
11 mm (ID)
30 μm
4.1 m
65 cm from und. exit
105 cm from und. entr.
2.36 m (d), 2.36 m (u)
99%
2 mm

Next, we performed time-dependent simulations using
We simulated the time-structure of the electron
bunch as Gaussian with rms width of 4 ps. A time window of six times the rms width has been used for simulating the electron bunch, which is discretized into 60
electron slices, the separation between slices being 4 radiation wavelengths. A total number of 96 such radiation
slices were used in the simulation. We studied the effectof cavity length detuning on the performance of the FEL.
Fig. 2 shows the dependence of out-coupled power on cavity length detuning ΔL c . Here, ΔLc is defined as the reduction in the cavity length compared to the synchronizedlength. We find that the optimum performance is obtainedat ΔLc = 27 μm. We used this value for further simulations
GINGER .

FEL projects

180

done at this wavelength.

76Micropulse energy (μJ)

Electron beam energy (E)Peak beam current (I)RMS energy spread (σ γ /γ)RMS normalised emittance
RMS pulse width (σz )Micropulse rep. rate
RMS e-beam size (σx , σy )Electron macropulse width
Undulator period (λ u )Peak und. parameter (K)Undulator length (N u λu )Undulator gap
Beam pipe diameter
Radiation wavelength (λ R )Optical cavity length
Location of down mirror
Location of up mirror
Mirror radii of curvature
Mirror reflectivity (power)
Hole radius in down. mirror

5
4
3
2
1
0
0

10

20

30

40

50

60

70

80

90

Cavity detuning (μm)

Figure 2: Energy in the out-coupled micropulse as a function of cavity detuning.

Next, we studied the growth of power starting from shotnoise, which is shown in Fig. 3. The saturated intracavity
average power is 5 MW, where averaging is done over effective electron pulse width, which is approximately 2.5
times the rms width for a Gaussian bunch. As seen in
Fig. 3, it takes around 150 round trips for the power to saturate. This means that the start-up time is around 4 μs sincecavity length is 4.1 m.
The time structure of the out-coupled power is shown in
Fig. 4. We find that the peak out-coupled power is 1.35
MW and the total energy in the micropulse is 6.9 μJ.
We thus find that assuming a modest set of design parameters mentioned in Table 1, it should be possible to laseand generate around 1 MW of peak out-coupled power at
30 μm. We have also performed preliminary simulationsat 12.5 μm and 50 μm and found that the lasing is possi-

Proceedings of FEL 2007, Novosibirsk, Russia

MOPPH074

50 μm
12.5 μm

Figure 3: Growth of average intracavity power from noise.
Parameters used in the simulation are given in Table 1.

Figure 5: Growth of average intracvity power from shotnoise for the 12.5 μm and 50 μm cases. Parameters used in
the simulation are discussed in the text.

DISCUSSIONS AND CONCLUSIONS
We have not included the effect of wave-guiding in our
calculation. Since we are planning to use a rather smaller
beam pipe ID, the effect of wave-guiding may become important. We plan to focus on this issue in the future.
To summarize, we have presented the results of preliminary design calculations for an IR FEL proposed to be built
at RRCAT. We find that with modest design parameters, it
should be possible to lase in the range 12.5 - 50 μm andobtain peak out-coupled power more than 1 MW. Detailed
design simulations and optimization are still underway.

ACKNOWLEDGEMENT
Figure 4: Time structure of the out-coupled power. A holeof radius 2 mm in the downstream mirror is used for thiscalculation.

It is a pleasure to thank Bill Fawley for many useful andstimulating discussions on FEL simulation using GINGER
and for his generous help by including the hole-outcouplingin this code.

REFERENCES
ble even at these wavelengths with these parameters. Fig. 5
shows the growth of power from shot noise for these twocases. Note that we have assumed an electron energy of
25.32 MeV (γ = 50.55) and K = 1.0 for the 12.5 μm simulation. For the 50 μm simulation, the electron beam energy is assumed to be 17.4 MeV (γ = 35.07) and K = 2.0.
We have used a peak electron beam current of 50 A for the12.5 μm simulation. Since the gain is less at shorter wavelengths, we have used a larger current for this case. Also,
we have taken the radius of the out-coupling hole in thedownstream mirror to be 1 mm since the radiation beam
size is smaller for this case. The peak out-coupled power
for the 12.5 μm case is around 3.2 MW and for the 50 μm
case, it is 1.1 MW.

[1] W. Fawley, A user Manual for GINGER and Its PostProcessor XPLOTGIN, LBNL-49625-Rev. I ed., Lawrence
Berkley National Laboratory (2004).
[2] S. Krishnagopal et al., Proceedings of FEL Conference(2006) 496.
[3] C. A. Brau, Free-Electron Lasers, Academic Press Inc., San
Deigo, 1990.
[4] N.M. Kroll, P.L. Morton, and M.R. Rosenbluth, IEEE J.
Quantum Elec. QE-17, (1981) 1436.
[5] W.M. Fawley, PRST-AB 5 (2002) 070701.
[6] S. Krishnagopal et al., Nucl. Instr. and Meth. A 318 (1992)
661.
[7] T. M. Tran, J. S. Wurtele, Computer Phys. Commun. 54(1989) 263.

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MOCAU01

Proceedings of FEL 2007, Novosibirsk, Russia

SHORT WAVELENGTH REGENERATIVE AMPLIFIER
FREE-ELECTRON LASERS
N. R. Thompson and D. J. Dunning, ASTeC, Daresbury Laboratory, Warrington WA4 4AD, UK ∗B. W. J. Mc Neil, SUPA, University of Strathclyde, Glasgow G4 0NG, UK
Abstract
In this paper we discuss extending the operating wavelength range of tunable Regenerative Amplifier FELs toshorter wavelengths than current design proposals, notably
into the XUV regions of the spectrum and beyond where
the reflectivity of broadband optics is very low. Simulation studies are presented which demonstrate the development of good temporal coherence in generic systems witha broadband radiation feedback of less than one part in ten
thousand.

INTRODUCTION
A regenerative amplifier free-electron laser (RAFEL) isa high-gain resonator FEL which achieves saturation in a
few round-trips of the radiation in a high-loss, and hence
low feedback, optical cavity. Because the radiation feedback fraction is low it is feasible that the use of low reflectivity optics in the resonator makes the RAFEL a candidate
for short wavelength operation [1]. Several RAFEL proposals have been made in the VUV [2, 3] and X-ray [4]and some experimental results obtained [5, 6].
There are several expected advantages of the RAFEL
over other types of FEL. The RAFEL should be less sensitive to radiation-induced mirror degradation than a low gain
oscillator FEL, and the small number of passes required
to reach saturation should relax the longitudinal alignment
tolerances. The optical feedback also allows the undulator
length to be reduced compared to a Self Amplified Spontaneous Emission (SASE) FEL, and it is expected that because of the feedback a RAFEL source can deliver higher
quality and more stable pulses than a SASE FEL.
The properties of the transverse modes within the cavity
differ from those of a low-gain oscillator FEL. Because of
the high loss of the resonator the radiation is not stored overmany passes, and because of the high-gain of the FEL theradiation does not propagate freely within the cavity but
experiences gain guiding. The cavity’s primary function isto return a small field to the start of the undulator to seed theinteraction with the subsequent electron bunch. For thesereasons it is equally valid to refer to a RAFEL as a HighGain Self-Seeding Amplifier FEL.
In this paper we present 1D modeling results for a systemwith a very low feedback factor that returns only ∼ 10 −5of the undulator output. Such low feedback may occur
when mirror reflectivities are very poor, for example into
the XUV and x-ray regions of the spectrum. The results∗ n.r.thompson@dl.ac.uk

FEL Theory

182

are encouraging and suggest that, in principle, a low feedback RAFEL may prove a viable source at these photon
energies.

A GENERIC HIGH-GAIN RAFEL
We now consider a generic high gain system shown
schematically in Fig. 1 and investigate the properties ofsuch a system when the feedback fraction is reduced to very
low levels. First we optimise the feedback fraction using
two criteria—the output power and the pulse temporal coherence should both be maximised. We work in the units of
the universal scaling [7] where z̄ = z/l g and lg = λw /4πρis the nominal gain length, with λ w the undulator periodand ρ the FEL parameter.
It can be shown from [8] that the electron beam equivalent shot-noise power is:
√
6 πρ
2

,
(1)
|A0 | ≈
Nλ ln (Nλ /ρ)where Nλ is the number of electrons per radiation wavelength. In the exponential gain regime the radiation intensity after a single pass through an undulator of scaled interaction length z̄ is then given by|A1 |2 (z̄) ≈√|A0 |2exp( 3z̄)
9(2)

and after returning a fraction F of the output power to thestart of the undulator, via some as yet undefined opticalsystem, the seed power at the start of the second pass is
F × |A1 |2 . The necessary condition for the developmentof longitudinal coherence is that this seed power is greaterthan the shot noise power, i.e.
F × |A1 |2 > |A0 |2 .
A feedback factor criterion to dominate the shot noise canthen be defined as:√
FN > 9 exp(− 3z̄).
(3)The feedback factor necessary to optimise the output
power in the steady state regime only has been determinedfrom 1D simulations, with the results shown in Fig. 2. A
fit to the numerical data, valid over the range 3 ≤ z̄ ≤ 12,
gives
√
(4)
FP ≈ 25 exp(− 3z̄).
It is seen from comparison of (3) and (4) that F P  3FN
implying that optimising feedback to maximise the output power will necessarily prove sufficient to dominate theProceedings of FEL 2007, Novosibirsk, Russia

MOCAU01

Figure 1: Schematic representation of a generic high gain RAFEL system.
propagation equations

0

10

−2

10

FP


−4

10

−6

10

−8

10

0

2

4

6
z̄

8

10

12

Figure 2: Results of one-dimensional steady-state simulations to determine the feedback factor F P that maximises
the output power. A fit to the numerical√ data over the range
3 ≤ z̄ ≤ 12, gives FP ≈ 25 exp(− 3z̄)electron beam shot noise and enable the development ofcoherent pulses. This postulate is tested with 1D timedependent numerical simulations in the next section.

∂∂+∂ z̄ ∂ z̄1



dθj
dz̄
dpj
dz̄
A(z̄, z̄1 )= pj ,= −(A(z̄, z̄1 ) exp[iθj ] + c.c.)= χ(z̄1 )exp[−iθ] ≡ b(z̄, z̄1 )where p is the particle energy p = (γ − γ r )/ργ with γr the
resonant electron energy in units of the electron rest mass,
θ the particle phase within the ponderomotive well, z̄ 1 isthe length along the electron bunch from the bunch tail inunits of the cooperation length l c = λr /4πρ and χ(z̄1 ) the
function describing the macroscopic electron current profile.
The feedback factor was varied from F = 10 −3 toF = 2 × 10−6 , and the cavity detuning value δ c , in unitsof z̄1 , varied from δ c = 0, defining cavity synchronism, toa detuned cavity length of δ c = 9.0. For each combinationof these parameters the system was allowed to evolve over
200 cavity round trips.
In order to compare the numerical results of the low
feedback RAFEL system with a SASE system, 200 separate simulations were done for an equivalent SASE systemwith z̄ = 14 where saturation of the pulse energy is seen to
occur.

Simulation Results
TIME DEPENDENT SIMULATIONS
Simulation Method and Parameters
We choose a low feedback factor of F P = 10−5 anduse (4) to derive the appropriate scaled interaction lengthof z̄ = 8.67. An FEL parameter of ρ = 2.9 × 10 −3 is used,typical of XUV FELs, with a peak number of electrons per
wavelength of N λ ≈ 3.8 × 105 . The macroscopic profileof the electron bunch is gaussian, and the input electron
beam is monoenergetic. The system is modelled using a
1D time dependent code FELO [9] which solves the 1D FEL

An analysis has been carried out to determine key parameters of the output pulses pass-by-pass. The parameters of interest are the peak intensity |A| 2peak , the rms pulse
length σz̄1 , the rms relative linewidth σ λ /λ and the time
bandwidth product ΔνΔt which is used to quantify the development of the temporal coherence. The definition used
is


1 Δλ
ΔνΔt =Δz(5)λλwith Δz the pulse width. The numerical value obtained
depends on the definition√ of width chosen. The choice usedhere here is Δx = 2 2 ln 2 × σx under which definition

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Proceedings of FEL 2007, Novosibirsk, Russia

1 × 10−3

5 × 10−4

8

6

5 × 10−5

4

1.5

4

|A|2

1
|A|2

4
|A|2

|A|2

6

2

2

2
0
0

1 × 10−4

0
0

100 200z̄1
2 × 10−50.5
00

100 200z̄1
1 × 10−5

100 200z̄1
5 × 10−6

0
0

0.03

1

1

1

0.02

|A|2
0.5
0
0

0.5

100
z̄1

200

0
0

|A|2

1.5

|A|2

1.5

|A|2

1.5

0.5

100
z̄1

200

100 200z̄1
2 × 10−6

0
0

0.01

100
z̄1

200

0
0

100
z̄1

200

Figure 3: Typical output pulses of the low feedback RAFEL system. The feedback fraction is shown above each plot, andvaries from F = 1 × 10 −3 (top left) to F = 2 × 10 −6 (bottom right). The cavity detuning value is δ c = 6.0 for all pulses.
a transform limited gaussian intensity pulse would give theresult obtained using FWHM values of ΔνΔt  0.44 (therelationship between√ σ and FWHM for a gaussian given by
FWHM(x) = 2 2 ln 2 × σx ).
SASE results The results of the SASE simulations are
as follows: the root mean square (rms) linewidth over 200
simulations was σλ /λ = 2.77 × 10−3 with an rms pulse
length σz̄1  = 14.01 giving a time-bandwidth product ofΔνΔt = 5.9. The peak intensity |A| 2peak  = 2.2.
Low feedback RAFEL Results To identify some features of the RAFEL output, pulse profiles for a feedback
fraction decreasing from F = 10 −3 to 2 × 10−6 are shown
first in Fig. 3 for a cavity detuning value of δ c = 6.0. It
is seen that for F = 10−3 the pulse profile is spiky witha peak intensity |A|2peak = 7. The bandwidth for theseparameters, averaged over 200 post-saturation passes, isσλ /λ = 4 × 10−3 , greater than the mean SASE valueof σλ /λ = 2.77 × 10−3 , and the time bandwidth product is ΔνΔt = 12 compared to the SASE value ofΔνΔt = 5.9. This data indicates that the RAFEL pulse
is over-saturated. The feedback fraction is too high so thatthe seed power is too great and the RAFEL saturates before
the end of the undulator.
Fig. 3 shows that as the feedback fraction is decreased
the pulse profile becomes cleaner, with the front and backof the pulse cleaning up first, leaving a spiky region in
FEL Theory184

the centre of the pulse. This behaviour is attributed to thegaussian electron current profile—the front and back of thepulse experience less gain and do not oversaturate whereas
the centre of the pulse oversaturates. The time bandwidth
product falls below the SASE value at a feedback fractionof F = 5 × 10−5 . For lower feedback, the time bandwidth
product continues to fall until it reaches a minimum valueof ΔνΔt = 1.0 at a feedback of F = 5×10 −6. Examination of the pass-by-pass data shows individual pulses withΔνΔt = 0.68, close to that of a transform limited gaussian
pulse. Finally, as the feedback fraction is reduced further
to F = 2 × 10−6 it is seen that there is insufficient feedback for growth to saturation, and the pulse shown represents a pre-saturation SASE pulse for an interaction lengthz̄ = 8.67. This conclusion is supported by the fact thatthe pulse parameters (except peak intensity) have reverted
back to close to their values for the SASE simulations.
The complete data for all simulations, in each case averaged over 200 post-saturation pulses, are summarised in
the contour plots of Fig. 4 and Fig. 5. In each of these plots
the vertical axis gives the feedback F and the horizontal
axis the cavity detuning δ c . The bold contour represents theaveraged value of the 200 SASE simulations so that, for example, in the top left plot showing time-bandwidth product,
the area below the bold contour represents all those feedback and detuning combinations in which the low feedback
RAFEL pulses have a lower time-bandwidth product, andhence improved temporal coherence, than the SASE case.

Proceedings of FEL 2007, Novosibirsk, Russia

Time Bandwidth Product

−3

11
10
9
8

12

8

11
10
9

7

9
5.

5
4

12

11 10
9
8 7

5.
9

4

3

F

3

1.5

1.5

2
1.25

5

1

2

1.5

1.5

.25
11.5
2
3
4
5

0

2

3

1.5

3
4

2

1.251
1.5
2
3
4

3

4

5

3
4

6

δc (z̄1 )7

8

9

Peak Intensity
2.21.5
98 4
33.
2 5

4.5

5

2

5

2.5198
2.

4
3.5
3

1.

3

4
4.53.5
3

5.5
5

44.5

5

5.5
4.5

4
4.5 3.5

3

6

5

6 5.5

5.55

5.5
4.5 5
4
3.5

3 3
.5

−3

5

2

2

10

3

4

2
−5

4

7

5.9

10

5

8

5

−4

10

1
8 1
7 910

7

5 .9

11109

12
12

10

MOCAU01

−4

2

F

1.

5

1

10

2.5
2.5

1.5

2.198
−5

10

2.198

2

1.5
1

1

1.5
1

0.5

1

0.5
0.5

0.1

0

1

2

0.1

0.1

3

4

5

δc (z̄1 )

6

7

8

9

Figure 4: The complete data for all simulations, in each case averaged over 200 post-saturation pulses, for time-bandwidth
product ΔνΔt (top), and peak intensity |A| 2peak  (bottom). In each plot the vertical axis gives the feedback F and thehorizontal axis the cavity detuning δ c . The bold contour represents the averaged value seen for the 200 SASE simulations.

FEL Theory

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MOCAU01

Proceedings of FEL 2007, Novosibirsk, Russia−3

rms Bandwidth × 10

3

4
62. 2.22
1 .8

2.8

3

2.8

3

2.6

1.2

F

1.6

1.2

1.4

1.4

2.4
2.2

1
−5

10

2
1.8

1.2
1.4

2.4

0

1

2.4

2

3

1.4
1.6
1.8

2

2.2

2.8

1.2

1

1.6
1.8

2

2.2
2.6

1.6

1.2

1.4

1.2

1.21.4

1.6
1.8

2

2.6

4

5

6

δc (z̄1 )

2.4

2.2
2.6
2.8

7

8

2

9

rms Pulse Length
22

22

21

21

21

21

20
19

1
20 2
19
18
17

21

−3

10

−4

3.8
3.2 33.
.46

1.6

−4

10

10

3.8

2.8
2.6 3
2.4 3.2 .6
1.282.2 3.4
3

3.22.28.

1.4

4.2
4

3.8
3.4 3.6

4

4

2.
6
2.4
2
1. 2.2810

2
3.

3. 3.6
4
3.2
3
2.82.622.
4
.2
2
1.81
.6

3. 3
4 .8
3.6

−3

17

19

16

18
17

F

15
1414

13
12

−5

8

10
11

7

9
11

1

2

8

3

9

10

4

5

δc (z̄1 )

11

10
9

8
7

9

15

1414

13
12

11

10

9

8

17

16

15

11

10

10

0

1414

13
12

9

20
19
18

20

18

16

21

6

8
7

9

8

7

10

9

11

7

8

9

Figure 5: The complete data for all simulations, in each case averaged over 200 post-saturation pulses, for rms bandwidthσλ /λ (top) and rms pulse length σ z̄1  (bottom). In each plot the vertical axis gives the feedback F and the horizontal
axis the cavity detuning δ c . The bold contour represents the averaged value seen for the 200 SASE simulations.

FEL Theory

186

Proceedings of FEL 2007, Novosibirsk, Russia

Discussion of Results
It is clear from these simulations that the feedback factor derived in (4), with a value F P = 10−5 and for interaction length z̄ = 8.67, is sufficient to significantly improve the temporal coherence of the output compared toSASE, over the full range of cavity detuning values. The
feedback corresponding to the best temporal coherence is
F = 5 × 10−6 which is a factor of two larger than the criterion derived in (3) required to dominate shot noise which
gives FN > 2.7 × 10−6 .
From examination of the contour plots in Fig. 4 andFig. 5, and considering the previous discussions, threebroad regimes can be identified:

MOCAU01[3] McNeil BWJ, Thompson NR, Dunning DJ, Karssenberg JG,
van der Slot PJM and Boller K-J 2007 New J. Phys. 9 239[4] Huang Z, Ruth RD 2006 Phys. Rev. Lett. 96 144801[5] Nguyen DC, Sheffield RL, Fortgang CM, Goldstein JC,
Kinross-Wright JM and Ebrahim NA 1999 Nucl. Instrum.
Methods Phys. Res. A 429 pp 125-30[6] Faatz B, Feldhaus J, Krzywinski J, Saldin EL, Schneidmiller
EA and Yurkov MV 1999 Nucl. Instrum. and Meth. Phys.
Res. A 429 pp 424-8[7] Bonifacio R, Pellegrini C and Narducci L 1984 Opt. Commun. 50 pp 373-8[8] Kim KJ 1986 Phys. Rev. Lett. 57 pp 1871-4• For F  10−4 : the output has the characteristics ofover-saturation;[9] McNeil BWJ, Robb GRM, Dunning D and Thompson NR
2006 Proc. 28th Int. Free Electron Laser Conf. (Berlin,
Germany) pp 59-62 Joint Accelerator Conferences Website,
http://www.jacow.org• For 10−4  F  5 × 10−6 : the applied feedback
improves the pulse coherence over SASE;[10] Bonifacio R, De Salvo Souza L, Pierini P and Scharlemann
ET 1990 Nucl. Instrum. Methods Phys. Res. A 296 787• For F  5 × 10−6: the feedback is insufficient to give
growth to saturation or improve the coherence, giving
unsaturated SASE output.

[11] Yu L-H 200 Science 289 932[12] McNeil BWJ, Robb GRM, Poole MW and Thompson NR
2006 Phys. Rev. Lett. 96 084801[13] McNeil BWJ, Robb GRM and Poole MW 2004 Phys. Rev.
E 70 035501(R)CONCLUSION
An overview of the properties of Regenerative Amplifier
FELs has been presented and a one-dimensional feasibility
study of a generic high-gain RAFEL system which functions using cavity feedback factors as low as 5 × 10 −6 . It
has been shown that such a system may generate radiation
pulses of greatly improved quality than that possible using SASE. The greatest temporal coherence is seen when
the power feedback is approximately double the shot noise
power. Here the time bandwidth product, averaged over
200 pulses, is ΔνΔt ≈ 1.0, approximately double thatof a transform limited gaussian pulse. This is more than
five times better than the equivalent SASE result, with individual pulses having a time bandwidth product as low as
ΔνΔt ≈ 0.68.
It is also seen that if the feedback factor is too high thepulses oversaturate and their properties are similar to, orworse than, the equivalent SASE case.
Methods of attaining the low feedback factors were notdiscussed, however the fact that they may be so small indicates that there is significant scope in extending the low
feedback RAFEL concept into the XUV and possibly further. The possibility of combining harmonic generation
methods [10, 11, 12, 13] and RAFEL also exists and these
exciting possibilities will be the subject of future research.

REFERENCES[1] McNeil BWJ 1990 IEEE J. Quantum Electron. 26 1124
[2] CCLRC 2006 4GLS Conceptual Design Report Council for
the Central Laboratory of the Research Councils (UK) online at http://www.4gls.ac.uk/documents.htm#CDR
FEL Theory

187

MOCAU02

Proceedings of FEL 2007, Novosibirsk, Russia

NUMERICAL SOLUTION OF THE FEL CORRELATION FUNCTIONEQUATION
O.A. Shevchenko# , N.A. Vinokurov,
Budker Institute of Nuclear Physics, 11 Acad. Lavrentyev Prosp., 630090, Novosibirsk, Russia
Abstract
The equation for two-particle correlation function in
FEL was derived recently to provide a new way of noise
calculations in SASE FELs [1]. In this paper this equation
is solved numerically for the simplest case of narrowelectron beam. Time independent solution with saturation
is obtained. It is compared with the results of quasilinear
theory and results of previous SASE linewidth estimates.

⎛ ∂∂F (1)∂ ⎞∂⎜⎟⎜ ∂θ + ν 1 ∂ z + ν 2 ∂ z ⎟G (1,2, θ ) = − N ∂Δ
1
2 ⎠
1
⎝

−N

∫ Φ(1,3) G(2,3,θ )d {3}−⎛∂F (2)∂∂ ⎞⎟ F (1) F ( 2)
Φ(2,3) G (1,3, θ )d {3} − ⎜⎜ Φ (1,2)+ Φ (2,1)⎟∂Δ 2 ∫
∂
Δ
∂
Δ
1
2 ⎠
⎝

(2)
where

(i ) = ( zi , Δ i ), d {i} = dz i dΔ i , ν i = (1 + 2Δ i ) , Δi .-relative electron energy deviation,

INTRODUCTION
High gain FELs operated in SASE mode are considered
now as one of the most perspective high-brightness
radiation source in the x-ray region. Therefore it is very
important to know the radiation properties of such FELs.
Parameters of radiation in a single shot are determined by
the shot noise in the beam current which has stochastic
nature. Because of that these parameters fluctuate fromshot to shot and they can not be determined without exact
solution of the particle motion and Maxwell equations.
On the other hand the parameters averaged over many
shots can be found by the methods of statisticalmechanics.
The statistical approach has been treated by many
authors but usually it was limited to the linear case when
one can introduce the Green function and the averaging
becomes straightforward [2,3]. Some authors considered
the averaged results of simulations obtained bymacroparticle based codes [4]. But in this case it is notevident that artificially constructed initial distribution ofmacroparticles leads to correct results at saturation stage.
The regular nonlinear approach to the start-up fromnoise has been proposed in [1]. It is based on the BBGKY
set of equations which is truncated to two equations for
single-particle distribution function and two-particle
correlation function. In this paper we obtain the numericalsolution of these equations for the simplest model ofnarrow beam comprised of charged disks with Gaussiantransversal charge distribution.

longitudinal coordinate in undulator, N - number ofelectrons in the beam, θ = 2γ ||2 (t − z ), (c = 1) - “time”
variable andγ ||- relativistic factor of electron

longitudinal motion. The longitudinal interaction force
Φ(1,2) can be determined from eq. (6) of [1]. In theconsidered model it should be averaged over transversal
distribution:Φ (1,2) ⊥ = −

⎞
re
K2 ⎛
e ik w ( z1 − z2 )⎜+ c.c.⎟⎟
22 ⎜2σ k wγ 1 + K ⎝ 1 + iαk w ( z1 − z 2 )⎠(3)here σ is r.m.s transversal beam size,re - classicalelectron radius, α = 1 2k0 kwσ - small dimensionless2

parameter which characterizes the beam “thickness”, k0 .radiation wave number and k w - undulator wave number.
We assume that undulator has constant deflection
parameter K and helical symmetry.
From this point we shell consider stationary case,therefore the time derivative in Eq. (1-2) can be omitted
and N should be replaced by the number of electrons perunit of length. In this case the single-particle distributionfunction has to be renormalized the following way:∫ν F (z , Δ )dΔ = 1
1

BASIC EQUATIONS

zi - electron

1

1

1

In the case of the charged disks model the equations (45) of [1] for the single-particle distribution function andtwo-particle correlation function have the following form:

To eliminate the fast oscillating terms it is convenient~
to introduce the slow varying complex amplitude G of
the correlation function:

⎛ ∂
∂ ⎞
⎜
⎟ F 1,θ+ν 1⎜ ∂θ
∂z1 ⎟⎠⎝~G ( z1 , Δ 1 ; z 2 , Δ 2 ) = 2 Re G (z1 , Δ 1 ; z 2 , Δ 2 )e i ( z1 − z2 )( ) = − N ∫ d {2}Φ(1,2) ∂ G(1,2;θ )
∂Δ1

(1)

(

) (4)

Here we have replaced k w zi by dimensionless variable___________________________________________#

O.A.Shevchenko@inp.nsk.su

FEL Theory

188

zi . Substituting (4) into (1-2) and neglecting fast
oscillating terms we obtain the final system of equations:Proceedings of FEL 2007, Novosibirsk, Russia

⎛ ∂
⎞
∂
ν1
F 1 = −2 Re⎜⎜I z1 , Δ1 ; z1 ⎟⎟
∂z1
⎝ ∂Δ1
⎠

()

(

)

(5)

⎛ ∂
⎛
1⎡
∂ ⎞
∂
∂ ⎞⎤ ~⎟ + (ν 1 −ν 2 )⎜ 2i +⎟⎥G (1;2 ) =+−⎢(ν 1 + ν 2 )⎜⎜⎟⎜2⎣∂z1 ∂z 2 ⎟⎠⎦⎝ ∂z1 ∂z 2 ⎠⎝=∂F (1) *I ( z1 ; z 2 , Δ 2 ) −
−
∂Δ1

−

∂F (2 )I ( z 2 ; z1 , Δ1 ) −
∂Δ 2

(6)

δI (z, t1 )δI (z, t2 ) ≡ J ( z,θ1 − θ 2 ) =
⎝

(7)

0 −∞

1
is renormalized complex amplitude
1 − iα z1⎛ 1
I K 2 ⎞3 of the longitudinal force (3) , ρ = ⎜⎟3⎜
I A k w2σ 2 ⎟⎠
⎝ 2γ

( )

Pierce parameter ( I - beam peak current, I A = mc 3 e -N λ0 - the number of electrons in the

beam on one wavelength.
The solution of eq. (5-6) can be obtained by numericalmethods which are described in the next section. It seems
natural that initial electron distributions in different shots
are not correlated. Then the boundary conditions for eq.
~~(5-6) are G |z1 = 0 = G |z 2 = 0 = 0 , F | z1 = 0 = F0 (Δ1 ) , where

F0 (Δ1 ) is the electron energy distribution at the entrance

to undulator. It is sufficient to find the solution only forz1 ≥ z2 as the symmetry of the correlation function
imposes additional condition~~
G (1,2 ) = G * (2,1)

where A is some constant and θ i = 2γ ||2 (ti − z ) . It can be⎛z ∞Alfven current),

δI ( z, t1 )δI ( z, t2 ) = A∫ν 1ν 2G2 (z , Δ1 , θ1 ; z, Δ1 , θ 2 )dΔ1dΔ 2= A∫ G ⎜ z −where function I ( z1 ; z 2 , Δ 2 ) is determined as~
Φ( z ) = −2 ρ 3

The beam current correlation function at given
longitudinal coordinate in undulator z can be found fromthe following expression:

shown that if we neglect the dependence of longitudinal“velocities” ν i on energy coordinates Δ i then

2π ⎛ ~ *∂∂ ⎞~⎜ Φ (z1 − z 2 )⎟ F (1)F (2 )+ Φ ( z 2 − z1 )⎜N λ0 ⎝∂Δ1∂Δ 2 ⎟⎠1~~I ( z1; z2 , Δ 2 ) = ∫ ∫ Φ(z1 − z3 )G(2;3)d {3},MOCAU021(θ1 − θ 2 ), Δ1; z + 1 (θ1 − θ 2 ), Δ 2 ⎞⎟dΔ1dΔ 2
2
2⎠

The current spectral density is determined by theexpression:Jν ( z ) = ∫ J ( z ,τ )ei (1+ν )τ dτ

NUMERICAL SOLUTION
The system of equations (5-6) has been solved
numerically using finite difference method. The
difference scheme was obtained by replacing of partial
derivatives by centered differences. The integral in Eq. (7)was approximated using method of central rectangles. The
numerical algorithm is illustrated in Fig. 1. Indexes(n, m) correspond to energy coordinates, index ( j ) isrelated to the coordinate z2 .
The letters “M”, “O” and “P” denote three layers in z1
direction. To find the solution at the layer “P” one has toknow the values of correlation function at two precedinglayers. Therefore it is required to keep in the computer
memory only these three layers. The solution above theline z1 = z2 is obtained from the symmetry condition (8).

(8)

It should be noted that one-time two-particle correlation
function allows to find only the radiation peak power
averaged over different shots. The averaged spectral
distribution is determined by two-time two-particle
correlation function which obeys the following equation:
⎛ ∂
∂ ⎞
⎜
⎟G2 1,θ1 ;2,θ 2
+ν 1
⎜ ∂θ
∂
z1 ⎟⎠
1
⎝

(

) = − N ∂F (1) ∫ Φ(1,3)G2 (3,θ1 ;2,θ 2 )d {3}∂Δ1(9)In the stationary case G2 (1,θ1 ;2,θ 2 ) = G2 (1,2;θ1 − θ 2 )and this equation has to be solved with the initialcondition G2 (1,2;θ1 − θ 2 ) |θ1 =θ 2 = G (1,2 ) .

Figure 1. The finite difference scheme.

FEL Theory

189

Proceedings of FEL 2007, Novosibirsk, Russia

SIMULATION RESULTSz = 5 Lg3

σ e = 0.2 ρ , α = 50ρ .
0,16

200

6,0

J ν x 10 , a. u.

In this section we present an example of simulation
results obtained for the following set of parameters:
Pierce parameter ρ = 0.01 , beam energy spreadz = 5 Lg

4,5

150

3,0

100

F(Δ)

MOCAU02

50

1,5

0
-4

-2

0,12

0

2

4

-1x10

-2

-5x10

-3

2πΝgν

a)

0

5x10

-3

1x10

-2

5x10

-3

1x10

-2

5x10

-3

1x10

-2

Δ

0,08
200

1,2
z = 10 Lg

0,04

z = 10 Lg
150

0,9Jν, a. u.

∫

0

5

10

15

F(Δ)

0,6

0,00

at the linear stage.
At Fig. 2 one can see the dependence of the beam
microbunching on the longitudinal coordinate inundulator. The amplitude gain length at linear stage
Lg ≈ 40λw , where λw is undulator period. Therefore
the Fresnel number 1 2αk w Lg [1] is small and the narrow

-4

12

-2

0

2

4

-1x10

-2

-3

0

Δ

200

6,0
z = 15 Lg

z = 15 Lg
150

4,5

3,0

100

50

1,5

0

0,0
-4

c)

-5x10

2πΝgν

b)

beam approximation is valid. The exponential growthstarts at z ≈ 4 Lg and comes to saturation at z ≈ 10 Lg .
Fig. 3 shows variation of the r.m.s. spectral bandwidthalong undulator. The final value of the bandwidth is invery good agreement with the asymptotic formula (21)obtained in [1].

00,0Jν, a. u.

Figure 2. Dependence of the microbunching square on thelongitudinal coordinate in undulator. Lg - the gain length

100

50

0,3

z/Lg

F(Δ)

G(z,Δ1,z,Δ2)dΔ1dΔ2

0,0

-2

0

2πΝgν

2

4

-1x10

-2

-5x10

-3

0

Δ

Figure 4. The spectral and energy distributions at different
longitudinal positions: a) – start of the exponential
growth, b) – start of saturation process, c) – saturation
stage.

2πNgσν

9
6
3
0
0

5

10

15

z/Lg
Figure 3. Dependence of the r.m.s. spectral bandwidth on
the longitudinal coordinate in undulator. N g - number ofundulator periods per one gain length.

FEL Theory

190

The saturation process is illustrated in Fig. 4. At the
beginning of the exponential growth the spectrum is wide
and the energy distribution function is unperturbed (a).
Before saturation the bandwidth reduces rapidly and theenergy spread starts growing (b). At the saturation stage
the energy distribution becomes wide and amplification
stops (c). The saturation mechanism is very similar to thequasilinear one [5].
Fig. 5 shows distribution of the correlation function
amplitude integrated over energy in the ( z1 , z2 ) plane.

Proceedings of FEL 2007, Novosibirsk, Russia

0,15
0,14
0,13
0,12
0,11
0,10
0,09
0,08
0,07
0,06
0,05
0,04
0,03
0,02
0,01
0

z2/Lg

15

10

MOCAU02

in FEL now. For the simplest case of narrow electron
beam we first obtained non-trivial solution for thecorrelation function nonlinear behaviour.
From the other hand, the SASE FEL is an explicit
illustration of fundamental ideas of statistical physics.
Indeed, the averaging over the abstract assembly ofmacroscopically equivalent systems is simply theaveraging over different electron bunches, which passthrough undulator. It is also the clear example ofergodicity, as the averaging over bunches is a kind oftime-averaging.

REFERENCES

5
5

10

z1/Lg

15

Figure 5. Two coordinate distribution of the correlation
function amplitude integrated over energy.

CONCLUSION
In this paper we developed the description forsaturation in SASE FEL based on rigorous statistical
approach. By our knowledge it is the only existing
method to consider nonlinear stage of noise amplification[1] O.A. Shevchenko, N.A. Vinokurov, NIM A507
(2003) 84-88.
[2] K. J. Kim. NIM A250 (1986) 396[3] S. Krinsky and L.-H. Yu, Phys. Rev. A35 (1987)
3406.
[4] E.L. Saldin, E.A. Schneidmiller, M.V. Yurkov, NIM
A407 (1998) 285-290.
[5] N.A. Vinokurov, Z. Huang, O.A. Shevchenko, K.-J.
Kim, NIM A475 (2001) 74.

FEL Theory

191

MOCAU03

Proceedings of FEL 2007, Novosibirsk, Russia

NUMERICAL PROPAGATION SIMULATIONSAND COHERENCE ANALYSIS OF SASE WAVEFRONTS*
O. Chubar#, M.-E. Couprie, F. Polack, SOLEIL, 91191 Gif-sur-Yvette, France
M. Labat, G. Lambert, O. Tcherbakoff, CEA, DSM/SPAM, 91191 Gif-sur-Yvette, France
Abstract
Examples of wavefront propagation simulation andcoherence analysis of Self-Amplified SpontaneousEmission (SASE), seeded and started-up from noise, arepresented. The calculations are performed using SRW –the wave-optics computer code optimized for Synchrotron
Radiation (SR), and the 3D FEL simulation code
GENESIS. To ensure easy inter-operation and dataexchange between the two codes, GENESIS has been
integrated into the “emission” part of the SRW, which isdedicated for calculation of initial wavefronts in the form
ready for subsequent propagation simulations. After eachrun of GENESIS in time-dependent mode, the resulting
electric field is transformed from time to frequency
domain, and the wavefront obtained this way isnumerically propagated, using Fourier-optics methods
implemented in SRW, from the exit of FEL undulator to a
destination plane of a beamline containing several opticalelements separated by drift spaces. Interferometer-type
optical schemes, which allow for “probing” spatial andtemporal coherence of SASE wavefronts, are used in theexamples. Intensity distributions of the propagatedradiation are extracted and analysed in time andfrequency domains. The presented examples show that
the SRW code can be used for optimization of opticalbeamlines for 4th generation synchrotron radiation
sources, which require accurate treatment of wave-opticalphenomena in frequency and time domains.
INTRODUCTION
Synchrotron Radiation emitted by relativistic electrons
in magnetic fields of storage ring sources of the 3rd
generation is a proven tool for research in many areas ofscience, from physics and chemistry to biology andmedicine. An outstanding feature of the SR is a verybroad emission spectrum extending from far infrared tohard X-ray range. Besides, undulator-based 3rd
generation SR sources offer relatively high average
spectral flux, brightness and degree of spatial coherenceof the output radiation, and a possibility to use thisradiation simultaneously for various experiments at alarge number of beamlines.
The new emerging sources of the 4th generation – freeelectron lasers and energy-recovery linacs – extend thedomain of SR applications to time-resolved research, by
providing femtosecond and, prospectively, evenattosecond time scale pulses of radiation with extremely
high peak brightness [1, 2].
To fully exploit all great SR features in the 3rd and 4th
generation sources, high-accuracy simulation tools for the____________________________________________*Work supported by EuroFEL#

oleg.chubar@synchrotron-soleil.fr

FEL Theory

192

processes of emission and wavefront propagation throughvarious optical elements of a beamline should be used. In
the frame of classical electrodynamics, such simulation
tools, dedicated both for the emission and propagation
parts, would operate with 3D electric field of radiation[3]. Whereas this requirement seems absolutely naturalfor the emission part, it is much less evident for the
propagation, where simple geometrical optics based
approximation exists and is extensively (and successfully)
used for incoherent sources and systems dominated by
optical aberrations. Nevertheless, with decrease ofelectron beam emittance in storage rings [4] andcontinuous progress in the quality of optical elements [57], the radiation gradually approaches diffraction limit for
shorter and shorter wavelengths, making physical-optics
approaches to simulation of wavefront propagation
increasingly important.
Two physical-optics based approaches to wavefront
propagation simulation are currently popular: Fourier
optics [8] and asymptotic expansions (mainly, thestationary phase method) [9, 10]. This paper deals with
the Fourier optics approach, as it is implemented in the
SRW computer code [11, 12].
The following are proven “strong points” of the Fourier
optics method:• very high CPU efficiency;• possibility to take into account multiple diffractive/
refractive/ reflective optical elements in “uniform”
way without any increase of the overall complexity;• stability in case of “noisy” wavefronts (these methods
are extensively used for simulation of scattering);• availability of large amount of data on electric field
after only one propagation pass.
Among “weak points” of this method one can mention:- large amount of memory required for “standard” nearfield propagator through free space, and- poor accuracy of the “thin” element approximation forsimulating grazing incidence optics and/or optics withvery wide angular apertures.
We note that for the 3rd generation sources, it is often
enough to simulate wavefront propagation through abeamline only in frequency domain – at one central oreventually at several different frequencies / photon
energies. On the other hand, the 4th generation sources
require a combined frequency- and time-domain analysis
because of the necessity to preserve (or at least to keep
track of) temporal characteristics of propagating
wavefronts. To profit of CPU efficiency of the Fast
Fourier Transforms (FFT), which are used by the freespace propagator and at changing the electric field
representation between the frequency and time domains,
it is preferable to keep in memory at each step ofProceedings of FEL 2007, Novosibirsk, Russia

propagation an entire “instant” wavefront, meshed not
only vs two transverse coordinates, but also vs frequency(or time). This makes the memory constraint even more
important. In the following sections, we show that despiteof this constraint, the Fourier optics method can be very
efficiently used for simulating propagation of timedependent SASE wavefronts produced by FELs.
BRIEF METHOD DESCRIPTION
Time- and Frequency-Domain Representations
Time- andr frequency-domain complex electric fieldsr rr
E ( r , t ) and E~( r ,ω ) are well known to be related by the
Fourier transform:
r

∞

r

r r

E~( r , ω ) = ∫ E ( r , t ) exp( iωt )dt

(1)

−∞

r r

E (r , t ) =

1

∞ r

~

r

∫ E ( r , ω ) exp( −iωt )dω
2π−∞where t is time, ω is cyclic frequency (linked to photonrenergy via the reduced Planck constant ε = hω ), r isobservation point.
Initial SASE wavefronts are often calculated in time
domain [13]; however, propagation of the electric field in
free space or in media is described in the frequency
domain [14]. Besides, it is often necessary to follow theevolution of both temporal and spectral characteristics ofa wavefront at different propagation steps. It is therefore
important to use an efficient algorithm for Eq. (1). Suchalgorithm can be based on a prime-factor FFT [15], which
would be applied “in place” to a “flat” (or “C-aligned”)
complexr electric field data structure – for many spacepoints r in parallel.
Fourier-Optics Propagators
The propagation of transverse components of thefrequency-domain electric field in free space is wellknown to be described by the Huygens-Fresnel principle,
which, for small emission and observation angles is [14]:rrE~⊥ ( r2 ,ω ) ≈

− iω

r

πc Σ

2

r

~
∫∫ E ⊥ ( r1 ,ω )
1

exp[

r

r

iω | r2 − r1 | c ]dΣ1 (2)r r| r2 − r1 |rwhere the integration is performed over surface Σ1 ; r1 is
point on that surface (varying at the integration), rr2 is anobservation point, c is speed of light. If Σ1 is a plane, e.g.
perpendicular to Z axis, and rr2 belongs to another plane,
located at distance Δz from Σ1 , then dΣ1 = dx1dy1 ,
r
r
2
2
12
r2 − r1 = Δz + x 2 − x1 + y 2 − y1
, and Eq. (2) is a
convolution-type integral, which can be quickly
calculated using 2D FFT.
In practice, direct application of the convolution
theorem to Eq. (2) for the case of propagation between
parallel planes may result in the necessity of very dense
sampling of the electric field vs transverse coordinates x1
and y1 (and/or x2, y2), because the phase of the field at
|

|

[

(

)

(

)]

MOCAU03some distance from source depends quadratically on thesecoordinates and all oscillations of the field within given
wavefront limits must be resolved (otherwise accuracy
may be lost). There are several possibilities to walkaround this problem. One consists in distinguishing more
economic (in terms of sampling) “special cases” ofpropagation, such as propagation to or from waist, when
Eq. (2) can be reduced to one Fourier transform andmultiplication of the field by phase factors which dependon the transverse coordinates.
More generally, if approximate values of wavefront
radii and centres with respect to transverse coordinates
are known, one can “subtract” the quadratic phase terms
from the initial wavefront; then, within the quadraticphase approximation, Eq. (2) can still be reduced to a
convolution, with the necessity to re-scale (and eventuallyshift) the resulting wavefront, and add a new (modified)quadratic phase term to it. This simple manipulation candramatically reduce the amount of memory required forthe propagation, while preserving high efficiency andaccuracy of the Fourier optics method.
Electric field transformation at propagation from atransverse plane before an optical element (e.g. lens,mirror, aperture, zone plate, grating,...) to a plane
immediately after it can be formally represented as:
r

E~⊥

out

(

x2 , y 2 , ω ) ≈ G( x2 , y2 , ω ) exp[iωL( x2 , y 2 ) c] ×r× E ⊥ ( x1 ( x 2 , y 2 ), y1 ( x2 , y 2 ), ω )
~

(3)

in

where, in general case, G( x2 , y2 , ω ) is a 2x2 matrix
function of the output transverse coordinates andfrequency, which can take into account eventual
anisotropy of the optical element with respect totransverse components of the input electric field; theoptical path function L(x2, y2) and the input/output
coordinate transformation x1 ( x2 , y2 ), y1 ( x2 , y2 ) can be
deduced from geometrical optics, or by applying thestationary phase method. We note that for a “thin” opticalelement, Eq. (3) is reduced to simple multiplication of the
input field by a complex transmission function.
Wavefront Resizing and Resampling
Transverse dimensions and/or oscillation rates ofelectric field may strongly vary during the propagation. In
order to keep the electric field sufficiently welldimensioned and resolved at each step of the propagation(as required by the propagators being used to simulate
optical elements and free spaces) and, at the same time,
stay within reasonable memory consumption, efficientmechanisms of wavefront resizing (changing limits) andresampling (changing steps of the grid) should be used.
The resampling can be performed either by using
interpolation, or by applying FFT and resizing the electricfield on the Fourier side. E.g., if there is a necessity todecrease step of transverse position(s), one can performforward FFT and increase limit(s) by padding zeros on the
Fourier side, and then perform backwards FFT. At
manipulations with time-dependent wavefronts, the use of

FEL Theory

193

MOCAU03

Proceedings of FEL 2007, Novosibirsk, Russia

the resizing and resampling procedures is particularly
important, and it should be used not only to transverse
coordinates (/angles), but also for time (/frequency).
APPLICATIONS FOR TIME-DEPENDENTSASE WAVEFRONTS
To illustrate application of the Fourier-optics based
method, as it is implemented in the SRW code, forsimulating propagation of time-dependent SASE
wavefronts, we use two simple interference-type opticalschemes, one of them being sensitive to spatial, and theother one to temporal coherence of an input wavefront. Of
course, the range of potential applications of the method
is not limited by these types of optical schemes.
Two different wavefronts are numerically propagatedthrough the optical schemes: (almost fully) saturated
radiation wavefront obtained at seeded FEL operation anda wavefront of unsaturated SASE.
All calculations described in this section were
performed on a regular laptop PC with 1 GB of memory
under 32-bit Windows. In all considered cases, thesimulation of wavefront propagation took small amountof CPU time (in the range of minutes) compared to thecalculation of initial time-dependent wavefronts.
Wavefronts at FEL Exit
The two initial wavefronts were calculated using
GENESIS (integrated into SRW) for the parameters
corresponding to the phase 2 of the ArcEnCiel project [16]:electron beam at 1 GeV energy, 1.5 kA peak current,
60 μm RMS bunch length, 1.2 π mm-mrad normalized
emittance; planar undulator with 30 mm period anddeflecting parameter ~2.06, composed out of five 2 mlong sections. In one case, a seeding radiation pulse of
50 kW peak power and 22 fs RMS duration, at 100.15 eV
average photon energy was used (the seed was assumed to
be produced by the process of generation of highharmonics in gas [17]). In the other case, no external seed
was applied. The results of time-dependent calculations(peak power, pulse profile, energy spectrum,
fluence/intensity distribution at FEL exit) obtained for thetwo cases are presented in Fig. 1.
Young’s Double-Slit Interferometer
The Young’s double-slit interferometer scheme, shownin Fig. 2, allows one to test transverse coherence of input
radiation [14].
Lens (M)Two Slits
Image
FEL
Plane

Figure 2: Double-slit interferometer scheme.
Spectral Fluence vs Photon Energy and Vertical Position (at x = 0)

Peak Power vs Longitudinal Position
Power Density vs Time and Vertical Position (at x = 0)

Power vs Time
Fluence (/Time-Integrated Intensity) vs Horiz. and Vert. Positions
Energy Spectrum

Fluence (Time-Integrated Intensity) vs Vertical Position (at x = 0)
Fluence

Figure 1: Radiation characteristics at FEL exit for twocases: seeded (left) and started up from noise (right).
FEL Theory

194

Figure 3: Wavefront characteristics in the image plane of
double-slit interferometer scheme for two FEL regimes:
seeded (left) and started up from noise (right).

Proceedings of FEL 2007, Novosibirsk, Russia

The following parameters of this scheme were used for
SASE wavefront propagation calculations: 20 m distancefrom the FEL exit to the slits, 1 mm vertical distance
between the slits, 0.1 mm slit widths, 2.6 m/18 m
vertical/horizontal focal distance of an astigmatic lens(mirror), and 3 m distance from the lens to the image
plane. The calculation results obtained for the image
plane in the two wavefront cases (as described above) arepresented in Fig. 3. One can see that in both cases, thevisibility of interference fringes, characterizing the degreeof spatial coherence, is ~1.
Double-Slit Interferometer with Grating
A simple scheme for probing temporal coherence canbe obtained by inserting a grating into the double-slit
interferometer, just before (or immediately after) the slits
and the mirror, as shown in Fig. 4.
Grating
FEL

Slits

MOCAU03

Spectral Fluence vs Photon Energy and Vertical Position (at x = 0)

Power Density vs Time and Vertical Position (at x = 0)

Power vs Time

M
Obs.
Plane

Figure 4: Double-slit interferometer with grating.
Simulation results on wavefront propagation to theobservation plane for the two cases of input SASE are
illustrated in Fig. 5. At this calculation, the vertical andhorizontal focal distances of the mirror were 3.7 m and100 m; the observation plane was at ~3.8 m from themirror. The grating was assumed to be flat, with groove
density of 150 l/mm; the incidence angle ~2.5° (invertical plane).
We see from Fig. 5 that for both wavefront cases, theinterference patterns are strongly modified by the grating.
Vertical positions of interference peaks depend now on
photon energy (see upper image plots), and this reduces
the visibility of fringes in the resulting frequency- (ortime-) integrated patterns. As one can see from the graphs,
the poor visibility of fringes in the seeded case has also
simple time-domain interpretation: because of the delay
introduced by the grating, the radiation pulses from thetwo slits almost don’t overlap in time.
We note that in the case of SASE started from noise,
the interference pattern depends on pulse micro-structure(having stochastic origin) and can therefore appear further“smoothed-out” after averaging over ensemble of pulses.
The corresponding analysis can be easily performed using
the described methods.
ACKNOWLEDGEMENTS
We would like to thank Dr. M. Bowler (4GLS) and Dr.
P. Dumas (SOLEIL) for precious help in benchmarking
and reviewing wavefront propagation functions of SRW.
REFERENCES[1] C. Pellegrini, S. Reiche, in Optics Encyclopedia,
Wiley-VCH Verlag, Berlin 2003, p. 1111-1134.
[2] A. Zholents, W. Fawley, Phys. Rev. Lett. 92, 224801 (2004).

Fluence (/Time-Integrated Intensity) vs Horiz. and Vert. Positions

Fluence (Time-Integrated Intensity) vs Vertical Position (at x = 0)

Figure 5: Wavefront characteristics in observation planeof double-slit interferometer with grating, for two FEL
regimes: seeded (left) and started up from noise (right).
[3] K.-J. Kim, Nucl. Instr. and Meth. A246 (1986) p.71-76.
[4] K.-J. Kim, Synchr. Rad. News, Vol. 19 (6), Dec. 2006, p. 2-6.
[5] A. Snigirev et. al., Nature 384 (1996) p.49.
[6] M. Hart, L. Berman, Acta Cryst. A54 (1998) p. 850-858.
[7] E. Di Fabrizio et. al., Nature 401 (1999) p. 895-898.
[8] J.W. Goodman, Introduction to Fourier Optics, 2nded., McGraw-Hill, 1996.
[9] J. Bahrdt, Applied Optics 36 (19) 1997, p. 4367.
[10] J. Bahrdt, Phys. Rev. ST - Acc. and Beams 10, 060701 (2007).
[11] O. Chubar, P. Elleaume, Proc. EPAC-98, p.1177-1179.
[12] O. Chubar et. al., Proc. SPIE Vol. 4769 (2002) p. 145-151.
[13] S. Reiche, http://corona.physics.ucla.edu/~reiche/.
[14] M.Born, E.Wolf, Principles of Optics, 4th ed.,Pergamon Press, 1970.
[15] S.C. Chan and K.L. Ho, IEEE Trans. Circuits andSystems 38 (8), 1991, p. 951-953.
[16] M.-E. Couprie et. al., these proceedings.
[17] Z. Chang et al, Phys. Rev. Lett. 79 (16) 1997, p. 2967.

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MOCAU04

Proceedings of FEL 2007, Novosibirsk, Russia

IMPACT OF LONGITUDINAL SPACE-CHARGE WAKE FROM FELUNDULATORS ON CURRENT-ENHANCED SASE SCHEMES
G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
We present a description of longitudinal wakefields in XFELs that is of relevance in relation
with Enhanced Self-Amplified Spontaneous Emission(ESASE) schemes. We consider wakes in XFELs, inthe limit when the electron beam has gone inside theundulator for a distance longer than the overtaking
length (the length that electrons travel as a light signal from the tail of the bunch overtakes the head of
the bunch). We find that the magnitude of the resulting energy chirp constitutes a reason of concern forthe practical realization of ESASE schemes. A moredetailed report of our study is given in [1].

INTRODUCTION
This article presents a description of longitudinal
wake fields in XFELs. Our study is of importance inconnection with ESASE schemes, demanding for a detailed study of longitudinal wake fields arising after
the dispersive section. For XFEL setups, the undulator parameter K obeys K2  1. As a result, the averagelongitudinal Lorentz factor γ̄z = γ/ 1 + K2 /2 is suchthat γ̄2z  γ2 , γ being the Lorentz factor of the beam.
Based on γ̄2z  γ2 , we demonstrate that the presenceof the undulator strongly influences the space-charge
wake. In contrast to this, in literature, wake calculations for the LCLS case are given in free-space, as
if the presence of the undulator were negligible. In
this paper we pose particular attention to the LCLS
case, for which ESASE schemes have been first proposed. We thus restrict our attention to a specificregion of parameters. First, the longitudinal size ofthe beam is much larger than the FEL wavelength,
i.e. σz    r . Second, we assume a long saturation length compared with the overtaking length, i.e.
Ls  2γ̄2z . Third, eﬀects of metallic surroundings
can be neglected, i.e. a  γ¯z . We present a general
theory based on these three assumptions. These aresatisfied for the LCLS case, together with an extraassumption on the transverse electron-beam size σ⊥ :σ2⊥  λw ,  being the reduced wavelength. Due tothis last condition, major simplifications arise in thegeneral theory. Radiation from the undulator is drastically suppressed and calculations of impedance andwake function can be performed considering a nonradiating beam, and thus accounting for space-chargeinteractions only. Space-charge impedance and wake
function is found to reproduce the free-space case.
FEL Theory

196

Only, γ must be consistently substituted with γ̄z . We
apply our theory to the ESASE setup referring to the
LCLS facility. We calculate the energy chirp associated with wakes inside the undulator and between
dispersive section and undulator. Subsequently, themagnitude of their eﬀect is estimated by calculating
the linear energy chirp parameter. We find that thegain of the FEL process is sensibly reduced, and that
longitudinal wake fields constitute a reason of concern
regarding the practical realization of ESASE schemes.

FIELD CALCULATION
Calculation of longitudinal wake field and
impedance from an FEL undulator first demand characterization of the electric field generated at a given
position by the bunch. We perform an analysis in =terms of harmonics, i.e. EĒ(r, ω) exp[−iωt] + C.C.,

the symbol ”C.C.” indicating complex conjugation1 .
The complex amplitude Ē(r, ω) can be considered as

the electric field in the space-frequency domain, ”thefield”. Transverse and longitudinal fields can befound by solving paraxial Maxwell’s equation in ther⊥ , ω)] = g(z, r⊥ , ω).
space-frequency domain: D[E(z,Here E⊥ = Ē⊥ exp [−iωz/c] is the electric field envelope that does not vary much along z on the scale of
the reduced wavelength  = λ/(2π). The diﬀerential
operator D is defined by D ≡ (∇⊥ 2 +(2iω/c)·∂/∂z), ∇⊥ 2
being the Laplacian operator over transverse cartesian
coordinates. The source-term g(z, r⊥ ) is specified by
the trajectory of the source electrons, and can be written in terms of the Fourier transform of the transverse¯ r⊥ , ω), and of the charge density,
current density, j(z,
 ρ).
ρ(z,
¯ r⊥ , ω), as g = −4π exp[−iωz/c](iω/c2j¯− ∇¯ Thus,we recognize current and gradient terms in the field.
Here j¯and ρ̄ are regarded as given data. They will betreated as macroscopic quantities, and can be writtenas ρ(
¯ r⊥ , z, ω) = ρo (r⊥ − r o⊥ (z)) f¯(ω) exp[iωso (z)/vo] andj = 
vo ρ. Here f¯(ω) is the Fourier transform of the longitudinal bunch-profile, while ρo is related with thetransverse bunch-profile. r o⊥ (z), so (z) and vo pertain areference electron with Lorentz factor γ that is injected
on axis with no deflection and is guided by the undulator field only. In particular, rox (z) = rw cos(kw z) and1 For simplicity we will consider ω > 0. Expressions for thefield at negative values of ω can be obtained based on the property∗Ē(−ω) = Ē (ω) starting from explicit expressions for Ē at ω > 0.

Proceedings of FEL 2007, Novosibirsk, Russiaroy (z) = 0, where the transverse amplitude of oscillations is rw = K/(γkw ). The correspondent velocity is
described by vo⊥ (z) = voxex + voye y . Finally, so (z) is thecurvilinear abscissa measured along the trajectory of
the reference particle. Solution of Maxwell’s equationis performed with the help of a perturbation theory inthe small parameter λr /λ  1. Calculations yield [1]:



 
iω f¯(ω)
iωzdr ⊥ ρo r ⊥ exp
E⊥ (z, r⊥ ) = −c2cγ̄2z⎧⎪√ | r⊥ − r ⊥ |
⎪
Kex
⎨
K0
2 √
×⎪
+ exp[+ikw z]
⎪
⎩
iγ
w

√ | r⊥ − r ⊥ |Kex
K0 − 2i √− exp[−ikw z]iγ w ⎡ √2K √2 |r√⊥ −r ⊥ | e1xw
icrw ⎢⎢⎢+ exp[+ikw z]⎢⎣ − √
ωw | r⊥ − r ⊥ |⎤√ | r⊥ − r ⊥ | ⎥⎥
2(x − x )(r⊥ − r ⊥ )
⎥⎥
K2
2 √
+
⎦

w | r⊥ − r ⊥ |2w
⎡ √2iK − √2i |r√⊥ −r ⊥ | e1xw
icrw ⎢⎢⎢− exp[−ikw z]⎢⎣ −√ωw | r⊥ − r ⊥ |⎤√ | r⊥ − r ⊥ | ⎥⎥2(x − x )(r⊥ − r ⊥ )K2 − 2i √+⎥⎥⎦w | r⊥ − r ⊥ |2
w

⎫

⎪
2
| r⊥ − r ⊥ | ⎪ic r⊥ − r ⊥
⎬
K1
−
(1)
⎪
⎪
⎭
ω | r⊥ − r ⊥ | γ̄z 
γ̄z 
and



 
iω f¯(ω)
iωzdr ⊥ ρo r ⊥ exp
Ez (z, r⊥ ) = −c2cγ̄2z
⎧
√


⎪
⎪
2
cK x − x⎨+ √exp[+ikw z]×⎪⎪⎩ωγ | r⊥ − r ⊥ |w
√ | r⊥ − r ⊥ |
2 √
× K1
√
 w

2i
cK x − x+ √exp[−ikw z]
ωγ | r⊥ − r ⊥ |w
√ | r⊥ − r ⊥ |
× K1
2i √
w
⎫
⎪


⎪
2
| r⊥ − r ⊥ | ⎬.
(2)+ 2 K0
⎪
⎪
⎭
γ̄z 
γ̄z
Terms not including exp[±kw z] are entangled withthe electron beam. We identify them as space-charge
terms. The formation length of the space-charge fieldis 2γ¯2z , while the correspondent diﬀraction size is γ̄z .
Terms including exp[±ikw z] are indicative of radiation
fields. Phase velocity of terms including exp[+ikw z] isslower than that of the beam harmonic. Phase velocity of terms including exp[−ikw z] is faster than that of
the beam harmonic. The formation length of radiation

MOCAU04

field terms√ is w , while the correspondent diﬀraction
size is w . The first and the second integral in thetransverse field are (radiative) current density terms.
The third and the fourth term are (radiative) gradientterms, while the last term is a (space charge) gradient term. As regards the longitudinal field instead,the third integral is a (space-charge) term originatingfrom a mixture of gradient and current sources. It is
possible to cross-check our expressions for the field = 4πρ.
 · Ē
with the help of Gauss law ∇¯ In particular,Ēsc separately verifies:
it can be seen that Ē = 
Ērad + 
 · Ērad = 0. This confirms that
 · Ēsc = 4πρ̄ and ∇∇radiation field is not entangled with sources, while
space-charge field is.

IMPEDANCEThe impedance is defined accounting for the transverse size of the beam as Z(ω, z) = 1/| f¯(ω)|2 ·z∗ ⊥j¯ · Ē. The integration volume is a cylindzdrA0
der of base A including the undulator up to positionz = z. Integration in z is performed from 0 to z,
because we are interested in impedance generated inside the undulator, that begins at z = 0. The wake
function can be obtained by Fourier transformation of
the impedance. Using Eq. (1) and Eq. (2) we obtainthe total impedance Z = Zr + Zsc . The real part ZR isgiven by
K2 πωz ⊥ ρ∗o (r ⊥ )ρo r ⊥drdr
ZR = −⊥
2⎞⎛ √ 4γ⎜⎜ 2 r ⊥ − r ⊥  ⎟⎟
⎜
⎟⎟ .
(3)
×J0 ⎜⎜⎝√⎟⎠
w

The imaginary part ZI amounts to




K2 ωz
 ⊥
d
r
dr ⊥ ρ∗o (r ⊥ )ρo r ⊥ZI = −22γ⎞⎞⎧⎛ √ ⎛ √  ⎪⎜⎜ 2 r ⊥ − r ⊥  ⎟⎟
⎪⎨ π ⎜⎜⎜⎜ 2 r ⊥ − r ⊥  ⎟⎟⎟⎟
⎜
⎟⎟
×⎪
√
√
⎪ Y0 ⎜⎝⎟⎠ − K0 ⎜⎜⎝
⎟⎠
⎩2
w
w
 ⎞ ⎫⎛ ⎪
4 + 2K2 ⎜⎜⎜ r ⊥ − r ⊥  ⎟⎟⎟ ⎪
⎟⎟ ⎬
+
(4)
K0 ⎜⎜⎝
⎪.
⎠⎪
⎭
γ̄z 
K2
ZR can be entirely traced back to the fast-wave part of
the transverse radiative field. ZI is composed of diﬀerent contributions instead. The term in Y0 follows fromthe fast-wave transverse radiative field. The second
term (in K0 ) follows from the slow-wave transverse
radiative field. The last term (also in K0 ) can be traced
back to the longitudinal space-charge field.

Asymptotic case for σ2⊥  w
It is interesting to derive asymptotic limits of Eq.
(3) and Eq. (4) in the case for σ2⊥  w . Bessel

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Proceedings of FEL 2007, Novosibirsk, Russia

functions in Eq. (3) and Eq. (4) can be expanded forsmall argument values. In particular, using J0 (x)  1
for x  1, the real part of the impedance becomes
ZR = −K2 πz/(4cγ2 ), independently of the choiceof ρo . Subsequently, we use K0 (x)  −γE − ln(x/2)
and Y0  2/π[γE + ln(x/2)], γE  0.577216 being the Euler Gamma constant in the imaginary
part of the impedance, Eq. (4). Weobtain ZI =√−K2 z/(cγ2 ) ln( /r ) + 2z/(cγ2 ) ln( 1 + K2 /2) +ZI free=2zγE /(cγ2 ) +ZI free ,  where
2ωz/γ2 dr ⊥ dr ⊥ ρ∗o (r ⊥ )ρo (r ⊥ ) ln[|r ⊥ − r ⊥ |/(2γ)].
ZI free is the only model-dependent part of the
impedance. Assuming a Gaussian transverse profile ρo (r⊥ ) = 1/(2πσ2⊥c) exp[−r2⊥ /(2σ2⊥)], we obtain
ZI free = 2zγE /(cγ2 ) + 2z/(cγ2 ) ln[σ⊥ /(γ)). Thus,
ZI free , is logarithmically divergent on σ⊥ . This is thefree-space impedance. The renormalized impedance,
i.e. the diﬀerence Z − i ZI free is independent of σ⊥ andconstitutes a result valid for any value of K. These
results are in agreement with limiting cases discussed
in literature.

Asymptotic case for σ2⊥  w
Transverse scales pertaining radiation field andspace-charge field are present in Eq. (3) and Eq.
(4). The first two terms in Y0 and K0 in Eq. (4),as well as the entire real part of the impedance, arelinked to the presence of transverse current density
and to radiation field. The last term in Eq. (4)is due to the presence of longitudinal space-charge
field, a combination of current and gradient terms.
The corresponding Bessel functions yield diﬀerent
characteristic transverse scales. Bessel functions
re"√lated with the radiation field yield w ∼ r γ̄2z .
Those related "with the longitudinal space-charge fieldγ¯2z . Since   r , it follows thatyield γ̄z ∼√w /2  γ¯z . By inspection of Eq. (3) and Eq. (4)
one can see that the value of r ⊥ − r ⊥  is limited byσ⊥ , because of the presence of the exponential functions under the integration sign. Therefore, assuming
constant total charge of the beam, when the electron√
beam transverse size σ⊥ increases beyond w theradiation contribution is suppressed with respect tothe space-charge one. Summing up, when σ2⊥  w ,we may neglect the real part of the impedance ZR andapproximate the total impedance with2ωz
Z = −i 2
γ̄z



dr



⎞
⎛

 ⎜⎜ r − r  ⎟⎟⎟⎟ . (5)dr ρ∗o (r )ρo r ⊥ K0 ⎜⎜⎜⎝⎟
γ¯z ⎠

This means that, in the limit σ2⊥  w , the only field
to be accounted for when calculating impedance (andwake), is the eﬀective longitudinal space-charge field.
FEL Theory

198

Figure 1: Plot of the universal function HA .

STEADY STATE WAKE FOR σ⊥2  W
Our derivations drastically simplify for σ2⊥  w .
We consider transverse and longitudinal gaussian
profiles. When σ2⊥  w , an expression for the wakecan be found by Fourier-transforming the impedance
given in Eq. (5). Eq. (5) is mathematically identical to
the free-space expression where γ is substituted by γ̄z .
We find that the antisymmetric part of the wake GA isgiven by√GA (Δξ)√ = γ̄z ηẑ/σ⊥ · HA (Δξ), where HA (Δξ) =−Δξ/(2 π) {2 π/|Δξ| − π exp[(Δξ)2 /4]erfc[|Δξ|/2]}.
Here we defined Δξ = γ̄z (Δs)/σ⊥ , η = γ̄z σz /σ⊥ andẑ = z/(2γ̄2z σz ). A plot of the universal function HA as afunction of Δξ is given in Fig. 1.
The energy change of a single particle at positions within the bunch due to the reactive part of thewake (averaged over
 ∞ transverse coordinates) is given
by ΔEA (s) = (−e) −∞ GA (Δs) f (s − Δs)d(Δs). An explicit
expression for ΔEA /Eo , with Eo = γme c2 , as a functionof ξ = γ̄z s/σ⊥ is:Imax ẑ
s
ΔEA s
;η =
F
;η
Eo σz
γIA
σz

(6)

and


  ∞


(Δξ)2
s
s
F
;η =
d(Δξ)ηHA η − Δξ exp −
. (7)
σz
σz
2η2
−∞


A plot of F is given as a function of s/σz in Fig. 2 fordiﬀerent values of η.

APPLICATION TO ESASE SCHEMES
We now calculate the impact of longitudinal wakefields on ESASE schemes. We propose an analysis
on a set of parameters referring to LCLS. Similarcalculations may be performed on other parameterProceedings of FEL 2007, Novosibirsk, Russia

MOCAU04

ESASE schemes at LCLS Ipeak = 18 kA, and we have
ρ1D  10−3 . Using an estimated peak-to-peak chirp of
50 MeV we obtain α̂  1. Thus, the saturation lengthis significantly modified. This is a reason of concern,
because ESASE schemes are based on the assumptionthat the nominal saturation length of about 80 m isshortened to about 50 m, that is only 37.5% less.

CONCLUSIONS

Figure 2: Plot of F for diﬀerent values of η.

sets like those for the European XFEL. We consider
a beam with normalized emittance after the dispersive section n  1.2 mm mrad. We take the averagebetatron function in the focusing lattice β f = 18 m,
and γ = 2.8 · 104 . This gives a transverse beam sizeσ⊥ = ( n β f /γ)1/2  30 μm. The longitudinal size of thebunch is σz = 50 nm. The maximal current is about the
Alfven current IA  17 kA; in fact, Ipeak  18kA. Finally, the undulator has a period λw = 0.03 m, K = 3.7,
and the vacuum chamber dimension is a = 2.5 mm.
We consider a wavelength   σz = 50 nm. We
can neglect the vacuum chamber influence, becauseγ¯z  = 500 μm, as γ̄z  104 , and γ̄z   a = 2.5
mm. The overtaking length is 2γ̄2z  10 m. The
saturation length is about Ls = 50 m. Thus ẑ = 5,
and we can use our asymptotic expression. Moreover η = γ̄z σz /σ⊥  16.7. From fig. 2 (or from direct
calculations) one can see that the maximal value assumed by F(s/σz , η) for η = 16.7 is about Fmax  6. It
follows that the energy-chirp peak-to-peak is given by
ΔEA,peak = 2me c2 (Imax /IA )· ẑFmax  30 MeV. In contrast
to this, estimations in literature indicate ”a swing inenergy of 2.4 MeV”. The reason for this large discrepancy is due to the fact that, in literature, the Lorentz
factor γ is incorrectly used in place of γ̄z . Energy
chirp is also accumulated in the free-space between
the dispersive section and the undulator, worsening
the situation even more. In the LCLS case the dispersive section is a dogleg located about 200 m from theundulator. The overtaking length is now 2γ2  80
m, so that ẑ = 2.5. Using the same procedure as forthe wake inside the undulator (but considering γ instead of γ¯z ), we obtain an extra energy chirp of about
ΔEA,peak  20 MeV. The sum of contributions from thestraight section after the dogleg and from the undulator amounts to about 50 MeV. In order to estimate themagnitude of the eﬀect we can use the linear energy
chirp parameter α̂ = −(γωρ21D )−1 · dγ/dt, where ρ1D isthe one-dimensional ρ-parameter in FEL theory. For

We presented a theory of wake fields in an XFEL
system. Specific constraints on parameters (fulfilled
in XFEL setups) were considered. We derived expressions for the steady state impedance, that is composedof a radiative and a space-charge part. Radiation fieldand space-charge field are characterized by diﬀerent
formation lengths: the undulator period w and theovertaking length 2γ̄2z respectively. As a result, thesteady state radiative part of the impedance can beapplied for any undulator system (with Nw  1).
The steady state space-charge part of the impedance
can be used only assuming that the saturation length
is long with respect to the overtaking length, which
limits its practical region of applicability. After having dealt with a generic expression for the steadystate impedance, we specialized our theory to the caseσ2⊥  w . Major simplifications arise: space-charge
contributions to impedance and wake dominate withrespect to radiative contributions. We showed thatthe (antisymmetric) wake can be given in terms of an
asymptotic expression for the wake generated by abeam in uniform motion along the longitudinal axis
provided that γ is consistently substituted with γ̄z . Final expressions are presented in the case of a planar
undulator. However, there are no specific eﬀects related with such choice, and our work may be straightforwardly extended to the case of a helical undulator.
In the limit σ2⊥  w radiation is suppressed, so thatthe beam can be considered as non-radiating, and only
space-charge impedance is present. Such impedance
amounts to the free-space impedance, where γ is consistently substituted with γ̄z . Eq. (5) gives the correct
impedance at position z inside the undulator, as an
asymptotic limit for σ2⊥  w of our general theory.
We used our theory to estimate the eﬀect on ESASE
schemes, and we found reason for concern. Our results are in contrast with literature, where the Lorentz
factor γ is incorrectly used in place of γ̄z in the calculation of the impedance.
For details on our work we refer the interested
reader to [1].

REFERENCES[1] G. Geloni, E. Saldin, E. Schneidmiller and M. Yurkov,
DESY 07-087 (2007) at http://arxiv.org/abs/0706.2280,
submitted to Elsevier Science

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Proceedings of FEL 2007, Novosibirsk, Russia

SPACE CHARGE EFFECT IN AN ACCELERATED BEAM ∗G. Stupakov and Z. Huang
Stanford Linear Accelerator Center, Stanford University, Stanford, CA 94309
Abstract
It is usually assumed that the space charge effects in relativistic beams scale with the energy of the beam as γ −2 ,where γ is the relativistic factor. We show that for a beam
accelerated in the longitudinal direction there is an additional space charge effect in free space that scales as E/γ,
where E is the accelerating field. This field has the same
origin as the “electromagnetic mass of the electron” discussed in textbooks on electrodynamics. We then consider
the effect of this field on a beam generated in an RF gun
and calculate the energy spread produced by this field in
the beam.

INTRODUCTION
Modern light sources such as free electron lasers andenergy recovery linacs require high-peak current, smallemittance beams. One of the important characteristics ofsuch a beam is its energy spread. It determines the limitsof a possible bunch compression, the stability against microbunching, and properties of the beam as a radiator ofphotons. There are several mechanisms that contribute to
the energy spread in radio frequency electron guns with thedominant one, for nanocoulomb bunches, being the spacecharge effect.
Traditionally in accelerator physics the space charge effect is computed as a self field of a beam moving with constant velocity along a straight line. The longitudinal fieldin such a beam causes the energy exchange between theparticles; it typically scales with the beam energy as γ −2[1, p. 128], where γ is the relativistic factor, and usually
becomes small for highly relativistic beams. In a broader
sense, the space charge effect might be understood as a self
field of the beam, even when it moves with acceleration.
With this understanding, acceleration adds to the beam self
field. One such contribution, that attracted a lot of attention lately, is due to the coherent radiation of the beam andis called the coherent synchrotron radiation wake (or CSRwake) [2]. The CSR wake is the radiation reaction force
that keeps balance between the electromagnetic energy thatis carried away by the radiation and the kinetic energy ofthe beam particles. It occurs when the beam is being accelerated in the direction perpendicular to the beam velocity
in bending magnets or undulators.
Another type of radiation reaction force has been considered in recent papers [3, 4]—it is a self field that arises
inside the beam during a violent longitudinal acceleration.
Such a field can play a role in plasma acceleration experi∗ Worksupported by Department of Energy contract DE–AC02–
76SF00515.

FEL Theory

200

ments, where the pace of acceleration is much larger thanin a conventional RF cavities.
In this paper we point out to a new component of thespace charge field that arises during longitudinal acceleration of the beam. We assume that the acceleration is notstrong enough to cause a noticeable radiation. What it does,
however, it changes the velocity of the beam. Because thebeam electromagnetic field depends on how fast it moves,
the electromagnetic energy of the beam field changes during acceleration. Similar to the case of a converging beam,
one should expect an additional component of the self fieldthat keeps balance between the beam and the field energy.
We call this field the acceleration field. Being proportional
to the acceleration, on average, it is equivalent to a renormalization of the mass; it is discussed in textbooks on electrodynamics in connection with a so called electromagnetic“mass” of a point charge [5, 6]. In this paper we are interested in the spatial distribution of the field and, more
specifically, the energy spread in the beam induced by theacceleration field.
The model that we consider in this paper assumes thatthe beam does not change its shape during the acceleration.
We neglect a component of self field that is associated withthe converging (or diverging) beams (see [7] and references
therein).

ENERGY OF ELECTROMAGNETIC
FIELD OF A MOVING GAUSSIAN BUNCH
Consider a Gaussian bunch of charged particles moving
with velocity v in the z direction with the particle distribution function given by
µ
¶
N
r2
ζ2
n(x, y, ζ) =
exp
−
−
, (1)
2
2
2σ⊥
2σz2
(2π)3/2 σz σ⊥where N is the number of particles in the bunch, r =px2 + y 2 , ζ = z − vt, σx = σy = σ⊥ is the rms bunch
size in the transverse direction, and σz is the rms bunch
length in the longitudinal direction. The electromagnetic
field of such a bunch can be calculated using the Lorentz
transformation from the beam frame, see, e.g., [8]. The
integrated electromagnetic energy over the whole spaceZ
E2 + H 2
dV ,
(2)
W =
8π
grows with γ, as shown in Fig. 1. Note that this energy
tends to infinity when γ → ∞. As a detailed analysis
shows, at γ À 1 the asymptotic expression for W isQ2
W =√log γ ,πσzγ À 1.

(3)

Proceedings of FEL 2007, Novosibirsk, Russia

This gives for the scalar potentialZ
d3 r 0φ(r, t) = e|r − r 0 |
µ
¶
1
0 0 0
2
× n x , y , z − z0 (t) + v(t)τ − a(t)τ
.
2

3

W

2

1

0

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0

25

50
Γ

75

100

Figure 1: Integrated electromagnetic energy density inunits Q2 /σ for a spherical Gaussian bunch (σ⊥ = σz = σ)as a function of γ.
Imagine now that the beam is being accelerated from rest
to velocity v corresponding to some value of γ. The increased electromagnetic energy is taken from the kinetic
energy of the beam via a longitudinal electric field Ez induced by the acceleration. Such a field is known from thetheory of the radiation reaction force [6, p. 386], where it is
responsible for the electromagnetic field contribution to themass of a charged particle. This force is linear in acceleration, and changes sign when the acceleration is reversed.
It is not related to the radiation; in addition to transferring
energy from the beam to the electromagnetic field during
acceleration (and transferring it in the opposite direction
during deceleration) it introduced an energy spread in thebeam. In the next section we derive an expression for Ez
using the retarded potentials.

SPACE CHARGE AND ACCELERATIONFIELDS
Consider a beam moving along the z axis with velocityv(t) that varies with time and is the same for all particles ofthe beam. If n(x, y, z) is the particle density at initial time,then at time t the charge density ρ and the current density jz
are: ρ = en(x, y, z − z0 (t)), jz = ev(t)n(x, y, z − z0 (t)),
with v = dz0 /dt, and e the elementary charge. The scalarand vector potentials of the beam are given by the following
equations [5]Z
ρ(r 0 , t − τ ) 3 0
φ(r, t) =d r ,|r − r 0 |Z1
j(r 0 , t − τ ) 3 0
A(r, t) =
d r ,
(4)
c
|r − r 0 |where the retarded time t − τ is defined by cτ = |r −r 0 | . We will assume that the acceleration a(t) = dv/dt
is small and expand the potentials in Taylor series keeping
only linear terms in acceleration. We have approximately
1z0 (t − τ ) ≈ z0 (t) − v(t)τ + a(t)τ 2
2v(t − τ ) ≈ v(t) − a(t)τ .

(5)

(6)

We now expand the function n to obtain φ ≈ φsc +φ̃, whereφsc is the space charge potential that does not depend on
acceleration, and φ̃ is a part of the potential proportional tothe acceleration:Zn (x0 , y 0 , z 0 − z0 (t) + v(t)τ ) 3 0
φsc (r, t) = ed r ,|r − r 0 |Z
τ2e
d3 r 0φ̃(r, t) = − a(t)2|r − r 0 |× ∂z n (x0 , y 0 , z 0 − z0 (t) + v(t)τ ) ,(7)with ∂z n = ∂n(x, y, z)/∂z. Similarly, we expand the vector potential A which has the z component only,Ze(v(t) − a(t)τ ) 3 0
Az (r, t) =d r
c|r − r 0 |
µ
¶
1
0 0 0
2
× n x , y , z − z0 (t) + v(t)τ − a(t)τ
, (8)2
to obtain A ≈ Asc + Ã, withZev(t)n (x0 , y 0 , z 0 − z0 (t) + v(t)τ ) 3 0
Az,sc (r, t) =d r
c|r − r 0 |ZeÃz, (r, t) = − 3 a(t)v(t) |r − r 0 |d3 r02c× ∂z n (x0 , y 0 , z 0 − z0 (t) + v(t)τ )
Z
ea(t)
− 2
n (x0 , y 0 , z 0 − z0 (t) + v(t)τ )d3 r0 .
(9)c
One can formulate conditions of applicability of the approximations used above by requiring that the terms discarded in the Taylor expansions are small compared tothose left. There are two such conditions¯ ¯¯ ȧ ¯c2¯ ¯¿ c,
a¿
,
(10)
¯a¯
l
l
where l is the characteristic size of the bunch. These conditions mean that the acceleration is not large and does notchange fast.
The electric field of the beam is a sum of the spacecharge field and a component that vanishes in the limit
when a = 0, E ≈ E sc + Ẽ, where E sc = −∇φsc −c−1 ∂Asc /∂t and Ẽ = −∇φ̃ − c−1 ∂ Ã/∂t. The electric field E sc (and related to it the magnetic field B =v ×E sc /c) is traditionally associated in accelerator physics
with the the space charge effect. The total energy of thisfield is plotted in Fig. 1.
In this paper, we are interested in the electric field Ẽ,and more specifically in the longitudinal component ẼzẼz = −∂ φ̃ 1 ∂ Ãz
−
,
∂z
c ∂t

(11)

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Proceedings of FEL 2007, Novosibirsk, Russia

that changes the kinetic energy of the beam particles. Using Eqs. (7) and (8) for calculation of Ẽz we find that inaddition to terms proportional to a it also contains terms
that involve ȧ and a2 . We discard the latter as being small
because of the conditions (10). This approximation gives
the following expression for Ẽz ,Zen (x0 , y 0 , z 0 + vτ ) 3 0
Ẽz = − 2 a
d r
(12)
c
|r − r 0 |Ze− 2 aβ (β|r − r 0 | − (z − z 0 )) d3 r02c× ∂zz n (x0 , y 0 , z 0 + vτ )¶Z µez − z0+ 2a−4β∂z n (x0 , y 0 , z 0 + vτ ) d3 r0 .
2c|r − r 0 |In this equation we set t = z0 = 0 (which means that thedensity distribution of the beam at the observation time is
now n(x, y, z)), and suppressed the argument t in a and v.
In what follows, for brevity, we call Ẽz the acceleration
field.

ACCELERATION FIELD FOR A
GAUSSIAN BUNCH
For a Gaussian bunch with the charge distribution function given by Eq. (1) the calculation of the acceleration field
can be reduced to a one dimensional integral. The expression for this field is derived in Ref. [9] and is given by thefollowing equations
µ
¶
eN a
r z
Ẽz (x, y, z) = − √
G
,
,
(13)
σ⊥ σz
2πc2 σzwith
G (R, Z) =Z ∞dvF (v, Z)
(14)
·
¸
R2 A2
Z2
× exp −−,2 (A2 + vγ 2 ) 2(v + 1)
0

where
γ2
F (v, Z) =×
(15)2(v + 1)9/2 (A2 + γ 2 v)
£ ¡ 2 ¡¢¢
v 5Z + 2(v − 2)(v + 1)Z 2 + v(v + 3)2 − vZ 4 γ 2
¡
¡
¢
¢
¤
+ v 4γ 2 + v Z 4 − (v − 4)Z 2 − v + 3 + 2 .
Using the relation between the acceleration and the rateof change of the gamma factor, a = (c/γ 3 β)dγ/dt, we canwrite the energy change of a particle in the beam due to theacceleration field as
Z γf
Z
dγ
I0
G , (16)∆E(r, z) = veẼz dt = − mc2
3
IA
γi γ
√
where I0 = N ec/ 2πσz is the peak current in the bunch,
IA = mc3 /e is the Alfvén current, γi and γf are the initialand final values of the gamma factor, and the function G isgiven by Eq. (14).
FEL Theory

202

20

Energy loss , keV

MOCAU05

0

15

1
10

2

5

3
0

0

2

4
r/σ |

_

Figure 2: Energy loss induced by the acceleration field for
four different slices in the bunch (z/σz = 0, 1, 2, and 3;
this number is indicated near the curves) as a function ofelectron radial position.
In the ultrarelativistic limit γ À 1, one can find from2
2
Eqs. (14) and (15) that G ≈ 2γ 2 e−z /2σz . The longitudinal acceleration field in this limit does not depend on radius. Taking into account that in the external field Eext theacceleration of a relativistic particle is a = eEext /mγ 3 wearrive at the following expression for Ẽz
r22
2 re NẼz = −
Eext e−z /2σz ,γ À 1,(17)
π σz γwith re = e2 /mc2 . We see that the acceleration field is directed against the external field Eext and scales as Eext /γ.
This contrasts to the usual scaling ∝ γ −2 of the longitudinal space charge forces. Note that due to the scalingG ∝ γ 2 the integral (16) diverges logarithmically when
γf → ∞. This is related to the fact that the electromagnetic energy of the bunch logarithmically tends to infinity when γ → ∞, as indicated by Eq. (3). In reality, thebeam is being accelerated inside a vacuum volume that hasa characteristic transverse size b. The electromagnetic energy of a relativistic beam propagating in a pipe of radiusb does not change with γ when γ & b/σz . To take into
account this shielding effect of the metallic pipe, for roughestimates, we will assume that γf = b/σz . Note that typically b/σz À 1, and because our result has only a logarithmic dependence on γ, it is rather insensitive to the exact
value of γf .
For a numerical example we consider now parameters of
the LCLS rf-gun beam. Because our model assumes Gaussian distribution and the LCLS beam has a flat longitudinal
profile, we choose the model parameters in such a way that
σx and σz are equal to the corresponding rms values for
the LCLS beam. We have σz = 0.86 mm, σx = 0.6 mm,
and Q = 0.72 nC (corresponding to the peak current of
I0 = 100 A). We also choose γi = 1 and γf = 20, corresponding to the beam pipe radius of about 1.2 cm. Using
Eq. (16) we calculated the energy loss of each particle inthe beam. Note that for the nominal LCLS rf gun accelerating field of 120 MV/m the applicability conditions (10)are reasonably well satisfied. The plot of the radial dependence of the function ∆E(r, z) for several values of z isshown in Fig. 2. The energy loss for the same beam aver-RMS energy spread , keV

Proceedings of FEL 2007, Novosibirsk, Russia

20

1

0

2

-20
-4

-2

0
z/σ z

2

4

RMS energy spread , keV

Figure 3: Energy loss induced by the acceleration field (averaged over transverse dimensions) as a function of electron longitudinal position, curve 1. For comparison, we
also show the energy loss introduced by the space charge
effect, curve 2.

6

2
4

MOCAU05

22.5 µJ. When we integrated the right side of Eq. (18) overtime from the initial to the final state, we found that thework of the acceleration numerically is equal to ∆W , inperfect agreement with the energy balance equation.
Computation of beam self-fields is a critical aspect innumerical simulations of high-brightness electron beam
generation. Many simulation codes (ASTRA, IMPACT,PARMELA) employ the quasi-static approximation andcompute only the space charge fields. There exist a few
codes that calculate the beam fields from the exact solutionsof Maxwell’s equations (i.e., the retarded potentials). A review of different computational approaches can be found in
Ref. [11]. In this paper, starting with the retarded potentials
and separating explicitly the self-fields into space charge
and acceleration ones, we give an analytical expression forthe longitudinal component of the acceleration field. Usinga Gaussian bunch model and typical (LCLS) RF gun parameters, we calculate the energy spread introduced by theacceleration field and show that it gives rise to a small correction of the energy spread introduced by the space charge
field. These results may be useful in guiding the simulation
studies of high-brightness beams.

References

2

1
0
-4

-2

0
z/σ z

2

4

Figure 4: RMS energy spread induced by the acceleration
field as a function of electron longitudinal position, curve
1. For comparison, we also show the energy spread introduced by the space charge effect, curve 2.
aged over the transverse coordinate is shown in Fig. 3 asa function of the position z. Finally, Fig. 4 shows the rms
energy spread in slices as a function of z. In Figs. 2 and
3 we also show the energy loss and the rms energy spread
introduced by the space charge forces (due to the longitudinal component of the field E sc ). The space charge effects
were calculated using the theory of Ref. [10].

DISCUSSION
As was mentioned in the introduction, the acceleration
field keeps balance between the electromagnetic energy ofthe beam and the kinetic energy of the particles. Mathematically, this property is formulated as the equality between
the rate of change of the electromagnetic energy W and thework of the field Ẽz on the moving particles
ZdW= −e Ẽz vnd3 r .
(18)
dt
Although we do not prove this statement here (see [9]), we
demonstrate its validity with the numerical example fromthe previous Section. We calculated the electromagnetic
energy difference for the beam at the final state with γf =20 and the initial state with γi = 1, which gave us ∆W =[1] A. W. Chao and M. Tigner. Handbook of Accelerator
Physics and Engineering. 3nd edition, 2006.
[2] L. V. Iogansen and M. S. Rabinovich. Sov. Phys.
JETP, 37, 83, 1960; Ya. S. Derbenev et al. DESY Report TESLA-FEL 95-05, 1995; J. B. Murphy, S. Krinsky, and R. L. Gluckstern. Part. Accel., 57, 9, 1997.
[3] G. Geloni et al. Nuclear Instruments and Methods inPhysics Research A, 578, 34, 2007.
[4] R. A. Bosch. Phys. Rev. ST Accel. Beams, 10, 050701,
2007.
[5] J. D. Jackson. Classical Electrodynamics. Wiley,
New York, third edition, 1999.
[6] W. Panofsky and M. Phillips. Classical Electricity
and Magnetism. Addison-Wesley, 2nd edition, 1962.
[7] K. L. F. Bane and A. W. Chao. Phys. Rev. ST Accel.
Beams, 5, 104401, 2002.
[8] G. Stupakov. Lecture notes on Classical Mechanics
and Electromagnetism in Accelerator Physics. The
US PAS, Lansing, MI, 4-15 June 2007.
[9] G. Stupakov and Z. Huang. Space charge effect in an
accelerated beam. to be published, 2007.
[10] Z. Huang et al. In Proceedings of the 2005 Particle
Accelerator Conference, page TPAT062, Knoxville,
Tennessee USA, May 2005.
[11] L. Serafini. In Proceedings of the 2nd ICFA Workshop
on the Physics of High Brightness Beams, page 27,
1999.

FEL Theory203

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Proceedings of FEL 2007, Novosibirsk, Russia

ELECTRON OUTCOUPLING SCHEME FOR THE NOVOSIBIRSK FEL
A.N. Matveenko*, O.A. Shevchenko, V.G. Tcheskidov, N.A. Vinokurov
Budker Institute of Nuclear Physics, Novosibirsk, Russia
Abstract
One of the main problems of contemporary high power
FELs is the mirror heating. One of the possible solutionsof this problem is the use of electron outcoupling [1, 2].
In this case the mirrors of optical resonator are nottransparent and the coherent radiation from an additional
undulator in the FEL magnetic system is used. To provide
the output of this radiation the electron beam in theauxiliary undulator is deflected from the optical resonatoraxis. To save bunching it is preferable to use theachromatic deflecting bend. The project of electron
outcoupling for the Novosibirsk FEL is described.
Simulation results are presented.

INTRODUCTION
The output power of high power oscillator FELs [3] arelimited by mirrors heating, leading to surface distortion.
Typical gain in oscillator FEL is tens per cent.
Correspondingly, optical cavity “quality factor” must beof the order of 10 to make losses lower thenamplification. Consequently, intracavity power is at least
an order of magnitude higher, than extracted power, andoptical cavity mirrors are most loaded compared tomirrors in the user beamlines. Electron outcoupling is oneof the possible ways to decrease the power density on the
mirrors at the same FEL output power.
The basic idea of electron outcoupling is to output thecoherent radiation of the bunched electron beam in thesecond undulator section (see Fig. 1.), while the bunchingis generated in the first section, which is put into opticalcavity. In this case the lasing power in the first section
can be limited some way (e.g. installing long undulator,
or using beam scraper to control cavity losses), but thebeam bunching can be preserved. An isochronous bend
between the sections brings the beam into the second
undulator.
The angle between undulators must be larger then2
undulator radiation divergence angle ~ 1 1 + K 2 ,γ
2Nwhere N is the number of periods in the undulator, γ is therelativistic factor, K is the planar undulator deflection
parameter.
Lengths of the undulator sections are chosen from a
condition 1 ~ 4π ΔE , where ΔE is the r.m.s. energyNE
spread of the electron beam.
Numerical simulations for different electron
outcoupling schemes were performed earlier in [4-7].
Here we present design and simulation results for
Novosibirsk high power FEL.

*

A.N.Matveenko@inp.nsk.su

High power FELs

204

e-

Undulator 1(energy modulation)e-

Undulator 2(radiation)

Fig. 1. Electron outcoupling scheme with two undulatorsand bending section between them. Electron beam pathand laser output are shown.

ELECTRON OUTCOUPLING SCHEME
OF NOFOSIBIRSK FEL
Electron outcoupling is planned to be used on the 4-th
track of the second stage of Novosibirsk FEL. Generallayout of the second stage is shown in Fig. 2. Mainelectron beam and laser radiation parameters are
summarized in Table 1.

Fig. 2. Layout of the second stage of Novosibirsk FEL.
Table 1. Electron beam and laser radiation parameters.
Energy, MeV
40
Peak current, A
100
Electron beam emittance (normilized), μm
20
Maximum K
2
Undulator period, cm
6
Number of periods in each undulator
28
Deflection angle in second undulator, mrad 3
Relative energy spread
3·10-3
Radiation wavelength, μm
15
Optical cavity length, m
40
Mirror radius of curvature, m25
Mirror reflectivity, %90
50
Optical cavity β x , β y on mirrors, m
Optical cavity β 0 (Raleigh length), m

10

The scheme of the electron outcoupling of Novosibirsk
FEL is shown in Fig. 3. It uses three undulators instead of
two. The idea lying behind this modification is that in thebasic scheme shown in Fig. 1 beam bunching reaches
saturation at the end of the first undulator, therefore theefficiency of radiation in the second undulator is reduced.
So, if one puts the third undulator (effectively, we divide
the first undulator into two) one gets best beam bunchingProceedings of FEL 2007, Novosibirsk, Russia

Q1

B1

Undulator 3(power limitation)

Undulator 2(radiation)

Undulator 1(energy modulation)e-

Q2

calculates bunching in axes of the first undulator. The
bunching in the second undulator in the axes of second
undulator is a little bit higher. (Since the bend between
undulators is achromatic, there is no bunching reduction.)
Total (eigenmode and coherent undulator) radiation
power growth is shown in Fig. 6.
0,5Bunching factor

inside the second undulator and better outcoupling
efficiency.
Planar permanent magnet undulators are used.
In order to reduce the length of the bends between
undulators, we use combined function elements. The
achromatic bend between first and second undulators
consists of two correctors on the nearest ends of theundulators and a quadrupole shifted off axis to provide
both bending and focusing. As the bend is achromatic(R16= R26=0), it has also R51= R52=0. The last conditions
are necessary to tilt electron slices in the bend, saving thebunching, obtained in the first undulator. Bend with shift
between second and third undulators is done similarly,
though it is not achromatic.
e-

0,4
0,3
0,2
0,1
0,0

B2

Fig. 3. Electron outcoupling scheme of Novosibirsk FEL.
Electron beam path is shown in black. Laser output isshown with red arrows.

the undulators (see Fig. 2) are necessary to provide
appropriate matching to external beamline.

Optical mode inside the second undulator is partiallyoverlapped with the electron beam, therefore the beam
radiates into the mode too. So, simulation of lasing isneeded to optimize the outcoupling.

SIMULATION RESULTS
Simulation of electron outcoupling is done with
GENESIS [8] and OPC [9] codes. GENESIS is used tosimulate the operation of FEL and electron outcoupling
itself. OPC is used to propagate radiation field in opticalcavity. Beam and optical cavity parameters from Table 1
are used in simulation.
Fig. 5 shows the bunching factor in undulators. The
bunching is maximal in the second undulator. GENESIS

1

2

3
4
z, m
Fig. 5. Bunching factor in undulators.

5

0

1

2

5

40
30
20
10
0

Fig. 4. Optical functions of the beam in undulators.

050
Total peak power, MW

Optical functions of the beam in undulators are shownin Fig. 4. All undulators focus in “y” direction withmatched β y 0 =0.529 m at K=2. 4 quads before and 4 after

TUAAU023
4z, m
Fig. 6. Total radiation power vs. length.

Figures 7 and 8 demonstrate the power distribution on
the optical cavity mirror and on the outcoupling mirror
surface (Intensity scales are different for visualisation
purposes). Outcoupling mirror is located near the mirrorof the optical cavity. Its edge is at the distance ofapproximately 2.5 cm from the optical axis. The profiles
at y=0 are shown in Fig. 9.
Red cross in Fig. 8 shows the expected center of theradiation spot from the second undulator. Circularinterference patterns we interpret as interference ofradiation from the first and the third undulators. A portionof radiation from the first and the third undulators is also
outcoupled. Basic mode in the optical cavity is distorted(it’s center moves off axes) which is seen in Fig. 9.
Total power and intensity on the optical cavity mirrors
and outcoupler are listed in Table 2. Given values are forbunch repetition rate 3.75 MHz (which is the opticalcavity fundamental frequency) and average current about
6 mA. It is seen that the ratio of the outcoupled power tothe intracavity power is more than 25%.

High power FELs205

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Proceedings of FEL 2007, Novosibirsk, Russia

-8
2

-6
Power density, W/cm

-4
-2
0
2
4

5

160

4

120

3

80

2

40

1

0
-16

6
8
-4 -2 02

4

6

8 10 12Fig. 7. Power distribution on the forward optical cavity
mirror surface. Transverse coordinates are in cm.

-8
-6
-4

-8

0
x, cm

8

16

0

Fig. 9. Intensity profiles: green - on the optical cavity
mirror surface, red – on the outcoupling mirror surface.
Scales are shown with arrows.
Table 2. Radiation parameters on the forward mirror of
the optical cavity and outcoupling mirror.
Total average power on the cavity mirror, W
990
Total outcoupled power, W
260
Max. intensity on the cavity mirror, W/cm2
170
Max. intensity on the outcoupling mirror, W/cm2 5

CONCLUSION-2

In this paper we considered the electron outcoupling
scheme with trajectory deflection in the second undulator(radiator). The scheme with deflection in the third
undulator was also simulated, but the FEL output power
was less for our beam parameters. The results ofcalculations look reasonable and understandable andshow that the chosen parameters of FEL magnetic system
are close to optimal.

0
2
4
6

REFERENCES

8
-4 -2

0

2

4

6

8 10 12Fig. 8. Power distribution on the outcoupling mirror(scraper) surface. Transverse coordinates are in cm.

High power FELs

206

200

[1] N.G. Gavrilov et al., NIM A304 (1991) 63-65.
[2] G.N. Kulipanov, A.S. Sokolov, N.A. Vinokurov, NIM
A375, (1996) 576-579.
[3] G. Neil et al., NIM A557, (2006) 9.
[4] D.D. Quick, et. al., NIM A341, ABS92, 1994.
[5] J. Blau, et. al., NIM A341, ABS94, 1994.
[6] S.J. Hahn, et. al., NIM A358, p. 167, 1995.
[7] S.J. Hahn and W.M. Fawley, Proc. of SPIE 2376, pp.
116-124, 1995.
[8] S. Reiche, NIM A429, (1999) 243.
[9] J.G. Karssenberg, et al., Proc. of FEL 2006, pp. 407410.

Proceedings of FEL 2007, Novosibirsk, Russia

TUAAU05

MODELLING MIRROR ABERRATIONS IN FEL OSCILLATORSUSING OPC
P.J.M. van der Slot∗ , J.G. Karssenberg, K.J. Boller
Mesa+ Institute for Nanotechnology, University of Twente, Enschede, NL
Abstract
Several high power free-electron lasers (FELs) are currently under design, operational or being upgraded. One
central issue is the beam outcoupling and mirror deformation due to absorbed power. Here we present an extension
to the OPC code that allows it to model mirror distorions.
We use this code to model the high average power vacuum ultra violet FEL oscillator of the 4th generation lightsource. Both Genesis 1.3 and Medusa are used to calculate
the gain provided by the undulator. Our findings indicatethat the high gain oscillator is quite resilient to thermal mirror deformation and operation well into the kW range of
average power can be expected.

INTRODUCTION
Several high average power Free-Electron Lasers (FELs)
are currently operational [1, 2] or planned [3]. One of theissues in these devices is the thermal distortion of the mirrors that can alter the optical mode and degrade performance. Including this and other mirror distortions in simulation of these devices is important to understand and further improve these devices. Several attempts have alreadybeen made to model thermal mirror distortions [4, 5, 6, 7],
however, a full integration of the FEL gain medium, optical propagation in the non-amplifying section and mirror
distortions for both steady state and time dependent simulations is not readily available. Here we present an extension to the OPC package [8] that allows it to model mirror
distortions. OPC implements paraxial optical propagationin the non-amplifying sections of a resonator, while either
Genesis 1.3 [9] or Medusa [10] is used to simulate the gain
provided by the undulator.
It is well know that various mirror distortions can be
described using the circle polynomials of Zernike [11].
Within OPC these polynomials are used to calculated aphase difference dθ according tocos(mφ)m≥0dθ = Anm Rn|m| (ρ) ×(1)
sin(mφ)m<0|m|

of order (n,m), ρ iswhere Rn is the circle polynomial
the scaled radial distance x2 + y 2 /ρc , ρc being a characteristic distance, φ is the angle tan −1 (y/x), and Anm is
the amplitude of the aberration. These aberrations define aphase mask that is applied to the optical field at the position of the corresponding optical component. The scaling∗ p.j.m.vanderslot@tnw.utwente.nl

constants Anm and ρc can either be kept constant or madedependent on certain properties of the optical field, e.g.,
the total power or the root-mean-square (rms) width of the
optical beam.
Different type of aberrations can be modeled using
Zernike polynomials. For example, n = 4 and m = 0
corresponds to spherical aberration, n = 3 and m = 1 tocoma and n = 2 and m = 2 to astigmatism [11]. A combination of Zernike polynomials can also be used to model
a cylindrical lens. Here we focus on the the use of Zernike
polynomials to model thermal mirror distortions [6, 4].
As an example of a high average power FEL we consider here the vacuum ultra violet FEL (VUV-FEL) oscillator that is part of the 4th generation light source (4GLS)
project of Daresbury laboratory [3]. This high gain oscillator uses a low Q cavity to generate coherent output withphoton energies in the range 3 to 10 eV. The VUV-FEL
will operate in the 600 MeV high average current branch of
the energy-recovery linac, and is driven by ∼ 80 pC electron bunches at multiples of 4 31 MHz up to a maximum of
1.3 GHz. A system of distributed bunch compression along
the beam line is expected to compress the bunch to lengths
as short as 100 fs, generating a peak current of ∼ 300 A
before injection into the VUV-FEL. The main system parameters used in the simulations are given in table 1. Since
the average output power will be of the order of 300 W or
multiples thereof, and the mirror only reflects 60 % of theradiation falling on the surface, significant mirror heating
is expected.
We will first briefly discuss the mirror thermal expansion
and the resulting phase distortion. We then continue witha simulation of the VUV-FEL with and without the mirror
expansion included.

MIRROR EXPANSION UNDER A
THERMAL LOAD
The mirrors considered for the VUV-FEL oscillator consist of a protected aluminium coating on a silicon substrate.
The reflectivity R of the mirror is expected to be 60 %[3]. Radiation is extracted at the downstream (DS) mirror
through a hole with a radius of r h = 1.8 mm. We approximate the mirror loading in the form of a train of opticalpulses by an average power and determine the steady state
displacement δz(r) of the reflecting mirror surface under
the assumption that the average absorbed power P abs will
have a Gaussian profile with rms width σ m .
We use the finite element program MultiPhysics with theStructural Mechanics Module [12] to calculate the temper-High power FELs207

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Proceedings of FEL 2007, Novosibirsk, Russia

Table 1: Baseline VUV-FEL parameters as used in the simulations.
Undulator
Undulator period λ u
Undulator parameter K (rms)
Periods per module
Number of modules
Electron Beam
Electron beam energy
Relative energy spread (rms)
Bunch charge
Peak current
Normalised emittance
Optical Cavity
Wavelength λCavity length Lcav
Upstream ROC r1
Downstream ROC r2
Mirror reflectivity R
Rayleigh length z r
Fundamental mode waist w 0
Waist position (from US mirror)
Outcoupling hole radius r hCavity stability g1 × g2

58 mm
1.9799523
549.3 MeV
0.1 %
80 pC
300 A
2 mm-mrad
123.89 nm
34.618067 m
14.5 m
21.7573 m
60 %3.67 m0.38 mm13.5 m
1.8 mm0.82

ature distribution and the resulting surface displacement,δz. The DS mirror considered here has an outer diameter of
20 mm and a thickness of 10 mm. The thermal conductivity and thermal expansion are taken to be 1.2 W/cmK and
2.8×10−6 K−1 respectively. Although taken constant here,
these can be allowed to vary with temperature. A heat flux
with a Gaussian profile having a rms width σ m and total
flux of αPo is used to load the reflecting surface of the mirror, where α is the absorption coefficient and P o is the average optical power incident on the mirror. Note that only
the fraction with r > rh will be absorbed by the mirror.
The mirror is cooled at the outer edge, where we assume
a heat transfer coefficient h T = 1000 W/m2 K to a thermal sink that is kept at 293 K. The heat transfer coefficientof the backside of the mirror is set to h T /1000. Mechanically, the mirror is considered to be mounted stress freewith the reflecting surface pushed against a stable reference plane. Hence, the outer edge of the reflecting surface
can only move radially. The rest of the mirror is allowed to
expand freely. Taking the spot size of the heat flux on the
mirror equal to the rms size of the optical beam found for
the VUV-FEL in stationary state without mirror distortions,and using Po = 300 W, α = 0.4, we find that Pabs and σmare 35.3 W and 2.3 mm respectively for r h = 1.8 mm.
For these numbers, the temperature profile, T (r), and mirror displacement, δz(r/2σ m ) are shown in figure 1. For
comparison, the profiles for the case r h = 2 mm are also
included. In this figure 1B δz is shown as a function of theHigh power FELs

208

Figure 1: Temperature profile (A) and surface displacement(B) of the mirror for P abs = 35.3 W (rh = 1.8 mm) andPabs = 25.5 W (rh = 2.0 mm). Here Po = 300 W andσm = 2.3 mm.

Table 2: Fit parameters for Zernike polynomials for theparameters of figure 1. The resulting δz is in [m].

A00
A20
A40
A60
A80

rh = 1.8 mm
2.446e-7-5.544e-8
5.480e-9-2.9344e-10
3.773e-12

rh = 2.0 mm
1.639e-7-5.641e-8
8.037e-9-6.050e-10
1.648e-11

scaled variable r/2σm , along with a fit to δz using Zernike
polynomials:

δz(r/2σm ) =n=8


An0 Rn0 (r/2σm )

(2)

n=0

where n only takes on even values. Figure 1 shows that thedifference between the calculated displacement and the fit
is far below λ/10. The fitting coefficients are given in table
2 for both r h = 1.8 mm and 2 mm. To convert the surface
displacement to a phase change we usedθ(r/2σm ) = −4πδz(r/2σm )λ(3)Since the phase shift is proportional to twice the surface
displacement and the minus sign has to be chosen to be inagreement with the phase advancement used in OPC.

Proceedings of FEL 2007, Novosibirsk, Russia

TUAAU05

VUV-FEL OSCILLATOR WITH MIRRORDISTORTION

Figure 2: Total power as a function of roundtrip (A) andcross section of the field at various places in the cavity forn = 25 (B) and n = 50 (C). frep = 4 13 MHz.
I (MW/cm2)
1400

50

1200

40
roundtrip

OPC is set up to use the fitting coefficients of table 2 to
calculate the mirror displacement and then convert it to aphase mask using eq. 3. This phase mask is then applied
to the DS mirror. As long as the spot size of the opticalbeam on the mirror does not significantly change, we do
not need to recalculate the temperature and displacement
profile. The amplitude of the phase shift can then be foundby multiplying δz(r) with the ratio P abs (t)/Pabs,0 where
Pabs (t) is the instantaneous average power absorbed by the
mirror and P abs,0 is the absorbed power used to calculate
the thermal expansion δz(r).
One problem with modeling the mirror’s thermal deformation is the difference between the time scale for the oscillator to reach saturation and the mirror to reach a stable
thermal profile. The latter is determined by the thermal relaxation time, which is estimated to be of the order of 1 s
for the DS mirror. On the other hand, the roundtrip time forthe cavity is about 230 ns and the laser reaches steady state
after about 20 roundtrips (∼ 4.6 μs). Ideally, one would
want to apply the absorbed energy of a single optical pulse
to the mirror, and use a time dependent analysis to determine T (r) and δz(r) at the arrival time of the next opticalpulse. The build up of the radiation and the thermal distortion would then be determined iteratively until a steadystate was obtained. Although such a simulation can be set
up with OPC using an appropriate finite element solver,thisrequires considerable computational resources and we havechoosen to demonstrate the effect of thermal mirror distortions in a different way.
In view of the short time the VUV oscillator requires
to produce a stationary output, we first let the oscillator
reach this state and then apply the full thermal distortion
instantaneously at the DS mirror and observe how the laser
reacts. Although this ignors the temporal development of
the distortions it gives a first impression of how the distortions affect the laser. Figure 2 shows the total power in andcross section of the optical field at various places along theresonator and in the far field (power only) after n = 25
and 50 roundtrips. The mirror distortion is applied after
30 roundtrips. Here Genesis 1.3 is used in steady statemode to propagate the optical field through the undulator
and frep = 4 13 MHz. It is clear that at these power levels
the laser quickly adapts to the distortions in the phase frontof the optical field without seriously affecting the powerin the field. We do observe that the surface expansion focusses the field more towards the upstream (US) mirror andhence the spot size on this mirror is decreased and the intensity increased (about a factor of 2 on axis). The profile
has changed as well and the intensity is now maximum on
axis. Figure 3 shows the cross section of the field at theundulator’s entrance as a function of the roundtrip. This
figure shows that only a few roundtrips are required for thelaser to adapt to the full mirror distortion.
The thermal load on the mirror increases when f rep is

1000
30

8000
6000

20

4000
10

2000
0
-2 -1.5 -1 -0.5 0 0.5
x (mm)

1

1.5

2

Figure 3: Cross section of the optical field at the undulator’s entrance as a function of the roundtrip n. The thermal
distortion is applied at n = 31 and f rep = 4 13 MHz.
increased. Figures 4 and 5 show the same data but now
for frep = 21 32 MHz. Again, the profiles at n = 25 areequal to the ones shown in figure 2B. Figure 4 shows thatwhen the distortions are applied, the total output power atthe undulator’s exit drops by almost a factor of 50. Still,after about 10 roundtrips the laser finds a new equilibrium,
albeit at an output level that is 70 % of the power without
mirror distortions. Although a realistic model of the temporal behaviour of the mirror’s thermal distortion is not used,
these results indicate that an average optical output powerof the order of several kW is feasible. This can still be further improved if the mirror can be cooled more efficiently.
OPC can also use Medusa [10] to calculate the gain andwe have also simulated the VUV-FEL oscillator using thiscode. As Genesis 1.3 can not start from noise in steadyHigh power FELs209

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Proceedings of FEL 2007, Novosibirsk, Russia

roundtrip

Figure 4: Total power as a function of roundtrip (A) andcross section of the field at various places in the cavity forn = 50 (B). frep = 21 32 MHz.

50

12

40

10
8

30
6
20

4

10

ponent in the resonator. Alternatively, the user may provide
an external file that defines an arbitrary phase mask. OPC
can easily be adjusted to interface with an apropriate timedependent finite element program that calculates the timedependent surface expansion resulting from a train of optical pulses incident on a mirror. Alternatively the instantaneous absorbed power based on the optical pulse energy
and frep can be weighted with a thermal relaxation timethat allows the mirror deformation to build up more slowly
than the instantaneous average power. As an example weapplied a simple implementaton of the thermal distortion
by applying instantaneously the full distortion to the DS
mirror of the 4GLS VUV-FEL oscillator after the oscillator
has saturated. We used both Genesis 1.3 and Medusa forthe gain calculation and there are some some differences intheir predictions related to the startup of the laser that are
currently under investigation. Nevertheless the case considered here shows that the laser is expected to be quite
resilient to the mirror’s thermal distortion.

ACKNOWLEDGEMENT
We would like to thank David Dunning, Brian McNeil
and Neil Thompson of the 4GLS design team for the useful
discussions, and Henry Freund and Buff Miner of SAIC for
the Medusa simulations and discussions.

20-2 -1.5 -1 -0.5 0 0.5
x (mm)

1

1.5

REFERENCES

2

Figure 5: Cross section of the optical field at the undulator’s entrance as a function of the roundtrip n. The thermal
distortion is applied at n = 31 and f rep = 21 32 MHz.
state mode, both codes used a seed power of 2 W based on
Ming Xie’s formula for shot noise [13]. Preliminary results
indicate that Medusa shows less optical guiding in the undulator during start-up. It predicts a larger spot size for the
optical beam at the undulator’s exit and consequently, thespot size at the DS mirror is found to be smaller. The feedback is then too small for the laser to start. Medusa can also
start from noise in steady state mode. In this case, the fieldin the oscillator builds up and saturates at about 366 MW
intracavity after about 40 passes without distortions. Thisis about double the number of roundtrips required by Genesis 1.3. Initial results with the mirror’s thermal distortion
turned on and using f rep = 4 13 MHz showed a similar behaviour. The differences found between Genesis 1.3 andMedusa are still under investigation.

[1] G. Neil, et. al., Nucl. Instrum. Methods Phys. Res. A557 9(2006).
[2] E.J. Minehara, Nucl. Instrum. Methods Phys. Res. A557 16(2006).
[3] B.W.J. McNeil, et. al., New J. Phys. 9 (2007) 239.
[4] S.V. Benson, et.al., Nucl. Instrum. Methods Phys. Res.
A407, 401 (1998).
[5] A.R.B. de Castro, and T. Möller, Rev. Sci. Instrum, 76,
063104 (2005).
[6] J.C. Goldstein, B.D. McVey, and B.E. Newman, Nucl. Instrum. Methods Phys. Res. A296, 288 (1990).
[7] H.P. Freund, M. Shinn, and S.V. Benson, Proceedings 28th
Free-Electron Laser Conference, FEL’06, Berlin, Germany,Aug. 2006, p. 444, http://www.JaCoW.org[8] J.G. Karssenberg, et.al., J. Appl. Phys. 100, 093106 (2006).
[9] S. Reige, Nucl. Instrum. Methods Phys. Res. A429, 243(1999)[10] H.P. Freund, S.G. Biedron, and S.V. Milton. IEEE J. Quantum Electron. 36, 275 (2000).
[11] M. Born and E. Wolf. Principles of Optics, 6th edition. Pergamon Press, 1980.

DISCUSSION AND CONCLUSIONS[12] Comsol Multiphysics V3.3a and Stuctural Mechanics
module are from Comsol AB, Stockholm, Sweden.
http://www.comsol.com

We have extended the OPC package to include mirror
distortions using Zernike polynomials. These distortions
are applied as a phase mask at the appropriate optical com-

[13] M. Xie. Nucl. Instrum. Methods Phys. Res., A445, 59(2000).

High power FELs

210

Proceedings of FEL 2007, Novosibirsk, Russia

TUBAU01

FLASH UPGRADED - PREPARING FOR THE EUROPEAN XFEL
H. Schlarb∗ for the FLASH and the XFEL Project Team,
DESY, D-20607 Hamburg, Germany
Abstract
Since 2005, the Free electron LASer in Hamburg,
FLASH, has delivered a high brilliance photon beam tousers with a wavelength range between 13 nm and 40 nm.
To meet the user demands for 4 nm wavelengths, sub-50 fs
timing stability, and better pointing stability, the accelerator will be continuously upgraded within the next few
years. The upgrade to an energy of 1.3 GeV, the development of a transverse and longitudinal intra-train feedback
system, and a 3rd harmonic cavity at 3.9 GHz are key prototype tests for the European XFEL. FLASH also serves asa test bench for an entirely new approach to accelerator facility synchronization involving optical pulses distributedin length stabilized fibres. Increased stabilization of theelectron beam peak current and its arrival time should provide the possibility to reliably seed the electron bunch withhigher laser harmonics. In this paper, an overview of theplanned upgrades for FLASH will be presented with respect to their usefulness for the European XFEL.

INTRODUCTION
Since 2005, the high-gain Free electron LASer in
Hamburg, FLASH, successfully delivers to user experiments in the VUV-wavelength range between 13 nm and40 nm ultra-short photon pulses (10-25 fs FWHM) withpeak power at the Gigawatt level [1]. The peak brillianceof the FLASH photon beam exceeds that of state-of-the-art
synchrotron radiation sources by seven orders of magnitude. Observations of the high degree of transverse and longitudinal coherence, intensity stability of the self-amplified
spontaneous emission process, amplification gain measurements along the undulator and the content of high harmonics down to 2.6 nm are in full agreement with theoreticalprediction.
The 13 nm wavelength achieved with this FEL is limited only by the 700 MeV maximum electron beam energy
and is an important milestone for FLASH and the European XFEL as they set goals of reaching wavelengths of
6 nm and 0.1 nm, respectively. Besides photon production
for users, FLASH serves as a small scale (∼ one tenth)
prototype for the larger XFEL facility. The layouts of the
facilities are shown in Fig.1 [3, 4].
The electron beam is produced in a laser-driven photoinjector using a normal conducting RF gun. The beamis accelerated in a linear accelerator comprised of eight 9cell superconducting cavities housed in cryogenic modules.
The kilo-Ampere’s peak currents are achieved though twomagnetic bunch compressors before the beam enters the∗ holger.schlarb@desy.de

main linac section. Passing beam cleaning and protecting
collimators, the electron bunches of typically 100 fs duration produce the SASE-FEL photons in long undulators.
Key parameters of the machines are listed in Tab. 1[3, 4].
Most of the accelerator parameters impacting the electron beam dynamics, beam instrumentation, mechanicalor RF tolerances are quite similar for the two facilities.
The main differences are related to the electron beam energy, the accelerator and undulator length, the electron andthe photon beam transport, and the photon diagnostics for
Angstrom wavelengths. The large number of devices in the
XFEL - about 100 acceleration modules - requires reliablemass-production by industry. FLASH can provide for the
prototyping of single XFEL units and, within certain limitations, can also provide long-term reliability tests.
Table 1: Key parameter of FLASH and the European XFELParameter
FLASH
XFEL
norm. emittance2 µm
1.4 µmpeak current
2.5 kA
5.0 kAbunch rep. rate
1(9) MHz
5 MHz
pulse rep. rate
10 Hz
10 Hz
bunch charge
1 nC
1 nC
beam energy
1.0 GeV17.5 GeV
photon wavelength
6.3 nm0.1 nmacc. freq.
1.3/3.9 GHz 1.3/3.9 GHz
flat top duration
800 µs650 µsfacility length
260 m
3.4 kmundulator length
30 m
250 m
orbit tolerance und.
5 µm
3 µm
Bunch compression for the XFEL takes place at beamenergies that are ∼4 times higher than in FLASH. The
higher energies and the smaller R56 of the XFEL chicanes
reduce the sensitivity to micro-bunch instabilities and relax the tolerances on the RF amplitude stability. Dedicateddiagnostics for temporal and spatial bunch profiling up to
the second bunch compressor - the most critical part of theaccelerator - are essentially the same. Therefore, almost
all critical accelerator sub-systems can be tested and prototyped at FLASH, allowing for reduced costs, a rapid XFEL
commissioning, and minimized risk. In this paper, the various FLASH upgrades relevant for the XFEL are described.

ENERGY UPGRADE TOWARD 1.3 GEVDuring the spring shutdown of 2007, a new accelerator
module ACC6 - almost the XFEL design module - has been
installed. The average gradient of ACC6 is 28.5 MV/m

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Proceedings of FEL 2007, Novosibirsk, Russia
Injector

Laser

BC1

BC2

Booster

Main accelerator

Collimator

Undulator

Exp.

3rd

RF gunFLASH:XFEL:

130MeV
500MeV

470M eV
2. 0 GeV

1.3GeV
17.5GeV

6.3nm
0.1nm

Figure 1: Generic layout of the Free Electron Laser FLASH and the European XFEL.
measured at the cryo-module test stand at DESY. In addition, the coupler of ACC5 has been repaired and module
ACC3 has been exchanged, allowing FLASH to reach thedesign beam energy of 1 GeV or 6 nm photon wavelength.
At the exit of the FLASH linac, space for a seventh acceleration module is foreseen. To meet the user demands
for shorter photon wavelength, the installation of ACC7 isplanned for 2009. This boosts the beam energy toward
1.3 GeV and allows the users to reach the water window
with wavelengths below 4.3 nm in the first FEL harmonics.
This new accelerator module (No. #8) will be assembled at DESY by industry. The four acceleration modules(ACC4-ACC7) correspond to a baseline RF section of the
XFEL. It will, therefore, allow for testing of the complete
high- and low-power RF control system, as foreseen for
the Angstrom machine; this includes the waveguide distribution and 32-cavity field regulation.

sufficient to remove non-linearities caused by accelerating RF, time-momentum correlations exiting the RF gun(Fig. 2(a)), higher order chicane momentum compaction(T566 ) and distortions due to collective effects. The XFEL
requires a total voltage of 108 MV at 3.9 GHz due to thehigher energy of 500 MeV at the first compressor. The
voltage can be achieved by 24 cavities at a gradient of
13.5 MV/m.
Cavity treatments, assembly and vertical performance
tests have been successfully carried out at Fermilab [5, 6].
The delivery of a complete cryostat housing the four cavities for FLASH ( Fig. 3) by Fermilab is foreseen for Spring2008 [7]. An integral test of the cryostat is planned at the
DESY cryo-module test bench before installation in 2009.
The preservation of the projected beam emittance requires an alignment of the cavities to each other better than
0.5 mm. In addition, a good orbit control through the cavity
string is needed.

3.9 GHZ LINEARIZING CAVITIES
Ultra-short FEL pulses of some ten femtosecond duration are produced at FLASH by inhomogeneous electron
bunch compression, causing a sharp leading high-peak current spike with a picosecond-long trailing tail. The longitudinal profile is mainly a consequence of the non-linear
energy chirp from the time-dependent RF fields and the linear shearing of the longitudinal phase space that occurs in
the magnetic bunch compressor chicanes.
Exit RF gun
100

Exit 3.9 GHz cavities
5000

a)

3000

50

Figure 3: Cryostat housing the four 3rd harmonic cavity
for FLASH.

2000
Pz [eV/c]Pz [eV/c]

b)

4000

0
-50

1000
0
-1000
-2000
-3000

-100

-4000
-150
-5

-5000
-4

-3

-2

-1

0
1
z [mm]

2

3

4

5

-5

-4

-3

-2

-1

0
1
z [mm]

2

3

4

5

Figure 2: Simulation of longitudinal phase space at the entrance of ACC1 and at the exit of the 3rd linearizer cavities.
Of significant importance for he bench marking of beam
dynamics and operational aspects of the XFEL with homogeneous bunch compression is the installation of thethird harmonic superconducting linearizer cavity operated
at 3.9 GHz (see Fig. 2(b)).
At FLASH, the first bunch compression takes place at
130 MeV beam energy. Four 3rd harmonic cavities operated at a gradient of 15 MV/m (20 MV voltage total) are
X-ray FELs212

DIAGNOSTICS DEVELOPMENTS
Intra-bunch train feedback
The long duration of the XFEL electron macro-pulses
enables active stabilization of the transverse beam offsets
by means of a fast intra-bunch-train feedback (IBFB) system. The Paul Scherrer Institute agreed to develop the
IBFB which will be tested in its prototype version at the
FLASH linac [8, 9].
The proposed IBFB topology, shown in Fig. 4, consists of two upstream beam position monitors (BPM) followed by two kicker magnets for each transverse plane
and two downstream BPMs. From position measurements

Proceedings of FEL 2007, Novosibirsk, Russia

TUBAU01a)
λ > λ1λ1>λ>λ0.
THz diffraction
gratings

Detectorarray

Figure 4: Topology of the intra-bunch train feedback systemof the upstream BPMs transverse kicks are applied witha latency preferably below the bunch spacing of 200 ns
and 1000 ns for the XFEL and FLASH. Optimization of
the feedback parameters is derived from the downstream
BPMs. The proposed IBFB system will damp perturbations
up to frequencies of some 100 kHz. The FPGA-based digital IBFB electronics include a DSP that enables adaptive
feed-forward correction of repetitive intra-train variations.
Resonant stripline pickups were developed to meet the desired orbit resolution of 1-2 µm and latency requirements.
A test of the IBFB at FLASH is planned for 2008.

Single-shot THz spectrometry
Coherent radiation produced at diffraction and transition
screens or bending magnets provides an excellent opportunity for diagnosing and controlling the bunch compression process. The radiation is emitted mid and far infrared wavelength range, corresponding to the electron bunch
length. To measure this radiation, a single-shot THz spectrometer based on three staged diffraction gratings has beendeveloped (see Fig. 5(a))[11, 12]. The diffracted radiationis recorded by an array of pyro-electric sensors (shown in
Fig. 5(b)), that can be read out simultaneously. To suppress
water absorption in air, the spectrometer and detector unit
is housed in a vacuum vessel.
Correlations between the FEL intensity and different
wavelengths ranging from 12 µm to 80 µm clearly showthat the spectral information reveals significantly more information than a simple integral power determination. For
example, the FEL intensity is correlated with the THz intensity at 30 µm, but anti-correlated to wavelengths around
12 µm, indicating a large destructive compression of thebeam. The measurements were carried out using a single
kicked bunch onto an transition screen. An online device
suited for macro-pulse operation that detects the coherent
synchrotron radiation emitted at the last bending magnet ofthe chicane is in preparation.

Fiber laser based electro-optic bunch profiling
The longitudinal bunch profile has been successfullymeasured by detecting the Coulomb field of the bunchwith electro-optics (EO) techniques. The Coulomb field isencoded into the polarization of a broadband laser pulse(Ti:Sa laser) and decoded by transforming the polarization variation into a laser intensity modulation. Cross-b)

Pyro-detectors
Pyro-detectors

Figure 5: (a) Scheme of single-shot spectrometer covering
12-80 µm radiation. (b) Pyro-detector array with 30 channels.
comparison with a transverse deflecting RF structure turning the longitudinal charge distribution into a transverse
streak on an observation screen[10] reveals a time resolution of 60 fs rms, limited by electro-optic crystal [13, 14].
Unlike the transverse deflector, EO-techniques are noninvasive and allow for single-shot detection of all bunches
in an macro-pulse. This requires the development of a fast
readout system for detection of the laser intensity modulation in a line-array, and, in a second step for intra-train
feedbacks, a high speed FPGA based profile processing.
grating mirror
QWP isolator

Yb-doped
fiber
SMF

linearly polarized beam

SMF

collimator

EOM/AOM

HWP
54 MHzWDM
couplerpolarizing
beamsplitter

to EO
crystal
1 MHz

QWP

collimator

diode
laser

SMF
PLL

PD

pulse picker

Figure 6: Scheme of Yb-fiber laser for EO bunch profiling.
Suited for tunnel installation and for every day operation, an ultra-broadband Ytterbium-fiber laser, sketched inFig. 6, is considered. The fiber laser has been developedin corporation with Bilkent Uni. [15]. The repetition frequency of the cavity is 54 MHz and will be reduced witha pulse-picker to match the bunch frequency. Fiber amplification allows for boosting of the pulse energy to 1-10 µJ
with pulse durations below 50 fs (FWHM).

Optical replica synthesizer
Femtosecond time-resolutions can be achieved with an
optical replica synthesizer (ORS), proposed in Ref. [16]. It

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Proceedings of FEL 2007, Novosibirsk, Russia

Figure 7: Scheme of optical replica synthesizer.
operates like an optical klystron FEL seeded by an infraredlaser (Fig. 7) [17]. In the modulator undulator, the interaction of the laser with electrons causes an energy modulation. A small chicane turns the energy modulation intoa density modulation at the wavelength of the laser light.
The micro-bunched beam radiates coherently in a radiator
undulator. The emitted light pulse with the same longitudinal profile as the electron beam is analyzed by a commercially available second-harmonic generation FROG (frequency resolved optical gating) device.
In a collaboration effort between Uni. Stockholm, Uni.
Uppsala, Uni. Hamburg, BESSY and DESY, the ORS experiment was assembled at FLASH. The commissioning of
the novel diagnostic device is scheduled for Autumn 2007.
Beside the diagnostics aspect, the ORS experiment will
provide valuable experience with the design and the operation of a laser heater, as foreseen in the XFEL design.

FEMTOSECOND SYNCHRONIZATION
A drift-free synchronization distribution system withfemtosecond accuracy is of key importance for the stabilityof X-ray FELs and is an indispensable prerequisite for laser
seeded FELs. The most critical devices of an FEL are thephoto-injector laser, the RF gun, the acceleration section
upstream of the bunch compressors, and pump-probe andseed lasers for user experiments. Their locations are separated by 260 m for FLASH and by 3.4 km for the XFEL.
Femtosecond accuracy at these large distances cannot be
achieved with conventional coaxial RF cable distributions.
Laser based synchronization, however, can provide the desired stabilities [18]. At FLASH, a prototype system for the
XFEL of a laser based synchronization is under construction [19]. The large complexity of such a system, comprised of multiple feedback loops, needs a careful designof the sub-components and optical devices to meet the reliability, stability and maintainability requirements.
The new synchronization system consists of an passively mode-locked Erbium-doped fiber laser producing
ultra-short pulses at central wavelength of 1550 nm anda repetition rate of 216 MHz. The fiber laser is narrowbandwidth locked to the low-noise RF master oscillator of
FLASH. The laser pulses are distributed throughout the facility in dispersion compensated optical length stabilized
fiber links. Length stabilization is accomplished by Piezotransducers. The error signal is generated by the precise
X-ray FELs

214

temporal overlap of pulses exiting the laser with pulses
back-reflected at the end of the fiber link in a balanced
second harmonic optical cross-correlator. A 400 m longfiber link test bench installed in an accelerator hall has been
setup to develop the link stabilization unit. First out-ofloop measurements show a short time (≈10 min.) link accuracy of 4.4 fs rms and drifts of 20 fs peak-to-peak during
12 hours are observed. At the same time, the optical fiber
length has changed due to environmental temperate change
by more than 40 ps [20].
At the link exit, three different front-end systems can beclassified: a) the synchronization of optical lasers using
sum-frequency optical cross-correlation; b) the direct useof the optical synchronization pulses for sub-50 fs bunch
arrival measurements [21], bunch position monitoring inlarge apertures [22], and RF signal sampling. The opticalpulses are also most suited as seeds for laser amplifier, e.g.
the ORS-experiment; c) the conversion to RF for the acceleration field control, for example, by means of a Sagnacloop interferometer [23].
Figure 8 shows the layout of the FLASH optical links
and their front-ends. The system will be suited to stabilize
the electron beam arrival by fast intra-train feedbacks for
the RF control and to synchronize all relevant devices.

LASER SEEDING (S-FLASH)
Implementation of a femtosecond stable synchronization system and further improvements of the RF controls
should produce a reduction of the electron timing jitter below 100 fs (FWHM). The 3.9 GHz linearizer cavities allows for longer electron bunches (400 fs FWHM) with uniform peak currents that are comparable to what we use today. This will enable the stable temporal overlap for external seeding of FLASH (s-FLASH) at VUV wavelengths.
A technical feasibility study to demonstrate electron
beam seeding with the high harmonics generated by an optical laser impinging on a gas target has been approved by
the German funding agency. The goal of s-FLASH is to initially reach saturation at 30 nm seed wavelength (29th harmonics) with 100 kW seed power. The desired FEL intensity fluctuation would be smaller than 5 % at the Gigawatt
level, the radiation would have full longitudinal coherencewith a SASE background below 1 % and the pump-probe
timing would be stable below 10 fs.
To avoid impacts on the normal FLASH user operation,
the layout of the experiment (Fig. 9) allows for parasitic
operation. The ten meter long, variable-gap undulator will
be installed after the collimation dogleg, providing the required wavelength tunability at fixed electron beam energies. The seed is transported from a neighboring laser
building and coupled into the electron beam line at the last
dogleg bending dipole. The Gigawatt seeded FEL pulses
with a duration of about 20 fs FWHM are coupled out a
few meters behind the undulator. The out-coupling mirror
is located in the center of a small chicane to vertically offset the electron beam by ∼ 10 mm. The FEL beam is thenProceedings of FEL 2007, Novosibirsk, Russia

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La s e r b u ild in g
EO, HHG a n d ORS

Ph o t o ca t h o d e
La s e r

Se e dL2 L

L2 L
ACC 1 BC2

CDR

ACC 2 3THz

ACC 4 5 6BC3

La s e r
L2 L

ISR

Un d u la t o r s
ORS

RF g u n

BPM
DWC
L2 RF BAM

Dia g.
BAM

DWC
L2 RF

BPM

CDR

LOLA

BAM

BAM

BAM

TEO

Dia g.

PPla s e r
L2 L
BAM

MLO
MLO

Dis trib ution

MO

ISR

L2 L

Beam arrival monitor
Laser to laser synchronization

Se e d Direct laser seeding
Op t- Cr o s s ..

DWC

High precision down converter

L2 RF Laser to RF conversion

Figure 8: Prototype of a laser based synchronization system for the XFEL at FLASH
transported to an experimental building outside of the accelerator tunnel. A portion of the optical laser is split after
the multi-pass amplifier and transported to the pump-probe
experiment. Installation of s-FLASH is planned for 2009.

[7] Private communication E. Vogel, DESY
[8] V. Schlott, et al., ”Intra Bunch Train Feedback for teh European X-FEL“, EPAC’06, Edinburgh, Scotland, p. 3017
[9] B. Keil, et al., ”Design of an Intra-Bunch-Train Feedback
system for the European X-ray FEL“, DIPAC’07, May
2007, Venice, Italy[10] M. Huning, et al., FEL’05, Aug. 2005, Stanford, CA, p. 538.
[11] H. Delsim-Hashemi et al., ”Single-Shot Longitudinal Diagnostics with THz radiation at the Free-Electron Laser
FLASH“, FEL’06, Aug. 2006, Berlin, Germany, p. 594[12] B. Schmidt, ”Overview on diagnostics for X- ad XUVFEL“, , FEL’06, Aug. 2006, Berlin, Germany, p. 761

Figure 9: Layout of the laser-seed FLASH (s-FLASH).

[13] G. Berden, et al., ”Benchmarking ultrafast electron bunch
length monitors“, accepted for publication, Phys. Rev. Lett.

SUMMARY[14] B. Steffen, et al., ”Single-Shot Longitudinal Bunch Profile
Measurements at FLASH Using Electro-Optic Detection“,
this conference, WEBAU04.

Future upgrades of FLASH will provide important opportunities for prototyping XFEL components such as acomplete RF section, the 3rd harmonic cavity, novel diagnostics for beam stabilization, a synchronization systemwith femtosecond accuracy, and an external seeding system.

REFERENCES[1] V. Ayvazyan et al.,”First operation of a free-electron laser
generating GW power radiation at 32 nm wavelength“, Eur.
Phys. J. D 37, p. 297-303 (2006)[2] W. Ackermann, et al., ”Operation of a free-electron laserfrom the extreme ultraviolet to the water window“, Nature
Photonics 1, 336 - 342 (2007)[3] J. Rossbach, ”A VUV Free Electron Laser at the TESLATest Facility at DESY“, NIM A375, (1996) 269.
[4] ”XFEL Technical Design Report“, DESY 2006-097,
http://xfel.desy.de.
[5] T. Khabiboulline, et al., ”3.9 GHz Superconducting Accelerating 9-cell Cavity Vertical Test Results“, PAC’07, June
2007, Albuquerque, USA, p. 2295
[6] E. Harms, et al., ”Status of the 3.9-GHz Superconducting
RF Cavity Technology at Fermilab“,PAC’07, June 2007, Albuquerque, USA, p. 2256

[15] A. Winter, O.̈ Ilday and B. Steffen, ”Femtosecond Yb-doped
fiber laser system at 1 µm of wavelength with 100-nm bandwidth“, DIPAC’07, May 2007, Venice, Italy[16] E. Saldin, E. Schneidmiller, M. Yurkov, ”A simple method
for the determination of the structure of ultrashort relativistic electron bunches“, NIM A539 (2005) 499.
[17] G. Angelova, et al., ”Installation of the Optical Replica Synthesizer in FLASH“, this conference.
[18] J. W. Kim, et. al., ”Large scale timing distribution and RF
synchronization for FEL facilities“, FEL’04, Trieste, Italy.
[19] A.Winter, et.al., ”High-precision laser master oscillators for
optical timing distribution systems in future light sources“,
EPAC’06, July 2006, Edinburgh, Scotland, p. 2747.
[20] F.Loehl, et al., ”Sub-10 Femtosecond Stabilization of a
Fiber Link Using a Balanced Optical Cross Correlator“,
PAC’07, June 2007, Albuquerque, USA, p. 3804
[21] F. Loehl, et. al., ”A Sub-50 fs Bunch Arrival Time Monitor
System for FLASH“ DIPAC’07, Venice, Italy, 2007.
[22] K. Hacker, et al., ”Large Horizontal Aperture BPM for use
in Dispersive Sections of Magnetic Chicanes“, EPAC’06,
July 2006, Edinburgh, Scotland, p. 1043.
[23] J. W. Kim, et. al., ”Long-Term Stable Microwave Signal Extraction from Mode-Locked Lasers“, Optics Express, July
2007, Vol. 15, Issue 14, p. 8951

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STATUS OF SCSS & X-RAY FEL PROJECT IN JAPANTsumoru Shintake# and XFEL/SPring-8 TeamRIKEN/JASRI/SPring-8, Hyogo 679-5148 Japan
Abstract
The XFEL/SPring-8 project has been funded in
FY2006, which is aiming at generating 1 Å coherent
intense X-ray laser using 8 GeV normal-conducting
accelerator. The construction period is scheduled 20062010, and FEL operation will start in 2011. XFEL/SPring8 is based on unique concept of SCSS: SPring-8 Compact
SASE Source. It requires low emittance and high peakcurrent electron beam, i.e., normalized emittance of 1π.mm.mrad and 3 kA peak current. We decided to employ
the thermionic electron gun, which generates 1 A beamfrom single crystal cathode, followed by the multi-staged
bunching system to achieve 3000 times compression. The
design is based on the “Adiabatic Bunch Compression”
scheme, i.e., compressing bunch length as inversely
proportional to the beam energy, thus the bunch length onelectron rest frame is kept constant, and as a result thelow slice emittance is preserved. To prove this concept,
the SCSS prototype accelerator of 250 MeV beam energy
was build. On June 2006, the first lasing has been
observed at 49 nm. From the FEL gain measurement, thebeam brightness was determined as high as 300
A/(π.mm.mrad)2, which is enough value for the beam
quality for the 8 GeV XFEL/SPring-8 project.

INTRODUCTION
We started SCSS project in 2001[1] for developing
technology required for X-ray FEL. SCSS stands for
SPring-8 Compact SASE Source, in which by means of
in-vacuum type short period undulator, the required
electron beam energy becomes lower, additionally the Cband accelerator drives the beam at high gradient as highas 35 MV/m, as a result, the total system length becomes“compact”, and it fits to available site length at SPring-8.
In the course of SCSS R&D, we developed a low
emittance electron gun using single crystal CeB6 cathodeshown in Fig. 2 and 500 kV gun driven by pulse
modulator power supply: We also developed various
hardware components required for SCSS: injector rf
system, C-band klystron modulator with oil-filled

Fig. 1 The XFEL will be build at SPring-8 site.

___________________________________________#

shintake@spring8.or.jp

X-ray FELs

216

compact design, high resolution beam position monitor,and digital rf signal processing system[2]. In order tocheck the developed hardware components and verify
system performance, especially the low emittanceelectron injector, we constructed SCSS prototype
accelerator in 2004-2005. The tunnel length is 60 m long,the maximum electron beam energy is 250 MeV, theshortest lasing wavelength is around 50 nm. In July 2006,
we observed first lasing. The user beam run will start in
October 2007.
On FY2006, the Japanese MEXT: Ministry of
Education, Culture, Sports, Science and Technology has
decided construction of XFEL at SPring-8 site. The
project is aiming at generating 1 Å coherent intense X-ray
laser, which is based on SASE using 8 GeV normalconducting accelerator. A big benefit to have XFEL at
SPring-8 site is to share human resources and facilities forsample preparation with existing 8 GeV synchrotron lightsource.
We have decided to use normal conducting linear
accelerator technology at C-band frequency (5712 MHz),
which was originally developed at KEK for the e+elinear collider project. It is “warm” technology, not super
conducting “cold” technology; therefore it can beconstructed with much lower cost. The C-band accelerator
is capable of running at high accelerating gradient, as
high as 35 MV/m. The 50 MW C-band klystron wasdeveloped and it is now available from industries as astandard component. C-band accelerator technology isavailable right now.

CHOICE OF ELECTRON SOURCESCSS is unique and beneficial, however, it requires
extremely low normalized emittance: ~ 1 π.mm.mrad andhigh peak current: 3 kA. We decided to employ thethermionic electron gun, which generates 1 A beam fromsingle crystal cathode, followed by the multi-staged
bunching system to achieve 3000 times compression(3000 = 20 x 5 x 10 x 3). The design is based on“Adiabatic Bunch Compression” scheme as shown in Fig.
3, i.e., compressing bunch length as inversely
proportional to the beam energy, thus the bunch length onelectron rest frame is kept constant, and as a result thelow slice emittance is preserved. We carefully manipulatebunch length and avoid “over bunching”, thus we do not
mix particle between head and tail within bunch. The
bunch length on the electron rest frame is kept almost
constant, in practice it is about 30 cm long, while thediameter of the beam is a few mm only, therefore theelectric field of space charge is fairly uniform and linear,and has only the radial component, as a result emittancebreak due to the space charge effect becomes negligibly
small.

Proceedings of FEL 2007, Novosibirsk, Russia

Fig. 2 CeB6 single crystal thermionic cathode for low
emittance electron source.
We use rod shape CeB6 of 3 mm in diameter as shownin Fig. 2. We extract 1 A beam by 10 MV/m acceleration
field in the gun (500 kV/5cm), which is in the temperature
limited condition. The theoretical normalized emittancedue to thermal motion at the cathode is 0.4 π.mm.mrad.
The emittance was carefully measured at the gun using
double slits. The measured emittance of core beam was
0.6 π.mm.mrad [3].

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length on the electron rest frame, and never overcompress, thus we can maintain “laminar flow” ofelectron beam from the gun down to the undulator.
In the SCSS prototype accelerator[5], the projected
emittance was measured as 3~4 π.mm.mrad, while it was
dominated by the resolution limit of profile monitor andalso including the tail component associated from beam
deflector right after the gun. To determine the emittancein the beam core, we performed FEL gain measurementby varying K-parameter of the undulator, and peak current,
from which we obtained beam brightness 300
A/(π.mm.mrad)2. To determine peak current, we
performed bunch length measurement by chirping thebeam energy in C-band accelerator, and observed thetransverse beam size variation in the downstream chicane.
The full width was 1 psec. Therefore we obtained thebeam current as 300 A, and the emittance derived as 1π.mm.mrad. This is enough beam quality for 8 GeVXFEL machine.
From the SCSS prototype accelerator to 8 GeV
XFEL/SPring-8, we need further bunch compression by

MACHINE CONFIGURATION
AND BEAM OPTICS
Figure 4 shows the machine configuration and its
parameter is listed in Table-1. The thermionic electron
gun generates only 1 A, and then we compress the bunch
length 3000 times in the injector and chicane magnets. We
designed the compression factor as 20, 5, 10, 3 in theinjector, the first, second and third bunch compression
systems, respectively. The highest compression is made in
the injector, it is basically velocity bunching using energy
chirping on rf field. In the optics design, we introduced
new concept “Adiabatic Bunch Compression Scheme”[4],where we maintain the longitudinal bunch length asconstant on the electron rest frame (moving frame) during
acceleration. In practice, we squeeze the bunch length as
inversely proportional to the beam energy, that is, 1 nsec,
500 keV, γ = 2 at the gun, followed by 0.6 nsec, 1 MeV, γ= 3 after booster, and 10 psec, 30 MeV, γ = 60 after bunch
compressor 1. In this scheme, we maintain constant bunch
Table-1. Machine parameter of SCSS prototype
accelerator and XFEL/SPring-8

Fig. 3 Adiabatic bunch compression scheme.
factor of 10. This is straightforward by simply adding
another two magnetic chicane bunch compressors asshown in Fig. 4.
One special care is taken in the design of 8 GeV
machine to make linear the beam shape in the (z, E) phasespace. Overlapping the higher order harmonic field on thedominant rf-field, we may flatten the effective
acceleration field. This technique will be applied in the
476 MHz booster cavity with L-band correction cavity
and L-band accelerator with C-band correction cavity.
The frequency of the rf acceleration is designed aslower in the injector and gradually raised higher in thefollowing accelerator. This is a part of the “Adiabatic
Bunch Compression” scheme, where the wavelength of
the rf field is also varied to maintain constant bunch towavelength ratio. Ideal way is to use static fieldeverywhere until beam energy reaches to 8 GeV, since thestatic field does not cause emittance dilution associatedfrom time varying transverse kick from radial electricfield or azimuthally magnetic field in the rf cavity.

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Fig. 4 Machine configuration.
In practice the attainable electric field gradient is lower
at lower frequency, especially at DC field. HV break
down is caused by avalanche mechanism driven by ion
bombardment on metallic electrode followed by gas
emission and successive ionisation, which results in more
ion bombardment. When the rf frequency becomes higher,
the field polarity changes faster than the ion reaches to theelectrode, thus the cycle gain of ion population becomes
lower, and HV breakdown stops. From this technicalpoint, the higher frequency is desirable for high field
acceleration. On the other hand, to minimize theemittance dilution due to the time varying transverse kick,lower frequency is desirable. To make an optimum designfor those two constraints under the “Adiabatic Bunch
Compression” scheme, we chose the rf frequency lower in

the injector and higher in main linac. We start 238 MHz in
the sub-harmonic buncher, and 476 MHz in the booster,then 1428 MHz (L-band) in bunch accelerator, 2856 MHz
415 MeV in the(S-band) in the upstream 30 MeV
main accelerator, at the last 5712 MHz (C-band) in themain linac up to 8 GeV. They are schematically drawn in
Fig. 5.
A question will be arise, why don’t we go even higher
frequency. In principle, the answer is “Yes”, but “No” inpractice. The high frequency accelerator requests smaller
size of accelerating cavity structure, whose fabrication
becomes harder and harder as frequency becomes higher.
The C-band is determined by the technical consideration
amount the higher gradient and the practical engineering
capability.

UNDULATOR

Fig.5 Accelerating structures.
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Figure 6 shows the undulator for 8 GeV XFEL/SPring8. The magnet array is hybrid type consist frompermanent magnet and iron yoke. It is in-vacuum design
with variable gap (2 mm ~ 40 mm). Nominal operation
point is gap = 4 mm and K = 1.9. One advantage to use invacuum undulator is that we have fairly wide beam
aperture by opening the gap to 40 mm, where we cantransport guide laser beam for alignment of cavity BPMs.
Temperature control of the permanent magnet is one of
the most important issue in precise undulator design, in
this point the in vacuum undulator design provides ideal
heat isolation from the environmental temperature change.
Figure 7 shows one example simulation results on the
SASE-FEL amplification with nominal beam parameter.

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entrance to the undulator. It was 46 fsec, which isreasonable value if we consider R56 (40 mm) parameterof chicane multiplying with the energy jitter. This is very
promising result for pump-probe experiment. And also,
this is a surprising result that we have such stable beamtiming even through the bunch was made after highcompression from a long pulse of thermionic gun.
To obtain 0.1 degree phase stability, we are currently
developing optical fiber link. For slow drift, phasedetection system in optical fiber by reflecting opticalsignal from one end, and apply feedback on fiber
mechanical stretcher. Recently, we stretched 2 km fiber
around the SPring-8 ring, where the phase drift wasmaintained within 10 fsec range.
Fig. 6 Undulator for 8 GeV XFEL/SPring-8. The magnet
array is hybrid type consist from permanent magnet andiron yoke.
It predicted that the FEL will be saturated within 120 mlong undulator line. The estimated saturation power is 2
GW.

STABILITY ISSUE
As discussed in previous sections, our system uses very
high bunch compression factor, thus the beam parameter,
such as peak current, is very sensitive to the machineparameter change in the upstream section. By simple
analysis, to make the peak current stability better than a
few %, it was shown that the voltage and phase stabilityon the rf acceleration field in the injector has to be 10-4
level and 0.1 degree, respectively. In order to achieve thisrequirement, we have been carrying out R&D on stablehigh-voltage power supply for klystron modulator. Bymeans of parallel operation of high-power fast invertertype power converter and a small power precise power
supply, we successfully demonstrated 10-4 level of pulseto-pulse stability in 50 kV, 35 kW power supply. Using
this type of power supply in the electron gun, and S-bandbuncher, the measured beam energy jitter in the SCSS
prototype accelerator becomes 6 x 10-4. The R&D will be
continued during the construction period to achieve 1 x
10-4. The beam arriving time jitter was measured at the

CONCLUSION & SCHEDULE
Our design concept on low emittance electron gun andinjector, based on thermionic cathode and adiabatic bunch
compression, has been proven at SCSS prototype
accelerator. XFEL/Spring-8 aiming at generating 1 Å Xray was designed and its construction has been started in
FY2006. The construction will be completed in FY2010
and the first X-ray beam test is scheduled in the end of
FY2010.

REFERENCES[1] T. Shintake et al., "SPring-8 Compact SASE Source",
SPIE2001, San Diego, USA, June 2001
[2] http://www-xfel.spring8.or.jp[3] K. Togawa et al., "Emittance Measurement on the
CeB6 Electron Gun for the SPring-8 Compact SASE
Source", FEL2004, Trieste Italy, August 2004
[4] T. Shintake, “Status of SCSS Project”, FEL2006
conference, Berlin, August, 2006.
[5] H. Tanaka et al., “Low Emittance Injector at SCSS”,
FEL2006 conference, Berlin, August, 2006.

Fig. 7 Simulated FEL power growth along undulator line.
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STARS—AN FEL TO DEMONSTRATE CASCADED HIGH-GAIN
HARMONIC GENERATION∗
M. Abo-Bakr, W. Anders, J. Bahrdt, K. Bürkmann, P. Budz, O. Dressler, H. Dürr, V. Dürr,
W. Eberhardt, S. Eisebitt, J. Feikes, R. Follath, A. Gaupp, R. Görgen, K. Goldammer,
S. Hessler, K. Holldack, E. Jaeschke, T. Kamps, J. Knobloch† , O. Kugeler, B. Kuske,
P. Kuske, D. Krämer‡ , F. Marhauser§ , A. Meseck, R. Mitzner¶, R. Müller, A. Neumann, M. Neeb,
K. Ott, D. Pflückhahn, T. Quast, M. Scheer, T. Schroeter, F. Senf, G. Wüstefeld
BESSY, Albert-Einstein-Strasse 15, 12489 Berlin, Germany
Abstract
BESSY is proposing a new facility to demonstrate thecascading of two high-gain harmonic-generation stages
for the generation of FEL radiation. This facility, called
STARS, is planned for lasing in the wavelength range 40
nm to 70 nm. A 325-MeV CW driver linac provides a peakcurrent of 500 A at a bunch charge of 1 nC. The linac consists of a normal-conducting gun, three superconducting
TESLA-type modules modified for CW operation, a thirdharmonic unit to linearize the RF potential and a singlestage bunch compressor. This paper discusses the facility
layout and the main operating parameters.

MOTIVATION
Femtosecond pulses from linac-based free-electron
lasers are unique tools for future time-resolved experiments. In March 2004, BESSY published the TDR for afree-electron laser user facility that covers the VUV to soft
X-ray range (BESSY FEL) [1]. This second-generation
FEL facility is seeded and uses the high-gain harmonic
generation (HGHG) [2] scheme to produce coherent radiation down to the 1-nm range. This scheme offers thepossibility to generate photon pulses of variable femtosecond duration, gigawatt peak power, full shot-to-shot pulse
reproducibility, wide-range tunability and full transverseand longitudinal coherence. To reach the highest energies,
HGHG cascades with up to four stages must be employed.
Following the evaluation of the TDR in 2005/06 by theGerman Science Council, it was recommended that the
BESSY FEL be realized on condition that its enabling technology, the HGHG cascade, be demonstrated beforehand.
To address this important issue, BESSY is therefore
proposing to build a two-stage HGHG cascade with a superconducting driver linac called STARS (Superconducting Test Accelerator for Radiation by Seeding) [3, 4]. Although its primary purpose is to validate the cascadingof HGHG stages, many components and technical issues
are nearly identical to those of the BESSY FEL. Hence,∗ Supported by the Bundesminsiterium für Bildung und Forschung, theState of Berlin and the Zukunftsfonds Berlin.
† knobloch@bessy.de‡ now at GSI, Darmstadt§ now at Jefferson Lab, Newport News
¶ Universität Münster

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STARS serves as an ideal test bed for operating CW superconducting technology, diagnostics, synchronization, andfor studying beam generation, manipulation and transport.
To demonstrate the capabilities and potential of seeded,ultra-short-pulse FEL radiation, prototype user experiments will also be installed at STARS. The location of
STARS is planned such that it will remain operational evenafter construction of the BESSY FEL. By expanding theexperiments, STARS will therefore migrate towards a fulluser facility to enhance the BESSY FEL and to enable theexploration of new techniques before they are adopted for
the BESSY FEL.

OVERVIEWSTARS will be located on the same site as BESSY-II in
Berlin-Adlershof, making use of some of the existing infrastructure while leaving room for the BESSY FEL facility to be built later. The philosophy behind the layout of
STARS, as depicted in Figure 1, is to adopt a conservative
configuration that provides for “safe” operation in view ofthe main goal of demonstrating the cascading of HGHG at
70 nm. Hence, components for the driver linac and systemparameters were adopted which have already been demonstrated experimentally elsewhere. Nevertheless, “optional
upgrades” of the linac are included, some from the outset,that will enhance the FEL’s performance to make STARS
attractive for future user experiments.
A normal-conducting photoinjector generates highbrightness electron bunches.
Three superconducting
TESLA-type cryomodules, modified for CW operation,then boost the energy up to 325–380 MeV.1 The cryomodules contain twenty 9-cell TESLA-type cavities with thepossibility to add four further ones at a later date. Bunch
compression is achieved in a magnetic chicane following
the second module. A collimator and diagnostic beam line
preceed the HGHG cascade, permitting linac commissioning before the beam is injected into the FEL section consisting of two HGHG stages and a fresh bunch chicane.
For bunch compression, off-crest acceleration is required. Non-linearities in the longitudinal bunch profile introduced by the RF potential result in a strongly peaked
current distribution after compression. STARS thus in1 The final energy depends on whether the third-harmonic cavities, discussed later, are in operation or not.

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BUNCH
COMPRESSORPHOTOCATHODE LASERSEED LASERTUBAU03

HGHG STAGE 1

STAGE 2γ

GUN

ACC: MODULE 1

MODULE 2

3rd
HARMONIC

MODULE 3 COLLIMATOR +DIAGNOSTICSe−FRESH BUNCH
CHICANE

Figure 1: Layout of the main components of STARS.

ELECTRON-BEAM GENERATION

1,0E+11

1.8 K

Cavity Quality

cludes a third-harmonic cavity system directly after the second module to remove the non-linearities. However, thedemonstration of cascaded HGHG is also possible without the linearizing cavities installed, albeit at longer wavelengths and lower power.

Targeted operating point for STARS
1,0E+10
0

5

10

15

20

E acc (MV/m)

The electron beam current is generated in an RF photoinjector. Here a modified PITZ normal-conducting system has been adopted [5], primarily because the required
beam paramters (slice emittance = 1.5 π mm mrad at 1 nC)
have already been demonstrated [6, 7]. A UV photocathodelaser illuminates a Cs2 Te cathode with flat-top laser pulsesof 20 ps width to release electron bunches of 1 nC charge.
The repetition rate of the STARS injector is a conservative 100 Hz with a pulse length of 25 μs. This is sufficient
to demonstrate cascaded HGHG, while operating the gun
cavity at a moderate thermal load of 7.5 kW. Stable gun
operation, critical to guaranteeing a jitter-free beam, is thus
much simpler than for high thermal pulsed loads. An RF
pickup is included in the gun-body design to further enhance the control of the RF field. First experiments at low
power have demonstrated that the required phase and amplitude stability of 0.3◦ and 0.1% can readily be achieved
and even improved upon [8].
In future, an upgrade to the full 1-kHz operation, as for
the BESSY FEL, is planned and the thermal loading will
increase to 75 kW. To handle this, the cooling of the PITZ3
gun cavity design was improved and a prototype of the new
design was tested successfully to 47 kW power dissipation,
limited only by available RF power at the gun [5].

BEAM ACCELERATIONSuperconducting RF technology developed by the
TESLA collaboration and as described in the BESSY FELTDR [1] has been chosen for the driver linac of STARS. Although TESLA was originally designed for pulsed operation, both STARS and the BESSY FEL will operate CW for
a number of compelling reasons. These include the flexibility to choose bunch patterns more freely and the enhanced
RF stability because the RF is alway on. The latter is especially critical to provide jitter-free electron bunches to the
HGHG cascade to ensure maximal output and synchronization capabilities for user experiments.
To study the CW operation of TESLA technology,
BESSY has already started an intensive R&D program.
The Horizontal Bi-Cavity Test facility (H O B I C AT) [9] hasbeen set up for this purpose.

Figure 2: Cavity quality of a CW operated TESLA cavity
with all ancillary components (coupler, tuner, HOM pickups, etc.) as measured in the HoBiCaT facility.
Tests of RF couplers [10] and tuners [11] as well as studies such as the optimum bath temperature required for reliable and economic CW operation, have been performed.
Simulations of the HGHG scheme have shown that abeam energy of 325 MeV is sufficient for lasing at wavelengths down to 40 nm. This energy can be reached withthree TESLA-type modules containing a total of 20 cavities
operating at a moderate 17.2 MV/m. Note that this value
takes into account a total decelerating voltage of about 30
MeV in the third-harmonic section. Measurements in H O B I C AT have already demonstrated that CW operation at
this field is possible while exceeding the STARS design
quality factor of 1.4 × 1010 by 65% (see Figure 2).
At 1 nC bunch charge and a repetition rate of 100 Hz,
beam loading in STARS is less than 2 W per cavity. Hence,
RF power will be needed primarily to compensate the microphonic detuning in the cavities. Microphonic detuningis also a significant contributor to RF instability and thus
should be kept to a minimum.
Measurements in H O B I C AT have shown that the RMS
microphonics are of the order of 3 Hz or less with peakexcursions around 15 Hz. A significant portion of thesemicrophonics are at frequencies below 1 Hz and are caused
by pressure fluctuations in the helium gas-return system, oforder 0.03 mbar RMS [12].
It is expected that the larger volume of the STARS helium system will reduce the level of microphonic detuning.
Still, it has already been demonstrated that the detuning canalso be compensated with a fast, piezo-based cavity tuner tolevels below 1 Hz RMS. Even high frequency components
at mechanical resonances have been compensated with thissystem (see Figure 3).
To provide for an ample safety factor, the RF system will
be dimensioned to handle microphonic detuning values of
5 Hz RMS and 25 Hz peak. The optimal bandwidth is 50
Hz, or an external coupling of 2.6 × 107 . At 17.2 MV/m
accelerating field this translates into an RF power requirement of Pave = 3.1 kW and Ppeak = 5.9 kW, which the

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Phase (deg)

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Proceedings of FEL 2007, Novosibirsk, Russia
50
40
30
20
10
0
-10
-20
-30
-40
-50

Open loop measurements

0

5

10

15

20

25

30

Time (sec)Figure 3: Open-loop measurements of the cavity phase stability. The dominant noise source is microphonic detuning resulting in a phase stability of 14.9◦ RMS (red curve).
When detuning compensation is activated with a fast piezo
tuner, the stability improves to 2.8◦ (blue curve).
existing TTF couplers can readily handle, as demonstratedin H O B I C AT [10]. The STARS system will consist of 20
individual IOT-based RF transmitters supplying one cavity each via coaxial transmission lines. RF control will be
performed by a digital FPGA-based system.

BEAM TRANSPORT
A single bunch compressor at 180 MeV is required to increase the peak current. A combination of off-crest acceleration and subsequent passage through a dispersive magnetic chicane is employed to compress the beam from 45 A
to 500 A.
Due to non-linearities in the accelerating RF potential,
a very high and short current peak with a long tail results after the compression. As the peak will generatestrong SASE background radiation, it limits the compression factor and hence the power of the HGHG output radiation. Although STARS is designed to be able to demonstrate HGHG in this mode, the quality and power is improved upon by installing third-harmonic cavities. They
remove most of the non-linearities of the RF potential andthe bunch compressor. A superconducting third-harmonic
module (with four 9-cell cavities) is currently being developed by Fermilab for the FLASH accelerator [13]. This
unit is compatible with the main acceleration modules andis planned for installation in March 2008. Preliminary
analyses of the input coupler system suggest that CW operation of the unit is also possible.
Start-to-end tracking of the electron beam, including allcomponents in Figure 1, have been completed. The photoinjector and the first four cavities were simulated withASTRA to take into account space-charge effects. ELEGANT was used for the remainder of the linac, while tracking in the undulators was performed with GENESIS.
The bunch profile at the entrance of the undulators is
depicted in Figure 4. A slice emittance of approximately
1 π mm mrad and an energy spread of 12 keV is predicted.
Very important for the HGHG process is the fact that a constant profile is maintained in the approximately 1-ps wide
peak-current region (500 A) used in the HGHG cascade.
Measurements at PITZ have demonstrated that a projected emittance of approximately 1.5 π mm mrad is readX-ray FELs

222

Figure 4: Simulated beam properties at the entrace of theundulator. Top left: Beam energy, top right: current profile, bottom left: slice emittance, bottom right: slice energy
spread.
ily achievable [6, 7]. Also, tests at FLASH have shownthat there the energy spread is below the measurement resolution limit of 20 keV [14]. Both results are compatible
with the predicted beam parameters for STARS. Nevertheless, for subsequent GENESIS simulations, the slice beamemittance was intentionally increased to 1.5 π mm mrad toprovide for an additional safety margin in case unexpectedbeam dilution occurs in the STARS linac. An improved
emittance will allow STARS to operate at higher power.
An important consideration for the HGHG cascade is thebunch-to-bunch stability of the beam. Due to the off-crest
acceleration, the bunches have an energy chirp of about
5 MeV/ps. Any time jitter of the bunches thus shifts thecentral energy of the slices used for HGHG which mustremain in the energy acceptance of the cascade (of order2 × 10−3 ). Hence the jitter of the seed laser to the bunch
may not exceed about 150 fs. Studies of the jitter are stillongoing, but first results based on the cavity performancein H O B I C AT have demonstrated that the required stability
can be achieved with the CW SRF system.

THE HGHG CASCADESTARS will cascade two HGHG stages to reach a photon
energy of up to 31 eV. Even higher energies can be accessedby tapping into the harmonic content of the radiation.
Figure 5 depicts the layout of the STARS HGHG cascade. STARS will be continuously tunable from 40 nm to
70 nm, the lowest wavelengths placing the most stringent
requirements on the electron beam quality. The flexibility is achieved by using different harmonics (three to five)in the cascades in conjunction with gap adjustments of theundulators and variation of the seed wavelength.
Modulators 1 and 2 and Radiator 1 are planar devices,while APPLE-III undulators for Radiator 2 provide fullvariability of the polarization between 40 nm and 50 nm[15]. APPLE-III devices yield a 35% higher field on
axis than APPLE-II undulators, so that at minimum gap

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Electron Beam
Modulator 1
Ti:Sa, 275 MW

Rad 1
Chicane

Rad 1

Modulator 2
FB Chicane

Rad 2

Rad 2

Rad 2

ChicaneFigure 5: Schematic of the STARS HGHG cascade (notethat the quadrupoles between undulators are not shown.)

Figure 6: Temporal profile (left) and spectrum (right) of
helical radiation at 40 nm.
(7 mm) 70 nm radiation is within reach. Here, the required
electron-beam quality is relaxed and STARS can even becommissioned without the third-harmonic cavity system.
Performance predictions for the HGHG process weremade using complete start-to-end simulations with thesame approach as for the BESSY FEL [16, 17, 18]. Importantly, the HGHG simulations with GENESIS 1.3 arebased on the actual electron bunch profiles obtained fromthe linac start-to-end calculations, only that the slice emittance has intentionally been increased by 50%. Also, bothradiating slices have been tracked through the first HGHG
stage to ensure that any (detrimental) spontaneous radiation
is taken in consideration.
Results for the most challenging case, radiation produced at 40 nm, are depicted in Figure 6 [18]. For helical polarization, an output power of order 140 MW is expected. The length of the seed-laser pulse (approximately
20 fs) is maintained and about 53% of the power is within
the 0.1% spectral bandwidth. Even more power is produced
at longer wavelengths—nearly 350 MW at 66 nm.
Significant flexibility has been designed into STARS for
the final radiator. Here three independent modules are used
to permit a wide range of operating modes. One benefit isthat STARS is very tolerant to variations of the electronbeam parameters, with saturation attained either after the
first or second module. Figure 7 underscores this point for
simulations at 40 nm (planar polarization). Two simulations were performed; one with the beam emittance andenergy spread as predicted by the start-to-end simulations(1 π mm mrad and 3×10−5, respectively) and one with theemittance and energy spread increased to 1.5 π mm mradand 10−4 , respectively. In the latter case, the strength ofthe dispersive section had to be increased and the second
module of Radiator 2 was closed. Nevertheless, nearly thesame output performance is achieved.
At the expense of spectral purity and by employing all
three radiator modules, the power can be increased further
by driving the cascade in the superradiance regime. Thismode is able to achieve peak powers above 1 GW at 40 nm(see [18] for more details). Wavelengths below 40 nm are

Figure 7: Simulated performance at 40 nm (planar polarization). The black curves were obtained with an emittance of 1 π mm mrad and an energy spread of 3 × 10−5 .
The calculations were repeated with degraded values of
1.5 π mm mrad and 10−4 , respectively (red curve) and the
2nd module of Radiator 2 was closed.
also within reach of STARS by tapping into nonlinear harmonic contents of the radiation field. For example, using
the third-harmonic (13 nm) approximately 700 kW is expected [18, 19].

REFERENCES[1] D. Krämer, E. Jaeschke, W. Eberhardt, (editors), “TheBESSY Soft X-Ray Free Electron Laser”, Technical Design
Report, ISBN 3-9809534-0-8, BESSY, Berlin, 2004.
[2] A. Doyuran et al., Phys. Rev. Lett. 86, 5902 (2001).
[3] J. Knobloch, E. Jaeschke, W. Eberhardt, (editors),“STARS—Proposal for the Construction of a Cascaded
HGHG FEL”, BESSY Report, Berlin, 2006.
[4] M. Abo-Bakr et al., Proc. PAC 2007, Albuquerque, NM(2007).
[5] F. Marhauser, Proc. EPAC 2006, Edinburgh (2006)[6] A. Oppelt et al., Proc. LINAC 2004, Lübeck (2004).
[7] F. Stephan, these proceedings.
[8] K. Ludwig, “Analog phase and amplitude controller”,
BESSY Report 2007.
[9] J. Knobloch et al., Proc. EPAC 2004, Lucerne (2004)[10] J. Knobloch et al., Proc. PAC 2005, Portland, OR (2005)[11] A. Neumann et al., Proc. EPAC 2006, Edinburgh (2006)[12] A. Neumann, “Characterization and Control of Superconducting CW Cavities in the BESSY FEL”, PhD thesis (to be
published), Humboldt University, Berlin, 2007.
[13] T. Arkan et al., Proc. PAC 2005, Knoxville, TN (2005).
[14] M. Röhrs, C. Gerth, M. Hüning, and H. Schlarb, Proc. EPAC
2006, Edinburgh (2006).
[15] J. Bahrdt, Proc. FEL 2006, Berlin (2006).
[16] B. Kuske et al., Proc. FEL 2004, Trieste (2004).
[17] M. Abo-Bakr et al., Proc. FEL 2005, Stanford (2005).
[18] B. Kuske, K. Goldammer, A. Meseck, these proceedings.
[19] K. Goldammer, “Studies on Harmonic Generation in Free
Electron Lasers”, PhD thesis (to be published), Humboldt
University, Berlin, 2007.

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TOWARDS A LOW EMITTANCE X-RAY FEL AT PSI
A. Oppelt∗ , A. Adelmann, A. Anghel, R.J. Bakker, M. Dehler, R. Ganter, C. Gough, S. Ivkovic,
F. Jenni, C. Kraus, S.C. Leemann, F. Le Pimpec, K. Li, P. Ming, B. Oswald, M. Paraliev,
M. Pedrozzi, J.-Y. Raguin, L. Rivkin, T. Schietinger, V. Schlott, L. Schulz, A. Streun, F. Stulle,
D. Vermeulen, F. Wei, A.F. Wrulich, Paul Scherrer Institute, 5232 Villigen PSI, Switzerland
Abstract
The Paul Scherrer Institute (PSI) in Switzerland is aiming to build a compact and cost-effective X-ray FEL facility
for the wavelength range 0.1 – 10 nm. Based on the generation of very low emittance beams, it consists of a lowemittance electron source followed by high-gradient acceleration, and advanced accelerator technology for preserving the initial low emittance during further acceleration andbunch compression. In order to demonstrate the feasibilityof the concept and the emittance preservation, a 250 MeV
test facility will be built. This machine has been designed
to be used as injector for the X-ray FEL at a later date. The
accelerator design of the 250 MeV linac will be presented
together with the status of the low emittance source andhigh gradient acceleration.

the required beam current can be reached with minor losses
in emittance. Research at PSI focuses on developing suitable field emitter arrays emitting a total current of 5.5 A
with an emittance of about 0.05 mm mrad. A scanningelectron microscope (SEM) image of such an array, produced in-house at PSI, is shown in figure 1. Currents up to∼ 10μA per tip have been extracted from such a FEA in
DC mode. The performances were studied at a 100 kV test
stand [1].

INTRODUCTION
In order to realize compact free electron lasers for the
Angstrom wave length range, electron sources with highbrilliance and ultra low emittance are required, allowing
for low beam energies and short undulator length, and thus
dramatically reducing the size and costs of such a project.
The proposed X-ray FEL at PSI is based on the development of new concepts that enable a substantial reduction insize and costs of the facility with respect to other existing
designs.
The successful operation of such a FEL depends on the
combination of high peak current, low energy spread, andhigh brightness of the electron beam. For the PSI-XFEL
performance, in order to reach the Angstrom spectral range,a peak current of 1.5 kA, a relative energy spread around10−4 , and a normalized transverse (slice) emittance as low
as technically possible (i.e. ε n < 0.1 mm mrad), are crucial. These stringent requirements shall be met by using
new techniques, which include a low emittance source,
a high gradient acceleration section, and a sophisticatedbunch compression scheme.

LOW EMITTANCE SOURCEElectrons emitted via field emission from micron sized
metallic tips have an intrinsic low emittance due to thesmall source size. Using a double gated emitter geometry,parallel beamlets are produced from these tips. Combining
the tips into a two-dimensional field emitter array (FEA),∗ presenting author: anne.oppelt@psi.ch

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224

Figure 1: SEM picture of a FEA produced at PSI: the pyramidal shaped Mo tips and the gate layer are clearly visible.
Needle cathodes (single tip field emitters) are also investigated at PSI. Currents up to 470 mA were extracted from a
ZrC needle via field emission (pulsed voltage, 2 ns FWHM,
30 Hz) [2]. Laser assisted field emission from needle cathodes allows increasing the extracted current further andoffers the possibility of pre-bunching the electron beam.
Figure 2 shows the measured current waveforms when applying different voltages (2 ns FWHM, 30 Hz) to a needle
cathode in combination with laser illumination (266 nm, 6
μJ, 16 ps RMS). In this way, a peak current of 2.9 A wasextracted [3]).
Since the fabrication and operation of the FEA [4] is very
challenging, the option of using a conventional photo cathode is also investigated. With the proper choice of parameters (material, bunch charge, peak current), emittances ofabout 0.1 mm mrad should be reachable. Therefore, a Cu
photo cathode will be chosen as start-up version for the injector. For both options, photo emission and field emission,
the parameters were chosen equally such that the design ofthe following accelerator sections is not affected.

Proceedings of FEL 2007, Novosibirsk, Russia

TUBAU04

diode at an accelerating gradient of 250 MV/m (1 MV
pulser, 4 mm gap between cathode and anode). The development of such a high voltage pulser is ongoing at PSI.
A 500 kV pulser was installed at the PSI site in summer
2007 and commissioning has started. After successfully
having passed the high voltage tests, high gradient tests arescheduled and we expect beam operation by the end of theyear. Figure 3 shows a photograph of this pulser in the test
bunker. Some basic diagnostics for electron beam characterization at 500 keV (mainly emittance and momentum
measurements) is being mounted. After demonstrating operation at 125 MV/m, this pulser will be upgraded to thefinal 1 MV pulser in order to realize the target acceleration gradient of 250 MV/m and produce a 1 MeV electron
beam.

EMITTANCE PRESERVATION AND
BUNCH COMPRESSION

Figure 2: Effect of the laser illumination on the extracted
current as function of different voltages applied to a ZrC
needle cathode (see text). Note: The photo current pulses
are broadened due to the low bandwidth of the oscilloscope(1 GHz).

HIGH GRADIENT ACCELERATION
In order to preserve the low initial emittance producedby the FEA, the field emitter will be operated in a pulsed

Figure 3: The high voltage high gradient test facility at PSI:
the 500 kV pulser is installed and being commissioned.

Even after the high gradient acceleration process, theelectron beam is still fragile at 1 MeV. A concept for preserving the small emittance is therefore necessary, since
space charge forces will blow up the beam emittance. Emittance conservation in the first 250 MeV of acceleration,
where space charge forces dominate, is therefore a challenging task.
The low beam current (5.5 A) and bunch charge (200 pC)
are beneficial to reduce the initial emittance and its dilution due to space charge forces in the low energetic region. But in order to obtain a peak current sufficient forlasing, a large bunch compression ratio of ∼270 is needed,which can be realized by controlling the longitudinal phasespace. Therefore, after the high gradient section, the electron beam is accelerated off-crest in a two-frequency RF
cavity [5]. The fundamental frequency (1.5 GHz) introduces thus an energy chirp which leads to ballistic bunching, while the third harmonic frequency (4.5 GHz) flattens
the accelerating field and thus allows controlling the longitudinal bunch shape. In the following L-band TW structure,
the RF compression is finished and the bunch length frozen,
see figure 4. At this stage, the electron bunches are shortenough to be further accelerated in an S-band TW structure,

Figure 4: Effect of the two-frequency cavity: current increase due to ballistic bunching (HOMDYN calculation).

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Proceedings of FEL 2007, Novosibirsk, Russia

Figure 5: Layout of the 250 MeV injector facility (top) with a detailed sketch of the first accelerating elements (bottom).
Target beam currents and energies along the machine are indicated.
running at 3 GHz. Afterwards, a 12 GHz harmonic cavity
linearizes the phase space before further bunch compression takes place in the magnetic chicane. Here, an energyof 250 MeV and a peak current of 350 A are reached. At
this stage of acceleration, space charge essentially no more
influences the electron beam.
After the injector, the beam will be further accelerated to∼6 GeV, always using normal conducting RF technology(mainly S-band). Another magnetic bunch compressor assures the peak current of 1.5 kA needed for the PSI-XFEL.
At the entrance of the 30 m long undulator, a target slice
emittance not larger than ε n = 0.2 mm mrad must be realized.

Figure 6: Site plan of the PSI-West area with the planned
infrastructure for 250 MeV injector (red) and PSI-XFEL(orange).
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226

250 MEV INJECTOR FACILITY
In order to experimentally verify the low emittance accelerator concept described above, a 250 MeV injector facility will be built and operated at PSI in the years 2008–2011. The detailed setup of the 250 MeV injector is described in [6]. Figure 5 represents a schematics of the machine and its space charge dominated beam optics.
If successful, the 250 MeV machine should then serve as
injector for the cost-effective 6 GeV PSI-XFEL. The proposed installation of the 250 MeV injector building and the
XFEL infrastructure on the PSI site (close to the SLS) is
illustrated in figure 6.
Beam dynamics simulations of the complete 250 MeV injector facility have been done using different tools [7]: envelope tracking codes (HOMDYN [8], BET [9]) and particle
codes (e.g. IMPACT-T [10]). The simulation results show
the feasibility of the accelerator concept: bunch compression and emittance preservation can be realized. As an example, figure 7 represents the emittance growth in the accelerator calculated with HOMDYN. The energy distribution
along the bunch as well as the current profile at the end of

Figure 7: HOMDYN calculations of projected emittance
growth along the 250 MeV injector.

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 8: Slice energy distribution (left) and current profile(right) after the bunch compressor at z=40 m.

TUBAU04

In addition to beam dynamics simulations for optimizing
accelerator components and beam optics, basic tolerance
and alignment studies were done using the BET code [3].
For the first beamline elements (pulsed diode, solenoid,
two-frequency cavity), the tolerance requirements are fairly
stringent: according to the simulation results, relative field
variations below 5 × 10 −3 have to be realized. For the elements further downstream, the requirements are more relaxed.
Misalignment studies show that the beamline element positioning is not critical: beam orbit correction using steerers
brings the emittance back to the ideal value (case of perfectalignment), see figure 10.

SUMMARY AND OUTLOOKThe PSI-XFEL concept is based on new technologies
such as field emission, high gradient acceleration, and a
two-frequency cavity, which are currently under development. In order to prove the sophisticated bunch compression scheme and the transport of low emittance beyond thespace charge dominated regime, a 250 MeV injector facility will be built. Its successful operation will allow theconstruction of an Angstrom range cost-effective XFEL at
PSI in the time period 2011 – 2016.

REFERENCES
Figure 9: Slice emittance growth as calculated with BET.

the 250 MeV injector are presented in figure 8. Figure 9shows slice emittances for various slice sizes as simulatedwith BET (an envelope code based on HOMDYN). These kindof 1D simulations are currently verified by a full 3D simulation of the 250 MeV injector [6].

[1] S.C. Leemann et al., Beam characterization for the fieldemitter-array cathode-based low-emittance gun, Phys. Rev.
ST Accel. Beams 10 (2007) 071302.
[2] R. Ganter et al., Nanosecond field emitted and photo-foield
emitted current pulses from ZrC tips, NIM A 565 (2006) 423429.
[3] Conceptual Design Report of the 250 MeV injector for the
PSI-XFEL, under preparation.
[4] E. Kirk et al., Development of All-metal Field Emitter Arrays for high Current Applications, Proceedings International
Vacuum Electronics Conference 2007, Kitakyushu, Japan.
[5] K. Li et al., A two-frequency rf cavity for the PSI-XFEL:
design and beam dynamics simulations, Proceedings International Workshop on Frontiers in FEL Physics and Related
Topics 2007, Elba island, Italy.
[6] Th. Schietinger et al., Beam Dynamics of the 250 MeV Injector Test Facility, Proceedings PAC 2007, Albuquerque, USA.
[7] R. Bakker, Ultra high brightness accelerator design, Proceedings FEL 2006, Berlin, Germany.
[8] M. Ferrario, HOMDYN user guide, available athttps://projects.astec.ac.uk/Plone/astec/Software/HOMDYN/HOMDYN%20User%20Manual.pdf.

Figure 10: Misalignment studies for the 250 MeV injector:
random offsets of beamline elements with σ = ±70μm
result in an emittance growth due to dispersion (red), butorbit correction (blue) can bring back the emittance to theideal value (black). On top of the plot, the accelerating
structures as well as the position of the corrector coils are
depicted.

[9] R. Bakker, PSI in-house development.
[10] S. Lidia et al., Phys. Rev. ST Accel. Beams 9 (2006) 044204.

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Proceedings of FEL 2007, Novosibirsk, Russia

HIGH ORDER MODE ANALYSES FOR THE ROSSENDORF SRF GUN
V. Volkov, BINP, Novosibirsk, Russia
D. Janssen, FZD, Dresden, Germany.
Abstract
High Order Modes (HOM) excited by the beam in asuperconducting RF gun (SRF gun) could destroy thequality of the electron beam. This problem is studied on
the base of frequency domain description by consideringof the equivalent RLC circuit contour for each HOM,
periodical excited by a pulsed current source [1].
Expression for the voltage, the field amplitude and thephase of the excited HOM has been obtained. The
equations for the coupling impedances of monopole TMHOM and TE-HOM in the RF gun cavity has been
derived. In this calculation the change of the particle
velocity due to acceleration is taken into account.
Resonance frequencies, coupling impedances, unloaded
and external quality factors, excitation voltages and field
distributions for each HOM including trapped HOM arecalculated for Rossendorf SRF gun up to the frequency of
7.5 GHz, using the complex field solver CLANS. The
dependence of the calculated parameters from a cavity
deformation has been studied.
The influence of the seven most dangerous HOM on the
beam quality has been estimated by particle tracking
using the ASTRA code.

DERIVATION OF THE THEORYIn the following considerations the electron beam isrepresented by a pulsed current with the repetition roundfrequency Ω. The time dependence of each pulse is givenby the Delta-function [2].

Excitation Voltage
The voltage ΔU=ω·(R/Q)·q of each HOM is excitedwhen a bunch pass through the cavity. It can be presented
as a vector in the complex space, which rotates with theround resonance frequency ω of the HOM:
(1)
U 0 (t ) = ΔU ⋅ e jωt −ωt 2QL ,whereas R/Q is coupling impedance of the HOM; ω/2QL
is attenuation factor; QL is loaded quality factor of the
HOM and q is bunch charge.
The voltage UN is the result of N bunch-HOM
interaction, where the voltage is changed each time by theamount ΔU and N phase rotation φ between theinteraction moments. This phase angle is determined by
the HOM and the bunch repetition frequency and givenby φ=2π·Fraction(ω/Ω). Finally for UN one obtains:N(

U N (t ) = ΔUei⋅(ωt +ϕ ) ∑ ei⋅2π ω Ω−2π ω Ω⋅2QL
n =0

).
n

(2)

where φ is phase angle at that time, when the bunch starts
at cathode of the SRF gun. In the stationary limit N→∞
the amplitude of excitation voltage U(t) becomes
constant. From (2) follows:High power FELs

228

ΔU
⋅ ei⋅(ωt +ϕ ) , (3)1− ei⋅2π (ω Ω ) ⋅ e −2π (ω Ω )/ 2QL
The time evolution of U in the complex plane isgraphical represented in Fig.1.
U (t ) = U N (t ) N →∞ =

Im(U)

40

0

20

20

ΔU

Φ

φ

Re(U)
40

60

φ

U
φ

40

60

80

Figure 1: Evolution of excitation voltage of all bunches
for low Q values of the HOM.
In the real cavity this excited voltage is equal to thechange of the particle energy due to the interaction with
the HOM field(4)
U≡∫dW/e,whereas W is the change of the kinetic particle energy
which can be measured in an experiment.

TM-HOM Excitation by Accelerated Beam
The energy exchange between the HOM and theparticles moving through the cavity is defined as:
r r
1
1
(5)
dW =
⋅ (dPθ ⋅ Pθ + dPr ⋅ Pr + dPz ⋅ Pz ) =⋅ dP ⋅ P
mγ
mγ
Here Pz, Pθ, Pr are particle momentum components
which commonly depend from the accelerating andfocusing fields in the cavity; The components of the d P
are the momentum transfer due to the HOM-particle
interaction. They are given by:urur
e ur ur(6)d P = e ⋅ E ⋅ dt +⋅ ⎡ P × B ⎤⎦ ⋅ dt ,mγ ⎣whereas e and m are the electron charge and the electronmass respectively, γ is relativistic factor, E and B is theelectric and magnetic RF field of the HOM.
For the monopole TM HOM field at cavity axis theequations B=0; Ē= Ez(z)·sin(ωt+φ) are hold. From (4) and(5) follow:(

TU = ∫ E z ( z )⋅ sin (ωt + ϕ )⋅ β (t )c ⋅dt

)

(7)

0

The integration interval T is the time of HOM-particle
interaction. Ez(z) is the electric field distribution of the
HOM on the cavity axis; β(t) and z=z(t) are the particle
velocity and its coordinate determined by the acceleration

Proceedings of FEL 2007, Novosibirsk, Russia
and can be obtained from (6) if Ē and B are theaccelerated and focusing fields. The phase φ must be
equal to phase of excited HOM when a multiple
harmonics n·Ω of the repetition is equal to the HOM
frequency ω. In that case U has the maximal possible
value. By this consideration and using (7) we obtain for U
and φ
U=

⎡T
⎤
⎢ E z z ⋅ sin ωt ⋅ βc ⋅ dt ⎥
⎣0
⎦

∫ ()

( )

2

⎡T
ϕ = arctan ⎢ Ez z ⋅ sin ωt ⋅ β t dt
⎣0

∫ ()

⎡T

⎤

+ ⎢ ∫ E z (z )⋅ cos(ωt )⋅ βc ⋅ dt ⎥( ) ()

⎣0

2

(8)

⎦

T

⎤ (9)

∫ E (z )⋅ cos(ωt )⋅ β (t )dt ⎥⎦0

Excitation of the TE Mode by Accelerated Beam

The TE mode has only one field component Ē≡Eθ, whichis responsible for the energy transfer between beam and
HOM field. Therefore from (4) and (5) follows:

( )

( [

HOM OF THE ROSSENDORF SRF GUN
In the next step we have calculated the field distributionof the HOM for the 3 ½ cell gun cavity using the CLANS
field solver. The external loading caused by the circuits
disposed immediately after the choke (QCC); by the Custem surface loses (QCu) and by the beam pipe (QBP),
which is responsible for the trapped mode dumping, istaken into account. The resonance frequency, the coupling
impedance, the unloaded and the three external quality
factors and the field distribution for the TM monopole
HOM up to 7.5 GHz has been calculated. The
corresponding values are given in Tab.1. Fig. 2 shows thefield pattern of a trapped TM HOM with the mentioned
three loads.

])

r r r
e r r
e
e
⋅ P ⋅ E ⋅ dt +⋅ P ⋅ P × B ⋅ dt =⋅ Pθ ⋅ Eθ ⋅ dt (11)mγmγ(mγ )2Pθ/mγ is the azimuthally velocity component. It is only
different from zero in the present of an external magnetic
field. Only in this case the TE HOM can be excited.
Therefore we propose the feed of a second TE mode withthe axis field Bzo(z,t)=Bzo(z)·sin(ωot+φo). This mode has
been used in [3] for focusing and emittance compensationof the electron beam. In the paraxial limit assuming
r=const the pulse is given by:r(12)Pθ (t ) ≅ −e ⋅ ⋅ Bzo ( z )⋅ sin (ω ot + ϕ o ) .
2
We assume here Bzo(z) >> Bz(z)·sin(ωt+φ) – the field of
excited TE mode. In the same approximation we obtain:rr ∂B (z )⋅ sin (ωt + ϕ )= − Bz (z )⋅ω ⋅ cos(ωt + ϕ ) (13)Eθ = − ⋅ z∂t22
From (11), (12) and (13) follows:
TU=

The excitation of TE HOM is possible only in thepresent of external magnetic field. The phase of excitation
TE HOM field φ depends from phases φo of the external
TE mode as ~φo. If the resonance frequency of theexternal TE mode is not equal to a multiple of therepetition frequency (ωo≠kΩ) then these phase φ changes
with the bunch number n as φ(n)~2π·(ωo/Ω)·n. Assuming
this n dependence in the vector sum of the excited
voltages (see fig.1) we find, that the voltage excitation of
TE HOM can be neglected. These modes could be ofinterest in the presence of a static magnetic field only.

zdJ = dq·U – exchanging of HOM field saved energy withthe particle energy according to energy balance;
dU = ω(R/Q)·dq – HOM voltage excited by the particles
in the equivalent circuit;
From previous follow dJ=U·dU/ω(R/Q), integration gets:
U2
(10)
R/Q =
2ωJ
The R/Q values of the Rossendorf SRF gun calculated
for different accelerating gradients are presented in table
1. Its values are decreased for a low accelerating gradient.

dW =TUPPH002

e r2
1⋅ ⋅ω ⋅ ∫ Bzo ( z )⋅ Bz ( z )⋅ sin (ω ot + ϕ o )⋅ cos(ωt + ϕ )⋅ dt (14)γm 40After averaging the radius r by <r2>= ρ2/2 we are able
to calculate the coupling impedances for the TE modes
using the same arguments as in the proceeding sections:
2(15)
R / QTE = Bmax
⋅ Bo2_ max ⋅ ρ 4 ⋅ω ⋅ f (ω ,ωo ,ϕ o ) 2 J

The expression f(ω,ωo,φo) is proportional to exp((ω+ωo))/γ2. Bmax and Bo_max are the maximum axis
magnetic fields for the excited HOM and for the external
focusing TE HOM respectively. Usually the values of(R/Q)TE are in the order of several nanoohms.

Choke

Cathode Cell

Accelerating Cells

CoaxialExternal
Circuite
Load
Beam pipe Load
Cathode Cu stem

Figure 2: The 3 ½ cell cavity of the SRF gun with thefield pattern of a trapped TM HOM.

These loads are simulated by low conducting materials
with ε=1, μ=1, tgδε=1.5, tgδμ=1.5. All incident RF power
is dissipated without of any reflecting.
The unloaded quality factor Qo is equal G/R(f), where G
is geometry factor of the HOM; R(f)=R1300·(f/1300MHz)2is the niobium surface resistance with R1300=23.2 nOhm at
a temperature of 2K.
The cathode Cu stem surface resistance is defined as
RCu(f)=2π·(10-7·f/σ77K)1/2 , where σ77K = 5.4·108 1/Ohm·m
is specific conductivity of copper at 77K.
Now we are able by means of (3) to calculate theexcitation voltage U in dependence on the repetition
frequency Ω. The result is given in Fig. 3. The upper partcontains the pass band modes. The repetition frequency Ω= 26 MHz is far from the resonance condition and theexcitation voltages for the HOM are lower than 25V. Alsoin the lower part of the picture no harmonics of 26 MHz
is close to a HOM frequency.

High power FELs

229

TUPPH002

Proceedings of FEL 2007, Novosibirsk, Russia

1010

Excited Voltage, [V]DEPENDENCE OF THE HOM SPECTRUM
FROM THE CAVITY SHAPE DETUNING

26 MHz Repetition Harmonics

109
108
107

In this section we examine the stability of the obtained
result by a simple model. SRF gun is equipped by themechanism allowing detuning of main resonancefrequency of 1300 MHz. The detuning is being due tochanging of total length of 3.5 cell cavity. We change thecavity shape by changing the inclination of the straightparts of the cavity cells marked by red colour in Fig.4.

106
105
104
103
100
10
1.26

1.265

1.27

1.275

1.28

1.285

1.29

Frequency Ω, [GHz]

1.295

1.3

1.305

Excited Voltage , [V]

10 7
10 6

Tuning length 400 mm

10 5
10 4
10 3

26 MHz Repetition Harmonics
100
10
1

2.4

2.45

2.5

2.55

2.6

2.65

Frequency Ω, [GHz]

2.7

2.75

2.8

100

Straight parts
10

26 MHz Repetition Harmonics

1

0.1
4.8

4.9

5

5.1

5.2

5.3
5.4
5.5
Frequency Ω, [GHz]

5.6

5.7

5.8

Figure 3: The voltages of the TM HOM.
Table1: Field parameters of the HOM. Trapped HOM
marked by blue color. 1/QL =1/Qo+1/QCC +1/QCu +1/QBP.
ω/2π
R/Q, Ohm
Qo
QL
MHz
β=1
E=25 E=12.5
1268 2.61e8 6.16e9 29.5
21.8
14.55
1283 3.65e9 9.98e9 4.35
2.98
1.694
1294 6.78e9 9.01e9 13.3
9.15
5.196
1300 9.35e9 1.0e10 168.6
170.2
171.2
2395 2.16e8 4.93e9 8.07
8.05
7.948
2487 1.13e7 4.27e9 16.8
12.6
9.957
2544 4.44e7 4.39e9
21.0
20.0
18.94
2690 7.36e6 4.67e9
5.86
5.82
4.536
2721 1.95e6 5.09e9
3.11
2.49
1.706
2758 1.63e6 5.43e9
1.55
1.28
1.243
2824 6.52e7 3.26e9
18.5
11.0
5.395
4043
4273
2.78e9
1.48
1.16
1.086
4853 4.48e4 2.36e9
3.49
1.27
0.22
5184
6631
2.35e9
0.87
0.89
0.641
5244 8.06e5 1.9e9
7.66
2.59
0.195
5257 9.07e6 2.22e9
1.66
1.14
1.383
5694 7.34e4 1.11e9
9.17
3.22
0.713
5811 3.63e7 1.57e9
4.13
1.57
0.291
5944 2.92e4 1.58e9
0.39
0.38
0.358
5992 745.4 2.57e9
1.21
0.89
0.657
6077 6.77e4 1.67e9
0.29
0.18
8.7e-26128
5060
1.83e9
0.44
0.37
0.253
6668 1.62e4 1.69e9
2.47
0.25
6.7e-37131 3.47e4 1.00e9
0.46
0.22
3.4e-27213 1.38e5 1.23e9
0.73
0.34
0.105
7467
4464
1.69e9
29.5
21.8
14.55
High power FELs

230

Figure 4: Change of the cavity shape.
Together with the cavity shape changes the HOM
frequencies ω and loaded quality factors in dependence ofthe length variation δ. For a given repetition rate thevoltages of (3) are also function of δ. In Fig.5 we plot thesum of all HOM voltages for different repetition rates andconstant current
1 10
1 10
Excited voltage, [V]Excited Voltage, [V]

10 3

1 10
1 10
1 10

Amplitude summ of all HOM vs tuning

7

2544

Repetition, MHz

65

f1300/48
f1300/49
f1300/50
f1300/51
f1300/52

5811

4

2824
2395
5811
4853

3

100
10

5244
1

5244
0.8

5694
0.6
0.4
Length variation δ, [mm]0.2

0Figure 5: Amplitude sum of all TM HOM excited by 2
mA beams with different repetition frequencies. f1300 is
accelerating mode frequency changing versus δ.
Again we obtain typical resonance behavior. But in thiscase the HOM voltages can achieve several MV if a
HOM frequency ω approaches to a harmonics of therepetition frequency. This result shows that a certain
HOM can destroy the beam quality at a special cavity
shape or cavity length and a special repetition rate. We
can avoid these approaches by switching between
different repetitions frequencies.
In the table 2 the change of HOM parameters in 3.5 cell
SRF gun cavity versus of –1 mm detuning is presented.
The loaded quality factors changes significantly. It shows
the high sensitivity of the trapped HOM with respect tothe cavity deformation.

Proceedings of FEL 2007, Novosibirsk, Russia

THE INFLUENCE OF THE HOM ON THE
BEAM PROPERTIES
The influence of HOM on bunch properties has been
estimated by particle tracking using the ASTRA code. For
this purpose the field of the seven most dangerous HOM
was added separately in ASTRA input file.
Bunch charges of 77 and 308 pC, an accelerating field of
12.5 MV/m and a laser spot size of 4 mm with σ=3.5 ps
Gaussian temporal distribution has been used in thecalculations.
In the first step the optimal values of the launch phaseand the field strength of a focusing solenoid disposed
after the RF gun are determined by the emittanceminimization without HOM fields. In the next step theinfluence of the HOM with an axis field Emax=1 MV/m is
calculated. The results are presented in table 3. The values
Δε and Δσw are the changes of the emittance and theenergy spread with respect to the undisturbed values.
It is interesting, that for certain HOM and for certain
Emax values the transverse emittance decreases. Theenergy spread is always diminishing. In figure 6 theemittance and energy spread dependencies from excited
voltage are shown for 2824 MHz HOM.

Table 3: Influence of TM HOM for Emax=1 MV/m on the
beam properties.

2395

1.65

77 pC
Δσw
%
-0.37

2543

2.27

-0.85

48.5

2.29

-5.46

48.3

2824

-11.7

-14.5

132*

0.93

-14.4

19.

4853

-0.8

-4.14

5.3

0.02

-4.8

5.11

5693

-1.11

-5.88

6.63

2.31

-7.11

6.13

5811

1.33

-6.82

6.01

0.39

-5.05

5.75

ω/2π

Δε,
%

%

308 pC
ΔW, U,
%
KeV

32.7

1.11

-4.12

32.7

U,
KeV

Δε,

5992

1.33 0.29 6.88 3.58 0.33 6.69
ε,
ε,
σw,
σw,
WithKeV
KeV
μm
μm
out
HOM 0.46 17.9
1.47 24.5* The excitation corresponds to minimum of emittance at
Emax=7.72 MV/m
Normalized transversal emittance

Energy spread (rms)

σw, [KeV]40

ε, [μm]Table 2: The change of HOM parameters in the 3.5 cell
SRF gun cavity at δ=–1 mm.
ω/2π,
Δ ω/2π,
ΔQ/Q,
ΔR/Q,
MHz
MHz
%
Ohm
1268
-0.72
-4.01
0.05
1283
-0.72
-5.388
0.046
1294
-0.68
-3.958
0.87
1300
-0.66
-0.465
-0.7
2395
0.86
1.431
0.054
2487
1.05
-0.0088
-0.01
2544
1.29
-1.075
-0.22
2690
0.63
-0.6233-0.0172721
0.73-1.786
0.016
2758
0.91
-2.017
0.007
2824
0.76
-0.848
-0.07
4043
1.34
-32.98-0.0394853
2.21-5.549-0.0114918
2.15-2.612-0.0158
5184
6.79
25.23
0.093
5244
5.23
5.901
-0.2025257
4.17-94.95
0.052
5694
2.56
1.148
-0.162
5811
9.36
15.88
0.274
5944
1.56
9.594
-0.02245992
3.89-17.51
0.016
6077
1.31
-30.89-0.0133
6128
1.96
2.292
0.00468
6668
7.02
405
-0.00757131
0.69-0.9913-0.001
7213
1.71
38.85
-0.01137467
2.9-3.5860.0028TUPPH002

ε=0.406 μm
U=0.14 MV

0.44

20

0.42

0.4

σw=3.96 KeV
U=0.115 MV

0

0.1
0.2
0.3
Excited Voltage, [MV]

0.4

0

0

0.1
0.2
0.3
Excited Voltage, [MV]0.4

Figure 6: Emittance and energy spread versus excited
voltage of the 2824 MHz HOM.

CONCLUSION
At a repetition (cw) frequency of 26 MHz themonopole TM-HOM of the 3 ½ cell SRF gun cavity
have no influence on the beam quality. But a relatively
small deformation of the cavity can change the situation
drastically. In order to avoid this situation it would be
useful to have a possibility to change the repetition
frequency in a dedicated area.
It is very interesting that for a specific parameter field
the excitation of special monopole TM-HOM improvethe beam quality.

REFERENCES[1] Fernando Sannibale, Collective effects. Single andMultibunch Instabilities. Fundamental Accelerator
Theory, Simulations and Measurement Lab –Arizona State University, January 16-27, 2006.
[2] This method is successfully used in the practice of
BINP by V.M. Petrov et al., Novosibirsk, Russia.
[3] Superconducting RF gun cavities for large bunchcharges. V. Volkov, K. Floettmann, D. Janssen.
PAC07, 2007.

High power FELs

231

TUPPH006

Proceedings of FEL 2007, Novosibirsk, Russia

FEL POTENTIAL OF THE HIGH CURRENT ERLS AT BNL *D. Kayran#, I. Ben-Zvi, V. N. Litvinenko, E. Pozdeyev,
Brookhaven National Laboratory, Upton, NY, USA,
A.N. Matveenko, O.A. Shevchenko, N.A. Vinokurov,
Budker Institute of Nuclear Physics, Novosibirsk, Russia.

Abstract
An ampere class 20 MeV superconducting Energy
Recovery Linac (ERL) is under construction at
Brookhaven National Laboratory (BNL) [1] for testing
concepts for high-energy electron cooling and electronion colliders. This ERL prototype will be used as a test
bed to study issues relevant for very high current ERLs.
High average current and high performance of electron
beam with some additional components make this ERL an
excellent driver for high power far infrared Free Electron
Laser (FEL). A possibility for future up-grade to a twopass ERL is considered. We present the status and ourplans for construction and commissioning of the ERL. We
discus a FEL potential based on electron beam provided
by BNL ERL.

rate, 50 mA average current. The electrons energy at theexit of the gun can be pushed upto 3.0-3.5 MeV by the
maximum field attainable in the super-conducting gun
itself.

INTRODUCTION
The R&D ERL facility at BNL aims to demonstrate CW
operation of ERL with average beam current in the rangeof 0.1-1 ampere, combined with very high efficiency ofenergy recovery. The ERL is being installed in one of thespacious bays in Bldg. 912 of the RHIC/AGS complex.
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) using
relativistic electron cooling of gold ion beams with energyof 100 GeV per nucleon. Furthermore, the ERL R&D
program extends toward a possibility of using 10-20 GeV
ERL for future electron-hadron/heavy ion collider, eRHIC[2].
These projects are the driving force behind thedevelopment of ampere-class ERL technology, which willfind many applications including light sources and FELs.
The intensive R&D program geared towards theconstruction of the prototype ERL is under way: fromdevelopment of high efficiency photo-cathodes [3] to thedevelopment of new merging system compatible withemittance compensation [4].

LAYOUT OF THE R&D ERL
Two operating modes are envisaged, namely the highcurrent mode and the high charge mode. The high current(0.5 A) mode will operate electron bunches with lower
normalized emittance, 0.7 nC charge per bunch at 703
MHz rep-rate. In this case, the full energy of electrons at
gun exit is limited by the available RF power 2.5 MeV. In
high charge mode electron beam will consist of buncheswith charge up to 5nC per bunch at 10MHz repetition___________________________________________* Work performed under the auspices of the US Department of Energy#
High power FELs
dkayran@bnl.gov

232

Figure1: Layout of the R&D energy recovery linac in theshielded vault with possible FEL setup. Dashed line
shows considered second pass upgrade.
The ERL design (shown in Fig. 1) has one turn:electrons are generated in the superconducting half-cellgun and injected into the main superconductive linac.
Linac accelerates electrons 15-20 MeV, which passthrough a one turn re-circulating loop with achromatic
flexible optics [5].
The photocathode is located in a high electric field for
immediate acceleration of the electrons to as high energy
as possible, reducing emittance degradation due to strong
space charge force. Furthermore, linear part of spacecharge effects is compensated by applying a suitable
external solenoid magnetic field.
In nominal recovery operation regime the path-length ofthe loop provides for 180 degrees change of the RF phase,causing electron deceleration (hence energy recovery)
down to injection energy. The decelerated beam separates
from the higher energy beam and goes to the beam-dump.

ERL Injector
The electron injector is a central part of any ERL thathas to deliver high brightness electron beam. The BNL
R&D ERL injector (see Fig. 2) consist of ½ cellsuperconducting RF gun with photocathode inside,solenoid, four dipoles and two solenoids turned on in
opposite direction (in order to match the electron beamwith linac entrance more accurately). The 4th dipole
mergers the high and low energy beams.

Proceedings of FEL 2007, Novosibirsk, Russia

TUPPH006

Figure 2: Detailed drawing of SRF Injector for the BNL R&D ERL.
For R&D ERL the superconducting 703.75 MHz RF(SRF) gun was selected (Fig.3). The gun design with ashort 8.5 cm cell was chosen in order to provide
reasonably high electric field at the cathode at this low
accelerating voltage. To provide effective damping ofhigh order mode (HOM) this gun has rather large iris
radius of 5 cm. More details on the SRF gun and its
photocathode system can be found elsewhere [6].

compensation. Hence, the use of combined function
magnets [7] with equal focusing strength in x- and ydirection is necessary.
Fig. 4 shows result of PARMELA [8] simulations of the
ERL injector for different charge per bunch. Due to thebends in vertical direction the effect of vertical emittance
growth is clear. But at the exit of Z-merger both: verticaland horizontal emittances become almost equal. In case of
5 nC per bunch this equality is broken, the next ordernonlinearity start playing a role.
The main expected electron beam parameters of thissystem obtained by PARMELA simulations are listed inTable 1.
15

Rms Normalized Emittances, mm mrad12.075Figure 3: The SRF gun, in helium vessel (cartesy
Advance Energy System) and SUPERFISH electric field
profile simulation.

MergerOne of the novel systems we plan to use for the R&D
ERL is a merging system providing achromatic condition
for space charge dominated beam and compatible with theemittance compensation scheme [4].
Table 1: Electron beam parameters of the R&D ERL
injector.

εxn1
εxn2
5

0

1.4

5

Injection energy, MeV

2.5

2.5

3

Max. beam energy, MeV

20

20

20

Average beam current, A

0.5

0.5

0.05

Bunch rep-rate, MHz

700

350

9.38

Normalized emittance ex/ey, μm

1.4/1.4

2.2/2.3

4.8/5.3

Rms energy spread, %

0.35

0.5

0.97

Rms bunch length ps

18.5

21

31

Focusing of the bending magnets in the merging section
has significant effect on the low energy electrons.
Different focusing in vertical and horizontal planes(astigmatism) makes impossible simultaneous emittanceRms Normalized Emittances, mm mrad

0.7

0

0

2

4

6

8

s0 , s0 , s1 , s1 , s2 , s2 , s3 , s3
Length, m

0101.925

Charge per bunch, nC

10

εxn0

10
8.312

120

100

εyn0
εyn1

80

60

εyn2
40

20
0

0

0
0

2

4

6

s0 , s0 , s1 , s1 , s2 , s2 , s3 , s3
Length, m

8

10
8.312

Figure 4: Evolution of normalized beam emittances (topfigure – horizontal, bottom figure- vertical) in the ERL
injector. Bunch charge: 0.7 nC-GREEN, 1.4 nC- RED,
5nC –BLUE.

High power FELs

233

Proceedings of FEL 2007, Novosibirsk, Russia

5-cell SRF linac
The heart of the ERL facility is 5-cell SRF linac, which isdesigned for operating with ampere-class CW beam
current [9]. The cavity was designed as a “single-mode”
cavity, in which all Higher Order Modes (HOMs)
propagate to HOM ferrite absorbers through the large
beam pipe. This design provides for very low Q’s for
HOMs and hence very high ERL stability. Measurementsof the damped Q and R/Q of the HOMs and simulations
show that in nominal operation regime the cavity is stable
to over 20 amperes in a one pass ERL and over 2 amperes
for two passes ERL.

Quadrupoles in the dispersion-free straight section
provides for matching of the β-function and for choosing
the desirable phase advances independently in horizontal
and vertical planes. The lattice functions for isohronus
operation regime are shown in Fig.6. The PARMELA
tracking result for 0.7 nC per bunch from the cathode to
the dump are shown in Fig.7 and Fig. 8.
6.0

RMS beam size, mm

TUPPH006

5.0

Horizontal
Vertical

4.0
3.0
2.0
1.0
0.0
0.0

10.0

20.0

30.0

40.0

Z, m

30.0

RMS normalized emittance
mm*mradFigure 5: The ERL cavity following BCP at JLab.
We plan to intentionally tune the lattice of the ERL to a
special mode to test the TDBBU predictions for our SRF
linac with current limited only to few hundreds ofmilliamps.
The cavity was built by AES and is undergoing chemistryat Jefferson Laboratory. Figure 5 shows the cavity at JLab
after the first BCP. The 5-cell SRF linac built by AES andis planned to be installed and tested in Bldg. 912 this year.

Figure 7: RMS beam size evolution from the cathode to
the beam dump as a PARMELA tracking (Q=0.7 nC perbunch).
Horizontal
Vertical

25.0
20.0
15.0
10.0
5.0
0.0
0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

Z, m

Figure 8: RMS normalized emittances evolution from thecathode to the beam dump as a PARMELA tracking(Q=0.7 nC per bunch).
The PARMELA simulation demonstrates what after theacceleration to 20 MeV the emitances are preserved (Fig.
8). There are effective horizontal emittance jumps due tononzero dispersion inside the banding arcs. However indispersion free straight section vertical and horizontal
emittances are equal again.
Figure 6: Lattice β and D functions of the R&D ERL
for the case of zero longitudinal dispersion Ds= m56. The
m12 and m34 elements are controlled independently using
quadrupoles in the dispersion-free straight section.

Loop lattice
The lattice of the ERL loop controls the parameters of a
symplectic transport matrix, which affect the stability andoperation conditions of the ERL. The lattice of the loop is
intentionally chosen to be very flexible for the R&D ERL
to be a test-bed of new ampere-range of beam currents in
ERL technology [10]. The adjustable part of the lattice
has two arcs and a straight section. Each arc is anachromat with adjustable longitudinal dispersion.
High power FELs

234

Beam dump
After a cycle of acceleration and deceleration back to
the injection energy 2.5 MeV electron beam goes to beam
dump. The beam dump has bullet like shape inside withfull water cooled jacket around. This beam dump is anexact copy of that is used for 1MW klystron water cooled
collector and this beam dump can accept electron upto 2
MW avrage power CW. In order to avoid very hot spots
on a surface of the beam dump the electron beam is overfocused by short focal length solenoid. The result of
simulation shows on Fig 9 what maximum power density
is less 200 W/cm2.

Proceedings of FEL 2007, Novosibirsk, Russia
250

CONCLUSSIONS

50
40

Collector contour

150

30

100

20

50

10

0
300

350

400

450

500

Aperture, cm

Power density, W/cm2

P, W/cm2
200

0
550

Z, cm

Figure 9: Power density distribution of 1 MW electron
beam in the beam dump.

FEL POTENTIAL OF THE R&D ERL
The availability of high current electron beam with low
emittance (see Tab. 1) opens new perspective of using
BNL R&D ERL as an electron beam provider for freeelectron laser. The simplest upgrade is to install in thedispersion free straight section bypass with one undulator
and mirrors from both side. For shorter wavelength we
consider the potential extension of this facility into twoturn configuration and installation of IR FEL. The
shielded vault is designed for ERL with maximum energyof 54 MeV to accommodate these future up-grades. The
loop of the ERL is designed to accommodate large energy
spread of electron beam in the case of operating a 100 kW
CW FEL [10].
An other option to use the high power electron beam in
optics-free (ring [11]) FEL. The simple schematic of such
type of FEL layout is shown in Fig. 10. There are two
undulators in straight section and isochronous 360 degrees
bend. Radiation from the second undulator (amplifier)produces energy modulation of the new coming beam
inside the first undulator (modulator). The isochronous
bend delivers the modulated electron beam in theamplifier. One of the big issues is to preserve
microbunching structure of the electron beam during the360 degrees turn.
eBeam

FIR FEL Light

Modulator

Amplifier

Back to ERL

From ERLTUPPH006

Figure 10: Schematic layout of optics free FEL
For 5 cm undulators period and 0.7 nC electron beam
(Tab. 1) at rep. frequency 9.38 MHz the GENESIS [12]simulation gives: wavelength 29 microns, peak power 2
MW and average power 400 W. For full current mode
operation rep. rate 703.75 MHz we obtain 30 kW far
infrared in CW mode.

We are designing, constructing, and commissioning asmall (about 20 meters in circumference) R&D ERL to
test the key issues of amp-class CW electron accelerator
with high brightness beams, required for future nuclear
physics experiments at RHIC-II and eRHIC. Extensive
R&D program on many novel components to be used in
the ERL is under way. The prototype ERL will
demonstrate the main parameters of the electron beamrequired for electron cooling.
This facility, planned to be commissioned in 2009, willserve as the test-bet for new range of beam parameters
whose application will extend well beyond the goals set
forward by Collider Accelerator Department at BNL.
The high avrage current and nice performance of theelectron beam makes BNL R&D ERL opens the potentialof using this machine as an electron source for kilowatts
class FELs.

REFERENCES[1] I. Ben-Zvi at al., “Extremely High Current, HighBrightness Energy Recovery Linac”, PAC2005.
[2] T. Hallman, T. Kirk, T. Roser and R.G. Milner,“RHIC II/eRHIC White Paper,” Submitted to the
NSAC Sub-Committee on Future Facilities, February
15, 2003,
http://www.bnl.gov/henp/docs/NSAC_RHICIIeRHIC_2-15-03.pdf[3] Multi-Alkali Photocathode Development at BNL, A.
Burrill et al., PAC2005.
[4] V.N. Litvinenko, R. Hajima, D. Kayran, NIM A 557,
(2006) pp 165-175.
[5] D. Kayran et al, Optics for High Brightness and High
Current ERL Project at BNL, PAC 2005, pp. 17751777.
[6] A. M. M. Todd et al., “State-of-the-Art Electron Guns
and Injector Designs for Energy Recovery
Linacs”,.PAC2005, p. 2292.
Rama Calaga, Ph.D. Thesis Stony Brook University,
2006.
[7] Wuzheng Meng et al., Unique features in magnet
designs for R&D Energy Recovery Linac at BNL,
PAC07 proceedings MOPAS097[8] L. M. Young, J. H. Billen, "Parmela documentation",
LA-UR-96-1835.
[9] R. Calaga et al., “High Current Superconducting
Cavities at RHIC”, TUPKF078, Proceedings of
EPAC-2004, Geneva, Switzerland, July 5-9, 2004[10] V. N. Litvinenko et al., FEL 2004, p. 570.
[11] N.A. Vinokurov, O.A. Shevchenko, NIM A528
(2004) 491-496.
[12] S. Reiche, NIM A429, (1999) 243.

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TUPPH008

Proceedings of FEL 2007, Novosibirsk, Russia

ELECTRON BEAM DYNAMICS UNDER COHERENT HARMONICGENERATION OPERATION AT UVSOR-II
M. Labat, CEA Saclay - 91 191 Gif-sur-Yvette, France
C. Bruni, G. Lambert, M.E. Couprie, Synchrotron SOLEIL - 91 192 Gif-sur-Yvette, France
A. Mochihashi, M. Shimada, M. Katoh, UVSOR Facility - Okazaki, Japan
M. Hosaka, Y. Takashima, Nagoya University - Nagoya , Japan
T. Hara, RIKEN SPring-8 - Hyogo, Japan

Abstract
In the Coherent Harmonic Generation Free Electron
Laser configuration, an external laser source is seeded inside a first undulator. The interaction between the electron beam and this seed induces energy modulation of thebunch, further converted into a density modulation, producing coherent radiation in a second undulator. The energy modulation enhances the energy spread of the electron
bunch, converted by the machine optics into a modification of its longitudinal distribution. In the case of a storage
ring FEL, the electrons are re-circulating: the same bunch
keeps interacting with the seeded laser, and relaxation of
the distribution is only allowed in between two laser injections. Such specific dynamics has been studied on the CHG
FEL of UVSOR-II storage ring (Japan). The electron beam
stored at 600 MeV is seeded using a 2.5 mJ, 1 kHz, 1.2
ps Ti:Sa laser at 800 nm wavelength, allowing radiation
at 266 nm (third harmonic). A Streak Camera is used torecord the evolution of the longitudinal profiles as a function of the repetition rate and average power of the seedinglaser, leading to bunch lengthening and distortion dynamical analysis. It appeared that because the heating inducedby the interaction remains local, the refreshment process ofthe electronic distribution is modified. The experimental
results are compared to simulations.

INTRODUCTION
The combination of an intense fs laser with synchrotron
electron beams now allows delivery of sub–ps light pulses
in an extendend spectral domain: from TeraHertz [1] to X–
rays [2]. The Coherent Harmonic Generation Free Electron
Laser (CHG FEL) results from this assembly. In the CHG
FEL [4, 5, 6], the electron beam is modulated in energy by
the laser pulse, within the magnetic field of an undulator-so–called ”modulator”-. Passing through a dispersive section converts this energy modulation into a density modulation, allowing in a second undulator -so–called radiator-,coherent emission at the seeding laser wavelength and its
harmonics. Inversely to HGHG FEL configuration[7], theinjected seed does not interact with a fresh bunch but a re–circulating synchrotron beam, which may drive degradation in time of the electronic distribution, and eventuallyof the output radiation properties. The effect of a ps laser
pulse on an electronic distribution has already been studied in oscillator FELs physics (lasing results from the pass
Storage Ring FELs

236

by pass amplification of the electrons spontaneous emission which is stored in an optical cavity). The light pulse
increases the energy spread of the electron beam, the so–called bunch heating [8, 9], inducing bunch lengthening
and shape distorsion [10, 11, 12, 13], until saturation isreached. Depending on the longitudinal overlap between
the electrons circulating in the ring and the laser pulse in
the optical cavity, the FEL can be operated in continuousor pulsed mode. In this last mode, the electron beam refreshes in between two pulses deliveries [14]. Q-switch
operation of oscillator FELs gave similar results on heating
dynamics and showed local effects on the electronic distribution [15, 16].
In this paper, we investigate the dynamical response ofan electron bunch from a storage ring to the excitation ofan external laser with shorter pulse duration (by one orderof magnitude) and higher peak power, as it is the case forboth Slicing and CHG schemes. A model is given for simulation of the electron-photon interaction inside the storage
ring. It is then used, together with experimental results obtained on UVSOR-II CHG FEL, to understand the evolution towards saturation of the electronic distribution under
the laser heating. Finally, local aspect of this interaction
and its consequence on the dynamics are presented.

BEAM HEATING SIMULATIONThe electron bunch distribution is simulated using a pass
to pass model following the stored particles in the longitudinal phase space [18]. The initial code [13, 17] has been
modified to include single pass interaction with an externallaser. The evolution of the j th particle at nth pass is drivenby:τn+1,j = τn,j − αT0 ²n,j(1)
²n+1,j = ²n,j −U0 +VRF,n,j −Dn,j +Rn,j +SE+Wmod,n,j(2)
with τn,j its relative longitudinal position and ²n,j its relative normalized energy with respect to the synchronous
particule. Energy variation is converted by the machine optics into a longitudinal displacement, which depends on the
momentum compaction factor α and the revolution period
T0 .
Along each revolution, the particule losses energy bysynchrotron radiation (U0 ), random emission (R) and spontaneous emission in the optical klystron (SE) [19]. D isthe damping term. The interaction with the external laser

Proceedings of FEL 2007, Novosibirsk, Russia

induces a maximum energy exchange of [20]:2πKN λ0(J0 (ξ) − J0 (ξ)) aLas
γλLas

105

(3)

where K is the deflexion parameter, N the number of undulator periods, λ0 the undulator period, aLas is the peakdimensionless potential vector of the laser electric field,
λLas = 2πc/ωLas its wavelength, γ the Lorentz factor, c
K2
the light speed, J the Bessel function and ξ = 4(1+K
2 /2) .
thSince the electric field experienced by the j electron depends on its relative position τn,j and phase Φj , the laser
induced energy change is:
2
τn,j
∆γmax
exp(− 2 ) sin(ωLas τn,j + Φj )
γ
2σLas
(4)
with σLas the laser pulse duration. This term is set to zeroif nT0 is not a multiple of the laser period. Finally, the RF
system provides an energy VRF,n,j to compensate the total
losses and ensure equilibrium.
Thanks to this model, simulation of the electron bunch
distribution evolution are performed, and compared to experimental results.

Wmod,n,j =BEAM HEATING
Streak camera
SR
Bending magnet(B7)

RF cavity
UVSOR-II
Storage Ring

Bunch length (ps-rms)∆γmax =

TUPPH008

100

95

90

85
0

200

400
Time (ms)

600

800

Figure 2: Bunch length measured with the streak camera.
Continuous line: a mechanical light chopper at 2 Hz enables periodic laser injection (the laser is seeded during 250
ms at frep = 1 kHz, and then cut off during the following
250 ms). Dotted line: laser OFF. I = 4.8 mA. The natural
bunch length at low current of this measurement is higher
than expected because the RF cavity electric field was not
optimised. Data are smoothed.
Table 1: Parameters for CHG operation at UVSOR-II.
SymbolValue
Electron beam
Energy (MeV)
RF frequency (MHz)RF voltage (kV)
Number of stored bunches
Period of revolution (ns)
Momentum compaction factor
Synchrotron frequency (kHz)Damping time (ms)Natural energy spread (10−4 )

E
fRF
VRF
nb
T0
α
fS
τS
σγ

600
90.1
94
1
178
0.028
19.4
20
3.4

N
λ0
Ld
K

9
11
33
6.06

P
σLas
frep
λLas

1.5
1.2
50 - 1000
800

Optical Klystron
Optical klystron
CHG
Seeding Laser

Figure 1: General scheme of the experimental setup for
CHG experiment on UVSOR-II storage ring. A Ti:Sa laser
is focussed inside the first part of the optical klystron. Coherent radiation (CHG) is collected at the output of the optical klystron and Synchrotron Radiation (SR) at the ouptut of B7 bending magnet for electron bunch profile measurements with a streak camera (Hamamatsu, C5680). Indeed, the distribution of the synchrotron radiation pulse isa replica of the electronic distribution.
The CHG experiments were performed on UVSORII [21] storage ring. A general scheme is given in Fig. 1,
and the main parameters of the electron beam and laser are
summarized in table 1. The intense Ti:Sa laser is focussed
inside the modulator onto the electron beam. Using a mechanical light chopper, the laser is alternatively switched
ON and OFF. The results are given in Fig. 2. This alternative injection drives clear oscillations of the bunch length

Number of periods
Spatial period (cm)Dispersive section length (cm)Deflection parameter
Laser
Average power (W)Pulse duration (ps-fwhm)
Repetition rate (Hz)Wavelength (nm)at the laser injection frequency. Indeed, since bunch length
can be assumed proportionnal to energy spread (operating
at low current in potential well distorsion regime [22]), thebunch lengthening can be correlated to a heating of the distribution. When seeding is enabled (laser ON), the bunch
length increases via laser heating (by 12 %); when seeding
is disabled, the bunch length decreases back to the laser
OFF value through the synchrotron damping process.

Storage Ring FELs

237

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Proceedings of FEL 2007, Novosibirsk, Russia

The longitudinal profile of the electron beam is thenrecorded with continuous seeding at 1 kHz, a standard
CHG operation. At 1 mA, an increase by 12 % is measured(from 83 to 93 ps-rms), in agreement with the results ofFig. 2. The model reproduces the bunch length laser OFF
at zero current, i.e. 80 ps-rms. In CHG operation (using
P =1 W, frep =1 kHz and σLas =1.2 ps-fwhm), it leads to abunch lengthening up to 107 ps-rms, a value slighlty higher
than the experimental one probably because of non perfectsynchronisation and alignment in the experiment.
Using 100 Hz repetition rate, still with 0.15 W seeding
power, bunch lengthening could no longer be detected experimentally. Indeed, the simulated bunch length at 100 Hz
repetition rate (and 0.1 W seeding power) only rises by 3.5
ps-rms, the limit of the experimental detection.
The simulations are found in good qualitative agreementwith the experimental results, allowing further dynamical
studies.

BEAM HEATING DYNAMICS
92

(a)

88

at 1 kHz.
Once saturation is reached, the electronic distribution reveals a double oscillating time structure. After each laser
injection, the bunch length suddenly increases, and thenslowly decreases back to its value before previous injection: the bunch length oscillates at the laser repetition rate.
In addition, all along CHG operation, synchrotron motion
drives fast oscillations of the distribution at the synchrotron
frequency.
Three levels of dynamics are found in the evolution of
the electronic distribution. When the laser is injected, theelectronic distribution responds to the laser periodic excitation by transiting to a pseudo equilibrium state. Once atsaturation, the distribution oscillates at the laser repetition
rate, refreshing in between two injections, and at the synchrotron frequency. The refreshment compensates the periodic bunch heating and allows to maintain equilibrium. In
addition, the final heated state depends on the initial electron beam quality, but can also be tuned using, for instance,
the seeding laser repetition rate. The bunch heating, i.e. energy spread can be controlled. This is of high interest since
the coherent output power strongly depends on the energy
spread at interaction [23, 24].

Bunch length (ps-rms)

84

LOCAL BEAM HEATING

80

(b)

100
95
90
85
80
110

(c)

100
90
80
0

10

20

30

40

Time (ms)Figure 3: Bunch length evolution from laser OFF to stable CHG operation. (a) frep =100 Hz, T90% ≈ 20 ms, (b)frep =500 Hz, T90% =18 ms, (c) frep =1 kHz, T90% =14
ms. Simulation with 15000 particules and the parametersof table 1. T90% is the time to reach 90% of the bunch
length at saturation.
Simulation of Fig. 3 investigates the evolution of theelectron beam from laser OFF initial state, to CHG operation state. When seeding is switched on, the average bunch
length gradually increases, performing oscillations at thelaser repetition rate, until a saturation is reached: the average bunch length becomes constant.
Whatever the simulated repetition rate, the rising time
to saturation remains below 25 ms. An upper limit of therising time of 100 ms is found using the mechanical chopper (see Fig. 2). A precise measurement would require afast shutter (to be able to neglect rising of the seeding average power) synchronised with the streak camera acquisition. The simulated rising time decreases with frep (seeFig. 3): it is 20 ms at 100 Hz, 18 ms at 500 Hz and 14 ms
Storage Ring FELs

238

We now investigate on the local aspect of the electronphoton interaction, since the seeding laser pulse is shorterby nearly two orders of magnitude than the electron bunch.
The profiles in CHG operation are simulated, and a typical example is given in fig. 4. Initially, laser is OFF andthe distribution starts from Gaussian shape (a). The first
injection of the laser causes a local distorsion in the centerof the distribution (b): a hole appears one turn after injection and remains only for a few turns (few tens of µs). The
edges of the distribution are not yet affected. Once saturation is reached (less than 25 ms later), each laser injection
still induces a hole remaining just for a few turns (d), but
the diffusion of the heated electrons causes a flattening of
the whole distribution, and a density displacement towards
the edges (c). The laser induces a local density defect in
the profile, which vanishes in between two laser injections.
The electron beam phase space can be recontructed [25]in two dimensions given by the electronic density N (τ ) and
its derivative. In the phase space, a defect in the profile, as
for instance a hole, will correspond to a large amplitude
oscillation Ahole .
Ahole reduces with the repetition rate. The hole canno longer be detected at repetition rate higher than 5 kHz(and P =5W, σLas =1.2 ps-fwhm). The heated particules are
diffused [13] over the whole bunch, causing strong bunch
lengthening. Ahole increases with the pulse duration (atgiven repetition rate and peak power). The digged holegets wider, still vanishing after a few turns, which eases
the diffusion towards edges and causes bunch lengthening.
The laser induces a local distorsion in the distribution atProceedings of FEL 2007, Novosibirsk, Russia

REFERENCES

120

Number of electrons

b

a

100

[1] K. Holldack, S. Khan, R. Mitzner and Quast T., Phys. Rev.
Lett. 96 (2006), 054801.

d

c

80

TUPPH008[2] R.W.Schoenlein, S. Chattopadhyay, H.H.W. Chong, T.E.
Glover, P.A. Heimann, C.V.Shank, A.A. Zholents and M.S.
Zolotorev, Science 287 (2000), 2237.

60
40
20
0
-200

-100

0
Time (ps)

100

200

Figure 4: Simulated longitudinal profiles: (a) Laser OFF
profile, (b) Profile two turns after first laser injection, (c)Profile in saturated regime 2 turns before a laser injection,(d) Profile in saturated regime two turns after a laser injection. Simulation parameters: frep =1 kHz, 4 W average
power, 4.8 ps-fwhm pulse duration for the laser (optimised
to produce a net hole in the distribution), 15000 particules,
and other parameters of table 1
each injection which, thanks to a fast diffusion, disappears
before next injection: even at saturation, the laser does notexperience local density defect. On the other hand, this diffusion increases the bunch length and consequently reduces
the electronic density all along the distribution. These local
dynamics studies reveal that the tunability of the externallaser parameters (frep , P and σLas ) offers attractive perspectives of adjusting beam heating and consequently CHG
ouptut power with possible optimisation between peak andaverage output power.

CONCLUSION
Electron dynamical response to an external short duration and intense laser has been investigated. Thanks tosimulations found in agreement with experimental results
obtained on UVSOR-II CHG FEL, we observed that theseeding of the laser causes -via bunch heating- a transition towards a saturated regime with double frequency oscillating structure (at the laser repetition rate and at thesynchrotron frequencies). The bunch heating, and consequently the equilibrium state at saturation, can be adjusted
using the laser parameters. This opens perpsectives to optimisation of the output radiation, especially in terms ofpeak or average power. While those results were obtainedin CHG FEL configuration, they can be easily extended toany scheme involving interaction between intense electricfield and stored electron beam.

ACKNOWLEDGMENTS
The authors would like to thank X. Epiard, J. Yamazaki,
S. Bielawski, C. Szwaj. A part of this work was supported
by Grant-Aid for Scientific Research of the JSPS and by
International Collaboration Program of IMS.

[3] A. A. Zholents and M. S. Zolotorev, Phys. Rev. Lett. 76(1996), 912.
[4] R. R. Freeman and B. M. Kincaid, AIP Conference Proceedings 119 (1984), p.277-292.
[5] R.Coisson and F. De Martini, Phys. of Quant. Electron. 9(1982) 939.
[6] R.Prazeres, J.M. Ortega, C. Bazin, M. Bergher, M. Billardon, M.E. Couprie, M. Velghe and Y. Petroff, Nucl. Instrum.
Methods Phys. Res. A 272 (1988), p.68-72.
[7] L.H. Yu et al., Phys. Rev. A 44 (1991) 5178.
[8] J.M.J. Madey, Nuovo Cimento Soc. Ital. Fis. 50 B (1979)
64.
[9] G. Dattoli and A. Renieri, Nuovo Cimento Soc. Ital. Fis. 59
B (1980) 1.
[10] Robinson K.E., Dissertation of the Stanford University,(1984).
[11] M.E. Couprie and P. Elleaume, Nucl. Inst. Meth. A 237(1987) 77-82.
[12] G.L. Orlandi, C. Bruni, D. Garzella, M.E. Couprie, C.
Thomas, R. Bartolini, C. Rippon and G. Dattoli, Phys. Rev.
ST. 7 (2004) 060701.
[13] G. De Ninno, M.E. Couprie, D. Nutarelli, D. Garzella, E.
Renault and M. Billardon, Phys. Rev. E 64 (2001) 026502.
[14] M. Billardon, D. Garzella and M. E. Couprie, Phys. Rev.
Lett. 69 (1992) 2368.
[15] Litvinenko V.N. and Burnham B. and Madey J.M.J. and Wu
Y., Nucl. Inst. Meth. Phys. Res. A 358 (1995) 334-337.
[16] I.V. Pinayev, V.N. Litvinenko, K. Chalut, E.C. Longhi and S.
Roychowdhurry, Nucl. Inst. Meth. Phys. Res. A 528 (2004)
283-286.
[17] R. Roux and M. Billardon, Nuovo Cimento Soc. Ital. Fis. A
112 (1999) 513.
[18] M. Sands, SLAC Report No. 121 (1970).
[19] J.M.Ortega, Cours de DEA, Rayonnement des onduleurs,
Universit d’Orsay, Paris XI (2004).
[20] L.H. Yu and J. Wu, Nucl. Inst. Meth. Phys. Rev. A 483(2002) 493-498.
[21] M. Katoh et al., Proceedings of the AIP’04 Conference 708(2004), p.49-52.
[22] G. Dattoli, L. Mezi, M. Migliorati, A. Renieri, M.E. Couprie, D. Garzella, D.Nutarelli, C. Thomas, G. DeNinno and
R. Walker, Nucl. Inst. and Meth. A 471 (2001) 403.
[23] R. Prazeres, PhD. Thesis, University of Paris XI, Orsay(1988) Chap.2-3, p.27-71.
[24] J. Wu and L. H. Yu, SLAC-PUB (2004) 10494.
[25] J.D.Farmer, Chaotic attractors of an infinite-dimensional dynamical system, Physica 4D (1982), p.366.

Storage Ring FELs

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Proceedings of FEL 2007, Novosibirsk, Russia

ANALYTICAL STUDIES OF TRANSVERSE COHERENCE PROPERTIES
OF X-RAY FELS
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron , DESY, Hamburg, Germany
EIGENVALUE EQUATION

Abstract
The explicit solution of the initial value problem for a
SASE FEL operating with a large ratio of electron beamemittance to the wavelength, ˆ = 2π/λ  1, is presented.
The degree of transverse coherence is explicitly calculated,too. It is shown to be dependent on the ratio of the numberof FEL gain lengths to the parameter ˆ. In particular, in themulti-mode limit the radiation from a SASE FEL has by
the squared number of gain lengths higher degree of transverse coherence than a synchrotron radiation generated bya beam with the same emittance.

INTRODUCTION
Free electron lasing at wavelengths shorter than ultraviolet can be achieved with a single-pass, high-gain FEL
amplifier. Due to a lack of powerful, coherent seeding
sources short-wavelength FEL amplifiers work in so called
Self-Amplified Spontaneous Emission (SASE) mode when
amplification process starts from shot noise in the electron
beam [1, 2, 3]. The first VUV FEL user facility FLASH(”F”ree-Electron-”LAS”er in ”H”amburg) [4, 5] operates
in SASE mode and produces GW-level, laser-like radiation
pulses with 10 to 50 fs duration in the wavelength range
13-45 nm. Present level of accelerator and FEL techniques
holds potential for SASE FELs to generate wavelengths asshort as 0.1 nm [6, 7, 8].
The condition ˆ < 1/2 is often formulated as necessary
one for an optimal design of a SASE FEL. It is meant that
under this condition the radiation from SASE FEL has afull transverse coherence. However, as it is shown in [9],the maximal degree of transverse coherence (and brilliance
as well) is achieved at ˆ  1. For smaller emittances thedegree of transverse coherence decreases due to the effectdiscovered in [10]. Moreover, the above mentioned condition is strongly violated in the project parameters of hard
X-ray FELs [6, 7, 8]: there the parameter ˆ is in the range 25. Even without discussing exotic proposals [11, 12], one
can notice a general trend towards lower energies of theelectron beam, i.e. cost-saving solutions. Since achievablenormalized emittance γ is limited by beam physics andtechnology issues, this would lead to a further increase of
ˆ. Thus, theoretical understanding of properties of a SASE
FEL, operating in this regime, becomes practically important. In this paper we present the main results of the theoretical analysis performed in Ref. [13] dealing with thelimit ˆ  1.
X-ray FELs

240

Let us have at the undulator entrance a continuous electron beam with the current I0 , with the Gaussian distribution in energy



−1/2
(E − E0 )2,
exp −F (E − E0 ) = 2π(ΔE)2 
2(ΔE)2 (1)and in a transverse phase plane

x2 + (x )2 /kβ2
f (x, x ) = (2πσ 2 kβ )−1 exp −
2σ 2


,

(2)

the same in y phase plane. Here kβ =√1/β is the wavenumber of betatron oscillations and σ = β.
Using cylindrical coordinates, in the high-gain limit weseek the solution for a slowly varying complex amplitudeof the electric field of the electromagnetic wave in the form
[14]:Ẽ(z, r, ϕ) ∝ Φnm (r) exp(Λz)e± i nϕ ,(3)where n is an integer, n ≥ 0. For each n > 0 there are
two orthogonal azimuthal modes and many radial modes
that differ by eigenvalue Λ and eigenfunction Φnm (r). The
integro-differential equation for radiation field eigenmodes[15, 16, 17] can be written in the following normalized
form:
 2
n2
1 d
d
− 2 + 2 i B Λ̂ Φnm (r̂) =+2r̂ d r̂
r̂
d r̂
∞

−4
0
∞

 



d r̂ r̂ Φnm (r̂ )Λ̂2T ξ 2× dξ 2− (Λ̂ + i Ĉ)ξexp −2
sin (k̂β ξ)0(1 − i B k̂β2 ξ/2)(r̂2 + r̂2 )× exp −
sin2 (k̂β ξ)
2(1 − i B k̂β2 ξ/2)r̂r̂ cos(k̂β ξ)
,
(4)
×In
sin2 (k̂β ξ)ξwhere In is the modified Bessel function of the firstkind. The following
notations are used here: Λ̂ = Λ/Γ,√r̂ = r/(σ 2), B = 2σ 2 Γω/c is the diffraction parameter, k̂β = kβ /Γ is the betatron motion parameter,Proceedings of FEL 2007, Novosibirsk, Russia
Λ̂2T = (ΔE)2 /(ρ̄2 E 2 ) is the energy spread parameter, Ĉ = kw − ω/(2cγz2 ) /Γ is the detuning parame−1 1/2
ter, Γ = A2JJ I0 ω 2 θs2 IA c2 γz2 γ
is the gain factor, ρ̄ = cγz2 Γ/ω is the efficiency parameter, ω is thefrequency of the electromagnetic wave, θs = Krms /γ,
Krms is the rms undulator parameter, γ is relativistic factor,
γz−2 = γ −2 +θs2 , kw is the undulator wavenumber, IA = 17
kA is the Alfven current, AJJ = 1 for helical undulator and2222/2(1 + Krms)) − J1 (Krms/2(1 + Krms))
AJJ = J0 (Krmsfor planar undulator. Here J0 and J1 are the Bessel functions of the first kind. Note that the efficiency parameter ρ̄is related to the corresponding parameter ρ [18] of the onedimensional model as follows: ρ̄ = ρB 1/3 . The equation(4) can be reduced to the integral equation by means of the
Hankel transformation [17] and then solved numerically.
Effects of emittance play the dominant role in X-ray
FELs. In this paper we will mainly concentrate on the casewhen beta-function is optimized for the highest FEL gain
as it happens in practice. Since diffraction parameter depends on beta-function, it is more convenient to go overto the normalized parameters other then those introduced
above. Indeed, diffraction parameter can be rewritten as
B = 2ˆ
/k̂β , where ˆ = 2π/λ. Then we can go from parameters (B, k̂β ) to (ˆ, k̂β ). In the following we will consider the case when ˆ  1, the energy spread effect can beneglected, and the beta-function is optimized for the maximum growth rate. We apply the variational method [17, 19]
to the Eq. (4) with the trial functions [13]
Φnm (r̂) = r̂n exp(−ar̂2 )Lnm (2ar̂2 ) ,(5)where Lnm are assotiated Laguerre polynomials. Solving
the obtained equations [13], we find the zeroth-order eigenvalueΛ̂0 

0.3695 + 0.2735 iˆ(6)

for the optimal betatron wavenumber k̂β  0.503/ˆ
2 andat the optimal detuning Ĉ0  0.391/ˆ. The diffraction
parameter for this operating point is B  3.98 ˆ3 . Then wefind [13] the next order correction (in ˆ−1 ) to the eigenvalueΛ̂nm  Λ̂0 −(1 + n + 2m)(0.3080 + 0.0988 i)
,
ˆ2

(7)

TUPPH011

Concluding this section, we should analyze some scaling relations. The FEL gain length in the case under consideration scales as Lg = (Re Λ̂0 Γ)−1 ∝ ˆ/Γ, while thebeta-function as β = kβ−1 ∝ ˆ2 /Γ. In other words, the betatron phase advance per gain length, kβ Lg , is of the orderof ˆ−1 . The size of a radiation mode scales as ˆ−1/2 , and atypical change of transverse coordinates of particles during
the passage of one gain length as ˆ−1 in units of the electron beam size. The rms size of the intensity distribution ofa fundamental mode (with n = m= 0) can be expressed indimensional units as σrad  1.07 βλ/(2π)  0.92 Lg
for the optimal beta-function.

INITIAL VALUE PROBLEM
The solution of initial value problem for a SASE FEL
with a parallel electron beam, accounting for diffraction effects, was obtained in [15, 20]. Initial value problem, that
also includes emittance effect, was solved in [21, 22, 23]
in a general form and then approximated in single-mode
limit. Here we present an explicit solution [13] for a large
emittance, ˆ  1, and the optimal (for the growth rate)2 . The normalized output power
focusing, k̂β  0.503/ˆ
(normalized FEL efficiency) in high-gain linear regime canbe expressed as [13]:0.0755 exp(2Ng )ηρ̄Nc ˆ2 Ng [f (Ng /ˆ) − 1]η̂ =(9)where η is the ratio of the radiation power to the electron is the number ofbeam power, Ng = Re Λ̂0 ẑ = 0.3695ẑ/ˆ
field gain lengths within a given undulator length, ẑ = Γz,
Nc = I/(eω ρ̄), and the function f is given byNg= 0.419 cosh 1.667
ˆ


Ng
.
+0.581 cos 0.535
ˆ


f

Ng
ˆ



(10)

Note that parameter ρ̄ for the given operating point is related to the corresponding one-dimensional parameter [18]as ρ̄ = B 1/3 ρ  1.58ˆ
ρ.
The expression (9) is valid when ˆ  1 and Ng  1,
 may take any value1 . In particular, for abut the ratio Ng /ˆ
sufficiently long undulator, Ng  ˆ  1, the fundamental TEM00 gives the dominating contribution to the total
power. In this case Eq. (9) reads

and the mode parametera  (0.4355 − 0.5123 i)ˆ
.

(8)Eqs. (5), (7) and (8) are the solutions for field distributions and growth rates of eigenmodes of a high-gain FEL
with optimized beta-function in the limit ˆ  1. We compared these asymptotical solutions with the exact solution[17] at the optimal detuning for different modes and founda good agreement for ˆ  1.

0.360
exp [2Ng (1 − 0.834/ˆ)]Nc ˆ2 Ng
0.36

exp(2Ng00 ) ,(11)
Nc ˆ2 Ng00η̂ 

1 In practice the maximal value of N is limited by saturation effectsgthat are not considered in the linear theory presented here. For any reasonable set of parameters Ng < 10 in linear regime of SASE FEL operation.

X-ray FELs241

TUPPH011

Proceedings of FEL 2007, Novosibirsk, Russia

where Ng00  Ng is the number of field gain lengths for
the TEM00 mode. This solution is identical to that given
in [23], taken in the limit ˆ  1 with the optimal betafunction, and integrated over FEL frequency band. Now
let us consider the multi-mode limit, ˆ  Ng  1. In thiscase the radiation power (9) is expressed as
0.151

η̂ 

5/2

Nc N gexp(2Ng ) .

(12)

Relative partial contributions to the total power of modes
with an azimuthal index n can be calculated as follows
[13]:

p0 =

f −1
f +1

√
2 f −1pn = √
f + 1(f + f 2 − 1)nf or n = 0(13)

f or n > 0(14)

For n > 0 we consider the sum of the contributions of
the two independently excited azimuthal modes with theangular dependence exp(± i nϕ). The contribution of theazimuthal-symmetric mode goes pretty linearly for Ng <ˆ:
Ngp0  0.5
ˆand asymptotically approaches unity when Ng  ˆ. Other
modes have maxima of which locations can be found fromthe equation

f

Ng
ˆ

√


=

n2 + 1n.

f or n > 0(15)

For instance, a possible contribution is limited by 34.3% for
n = 1, by 18.0% for n = 2, etc. For large n a maximum
  n−1 and takes the value max(pn ) is located at Ng /ˆ
−1(ne) , e being the base of natural logarithm.
Especially simple relation for the partial contributionsof azimuthal modes can be deduced for the point wherep0 = p1 . There we have:
p0 =

1
,
3

pn =

1
2n−1 3.

(16)

Note that the results (15) and (16) are universal since they
do not depend on a specific choice of the function f .
X-ray FELs

242

The definition of a degree of transverse coherence wasintroduced in [9]:

|γ1 (r⊥ , r ⊥ )|2 I(r⊥ )I(r ⊥ ) d r⊥ d r ⊥.
[ I(r⊥ ) d r⊥ ]2(17)
where I(r⊥ ) = |Ẽ(r⊥ )|2 is the radiation intensity,ζ=

γ1 (r⊥ , r ⊥ ) =Ẽ(r⊥ )Ẽ ∗ (r ⊥ )

1/2

(18)

|Ẽ(r⊥ )|2 |Ẽ(r ⊥ )|2 is the transverse correlation function, Ẽ is the slowly varying amplitude of the electromagnetic wave, and < ... >means ensemble average. The definition (17) is valid forany stationary (or quasi-stationary [14, 24]) random process, in particular for the radiation from a SASE FEL witha long electron bunch [14] operating in linear and nonlinear
regimes.
The radiation of a SASE FEL, operating in the linear
regime, holds properties of a completely chaotic polarized
light [14, 24]. In this case, as it was shown in [9], the definition (17) is equivalent to that given by the variance of theinstantaneous power [10, 14]:
< (P − < P >)2 >,(19)
ζ = σP2 =< P >2
where P = I(r⊥ )dr⊥ . The degree of transverse coherence ζ can be thought of as an inverse number of transverse
modes [9, 10, 14]:ζ=Maximal partial contribution of n−th azimuthal mode in
linear regime of SASE FEL operation is given by√
2nn ( n2 + 1 − n)max(pn ) = √( n2 + 1 + 1)n

DEGREE OF TRANSVERSE COHERENCE

1
.
MT

(20)

However, the definitions (17) and (19) cannot be directly
used for the purpose of this paper, namely for analytical calculations of the degree of transverse coherence of a
SASE FEL. Nevertheless, analyzing the results of numerical simulations in Ref. [9], we found out that the degreeof transverse coherence according to the definition (17) is
well approximated by the squared partial contribution of
azimuthal-symmetric mode:ζ  p20 .

(21)

Accuracy of this approximation is connected with the residual effect [10] on transverse coherence originated from thefinite frequency bandwidth of a SASE FEL. Indeed, for a
sufficiently long undulator the only fundamental TEM00
mode survives (other modes are exponentially suppressed),i.e. perfect transverse coherence would be achieved for a
monochromatic wave. However, the amplitude and phase
distributions of this mode change within the FEL bandwidth. As a result, the degree of transverse coherence approaches unity as [10]: 1 − ζ  δr /Ng but not exponentially as in (21). A numerical factor δr is of the order ofProceedings of FEL 2007, Novosibirsk, Russia

TUPPH011

accepted in this paper) for the case of the optimal betafunction. Note that in the case of synchrotron radiation foran axisymmetric beam one would have in the limit ˆ  1
2
for optimal focusing: ζ = 1/MT  (λ/4π) . Thus, theradiation from a SASE FEL has Ng2 higher degree of transverse coherence in this limit.
The asymptotes (24) and (25) are plotted in Fig. One < 1, andcan see that Eq. (25) is pretty accurate for Ng /ˆ > 3.
Eq. (24) - for Ng /ˆ
Finally, we present an estimate of the degree of transverse coherence at saturation for the case ˆ  Ng  1.
Number of gain lengths at the end of linear regime (where
the formation of transverse coherence stops) can be esti). Thus, using (25) we get:mated [13] as Ng  12 ln(Nc /ˆ
Figure 1: Degree of transverse coherence versus parameter
. The asymptotes (24) and (25) are shown as dot andNg /ˆ
dash lines, respectively.
one for ˆ  1 [9] and strongly increases in the limit ofsmall electron beam size. However, for considered herecase ˆ  1 we have found analytically [13] that δr  0.026
for the optimal beta-function:
ζ 1−

(22)

i.e. this effect is negligible for large Ng . We have seen fromnumerical simulations [9] that the relative difference between (17) and (21) is indeed very small for large ˆ and Ng
in both linear and nonlinear regimes. Thus, despite the definition (21) was introduced heuristically, it is sufficiently
accurate and adequate for our purposes. We rewrite it, using (13), in a more explicit form
f −1
.
(23)
f +1
The plot of the degree of transverse coherence versus
 for the function f from (10) is presented in Fig 1.
Ng /ˆ
For Ng  ˆ  1 the degree of transverse coherence isclose to one:
ζ



Ng
2
,
ζ  1 −  1 − 9.54 exp −1.667
f
ˆ

(24)

Ng
ˆ

2
.

(27)

REFERENCES[1] A.M. Kondratenko
10(1980)207.

and

E.L.

Saldin,Part.

Accelerators[2] Ya.S. Derbenev, A.M. Kondratenko and E.L. Saldin, Nucl. Instrum.
and Methods 193(1982)415.
[3] J.B. Murphy and C. Pellegrini, Nucl. Instrum. and Methods A
237(1985)159.

,[5] W. Ackermann et al., Nature Photonics 1(2007)336[6] M. Altarelli et al. (Eds.), XFEL: The European X-Ray FreeElectron Laser. Technical Design Report, Preprint DESY 2006-097,
DESY, Hamburg, 2006 (see also http://xfel.desy.de).
[7] J. Arthur et al., Linac Coherent Light Source (LCLS). Conceptual
Design Report, SLAC- R593, Stanford, 2002 (see also http://wwwssrl.slac.stanford.edu/lcls/cdr.
[8] SCSS X-FEL: Conceptual design report, RIKEN, Japan, May 2005.
(see also http://www-xfel.spring8.or.jp).
[9] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, ”Coherence
Properties of the Radiation from X-ray Free Electron Laser”, DESY
report DESY-06-137, August 2006; submitted to Opt. Commun.
[10] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt. Commun.
186(2000)185[11] F. Gruener et al., Appl. Phys. B86(2007)431[12] A. Bacci et al., Phys. Rev. ST Accel. Beams 9(2006)060704[13] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, ”Analytical Description of Coherent Properties of X-ray Free Electron Lasers”, tobe published[14] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, “The Physics ofFree Electron Lasers”, Springer, Berlin, 1999[16] L.H. Yu and S. Krinsky, Physics Lett. A129(1988)463[17] M. Xie, Nucl. Instrum. and Methods A445(2000)59[18] R. Bonifacio, C. Pellegrini and L.M. Narducci, Opt. Comm.
50(1984)373

2
(25)

or, in dimensional units
1

ζ=
MT



ln(Nc /ˆ)4ˆ[15] K.J. Kim, Phys. Rev. Lett. 57(1986)1871

but one should keep in mind the residual effect (22). In thelimit ˆ  Ng  1 we get[4] V. Ayvazyan et al., Eur. Phys. J. D 37(2006)297.

0.026
,
Ng

1
ζ=
 0.25MTζsat[19] M. Xie and D. Deacon,
A250(1986)426

Nucl. Instrum. and Methods[20] S. Krinsky and L.H. Yu, Phys. Rev. A35(1987)3406



λNg
4π

2

[21] Z. Huang and K.J. Kim, Phys. Rev. E62(2000)7295

.

(26)

Amazingly, a numerical factor in front of the last expression is equal to one (with the accuracy of the order of 10−3 ,[22] M. Xie, Nucl. Instrum. and Methods A475(2001)51[23] Z. Huang and K.J. Kim, Nucl. Instrum. and Methods A475(2001)59[24] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Opt. Commun.
148(1998)383

X-ray FELs

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Proceedings of FEL 2007, Novosibirsk, Russia

COMPACT X-RAY FREE ELECTRON LASE BASED ON AN
OPTICAL UNDULATOR
C. Maroli, V. Petrillo, Dipartimento di Fisica dell’Università di Milano-INFN Sezione di
Milano Via Caloria,16, 20133 Milano, Italy
L. Serafini, A. Bacci, A Rossi, P. Tomassini, INFN-Sezione di Milano, Via Celoria,16, 20133
Milano, Italy
Abstract
The interaction between a very high-brilliance electron
beams and a relativistically intense counter-propagating
laser pulses produces X rays via FEL collective
amplification. The phenomenon is, however, very
selective, so that the characteristics of both electron andlaser beam must satisfy tight requirements in terms ofbeam current, emittance, energy spread and laser
amplitude stability within the pulse.
The threedimensional equations governing the radiation
phenomenon have been studied in both linear and non
linear regime and solved numerically for the particularinteresting values of wavelengths of 1 Ang, 1nm and 12
nm. The performance of the collective Thomson source
has been compared with that of an equivalent static
undulator.

INTRODUCTION
The collective effects that develop in the classicalThomson back-scattering give rise to intense X-ray pulses
easily tunable and highly monochromatic at a level a few
orders of magnitude larger than the incoherent radiation.
Due to recent technological developments in the
production of high brilliance electron beams and highpower CPA laser pulses, it is now even conceivable to
make steps toward their practical realisation.
The phenomenon of the impact between the electron
beam and the laser pulse has characteristics similar to thefree electron laser and has been studied in previous
papers[1-2]. The lasing is rather difficult to start up andthe power saturation level is lower than that achieved inconventional static wigglers. It is however large enoughto be interesting for application as fast probing forchemical process, monochromatic X imaging, phase
contrast imaging, deep probing for inertial fusion
research, considering moreover the fact that this kind of
set-up is compact and considerably less expensive thanstatic FEL.
In this paper we present several details about this X-ray
production phenomenon, analysing various beam lines
producing different electron bunches as well as various
situations relevant to the synchronization between theelectron beam and the laser pulse. Finally, we havecompared the results of the radiation levels obtained withour ‘ad hoc’ radiation code EURA (for Electromagnetic
Undulator Radiation Analysis) with those provided by thecode GENESIS 1.3 currently used in FEL simulations [3],X-ray FELs

244

which is however not presently able to model electromagnetic undulators. The answers given by both codes
are qualitatively similar and also the quantitative
estimates of saturation power and gain length are very
close, when magnetostatic undulators are considered.

NUMERICAL SOLUTION OF 3D
EQUATIONS
We have first studied the use of a CO2 laser ofwavelength λL=10 micron. High power lasers of thisfrequency are characterized by 70-100 GW of power and
up to 300 psec of time pulse length.
By fixing the mean energy of the electron beam aroundthe value <E>=30 MeV, i.e. <γ>=60, using the resonanceconditionfortheback-scattering
Thomson,
λR=λL(1+aL02)/4γ2 and assuming the laser parameteraL0 ≤ 0,5, X rays of wavelengths λR of the order of 7-9
Angstrom can be obtained. For this case, collective
effects and FEL instability develop when the beamtransverse normalized emittance does not exceed thevalue εx=0.5, and if the energy spread Δγ/γ is contained infew 10-4. Values of this kind are out of the current stateof-the-art of high–brightness beams but represent aninteresting challenge for a possible future operation
scenario.
Our numerical simulations for the case of theelectromagnetic undulator have been performed with the
3D code EURA, which is a three-dimensional, timedependent code that integrates equations (2-5) using aforth order Runge-Kutta method for the particles and an
explicit finite difference scheme for the radiation
equation. The bunching factor is calculated along thebeam by selecting, around each point, a moving portion of
the bunch including several buckets.
The data obtained with EURA for a static undulator havebeen compared with similar data produced with the code
GENESIS 1.3 widely used in the FEL analysis. The
comparison is presented in Fig 3 where data from EURA
(black curve (b)) and from GENESIS 1.3 time dependent(red curve (a)) are reported.
The data chosen for the comparison are: undulator
parameter aw=0.3, undulator period λw=10μm, radiation
wavelength λR=1.515 nm, εx=0.3 mm mrad, r.m.s.
transverse dimension σx=12.5 μm (corresponding to aProceedings of FEL 2007, Novosibirsk, Russia
maximum radius of 25 μm), a constant external magnetic
field. EURA simulates the entire bunch, which has beentaken 1 mm long, while GENESIS 1.3 simulates afraction of N=1000 slices of width λR, separated by
zsep=NsepλR with Nsep=20, corresponding to approximately
75 cooperation lengths.
We note that in both simulations with EURA and
GENESIS 1.3 it is very important to set the correct
detuning with respect to the nominal resonancefrequency, because otherwise the growth of the instability
is strongly damped. The computed gain lengths are of Lg=3,6 mm for EURA and Lg =4.08 mm for GENESIS 1.3,
while the analytical expressions by Ming Xie [3] give(1)
Lg=L1D(1+η)
with L1D, the one-dimensional gain length, estimatednumerically as about 1.97 mm,
η=(0.45η

0.57
d

1.6

+0.55η

2+3η +…)
γ

ε

(2)

and:

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7

10

6

10

(b)

5

(a)

10

P

4

10

3

10

2

10

1

10

0,00

0,01

0,02

0,03

0,04

0,05

z

Fig 1: Radiated power P in Watt versus z coordinate inmeter for (a) simulations made with GENESIS 1.3 and (b)with EURA for aw=0.3, λw=10 μm, λR=1.515 nm, εx=0.3
mm mrad, σx=12.5 μm (corresponding to a maximum
radius of 25 μm), a constant external static magnetic field.

2

η =L λR/(4πσ )
d

1D

(3)

x

2

ηε= L 2πε1D,x2/(γ2σx λR)(4)

ηγ= 4π L (δγ/γ)/λ .
(5)1Dw
It can be seen that for the case analysed ηd is about 1,510-3 , η =0.24, negligible respect to η which in this caseγεcan be evaluated through (24) as η =1.31 yielding on theεwhole to L =3,96 mm.
g

As shown in fig 3, EURA gives a gain length slightly
shorter than GENESIS 1.3, with a faster saturation, but ata smaller power level. Other characteristics are an initial
growth in the first gain length less steep and stronger
post-saturation power oscillations due probably to a
deeper entrapment of the particles. A zero-ordercomparison on the time independent behaviour isimpossible, because EURA is, for its nature, only timedependent. The scenario is similar to that pointed out in
the GENESIS 1.3 versus GINGER comparison [4,5].
Other data relevant to the analysis made with GENESIS
1.3 are reported in Fig 2 where the signal on the bunch at
z=3 cm is presented.
In fig 3 the radiation obtained with a conventional static
undulator (already presented in fig 3) has been plotted
together with the case of an electromagnetic wiggler of
equal intensity and wavelength, in the case of aw=aL0=0.3,
λw=λL=10 μm, εx=0.3 mm mrad, σx=12.5 μm(corresponding to a maximum radius of 25 μm).The
differences introduced by the resonance condition lead,
however, to a radiation wavelength smaller than a factorof two respect to the static undulator, so that, for theelectromagnetic undulator, λR=0.7578 nm. The
simulations show that the electromagnetic undulator
produces a power saturation value of 1.93 MW in lessthan 2.5 cm, with an average gain length of about 1.8 mm,
while the static undulator reaches 1.33 MW of power inabout 3 cm, with a gain length near to 3.5 mm.

Fig 2: Radiated power P (in Watt) versus the coordinate
along the bunch s (in microns) at z=3 cm and for the samecase as fig 5. Simulation made with GENESIS 1.3

In fig 4 a case analogous to fig 3 is presented, but theemittance value, that in this case has been increased to
0.6. In this case the power level achieved byelectromagnetic and static undulators are respectively
0.36 MW and 0.26 MW, with gain lengths of respectively
2.9 and 5.08 mm. In Fig 5 a summary of data is presented
showing the gain lengths ((a) and (b)) deduced by a fittingof the numeral data (on the left scale) and the saturation
radiation intensity ((c) and (d)) (on the right scale) for
both electromagnetic (in blue) and static (in black)undulators. A case particularly important for its
applications is the production of radiation characterized
by wavelength λR of about 1 Angstrom. . This value canbe reached with a Ti:Sa laser with λL=0.8 μm, aL0=0.8,<γ>=55, Lb=300 μm, rb=7 μm, a total charge of 3 nC, fora current of 3 KA.

X-ray FELs

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TUPPH012
10

Proceedings of FEL 2007, Novosibirsk, Russia(c)) are presented in Fig 6, where the power obtained in
Watt is plotted versus z (in meter).

6

(b)

1

1 ⎛ ω a ⎞3
The factor ρ = ⎜⎜ b L20 ⎟⎟γ ⎝ 16ω L ⎠
2

10

4

10

2

(a)

P

0

10
0,00

0,01

0,02
z

0,03

0,04

Fig 3: Radiated power P (in Watt) vs z (in meter) for (a)static undulator and (b) electromagnetic undulat
aw=0.3, λw=10 μm, εx=0.3 mm mrad, σx=12.5 μm
or.
(corresponding to a maximum radius of 25 μm).For thestatic undulator λR =1.515 nm, while for the e.m.
undulator λR =0.7578.
10

6

(b)
10

4

10

2

10

0

(a)

P

-2

10
0,00

0,01

0,02

0,03

0,04

z

2

(ωb being the plasma

frequency of the beam and ωL the laser frequency) is 4.17
10-4 and the radiation wavelength is λR =1.13 A. In thiscase we are at the limit of validity of the classical model,
because the quantum factor q is 0.9, and quantum effects,
arising when q>1, can play an important role [7,8].
However, the previous condition on q relies on onedimensional models. Three-dimensional considerations[9] seem to point out a relaxation of the above condition
due to the enlargement of the bandwidth associated to
non-ideal and geometrical effects so that the requirementq>1 should be rather replaced by qρ > max(ρ, Δγ/γ,εn,x2/σx2), where qρ is the relative energy separation
between the quantum lines, ρ is the one-dimensional
natural bandwidth and Δγ/γ and εn,x2/σx2 are respectively
the inhomogeneous line broadening due to energy spreadand emittance effects [10]. In our case we have qρ=4 10-4,
but for the case (a) εn,x2/σx2 does never go under 7 10-4.
The cases with larger emittance are, in this sense, evenless critical respect to the presence of quantum effects.
The cases presented require an amount of laser poweroutside the present status of the art, but achievable in thenear future [11]. In fact, for instance, in the case (b) withemittance εx =0.54 mm mrad, at saturation the beam has amaximum radius of about 15 μm; assuming for the laser
in the waist a spot size of 20 μm, we obtain the needed
laser power of more than 17 TW for at least 1.5 mm,corresponding to a total laser energy of about 85 J.

Fig 4: Same as Fig 3 but with εx=0.6 mm mrad.
6

10

10

8
7

(a)

(c)

2

10

6

10

5

10

(d)

4

0,000

3
2

(b)

(c)

1
0,0

0,2

0,4

εx

0,6

0,8

1,0

Fig 5: Gain length Lg in mm (left scale) versus εx in
mmmrad. Radiation power P (in Watt) versus εx in
mmmrad on the right scale for aw=0.3, λw=10 μm,
σx=12.5 μm (corresponding to a maximum radius of 25μm). (a) and (c) refer to a static undulator case, while (b)and (d) to an electromagnetic one.
Cases with emittance εx=0.26 mm mrad (curve (a)) εx=0.54 mm mrad (curve (b)) and εx =0.8 mm mrad (curve

246

10

P

5

X-ray FELs

4

7

P

6

Lg

(b)

(a)

9

0,001

z

0,002

Fig 6: Radiated power P (in Watt) vs z (in meter) for anelectromagnetic undulator. aL0=0.8, λL=0.8 μm, σx=3.5μm, (corresponding to a maximum radius of 7 μm),Δγ/γ=10-4, λR=1.13 Angstrom. (a) εx=0.26 mm mrad .(b)εx=0.54 mm mrad (c) εx=0.8 mm mrad.
Also the properties of the electron beam are extreme, due
to the required condition of large current, low emittance,
minimum energy spread, high focusing and relatively
small γ.
A case equally interesting, but less difficult to realise is aradiation wavelength of about 1 nm. In addition to thecase presented in the previous paragraph relying on theProceedings of FEL 2007, Novosibirsk, Russia

use of the CO2 laser (characterized by a radiation
wavelength λR of about 7.57 A), we present here thepossibility of producing X-rays in the range of thenanometer with the Ti:Sa laser.
6

10

5

10

6

30

10
P

4

20

10

2

(b)
(a)

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σx

10

10

4

(c)

10
P

0

10
0,000

3

10

2

0,005

z

0,010

0

Fig 8: Left axis: radiated power P in Watt vs zin meter.
Right axis: rms radius (in micron) vs z.

10

1

10

0,00000,0005z

0,00100,0015

Fig 7 Radiated power P (in Watt) vs z (in meter) for anelectromagnetic undulator. aL0=0.8, λL=0.8 μm, σx=5 μm,(corresponding to a maximum radius of 10 μm), I=600 A,
Δγ/γ=10-4, λR=1.06 nm. (a) εx=0.26 mm mrad .(b)εx=0.54 mm mrad (c) εx=0.8 mm mrad..
In this case, in fact, the factor γ has been assumed
γ=18.11 and aL0=0.8, the resonant wavelength being about
1 nm. The total charge is Q=2 10-9 C, Lb=1 mm, so thatthe current I is I=600 A. Cases with different emittanceare presented in Fig 11. The radiation power reaches 1
MW for the case with εx=0.26. The requirement of laser
power can be evaluated by assuming a channel of 17 μm
of maximum radius with a length of 1.1 mm for a powerof 12 TW and a total energy of 48 J.
Finally, we present the possibility of producing 12 nm
radiation by means of the CO2 laser. For this case, theproperties of the electron beam have been relaxed. In fact,
we have assumed a γ of 16.5, a current of 150 A, anemittance of ε,x=1.06 mm mrad , a maximum radius of 30
μm (σx=15. μm), an energy spread of 1.3 10-4, conditions
inside the present status of the art of the production ofhigh brightness electron beams. The saturation value ofthe radiation power is very low, namely ten Kilowatt, butlarger by a factor 20 than the incoherent radiation
produced in the same bandwidth. The power saturation
value can be considerably incremented up to 10 MW byshifting the focus of the beam. In Fig 8 the radiation
power and the rms radius are presented for aL0=0.5 andfor the focus of the beam shifted at z=0.68 cm incorrespondence of the middle of the exponentiation
phase.

The laser power required is in this last case 100 GW withtotal energy 2.3 J, but considerable value of powerradiation (namely P= 100 KW at 1 cm) can be reachedalso by limiting the laser parameter to aL0=0.2,
corresponding to 16 GW of laser power and 0.6 J of totalenergy.

REFERENCES[1] A.Bacci, C. Maroli, V. Petrillo , L. Serafini: ‘Eur.
Phys. Jour. Appl. Phys’, (2006), 2006080[2] A.Bacci, M Ferrario, C. Maroli, V. Petrillo,
L.Serafini: ‘PRST AB’,Vol.: 9 , (2006) 060704[3]S. Reiche: Genesis 1.3
http:// pbpl.physics.ucla.edu/~reiche/[4] Ming Xie, "Design Optimization for an X-Ray Free
Electron Laser Driven by SLAC Linac," Proc. 1995
PAC, Dallas, May 1-5, 183.
[5] William M. Fawley, "A user manual for GINGER and
its post-processor XPLOTGIN" (February 19, 2002).
Lawrence Berkeley National Laboratory. Paper LBNL49625.
http://repositories.cdlib.org/lbnl/LBNL-49625[6]W.M. Fawley: ‘X-Ray FEL Simulation:BeamModeling’ ICFA 2003 Workshop on Start to end
Numerical Simulations of X-RAY FEL’s FawleyICFA03Zeuthe..>http://citeseer.ist.psu.edu/xie95design.
[7] J.B. Murphy and C. Pellegrini: ‘J Opt.Soc. Am. B’,Vol.: 2, (1985), pg.:259 .
[8] R. Bonifacio et al.: ‘Nucl. Instrum. And Meth. A’,
Vol.: 543 ,(2005), pg.:645.
[9] Smetanin, I.V., Nakajima, K, Proceedings of theSecond Symposium on Advanced Photon Research(JAERI-Con 2001-011) : 236-40, 2001[10] Winthrop J. Brown and Frederic V. Hartemann:‘Phys.Rev. ST A B‘, Vol.:7 (2004), 060703.
[11] M. D. Perry et al., "Petawatt Laser Pulses," Optics
Letters, Vol. 24 (1999), p. 160, E. Hugonnot, J. Luce,and H. Coïc, "Optical parametric chirped-pulse
amplifier and spatiotemporal shaping for a petawatt
laser", Appl. Opt. 45, 377-382 (2006)

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Proceedings of FEL 2007, Novosibirsk, Russia

PRODUCTION OF FEMTOSECOND PULSES IN A FREQUENCYDOUBLER AND PERSPECTIVES OF FLASH USER FACILITY FOR
PUMP-PROBE EXPERIMENTS WITH FEMTOSECOND RESOLUTION
E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
Abstract
Free Electron Laser in Hamburg (FLASH) operates successfully since the year of 2000. Permanent upgrades ofthe facility did allow to reduce operating wavelength from
100 nm in 2000 down to 13 nm in 2006. An upgrade of
the year of 2007 is in the progress, and after its completition FLASH will reach design value of the wavelengthof 6.4 nm. An attractive feature of FLASH is productionof intense, ultra-short radiation pulses of sub-10-fs duration. In this paper we describe perspective upgrades of
FLASH aiming at extension of the operating wavelength
range while conserving the feature of ultra-short pulse production. We show that an upgrade of FLASH with a frequency doubler will allow to reduce the wavelength down
to 3 nm, thus covering the ”water window” – the wavelength range that is crucially important for the investigationof biological samples. We show also that recent installations at FLASH of far infrared undulator (FIR) and optical
replica synthesizer (ORS) open up the possibility for implementation of schemes allowing to perform pump-probe
experiments with 10 femtosecond temporal resolution.

INTRODUCTION
During last years we observe rapid progress of SelfAmplified Spontaneous Emission Free Electron Lasers(SASE FELs) [1–3]. Jump in the wavelength was by about
three orders of magnitude, from 12 μm in 1997 down to 13
nm in 2006 [4–9]. Presently FLASH (Free Electron Laser
in Hamburg) has produced unprecedented powers for EUV
radiation at a fundamental wavelength of 13.7 nm, and harmonics with wavelengths as low as 2.75 nm [9]. After anenergy upgrade to 1 GeV of the FLASH driving linac minimum wavelength in the fundamental harmonic of FLASH
will be 6.4 nm.
FLASH demonstrated unique femtosecond mode of operation [6–9] which was not considered at an early design
stage of the project [10]. Thorough analysis has shownthat due to nonlinear compression and small local energy
spread the short high-current leading peak (spike) in thebunch density distribution was produced by beam formation system. Despite strong collective effects (of which themost critical was the longitudinal space charge after compression) this spike was bright enough to drive FEL process up to the saturation for the wavelengths down to 13
nm. Analysis of the latest experimental results [9] indicate
X-ray FELs

248

that the peak current in the spike is 2 to 2.5 kA, the FWHM
length of the high current spike is approximately 30 fs andthe normalized emittance is 1 to 1.5 mm-mrad. Note thatthe latter value is significantly less than the project one of
2 mm-mrad [10], and encouragingly approaches to the values predicted by start-to-end simulations. For FLASH thisresult is of crucial importance allowing to reach shorter
wavelengths with fixed electron energy of 1 GeV. The firstscenario for reaching ”water window” at FLASH equippedwith efficient frequency doubler has been analyzed a few
years ago [11, 12]. That analysis has been based purely
on refined start-to-end simulations. Now, with an experimentally proven update of the beam parameters we present
further development of a concept of frequency doubling for
generation of powerful femtosecond pulses. Application of
frequency doubler at FLASH will allow to cover the water window (wavelength range between the K-absorption
edges of oxygen (λ = 2.34nm) and carbon (λ = 4.38nm))
that is crucially important for the investigation of biologicalsamples.
Two-color pump-probe experiments are very attractive
for time-resolved studies. In this paper we show that
present configuration of FLASH holds great potential forpump-probe experiments with 10 femtosecond temporal
resolution. This potential stems from recent installation at
FLASH of far infrared undulator (FIR) and optical replica
synthesizer (ORS) [13–16]. In the case of FIR undulator optical pulses from FIR and XUV pulses from FEL
are naturally synchronized since they are produced by thesame electron bunch. In the case of pump-probe experiments with an external optical laser an ORS setup is used asa selection trigger for perfectly synchronized pump-probe
pulses.

CONCEPT OF FREQUENCY DOUBLER
An idea of using two undulators, with the second undulator resonant to one of the harmonics of the first one, wasconsidered in [17–19] (it is also referred to as the “afterburner” method). The first undulator is long enough toreach saturation and produce strong spatial bunching inharmonics. The bunched beam generates coherent radiation in the second undulator which follows immediately
the first one. The main problem with this approach is thelarge induced energy spread which significantly degrades
the performance of the radiator section at the harmonic fre-Proceedings of FEL 2007, Novosibirsk, Russia
quency [11, 12]. Another method to generate higher harmonics is high-gain harmonic generation scheme from theexternal seed (see [20] and references therein). However,
it is technically complicated and is not flexible enough for
production of tunable radiation.
The concept of effective frequency doubler scheme for
SASE FEL has been proposed in [11, 12]. This scheme essentially exploits the feature of a small local energy spreadin the driving electron beam of SASE FEL. It consists ofundulator tuned to the first harmonic, dispersion section,and undulator tuned to the second harmonic. The latter one
can be also tapered in order to increase output power above
saturation level. The first stage is a conventional SASE
FEL. The gain of the first stage is controlled in such a
way that the maximum energy modulation of the electron
beam at the XFEL exit is about equal to the local energy
spread, but still far away from saturation. When electron
bunch passes through dispersion section this energy modulation leads to effective compression of the particles. Thenbunched electron beam enters the 2nd harmonic undulator,and from the very beginning produces strong radiation because of a large value of spatial bunching, low value of theemittance and relatively small induced energy spread. Saturated power has the same level as for conventional SASE
FEL, but is reached in significantly shorter undulator.

PRODUCTION OF ELECTRON BUNCHES
We illustrate operation of the frequency doubler for theenergy of the driving beam of 1 GeV (see Fig. 1). The
electron beam is produced in a radio frequency gun andbrought up to an energy of 1000 MeV by six accelerating
modules ACC1 to ACC6. At energies of 130 and 380 MeV
the electron bunches are compressed in the bunch compressors BC1 and BC2. The electron beam formation system
is based on the use of nonlinear longitudinal compression.
When the bunch is accelerated off-crest in the accelerating module, the longitudinal phase space acquires a radio
frequency induced curvature. Downstream of each bunch
compressor, this distortion results in a non-Gaussian distribution within the bunch and in a local charge concentration.
It is the leading edge of the bunch, with its high peak cur-

Figure 1: Schematic layout of the FLASH facility equippedwith frequency doubler. Undulator of frequency doubler isplaced just after the main undulator. Abbreviations ACC,
BC, and DS stand for accelerating module, bunch compressor, and dispersion section, respectively. The scheme also
shows far infrared undulator (FIR) and optical replica synthesizer (ORS) setups installed at FLASH in 2007.

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Figure 2: Structure of the electron bunches at FLASH: current I (solid line) and mean energy E (dashed line) along
the electron bunch at the undulator entrance (simulationsof [9] scaled to 1 GeV). The bunch head is located at theright hand side of the figure.
rent, which is capable of driving the high intensity lasing
process (see Fig. 2). Collective effects play a significant
role in the bunch compression process for short pulses. One
can see on Fig. 2 that an increase in the peak current and anarrowing of the width of the spike leads to an increase in
the induced energy chirp due to space charge effects.

PROPERTIES OF THE RADIATION
We illustrate operation of the frequency doubler at
FLASH for the case of FEL process driven by short-spikeelectron bunch with energy of 1 GeV (see Fig. 2). The
main undulator of FLASH is a fixed 12 mm gap permanent magnet device with a period length of 2.73 cm anda peak magnetic field of 0.48 T. The frequency doubler
is 9 m long undulator (1.95 cm period and 0.39 T peakmagnetic field). Simulations have been performed with
time-dependent code FAST [21] upgraded for simulationof higher harmonics. Prior presenting results for the frequency doubler it is worthwhile to overview operation of
SASE FEL with a uniform undulator. Simulations of the
femtosecond mode of operation of FLASH at 6 nm showthat present undulator length of 27 meters is sufficient toreach deep saturation in the main undulator. Expected levelof the average energy in the radiation pulse is up to 70 μJ
for an ideal tuning of the machine and emittance in thebunch head of 1.4 mm-mrad. Expected radiation pulse duration is in sub-10 fs range.
Electron bunch quality is high enough to drive SASE
FEL optimized for production of 3 nm radiation (seeFig. 3). Saturation is achieved at the undulator length ofabout 30 meters with the level of the energy in the radiation
pulse about 15 μJ. We present this number for the further
comparison with the frequency doubler.
When operating as a frequency doubler, the level of output radiation energy in the main undulator should be tuned

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Proceedings of FEL 2007, Novosibirsk, Russia

Figure 3: Energy in the radiation pulse in the frequency
doubler (solid line). Electron energy is 1 GeV, undulator
period is 1.95 cm, and peak magnetic field is 0.39 T. Radiation wavelength is 3.2 nm. Dashed line shows operationof SASE FEL with the same undulator.
to the value about one microjoule. At this stage of amplification process induced energy modulations become to
be about local energy spread in the lasing spike. Thenelectron bunch passes dispersion section with the net compaction factor about one micrometer, and energy modulations transforms to the density modulation with high content of the second harmonic. Finally, electron bunch is
directed to the undulator resonant at the second harmonic(frequency doubler undulator) and readily starts to produce
powerful radiation from the very beginning. Since the electron beam still has high quality, a self-consistent process ofradiation amplification takes place. Peak radiation intensity
is nearly the same as in conventional SASE FEL, but saturation occurs at a shorter undulator length. We see from
Fig. 3 that the level of the average radiation energy is 5 μJ
at the undulator length of 9 meters. Temporal and spectral
properties of the radiation pulse at this point are illustrated
with Fig. 4. FWHM pulse length is well below 10 fs, andaverage power exceeds gigawatt level. Contribution of the
3rd harmonic into the full radiation power is about 0.08%,
and peak power is in a megawatt range.

Figure 4: Temporal (top) and spectral (bottom) propertiesof the radiation pulse at the length of the frequency doublerof 9 meters. Bold lines show averaged values, and thin lines
are single shots.

ter may be introduced by mechanical vibrations of opticalcomponents because different beamlines are used for transport of VUV and FIR pulses. Here we propose jitter-freescheme (see Fig. 5). Combination of modulator of ORS
and FIR undulator as a radiator will allow to produce powerful pulses of coherent radiation with the wavelength ofdriving laser around one micron. Then both pulses aretransported to the experimental area using the VUV opti-

PERSPECTIVES FOR PUMP-PROBE
EXPERIMENTS ON A 10-FS TIME SCALE
Recently FLASH facility has been extended with the
far infrared undulator (FIR) and optical replica synthesizer(ORS) [13–16]. These devices hold great potential for organization of pump-probe experiments on a 10-fs pulse
scale at FLASH operating in a femtosecond mode.
Current plans for FIR undulator foreseen pump-probe
experiments with VUV and FIR pulses (wavelength range
from a few to 200 μm) [14]. While initially FIR and VUVpulses are synchronized on a 10 fs timescale (they bothare produced by the same electron bunch), additional jitX-ray FELs

250

Figure 5: Scheme for pump-probe experiments with VUVFEL pulses and pulses produced by infrared undulator. Operation of the scheme is based on production by the same
electron bunch of naturally synchronized VUV FEL pulses
and pulses produced by the infrared undulator. Relativesynchronization of the pulses is preserved by means of using the same optical system for transportation of the pulses
to the experiment.

Proceedings of FEL 2007, Novosibirsk, Russia

TUPPH013

output power extends an opportunity for studies of timedependent processes on a sub-10-fs time scale describedabove. In addition, the frequency doubler setup produces
two radiation pulses of different frequencies which are naturally synchronized on a few femtosecond scale. The frequency doubler scheme is rather flexible allowing to negotiate with the intensity of the radiation pulses. In particular,
it is rather simple to produce VUV pulses (with fundamental and doubled frequencies) with similar intensity in therange of a few microjoules which reveals an opportunity for
performing pump-probe experiments with powerful VUVpulses of different colors.

ACKNOWLEDGEMENT
We thank R. Brinkmann, J. Rossbach, and J.R. Schneider
for interest in this work.

REFERENCES
Figure 6: Scheme for pump-probe experiments with VUVFEL pulses and optical pulses from external femtosecond
laser (top). ORS setup driven by the same external laser
produces selection trigger for well synchronized pulses.
Bottom plot illustrates overlapping of electron pulse (solidline) and optical pulse (dashed line) in the modulator of
ORS setup.

[1] A.M. Kondratenko and E.L. Saldin, Part. Accelerators 10(1980)207.
[2] Ya.S. Derbenev, A.M. Kondratenko, and E.L. Saldin, Nucl.
Instrum. and Methods 193(1982)415.
[3] J.B. Murphy and C. Pellegrini, Nucl. Instrum. and Methods
A 237(1985)159.
[4] M. Hogan et al., Phys. Rev. Lett. 81(1998)4867.
[5] S.V. Milton et al., Science 292(2001)2037.

cal system which conserves mutual synchronization. Calculations of the photon beam transport show that both radiation pulses, VUV and infrared one, can be effectivelytransported through existing optical system. Separation of
infrared and VUV pulses and organization of required timedelay is performed just near the experimental sample.
ORS setup can be also used for organization of pumpprobe experiments involving femtosecond pulses fromVUV FEL and powerful optical pulses from femtosecond
optical laser. Key problem of such experiments is precise
synchronization of laser and electron pulses having timing jitters of different physical nature. Instead of solving
synchronization problem we propose to use pulse selection
scheme based on ORS setup. Operation of this scheme
is illustrated in Fig. 6. An optical beam from fs-laser issplit into two beams, one is directed to the sample, and another one is used as a seed for ORS. Output signal fromthe ORS exhibits strong dependence on the time jitter between the lasing spike and short laser pulse, and achieves
maximum value at perfect overlapping. Selection signal isgenerated in this case which marks events with perfectly
synchronized pump-probe pulses.
Installation of frequency doubler at FLASH is natural,
cost-effective way for complete covering of the ”water window”, the wavelength range which is of crucial importancefor studying biological samples. But it is not just simple
extension of the operating wavelength range of the facility: production of ultra-short pulses with gigawatt level of[6] V. Ayvazyan et al., Phys. Rev. Lett. 88(2002)104802.
[7] V. Ayvazyan et al., Eur. Phys. J. D 20(2002)149.
[8] V. Ayvazyan et al., Eur. Phys. J. D 37(2006)297.
[9] W. Ackermann et al., Nature Photonics, 1 (2007)336.
[10] T. Åberg, et al., A VUV FEL at the TESLA Test Facility
at DESY, Conceptual Design Report, DESY Print TESLAFEL 95-03 , May 1995.
[11] J. Feldhaus et al., DESY Print DESY 03-092, July 2003.
[12] J. Feldhaus et al., NIM A528(2004)471.
[13] B. Faatz et al., Nucl. Instrum. and Methods A475(2001)363.
[14] M. Gensch et al., ”New THz undulator beamline at the VUVFEL FLASH”, submitted to Infrared Physics & Technology.
[15] E.L. Saldin, E.A. Schneidmiller and M.V. Yurkov, Nucl. Instrum. and Methods A539(2005)499.
[16] P. van der Meulen et al., Proc. of FEL 2006 Conference,
Berlin, 2006, p. 296.
[17] R. Bonifacio, L. De Salvo, and P. Pierini, Nucl. Instrum.
Methods Phys. Res. A 293, 627(1990)[18] Ciocci, et al., IEEE J. Quantum Electron. 31 (1995)1242[19] W. M. Fawley et al., Proceedings of the IEEE 1995 Partice
Accelerator Conference, 1996, p219
[20] I. Ben-Zvi et al., Nucl. Instrum. Meth. A304(1991)151.
[21] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Nucl. Instrum. and Methods A 429(1999)233.

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Proceedings of FEL 2007, Novosibirsk, Russia

GENERATION OF X-RAY FEL LIGHT USING LASER WAKEFIELDACCELERATED ELECTRON BEAMS
O.A. Shevchenko# , N.A. Vinokurov, Budker Institute of Nuclear Physics, 11 Acad. Lavrentyev
Prosp., 630090, Novosibirsk, Russia
Kim Ta Phuoc, Antoine Rousse, Laboratoire d'Optique Appliquée, ENSTA, CNRS UMR 7639,
Ecole Polytechnique, Chemin de la Hunière, 91761, Palaiseau, France
Abstract
We consider a new class of high gain FELs based on
femtosecond electron bunches with extra high current
density produced by Laser Wake Field Acceleration(LWFA). The FELs of this kind can be used forgeneration of high power femtosecond x-ray pulses. We
present the results of simulations of FEL operation withsome reasonable beam parameters which will be obtainedin future. We focus our attention on the advantages which
can be gained from the unique possibility of the use of
femtosecond hundred-kiloamperes bunches, generated by
LWFA. We also consider the impact of the relatively poor
electron beam properties on FEL characteristics.

be achieved in LWFA we obtain the FEL radiation
parameters.

DESCRIPTION OF THE ACCELERATOR
AND FEL LAYOUT
Based on the X-ray FEL requirements one can imagine
the scheme of the experimental setup which is shown in
Fig. 1.

INTRODUCTION
The possibility of the laser wake field acceleration(LWFA) of electron beams in plasma was explored indetail many years ago [1]. Until the present time practicalapplication of this acceleration technique was impossible
because of absence of lasers with required parameters.
The rapid development of high power laser techniquerecently gave rise to intensive experimental investigationof LWFA [2]. At present one can obtain the laser peak
power up to 1 PW with the pulse duration several tens offemtoseconds. This enables one to expect the creation oflaser-plasma accelerators which can provide the peakcurrents several hundreds of kiloamperes with relatively
small slice emittance and energy spread. Suchaccelerators could have very compact design as thegradient in the laser wake field can reach 300 GeV/m.
They certainly would find many applications. One ofthem could be a source of electron bunches for thecompact (tabletop) X-ray FEL [3].
The FEL operation may strongly depend on the detailsof the 6-D electron distribution function which can not bemeasured directly. Therefore it seems reasonable to makethe LWFA experiments simultaneously with observationof the electron beam radiation from undulator. This way
one can optimize the plasma accelerator parameters forthe requirements of the X-ray SASE FEL.
In this paper we consider a possible scheme of the
combined LWFA and SASE FEL experiment. We discuss
some essential physical and technical problems of thisexperiment. They include space charge and wakefield
effects, beam transport and undulator construction.
Assuming some reasonable beam parameters which can___________________________________________#

O.A.Shevchenko@inp.nsk.su

X-ray FELs

252

Figure 1. Possible scheme of the combined LWFA and Xray FEL experiment.
In most of the existing LWFA experiments plasma
volume is created in a gas jet or capillary and thetransverse laser beam size does not exceed 10 microns[2]. For the laser pulse energy available now it seems
worthwhile to increase the transverse laser beam size oneorder of magnitude and use the gas volume with
optimized pressure profile. In addition one can use the gas
focusing in the beam transport line after accelerator andinside undulator which matches very well with theelectron acceleration in the same gas.
At the scheme presented in Fig. 1 the accelerator regionis separated from the vacuum channel by narrow orificethrough which the laser radiation is injected into the gas
volume. To minimize multiple scattering the gas ishydrogen. The gas pressure is chosen to be ~ 5×10-3 atm
so that acceleration up to 1 GeV occurs at the distance 10
cm.
Additional diaphragms are placed along theaccelerator axis. It allows to optimize the pressure profile.
For the compactness of the experimental setup it isdesirable to obtain the FEL gain length no more thenseveral tens of centimetres. The electron beam β-functionin undulator should be of the same order of magnitude. It
can be achieved by applying of gas focusing which works
effectively at high beam peak currents. The focusing
occurs because the beam electrical field is partly screened
due to gas dielectric permeability and beam focuses itself
by magnetic field (at high beam currents collective
electric field may ionize atoms, and therefore effective
permeability will increase). Usually the gas permeability

Proceedings of FEL 2007, Novosibirsk, Russia

influence is very small but for such big peak currents
which can be obtained in LWFA it is sufficient to focus
the beam. In our case the required gas pressure isrelatively small (~ 100 Pa) and beam scattering can beneglected. To match the beam β-function from theaccelerator exit to the undulator entrance one can also use
superconducting solenoid.
To obtain X-ray radiation with 1 GeV electron beam
one has to use undulator with the period several
millimetres. The staggered array undulator seems to be
the optimal choice for such small period [4]. The
vanadium permendur poles of the undulator can be placed
directly to the gas-filled volume. It should be noted that
longitudinal impedance of vacuum chamber does notdepend on its roughness in the case of short beam andrelatively low conductivity of vacuum chamber material.
The critical value of the conductivity is determined by the2

1 ⎛ a ⎞ c wherelb is the bunch⎜ ⎟2π ⎜⎝ lb ⎟⎠ lb
length, a - radius of vacuum chamber, c - speed of light.
Taking lb ~ 1 μm and a ~ 0.5 mm we obtain σ cr ~ 1019

expression σ cr ~which is much higher then copper conductivity. Therefore
the undulator poles do not require shielding by smoothmetallic plates and thus the gap can be increased whichslightly reduces the “resistive” wakefield.
Undulator parameters which have been used insimulations are listed in Table 1.
Table 1: Undulator parameters
Undulator period, mm

3.6

Undulator gap, mm

1.0

Undulator K - parameter

0.3

Longitudinal field, Tesla

1

ASSUMED ELECTRON BEAM
PARAMETERS AND SOME KNOWN
PROBLEMSElectron beams obtained by LWFA should have verylarge correlated energy spread. Electron energy canchange from zero to maximum value at the distance equal
to the quarter of plasma oscillation wavelength. For theassumed gas pressure λ p ~ 100 μm . So the energy
difference at distance 1 μm can reach 5 %. On the other
hand the local energy spread should not be very large.
Therefore in our simulations we assume zero local energy
spread and energy chirp 5 % at distance 1 μm.
Utilization of laser beam with larger transverse size
allows one to hope that the beam slice emittance canbecome noticeably smaller then in present experiments.
There also may be some correlations between longitudinal
and transverse electron motion which can improve FEL
operation.
Taking into account all these considerations we assume
the beam parameters which are summarized in Table 2.

TUPPH014

We also assume homogeneous focusing and constanttransverse size of the beam in undulator. As it was
mentioned above the focusing in our scheme is realized
by beam magnetic field due to the partial screening of
beam electrical field in gas. Therefore the transverse
space charge defocusing is automatically taken into
account.
Table 2: Electron beam parameters
Electron energy, GeV

1

Beam charge, nC

0.8

Pulse duration (r.m.s.), fs

1.5

Peak current, kA

200

Normalized slice emittance, mm×mrad

0.5

Beam transverse size in undulator, μm

8.75

Local energy spread0

Energy chirp, %/ μm

5One has to consider carefully the space charge
longitudinal wakefield. In our case it is smaller thenresistive wakefield and we do not include it in simulations(it depends on current derivative and can be reduced byincrease of the bunch length). There is also fast oscillating
component of the longitudinal field which is created by
microbunching. Its influence is also not very significant
because the plasma oscillation length is larger then thegain length.
Another space charge effect which we do not take into
account is that the particles with large amplitudes ofbetatron oscillations gain additional energy in transverse
electrical field. This effect creates correlations between
electron energy and betatron amplitude which can befavourable for the FEL operation. Unfortunately in ourcase it is not strong enough for that.
The strongest collective effect which we include in our
simulations is resistive wakefield. As the beam length issmall we assume that the wakefield is simply proportional
to the charge in front and proportionality constant isdetermined by the undulator gap [5]. The gas pressure is
to be low enough to decrease the Cherenkov wakes.

SIMULATION RESULTS
To simulate FEL operation we used the code GENESIS[6]. The results are presented below.
In Fig. 2 one can see the increase of FEL radiation
pulse energy (expressed in terms of photon number) inundulator. The gain length at the exponential growth stage(from 1 to 1.75 m) is about 28 cm. Difference between
straight and dotted curve illustrates the efficiency
degradation due to the resistive wakefield. Influence ofthe fast component of longitudinal electrical field createdby microbunching is illustrated by dashed curve.

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Proceedings of FEL 2007, Novosibirsk, Russia

The peak power at saturation (3 m from the beginningof undulator) is about 1.5 TW. The spectral bandwidth israther large which is typical for SASE FELs.
Beam bunching distribution at different stages ispresented in Fig 4. The bunching reaches its maximal
value at linear stage and starts dropping down atsaturation.

13

Number of photons

10

12

10

11

10

10

10

9

10

0,3

8

10

7

0,0

0,5

1,0

1,5
z, m

2,0

2,5

3,0

Figure2. Number of photons in the FEL radiation pulse as
a function of longitudinal coordinate in undulator. Dottedcurve corresponds to the resistive wake free case; dashedcurve includes the influence of space charge.

Bunching

10

0,2

0,1

Radiation power and spectral distributions at different
positions in undulator are shown in Fig. 3.
z=1m

z=1m

0,8

0,2

Power, a.u.

0,1

0,5

1,0

1,5

2,0

0,40

0,45

0,50

0,55

0,60

λ, nm
1,0

0,4
z=2m

0,1

δγ/γ0, %Power, a.u.

0,2

0,6
0,4
0,2

0,0

0,0
0,0

0,5

1,0

1,5

2,0

0,40

0,45

s, μm

b)

0,50

0,55

0,60

z=3m

z=3m

0,8

Power, a.u.

1,2

0,8

0,4

0,0

s, μm

1,5

2,0

0,40

0,45

0,50

0,55

0,60

λ, nm

Figure 3. Radiation power and spectral distributions at
different distances from the undulator entrance.

X-ray FELs

-5

120

-10

80

-15

40

0,5

1,0

1,5

0
2,0

Figure 5. Relative energy deviation created by resistive
wake in undulator and initial energy chirp (pink) andbeam current profile (violet). Dotted pink curve
corresponds to initial energy chirp and green curve shows
beam bunching distribution in the middle of undulator.

0,4

0,0

c)

160

s, μm

0,6

0,2

1,0

0

-20
0,0

1,0

0,5

200

λ, nm

1,6

0,0

5

z=2m

0,8

0,3

Power, TW

2,0

Figure 4. Beam bunching distribution at the distance 1 m(blue), 2 m (green) and 3 m (red) from the undulator
entrance.

0,4

s, μm

a)

Power, TW

1,5

0,0
0,0

254

1,0

s, μm

0,6

0,2
0,0

0,5

Peak current, kA

Power, GW

0,0
0,0

1,0

0,3

The resistive wakefield is illustrated in Fig. 5. It is seenthat microbunching grows only in front of the beam
where the energy deviation is not very large.
The basic FEL parameters are summarized in Table 3.

Proceedings of FEL 2007, Novosibirsk, Russia

Table 3: FEL parameters

TUPPH014

parameters for accelerator optimization. From the other
hand, the available peak power of femtosecond lasers andtheir energy per pulse are increasing from year to year.
This gives us the possibility of further LWFA beam
parameters improvement (for example, by the increase of
the laser beam transverse size for having morehomogeneous accelerating field and less focusing
aberrations).

Gain length, cm

28

Saturation length, m~3

Radiation wavelength, Å5

Number of photons

1012

Peak power, TW

1.5

Spectral bandwidth (r.m.s.), %2

REFERENCES

Pulse duration (r.m.s), fs

0.37[1] T. Tajima and J. M. Dawson, Phys. Rev. Lett. 43,
267 (1979).
[2] J. Faure et al., Nature 431, 541 (2004); C. G. R.
Geddes et al., Nature 431, 538 (2004); S.P.D.
Mangles et al., Nature 431, 535 (2004).
[3] F. Grüner et al., Appl. Phys. B 86, 431-435 (2007).
[4] A. Ho, R. H. Pantell, J. Feinstein, and Y. C. Haung,IEEE J. Quantum Electronics 27, 2650 (1991).
[5] A. W. Chao, Physics of collective beam instabilities
in high energy accelerators (John Wiley & Sons,
New York, 1993); K. Bane, G. Stupakov, SLACPUB-10707[6] S. Reiche, Nucl. Instrum. Methods Phys. Res. A 429,
243 (1999).

CONCLUSION
In this paper we proposed the scheme of test
installation for compact x-ray FEL based on laser-plasma
accelerator. The main idea is that it is easier to optimize
acceleration parameters (laser beam size, plasma pressure
longitudinal dependence, etc.) looking at measured x-ray
parameters, than to measure details of electron
distribution in extremely short bunch with hopefully low
slice emittance and energy spread. The lack of reliabledata on beam parameters in LWFA makes impossible topredict gain length and power of FEL. Therefore our
calculations demonstrate only some set of beam

X-ray FELs

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Proceedings of FEL 2007, Novosibirsk, Russia

DIFFRACTION EFFECTS IN THE COHERENT TRANSITION RADIATIONBUNCH LENGTH DIAGNOSTICS *G. Kazakevich, V. Lebedev, S. Nagaitsev,
FNAL, P.O. Box 500, Batavia, Illinois 60510, USA
Abstract
Diffraction effects in the Coherent Transition Radiation(CTR) bunch length diagnostics are considered for the A0
Photoinjector and the NML injection module. The effects
can cause a noticeable distortion of the measured CTR
spectra depending on the experimental setup and thebunch parameters and resulting in errors of the bunch
length measurenents. Presented calculations show
possible systematic errors in the bunch length inmeasurements based on the CTR spectra at A0 Photoinjector and the NML injection module.

INTRODUCTION
Application of the CTR diagnostics for the subpicoseconds bunch length measurements was proposed
more than 10 years ago and a number of articles havebeen devoted to the experiments in this field. The
diagnostics employing the Transition Radiation (TR), [1],are based on the measurements of the CTR spectra to
restore the bunch length through the Fourier transform. In
this article we consider low-frequency TR range where
the coherent part of the spectrum dominates and thewavelengths are about the bunch length. For such lowfrequency harmonics one should not neglect thediffraction effects in the coherent radiation diagnostics,[2, 3, 4]. They can strongly distort the measured CTR
spectra depending on the beam energy and theexperimental setup. We discuss computations of the CTR
diffraction effects in application to the measurements at
A0 Photoinjector, [5], and the NML injection module [6].

ELECTRIC FIELD OF THE TR AND CTR
Most experimental techniques using CTR spectra forthe bunch length measurements employ backward TR
generated at 450 incidences of electrons on the mirrorquality metallic screen. This radiation has a spectral
density practically similar to the one for the backward TR
at the normal incidence. For simplicity we consider only
this case. To estimate the diffraction effects we assume afinite radius a of the TR screen. Finite size of vacuum
chamber we do not consider for sake of simplicity though
it also affects the bunch longitudinal profile. We also
assume that the screen is located at the origin of thecylindrical frame η : ( ρ , φ , z = 0) , and the z axis isdirected along the momentum of the electron beam. The
observation point is displaced at a distance D>>a along z.
A derivation of required formulae generally follows toRef. [4], where the consideration is based on the virtualphoton method applicable for ultra relativistic electrons.
The Fourier harmonic of the radial electric field for theincident single electron is expressed as, [7, 4]:~
E r (ω , ρ ) =*Work supported by Fermi Research Alliance LLC. Under DE-AC0207CH11359 with the U.S. DOE#
kazakevi@fnal.gov

X-ray FELs

256

( 2π ) ε 0 β c γ222⎛ ωρ ⎞⎟⎟,⎝ β cγ ⎠K 1 ⎜⎜(1)

where: ε 0 is the permittivity of vacuum, K 1 (u ) is thesecond kind modified Bessel function. We assume that thevirtual photon constituting the electron self-field isconverted into the real TR photon. Considering continuityof the normal components of the electric induction andtangential components of the electric field of the virtualand real (reflected) photons, [8], one can conclude that theamplitudes of the radial components of virtual and real
photons are same, i.e. the electric field of an ultra
relativistic electron is almost completely reflected frommetal screen. The small element of the TR screen withcoordinates ( ρ , φ ,0) gives following contribution to thefield (this field is also radial) in the point of observation(x,0,D) :iω R 'ce− iω ~~
d E x ( x ,0, D , ω ) =E r (ω , ρ ) cos φρ d ρ d φ . (2)2πcR'Here: R is a distance between the points ( ρ , φ ,0) and(x,0,D),'R ' = D 2 + ( x − ρ cos φ ) 2 + ( ρ sin φ ) 2 ≈R−xρ cos φ ρ 2
,
+
R
2R

(3)

and: R =D 2 + x 2 . Substitution (1) and (3) into (2)with x R = sin θ and integration over the TR screen
area yields for the electric field in the point (x,0,D):~E x ( x,0, D, ω ) ≈

∫ ∫

iωR

ieω 2

e c
⋅
×
5
( 2π ) 2 ε 0 β 2 c 3γ R

⎡ 2π
⎛ ωρ ⎞⎟⎟ cos φ ⋅ e⎢ K 1 ⎜⎜
⎝ β cγ ⎠0 ⎣ 0a− iωρ sin θ cos φ
c

iωρ 2

⎤
dφ ⎥ ⋅ e 2 cR ρ dρ . (4)⎦In this expression the integration over angle φ gives thefirst kind Bessel function J1(z):2π∫e− iωρ sin θ ⋅cos φc0___________________________________________− eω3That yields:cos φ ⋅ dφ = −i 2π ⋅ J1 (ωρ sin θc),Proceedings of FEL 2007, Novosibirsk, Russia~
E x ( x,0, D, ω ) ≈

∫J (
1

0

ωρ sin θc

one can write:

e c
⋅
×
3
(2π ) 2 ε 0 β 2 c 3 γ R

j kω =iωρ 2⎛ ωρ ⎞⎟⎟ ⋅ e 2 cR ρ dρ .
) K 1 ⎜⎜
β
c
γ
⎝
⎠

(5)

The flow of the TR energy in the observation plane is:~ ~S z = (1 2 μ 0 ) E x B y∗ , where the magnetic field Fourier

~

2
d 2U
~
= I (ω , θ ) = 2ε 0 cR 2 E x (ω , θ ) ,d ω dΩ

(6)

where: ds = R 2 dΩ .
Eqs. (5) and (6) include both: the Fraunhofer diffraction
in far-field zone and the Fresnel diffraction in the nearfield zone. The inequalities: a < γλ and D < γ 2λ (λ is the
wavelength of the TR harmonic), [9], give a region where
the Ginzburg-Frank formula [1] has to be corrected for thediffraction. The Fraunhofer diffraction approximationconsidering finite size of the TR screen neglects the third
term in Eq. (3); while the Fresnel diffraction
approximation neglects the second term in Eq. (3). For the
far-field measurements one can omit the Fresnel
diffraction effect.
In ultra relativistic case and a
results obtained from
Eq. (5) for far-field zone coincide with those obtainedwith Ginzburg-Frank formula, therefore, for TR in the
optical wavelength range at the electron energy of tenshundreds MeV the diffraction effects are negligible andthere is no need to use the above expressions to calculate
the angular distribution of the radiation, however at the
TR wavelength in the sub millimeter-millimeter range thediffraction effects become noticeable.
Using Eq. (5), derived for point like charge, one canobtain an expression for finite size bunch with charge Ne
using the following method. First, we consider Fourier
spectrum of the current of point-like bunch moving withrvelocity of v along z axis. The corresponding Fourier
harmonics are:rr∞
Nev ⋅ δ ω − ( k v )i (ωt − kr ) dtdr
j kω = ∫ Nevδ (r − vt )e=.
(2π )4(2π )4−∞
Then we consider Fourier spectrum for a bunch with
Gaussian distribution along z axis and infinitely smalltransverse sizes:

→∞

(

Nev
e
(2π )4 2π σ −∫∞( z −vt )2
−
2σ 2

rr

⋅ ei (ωt −k r ) dtdr 3 .

Introducing new variable: z`=z-vt and taking into account2⎛ ( z `)
that: ⎜
2
⎜
⎝ 2σ
∞

∫e

−∞

− 2 i⋅π ⋅kx

j kω =⎞+ ik ( z `) ⎟⎟ =⎠∞dk =δ ( x), ∫ e−∞(z`−iσ k ) + σ k ,
2

2

4

2

∞

dx = π = ∫ e−∞− ( x + ai ) 2⎛ −σδ (ω − k z v0 ) exp⎜⎜
4

(2π )

⎝

2

k 2 (1 − θ 2 ) ⎞
⎟.
⎟
2
⎠

Comparing this expression with the Fourier harmonics ofthe point-like bunch current one obtains the term
describing TR for finite size bunch. The term in afrequency domain is expressed as:()

S (ω ) = N exp − ω 2 (1 − θ 2 ) 2σ ω2 .

(8)Thus in the case of longitudinal Gaussian distribution Eqs.
(5) and (7) have to be supplemented by term S(ω). For
θ<<1 it results in,()

S (ω ) ≈ N exp − ω 2 2σ ω2 .

Corresponding form-factor for spectral density ofcoherent radiation of the N electrons is:

F (ω ) = (S (ω ) ) .
2(9)That yields the total CTR spectral power within the angle
θ0 to be equal to:θ0

I cd (ω ) = 2π ∫ F (ω ) ⋅ I (ω ,θ ) sin θ ⋅ dθ .

(10)

0

Using this spectral power one can determine the bunch
length through the inverse Fourier transformation.

DIFFRACTION EFFECTS IN THE
SINGLE ELECTRON TR
Angular distributions of the backward TR generated bypassage of single electron through the TR screen werecomputed using Eqs. (5), (6). The results for the
wavelengths, λ, of 1, 0.3, 0.1 mm and the electronenergies of 15 and 40 MeV are plotted in Figs. 1, 2.
The TR screen radius, a=12.5 mm of existing real setup
and the distances R =250 mm and R >>250 mm (far fieldzone) were used in the computations.
1.20E-013

8.00E-014

4.00E-014

B
C
D
E
F

0.00E+000-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

θ, rad

2σ 2

− x2

r

Nev

21

jkω =

∞

)

(2π )

k z2 ≈ k 2 (1 − θ 2 ) , this results in:~component is: B (ω ) = E (ω ) c , and μ 0 is thepermeability of vacuum. Total energy per unit area
radiated through element ds=dx·dy is [8]:⎛ − σ 2 k z2 ⎞
⎟⎟.
⎝ 2 ⎠

δ (ω − kv0 ) exp⎜⎜
4

Nev

Here: k z is projection of k on z axis. For small angles

x 6.25 x 10 , J / rad x 1/s

a

iωR

eω 2

TUPPH015

dx,

Fig. 1. Angular distribution of the backward TR for
different wavelengths and 15 MeV electrons. C- λ=1 mm,
far-field zone; D- λ=1 mm, R=250 mm; E- λ=0.3 mm,

X-ray FELs

257

Proceedings of FEL 2007, Novosibirsk, Russia

21

x 6.25 x 10 , J / rad x 1/s

R=250 mm; F- λ=0.1 mm, R=250 mm. Curve B was
computed using Ginzburg-Frank formula.
8.00E-013

6.00E-013

4.00E-013

B
C
D
E
F

2.00E-013

Normalized CTR spectra

TUPPH015

1.0 15 Mev,
a=25 mm,
R=25 cmθ0=0.1 rad

0.5

B: σt=0.15 ps
C: σt=0.5 ps
D: σt=1.5 ps

0.0
1E10

1E11

0.00E+000-0.10 -0.08 -0.06 -0.04 -0.02 0.00 0.02 0.04 0.06 0.08 0.10

For comparison the angular distributions of the
backward TR calculated using the Ginzburg-Frankformula (where the spectral density does not depend on
the frequency in a wide range) are also shown in thesefigures.
The plots show that the diffraction effects caused byfinite TR screen size noticeably change the angular
distribution of the TR especially for low frequencies.
Computation of the angular distribution using Eq. (5) and(6) for the TR screen radius a>γλ and detection of the TR
in the far-field zone results in excellent agreement withcalculation using the Ginzburg-Frank formula; but for a <γλ and/or detection of the TR at D < γ 2λ a noticeable
difference appears. An increase of the energy of electrons
magnifies the difference for long-wavelength TR due todiffraction effects, in spite of the narrower angular
distribution of the TR at higher energy. The diffraction
phenomenon becomes apparent in a broadening of the TR
angular distribution for longer waves.
Since the CTR exists in long-wave part of spectrum,
the broadening in the angular distribution causes a
distortion of the measured CTR spectra in a realexperimental setup. This additionally complicates
determination of the bunch length in methods employing
the CTR techniques.

DIFFRACTION EFFECTS IN THE CTR
SPECTRAThe spectra for the Gaussian distributions with rms
bunch duration of σt = 1.5 ps, 0.5 ps. and 0.15 ps arepresented by Gaussians with rms frequency width σf =0.107 THz, 0.322 THz and 1.07 THz, respectively.
The CTR spectra corresponding to real setups were
calculated using Eqs. (5), (6) and (10) for θ0 = 0.05 rad.
and 0.1 rad. Dependences of the spectra on the σt of thebunch, beam energy and setup condition are shown in
Figs. 3-5.
X-ray FELs

258

Normalized CTR spectra

Fig. 2. Angular distribution of the backward TR for
different wavelengths and 40 MeV electrons. C- λ=1 mm,
far-field zone; D- λ=1 mm, R=250 mm; E- λ=0.3 mm,
R=250 mm; F- λ=0.1 mm, R=250 mm. Curve B was
computed using Ginzburg-Frank formula.

Fig. 3. Calculated normalized CTR spectra for 15 MeV
for different σt at a=25 mm, θ0=0.1 rad.
B: σt=0.15 ps
C: σt=0.5 ps
D: σt=1.5 ps

1.0

15 Mev,
0.5 a=12.5 mm,

R=25 cmθ0=0.05 rad
0.0
1E10

1E11

1E12

f, Hz

Fig. 4. Calculated normalized CTR spectra for 15 MeV
for different σt at a=12.5 mm, θ0=0.05 rad.
Normalized CTR spectra

θ, rad

1E12

f, Hz

B: σt=0.15 ps
C: σt=0.5 ps
D: σt=1.5 ps

1.0

0.5

40 Mev,a=12.5 mm,
R=25 cmθ0=0.05 rad

0.0
1E10

1E11

1E12

f, Hz

Fig. 5. Calculated normalized CTR spectra for 40 MeV
for different σt at a=12.5 mm, θ0=0.05 rad.
The plotted curves show significant variation of the
CTR spectra with parameters of the experiment becauseof diffraction effects. The effects noticeably shift low
frequency boundary of the CTR spectra to higher
frequencies at limited size of the TR screen and limited
detector acceptance. In fact these phenomena lead to the“shortening” of the electron bunch length if it is computed
using the inverse Fourier transform. Corresponding results
are shown in Fig. 6 for different σt values at 15 MeV,
a=12.5 mm and θ0=0.05 rad.
We introduce the dimensionless relative σr as the ratioof the computed (using inverse Fourier transform of theProceedings of FEL 2007, Novosibirsk, Russia

CTR spectra) σt value to the real σt value of the bunchwith Gaussian longitudinal distribution. It is plotted inFig. 7 for different beam energies and setup parameters.

0.6
0.4

15 MeV
0.2 a=1.25 cm
θ0=0.05 rad
0.0-6.00E-012-3.00E-012

0.00E+000

3.00E-012

Systematic error, %Charge, r.u.

0.8

of the bunch length calculations caused by diffraction for
Gaussian longitudinal bunch profiles.

25"Shortened"
distributions
B
C
E
Gaussians
G: σt=0.5 ps
H: σt=1.5 ps
J: σt=5 ps

1.0

20
15
10
B: FWHM ~ 0.3 mm
C: FWHM ~ 1 mm

5

0

150

0.8

B: 15 Mev, a=2.5 cm, R=25 cm, θ 0 =0.1 rad
C: 15 Mev, a=1.25 cm, R=25 cm, θ 0 =0.05 rad
D: 40 Mev, a=1.25 cm, R=25 cm, θ 0 =0.05 rad
1

2

200

250

Fig. 8. Systematic errors caused by diffraction effects infinding of the bunch length based on the CTR techniques
for different beam energies.

≤

≤

0.9

σr, r.u.

100

The presented plots were calculated at a =1.25 cm, R = 25cm, θ0 =0.05 rad. As follows from Fig. 8 those setup
parameters provide systematic errors 5% for the bunch
length 0.3 mm at the beam energy up to 15 MeV and ~12% at the beam energy of 250 MeV. Increase of thebunch length causes a stronger distortion of the result.
Increase of the beam energy also amplifies a distortion of
the result.

1.0

0.5

50

Beam energy, MeV

Fig. 6. “Shortening” in the bunch duration caused bydiffraction. Curves B, C, E correspond to σt=0.5, 1.5, 5 ps,
respectively.

0.6

D: FWHM ~ 1.8 mm
E: FWHM ~ 3 mm

06.00E-012

Time, s

0.7

TUPPH015

3

4

5

Bunch σ t, ps

SUMMARY

Fig. 7. Bunch “shortening” caused by diffraction effects
for different bunch durations, setup geometries and beamenergy.
Presented plots evaluate systematic errors in the bunch
length caused by diffraction, if distortion of CTR spectra
is unaccounted. The effects become noticeable at low
frequencies (longer bunch length) and they are caused byboth: the finite size of the TR screen (the Fraunhofer
diffraction) and the finite distance to the detecting device
at finite acceptance of the detecting device (the Fresnel
diffraction) as well.
Note that the same systematic errors are inherent to all
methods based on the measurements of the coherent
radiation, including methods utilizing non-linear opticalcrystals.
The ordinary experimental setup employing the TR
screen of 25 mm in diameter at detection of the CTR in
the range of ± 0.05 rad. gives relative systematic error in
the bunch length of 10% at the bunch length of 0.5 mm
and at the electron beam energy of 15 MeV. At longer
bunch the diffraction more distorts the CTR spectra andsystematic error in the bunch length should be bigger if
the CTR diagnostics are used. For the bunch length of 3mm the relative systematic error is increased up to ~24%
for Gaussian longitudinal bunch profile. Higher energy ofthe electrons causes bigger distortion of the CTR spectra
and, correspondingly, bigger systematic error in the bunch
length determination. Figure 8 presents systematic errors≈≈

If uncounted, the diffraction distortions of the CTR
spectra result in systematic errors of the bunch length
measurements depending on the setup and the bunch
parameters. The diffraction corrections should beconsidered in the planned experiments at the A0
Photoinjector and the NML injection module.

REFERENCES[1] V.L Ginzburg and I.M. Frank, J. Exp. and Theoret.
Phys., Vol. 16, pp. 15-21, 1946
[2] M. Castellano and V.A. Verzilov, PRST-AB V1,
062801, (1998)[3] M. Castellano et al., NIM A 435, (1999), 297-307[4] S. Casalbuoni et al., TESLA Report 2005-15[5] J.P. Carneiro et al., “First Results of the Fermilab
High-Brightness RF Photoinjector”, Proc. of the 1999
PAC Conference, NY, 1999, pp. 2027-2029[6] M. Church et al., “Plans for a 750 MeV Electron
Beam Test Facility at Fermilab” PAC 2007 report,
PAC Conference, Albuquerque, New Mexico, 2007[7] J.D. Jackson, Classical Electrodynamics, J. Wiley &Sons, 1998
[8] L.D. Landau and E.M. Lifshitz, Electrodynamics ofContinuous Media, Pergamon, New York, 1960
[9] V.A. Lebedev, NIM A 372, (1996), 344-348

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Proceedings of FEL 2007, Novosibirsk, Russia

SIMULATIONS FOR THE LCLS INJECTOR
C.Limborg-Deprey*, D.H. Dowell, P.Emma, R.Iverson, J.Frisch, H.Loos, J.Turner, J.Schmerge,
J.Welch, J.Wu, Y.Ding, Z.Huang, J.Castro, G.Hays, P.Hering, S.Gilevich, A Miahnahri, W.WhiteSLAC#, MS 18, SLAC 2575 Sand Hill Road, Menlo Park, CA , U.S.A.
Abstract
The Linac Coherent Light Source (LCLS) Injector has
now been commissioned for five months. Measurements
made at the end of the Injector beamline show that thebeam quality meets the specifications. The transverse
projected emittances at 135MeV are in the range of 1.2
mm-mrad for 1nC/100A and thehorizontal slice
emittances are below 1 mm-mrad. In this paper, we
discuss the validity of both emittance and bunch length
measurements by comparing them with results fromsimulations made with a multi-particle tracking code.

In the second part of this paper, we report on theeffort made to benchmark the simulation code IMPACT[2] to the experimental data. Multi-particle tracking
codes [3,4] had been used intensively at the design
stage of the LCLS injector to specify tolerances of thebeamline components and of the drive laser [5]. In thispaper, we present results calculated with the 3D
algorithm of the IMPACT code. 3D simulations are
essential to represent our asymmetric beam. IMPACT
can run on parallel processors, making 3D calculations
time efficient.

INTRODUCTION
The LCLS Injector commissioning started on April 5th
2007 after several years of design, manufacturing andinstallation. After a few months of commissioning, thebeam quality at 135 MeV reached design performanceswith projected emittances varying from 1 to 1.5 mm-mrad
at 1nC and peak current of 100A [1] .
A bunch charge of 1nC charge was obtained after“passive” and “active” laser cleaning were done.
“Passive” cleaning is done at nominal laser fluence while
operating. In particular, when the laser radius wasdecreased from 1.0 to 0.7 mm, to minimize the transverse
emittances, a factor two increase in quantum efficiency
was obtained after one week of operation at that new
setting. “Active” cleaning was then performed switching
off the RF and forcing the laser fluence to 2.5 times
higher levels than nominal while scanning the cathodeposition. It then allowed us to reach 1nC at 300 μJ on thecathode and 30 degrees laser injection phase.
In this paper, we discuss the validity of transverse
emittance numbers deduced from the measurements bycomparing them to numbers obtained from simulated data
after processing those latter following the same method asthat applied to measured data. In the 135 MeV section of
the LCLS Injector, the emittance can be obtained byeither determining beam sizes at three screens (separated
by 60 degree phase advance) or at a single screen while
scanning an upstream quadrupole (quad scan). The beam
sizes are measured using OTR screens or wire scanners.
All combined, this gives at least four types ofmeasurements. The rms beam sizes can be extracted
following various algorithms which truncate the tails of
the distributions at different levels. Similar truncationlevels were applied to the simulated data. The first part ofthis paper shows that the emittance value rapidly
decreases when long tails are truncated. Emittances as low
as 1.2 mm-mrad in both planes for 1nC seem realistic for90-95% of the particles constituting the core of the bunch.
* Corresponding author: limborg@slac.stanford.edu#
SLAC is operated by Stanford University for the Department ofEnergy under contract number DE-AC03-76SF00515

X-ray FELs

260

Figure 1: Beam size and 100% projected emittance for
optimized beamline – the beam is matched to the 3screens – the three OTR screen locations are shown

EMITTANCE
Transverse Tails
The initial distribution used in the simulations
presented in this chapter uses the virtual cathode drive
laser image as a transverse profile. The laser spot on thecathode, and thus the virtual cathode, is the image of anaperture limiting our transversally Gaussian laser profile.
Even if the emission profile has hard edges, see figure2-a,
the photo-electron beam develops large transverse tails.
To evaluate the effect of those tails on the emittancecalculations, simulations with 2 levels of meshing wereused: 32 x 32 x 32 or 128 x 128 x 64. The first set was run
with 200k particles and the second one with 4 million
particles. No noticeable difference was seen in thegeneration of transverse tails and emittance results were
within a few percent. In both cases some islands of higher
density were preserved down the beamline as shown in
the three screen profiles of figure 3. The 4 million
particle distribution case shows finer structure in the
profile than the 200k distribution. But, the 12μm

Proceedings of FEL 2007, Novosibirsk, Russia
resolution of the screens sets the limit to the fine structure
visible on the experimental data. The long transverse tails
seen in the simulations are similar to those observed in theexperiment (see figure 3d). The longitudinal profile usedin the simulations (see figure 2-b) is directly the laser one
measured with the cross-correlator.
(a)

(b)

Figure2:
Laser
profilesJuly(a) virtual cathode (b) Longitudinal profile

13th

2007

TUPPH019

Three Screen Emittance Measurement
The beamline quadrupoles are tuned such that the beamsees a 60 degree betatron phase advance between eachsuccessive screen of the three screen emittance station.
The transverse phase space is then probed optimally insize and angle. Both experimental and simulations data
correspond to a well matched beam as the one presented
in figure 1. Slightly different magnet settings were used in
the simulations compared to the experimental one in order
to compensate for small inaccuracies in the beamline
model and beam characteristics. In figure 4, the emittancenumbers are computed from the three profiles after
appropriate truncation. Figure 4 shows that the horizontal
and vertical emittances get respectively close to 1.2 and1.5 mm-mrad in the horizontal plane for 5% cut area,
while the numbers are 1.8 and 2.6 mm-mrad for the
distribution containing all the particles.

Quadrupole Scan Emittance Measurement
(a)

(c)

(b)

(d)

A simulation of the quadrupole scan using QE04 (seefigure 1) was performed. For each of the quadrupole
setting, the appropriate truncation levels were applied tothe profiles. The numbers obtained are nearly identical tothose obtained for the 3-screen emittance calculations andare plotted in figure 4. Once again, the simulations weredone starting from a matched configuration. Running 4
million particles instead of 200k did not change the resultsby more than a few percent.

Figure 3: Transverse profiles ; Simulations data (a) OTR1;(b) OTR2 ; (c) OTR3 ; Experimental data (d) OTR2 (scaledifferent to show graininess)

Rms Beam Size Calculation
The rms beam size of the profiles can be computed
following various methods, but the “rms area cut” is mostcommonly used.
The rms beam size is typicallycomputed by integrating each measured 1D transverse
profile and cutting out 2.5% of the area (charge) on eachside. Accordingly, the truncated profile then contains
95% of the charge at the beam core. Other methods areapplied less commonly, including Gaussian fits, and full
100% rms calculations, but the 95% core emittance value
is less sensitive to baseline profile noise as well as weak
beam tails, which will likely not contribute to the FEL
gain in any case. Applying the same robust method
uniformly in both measurement and simulation allows afair, reproducible comparison. Accordingly, the intensity
profile, after these cuts, should then contain 95% of thecharge.

Figure 4: Emittance calculated from simulations fordifferent levels of area cut on the transverse profile; thecurves are identical for both quadrupole scan simulated
data (using 7 profiles) and the three screen simulated data

SIMULATIONS VS EXPERIMENT
Initial Distribution
The initial particle distribution needs to be as close as
possible to the emitted photo-electron distribution.
In the transverse plane, the intensity of the emission
profile can differ dramatically from that of the virtual
cathode image due to variation in quantum efficiency
across the cathode. To measure the emission profile, apoint-to-point imaging of the cathode is performed at
extremely low charges. Such images show that our

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Proceedings of FEL 2007, Novosibirsk, Russia

cathode presents some high density emission spots. It is
not clear that those emission spots were generated by highintensity spots in the drive laser beam or by some RF
arcing in the gun at the early stage of commissioning.
Since we operate in the space charge limit regime, it is notcertain that the intensity emission profile is the same athigh charge and at low charge [6]. However, in thesimulations presented below, we used the intensity profile
measured at low charge on the first imaging screen andtransported back to the cathode.

Figure 7: Schottky scan; charge vs laser injection phase

Operating Parameters

Figure 5: (a) virtual cathode; (b) emission scaled androtated from point-to-point image at first screen
In the longitudinal plane, we used directly the laser
longitudinal profile measured with the cross-correlator(mixing the UV and the IR of the Ti:Sa laser), see figure
6. This profile should in theory be corrected for Schottky
effect, see figure 7, but the intensity variation is small
over the 6 ps, i.e. the 6 degrees of the bunch extent.

The nominal parameters are• Laser pulse (6ps FWHM, 1.66 mm diameter)• Charge from 200pC to 1nC• 30 degrees injection phase• Gun gradient 110MV/m (more recently 115
MV/m)• Linac sections 20 MV/m , 24 MV/m

Machine Tuning
The standard procedure for tuning the LCLS Injector
follows these steps:(1) verify laser injection phase to 30 degrees byperforming a Schottky scan (charge vs laser
injection phase)(2) realign the laser on the solenoid axis (the solenoid
was aligned to the gun very accurately before
installation)(3) matching to emittance station(4) perform emittance minimization by scanningsolenoid, steering into the linac section

Solenoid Scan Emittance Measurement
Figure 6: Longitudinal profile measured at the crosscorrelator
The distributions of the transverse momenta are
Gaussian with rms values giving a thermal emittance of
0.6 mm-mrad per mm of cathode radius. Thermal
emittance measurements were done early in the run
confirming this level.
A six-dimensional distribution is then generated
numerically using a quiet start algorithm based on Haltonsequences [7].

Beamline Model
The beamline components have been described in [5]and are briefly summarized at the bottom of figure 1.
Other magnetic fields present in the gun region have been
ignored as of now, but will be included in a second roundof simulations. The beam is assumed to be on axis and not
perturbed by wakefields. The beam is usually steered into
the linac section to prevent wakefield-based emittance
growth.
X-ray FELs

262

Solenoid scans are done on a regular basis for operating
the LCLS Injector. The optimum solenoid value changes
mostly when gun RF parameters and slightly with charge.
Figure 8 and Figure 9 show the same measurement ofemittance as a function of solenoid value but for two
types of analysis. Figure 8 shows the result using the
100% rms, i.e for no truncation of the tails of the profiles.
The shape of the curve of measured horizontal emittanceis very similar to that obtained with the simulations andcomputed with 0% truncation level. But the mimimum
value differs by 25%. A better agreement on the minimum
emittance value is obtained if a 2.5% level cut is appliedon the simulated data, in particular for the vertical plane.
Figure 9 shows the results from the measurements when
the standard 5% rms cut area is used on the profile.
Simulations results based on the 5% level give slightly
higher emittance numbers. However, if a truncation at 7.5% level is applied on the simulated data, the agreementwith the measurements becomes quite good.
The solenoid currents used in the simulations werescaled by a factor 0.986 to make the solenoid values

Proceedings of FEL 2007, Novosibirsk, Russia
giving the minimum emittance coincide in both cases.
Such an error of 1.4% is within the tolerance of the gunenergy measurement done at the gun exit.

TUPPH019

calculated at the design stage. The design laser pulse for
1nC was 10ps FWHM and 1mm radius.

Figure 10: rms bunch length measured compared toresults from simulations
Figure 8: Emittance vs solenoid- Comparison between
experimental and simulated data for rms values calculatedwith no cut on the tails- simulations results at 2.5 % cut
level have also been superimposed

CONCLUSION
This first series of simulations seem to validate theacceptable emittance numbers measured at 1nC during thefirst LCLS Injector run. A fairly good agreement isobtained between measurement and simulations. Moreexperimental data are required to characterize the physics
of the emission in the space charge limited regime inwhich we are running. The related physics might explain
the 25% higher emittance numbers obtained in thesimulations. A second series of simulations remains to bedone including the complete set of known magnetic fields.
Further comparisons will include longitudinal phase spacecharacterization and data for low charges.

ACKNOWLEDGEMENTS
Figure 9: Emittance vs solenoid- Comparison between
from experimental data and simulations based on the 5%
rms cut area - simulations results at 7.5 % cut have also
been superimposed

Bunch Length vs Charge
Bunch lengths are measured using a transverse
deflecting cavity. A careful calibration is regularly
performed to accommodate the effects of the variation in
klystron power. The experimental data presented in figure
10 were taken within less than an hour. Simulations werebased on the optimization of the beamline for 200 pC as
was the case the day of that measurement. The agreement
between the measurement and the simulations is quitesatisfactory. The measured longitudinal laser profile usedin the simulation was that measured with the crosscorrelator and had a 5ps FWHM, i.e. it was slightly
smaller than the nominal 6ps long laser pulse used formost of our 2007 run.
At 1nC, when the laser pulse is 6ps long, the rms bunch
length of the electron beam at 135 MeV is 1.05mm. It islarger than the design value of 0.84 mm. The space charge
induced bunch lengthening is stronger when starting withboth a shorter laser pulse and a smaller radius than those

The authors would like to thank Ji Qiang (IMPACT) for
his very valuable help in setting up the LCLS deck in
IMPACT. The authors are indebted to L.Young(PARMELA) and K.Floetmann (ASTRA) for their great
support over the years and for the development ofmultiparticle tracking codes for photo-injectors. The
authors are also very grateful to the engineers, techniciansand operators involved in the Injector construction andcommissioning.

REFERENCES[1] D.Dowell, “LCLS Injector Commissioning Results”
these proceedings[2] J.Qiang , IMPACT-T User Document Version 1.5,
LBNL, rep 62326,2007[3] L.Young, J.Billen, PARMELA, LANL codes,
laacg1.lanl.gov/laacg/services/parmela.html[4]
K.Floettmann,
ASTRA,
K.Floetmann,
http://www.desy.de/~mpyflo/Astra_dokumentation/[5] C.Limborg-Deprey, “Modifications of the LCLS
Injector Beamline”, EPAC 04, Lucerne, Switzerland[6] J.Rosenzweig, “Initial Measurements of the UCLA RF
PhotoInjector ”, NIM A 341 (1994) 379-385[7]
Haltonsequences,
http://orion.math.iastate.edu/reu/2001/voronoi/halton_seq
uence.html

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Proceedings of FEL 2007, Novosibirsk, Russia

PRELIMINARY STUDY OF QUIET START METHOD IN HGHG FELSIMULATION*
Y.Hao#, L.H.Yu, BNL, Upton, NY 11973, U.S.A.
Y.Hao, Indiana University, Bloomington, IN 47405, U.S.A.
Abstract
Quiet start scheme is broadly utilized in Self Amplified
Spontaneous Radiation (SASE) FEL simulations, which isproven to be correct and efficient. Nevertheless, due to theenergy modulation and the dispersion section, the High
Gain Harmonic Generation (HGHG) FEL simulation will
not be improved by the traditional quiet start method. A
new approach is presented to largely decrease the numberof macro-particles per slice that can be implemented inboth time-independent and time-dependent simulation,accordingly expedites the high order harmonic cascade
simulation or other small modulation HGHG cases.

INTRODUCTION
Great interest has been focused in single pass freeelectron laser (FEL) for many years for the capability ofgenerating coherent radiation with high intensity and shortpulse duration in short wavelength from deep ultraviolet(~100 nm) to hard x-ray (~0.1nm). The scheme, self
amplified spontaneous radiation (SASE), has been
carefully study in both theory and experiment. The
simulation of SASE FEL process is achieved by using thequiet start method[1,2], which reduces the macro particle
number and simulation time dramatically. However,SASE FEL is seeded by the shot noise of electron bunch;hence produce limited temporal coherence and large shotto-shot intensity fluctuation.
An alternate approach for SASE FEL is the high gain
harmonic generation (HGHG) FEL. As the first HGHG
FEL experiment is accomplished successfully andovercome the limit of SASE FEL [3], increasing projects
were proposed to produce fully coherent VUV and soft Xray radiations sources using cascade HGHG scheme.
The Quiet Start scheme, which reduces the number ofmacro particles largely in SASE simulation, uses only
small number of distinguished phase ψ (usually 4). Each
phase is filled with identical macro particle distribution ofother 5 dimensions (γ, x, y, px, py), which is generated bypseudo random number generator or Hammersley quasirandom sequence. However, the quiet start scheme does
not lead to correct bunching factor in terms of HGHG
process.
A quiet start method scheme for HGHG is introduced in[4]. In the article, we consider a more dedicate method torealize ‘Quiet Start’ initial particle loading in small
modulation case when the modulator and dispersion
sessions exist, in order to achieve correct bunching factor
at the entrance of radiator. When energy modulation is___________________________________________*Work supported by U.S.DOE under contract No DE-FG0292ER40747 and NSF under contract No PHY-0552389#
yhao@bnl.gov#
yhao@bnl.gov

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264

small because of a weak seed laser, the beam energy
spread is large or dispersion effect is large so that thebeam is over bunched, the signal (bunching factor)
generated by modulator and dispersion section will besmall. Such small bunching factor will be overwhelmedby the noise of initial loading method such as
Hammersley sequence, if the number of macro particles is
not large enough. The quiet start loading method is tofind a way to generate less noise with same number ofmacro particles compared with normal loading methods.
To introduce our method on the small modulation HGHG
FEL simulation, first we will derive the bunching factor
errors produce by this quiet start scheme in 1-D casetheoretically. Then 3-D scheme is carried out withutilizing Hammersley sequence on transverse dimensions
to reduce noise. One example of small modulation
HGHG scheme is demonstrated to show the effectivenessof the method in the last section.

ONE DIMENSION ANALYSIS
In the HGHG FEL scheme, the bunching factor after
energy modulation and dispersion section can becalculated theoretically using a simplified one dimension
model. Assuming that the phase space distribution is
described by distribution written in variable 𝛾 =𝐸/𝑚𝑐 2 − 𝛾𝑐 , 𝜃 = 𝑘0 + 𝑘𝑤 𝑧 − 𝜔0 𝑡 , where 𝐸 is theenergy of electron, 𝑚𝑐 2 is electron mass, 𝛾𝑐 corresponds
to the resonance energy, 𝑘0 and 𝜔0 is the resonance wave
number and resonance angular frequency, 𝑘𝑤 is theundulator wave number.
The initial distribution function can be written as Eq.
(1), with energy spread 𝜎𝛾 ,1
𝛾02
𝑓 𝛾0 , 𝜃0 =exp − 2
(1)
2𝜎𝛾
2𝜋𝜎𝛾
After the modulator, the electron bunch energy ismodulated to (𝛾 ′ , 𝜃 ′ )
𝛾 ′ = 𝛾0 + Δ𝛾 sin 𝜃0𝜃 ′ = 𝜃0(2)

The energy modulation strength Δ𝛾 can be calculated
from the modulator strength and seed laser power.
The dispersion section gives rotation on thelongitudinal phase space and change the energy
modulation to density modulation. The new coordinate(𝛾 ′′ , 𝜃 ′′ ) is given by𝛾 ′′ = 𝛾 ′ = 𝛾0 + Δ𝛾 sin 𝜃0𝑑𝜃𝜃 ′′ =
𝛾 + Δ𝛾 sin 𝜃0 + 𝜃0
𝑑𝛾 0

(3)

Proceedings of FEL 2007, Novosibirsk, Russia
Before the bunch enters the radiator, the distributionfunction is shown in Eq.(4). Here we change the notation(𝛾 ′′ , 𝜃 ′′ ) to (𝛾 + 𝛾0 , 𝜃) for simplicity.
𝑓 𝛾, 𝜃
=

1
2𝜋𝜎𝛾

exp −

2

𝑑𝜃
𝛾 − Δ𝛾 sin 𝜃 −
𝛾
𝑑𝛾

(4)

2𝜎𝛾2

The bunching factor after modulator and dispersion
section can be calculated as
𝑏𝑚 = 𝐽𝑚 𝑚𝑑𝜃𝑑𝜃Δ𝛾 exp −(𝑚𝜎 )2 /2
𝑑𝛾
𝑑𝛾 𝛾

(5)

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In HGHG simulation, the traditional quiet start method
does not produce the desired bunching factor as derived inequation (5) using finite number macro-particles. To
obtain the correct bunching factor after energy modulationand dispersion section, we must carefully consider two
dimensional initial longitudinal phase space variables
𝛾0 , 𝜃0 to choose the macro-particles used in thesimulation. Assuming the initially configuration is evenly
distributed in phase variable 𝜃 , and has Gaussian
distribution with energy spread 𝜎𝛾 in 𝛾. We choose thephase to be some equal-space discrete value 𝜃0𝑗 = 2𝜋 ×
𝑗/𝑁𝑗 , where 𝑁𝑗 is the total number of discrete value 𝜃0𝑗 .
In each 𝜃0𝑗 , same configuration of energy 𝛾0𝑘 ,totally 𝑁𝑘 energy values, is assigned.
Using thisconfiguration, we need 𝑁𝑗 × 𝑁𝑘 macro-particles for 1-D
analysis.

Figure 1. Bunching factor error as function of 𝑵𝒋
Now we can find the bunching factor of these 𝑁𝑗 × 𝑁𝑘
particles before entering the radiator, using the Eq (3).
Here we use 𝜃𝑙 as the final phase of 𝑙 𝑡ℎ particle after
energy modulation and dispersion section, where 𝑙 varies
from 1 to 𝑁𝑗 × 𝑁𝑘 . Parameter 𝛼 = 𝑑𝜃/𝑑𝛾 × Δ𝛾 isintroduced for simplicity.
𝑁 𝑗 ×𝑁𝑘

𝑏𝑚 = 𝑒
1
=
𝑁𝑗 𝑁𝑘

𝑁𝑗

𝑁𝑘

𝑖𝑚 𝜃 𝑙𝑒 𝑖𝑚 𝜃 𝑙

=

(6)

𝑙=1
𝑑𝜃
𝑖𝑚 (
𝛾 +Δ𝛾 sin 𝜃 0𝑗
𝑒 𝑑𝛾 0𝑘

1
=
𝑁𝑗 𝑁𝑘

𝑁𝑗

𝑁𝑘

𝑒 𝑖𝑚 𝜃 𝑜𝑗 +𝑖𝑚𝛼 sin (𝜃 0𝑗 )
𝑗 =1

𝑒

𝑖𝑚

𝑑𝜃
𝛾
𝑑𝛾 0𝑘

𝑘=1

Now the two sums are decoupled and can be evaluatedseparately. The first sum only depends on 𝑁𝑗 ; while thesecond relies on each 𝛾𝑜𝑘 .
The first sum in Eq. (6) can be calculated easily using𝑖𝑝𝜃 ,Jacobi-Anger expansion 𝑒𝑖𝑧𝑠𝑖𝑛(𝜃) = +∞𝑝=−∞ 𝐽𝑝 (𝑧)𝑒where 𝐽𝑝 (𝑧) is Bessel function of the first kind.

+𝜃 0𝑗 )

𝑗 =1 𝑘=1

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Proceedings of FEL 2007, Novosibirsk, Russia
𝑐𝑘 is the small deviation from the number calculated in(10). The requirement can be listed in (15). All sums in(15) are added from 1 to 𝑁𝑘 .

𝑁𝑗

1
𝑁𝑗

𝑒 𝑖𝑚 𝜃 𝑜𝑗 +𝑖𝑚𝛼𝑠𝑖𝑛 𝜃 0𝑗
𝑗 =1

1
=
𝑁𝑘

𝑁𝑗

+∞

𝐽𝑝 (𝑚𝛼) 𝑒𝑖 𝑝+𝑚 2𝜋𝑗
𝑁𝑗

(7)
1
𝑁𝑘

𝑗 =1 𝑝=−∞After simple steps, the bunching factor gives
𝑁𝑘

+∞

𝑏𝑚 =

𝐽𝑡𝑁𝑗 −𝑚 (𝑚𝛼) ×
𝑡=−∞

𝑒

𝑖𝑚

𝑑𝜃
𝛾
𝑑𝛾 0𝑘

(8)

𝑘=1

Equation (8) shows the criteria of choosing 𝑁𝑗 .
Quantitatively, we can define the bunching factor errorE(m,α) by comparing Eq. (8) and (5).
𝐸1 (𝑚, 𝛼) =∞𝑡=−∞ 𝐽𝑡𝑁𝑗 −𝑚𝑚𝛼− 𝐽𝑚 𝑚𝛼

𝐽𝑚 𝑚𝛼

(9)

Figure 1 is the bunching error of the first sum withrespect to 𝑁𝑗 , at different harmonic number m andparameter 𝛼 . It shows that, as 𝑁𝑗 increases, the error
decrease dramatically. For large harmonic number m,more discrete phase values are needed to maintain thesame error value. Also, larger 𝑁𝑗 is chosen as parameter𝛼 increases. If the dispersion strength is optimized toyield maximum bunching factor, the parameter 𝛼 makes
𝐽𝑚 (𝑚𝑎) reach the maximum at around 𝛼~1. For example,
if harmonic number is 3, other parameters are optimize toachieve maximum bunching factor, 𝑁𝑗 is selected to be noless than 16 to keep the error less than 1%. This also
explains why quiet start for SASE FEL process(usually 𝑁𝑗 = 4) does not yield correct result.
The accuracy of second sum in Eq. (8) depends on the
distribution of 𝑁𝑘 energy values deviated from ideal
Gaussian distribution. Just follow the method which wetreat the first sum, we use sequence 𝑎𝑘 = (𝑘 −1/2)/𝑁, (𝑘 = 1 ⋯ 𝑁𝑘 ) to represent uniform distribution
in [0,1]. A transformation as (15) forms uniform
Gaussian distribution.
𝑏𝑘 = 2𝐸𝑟𝑓 −1 (−1 + 2𝑎𝑘 )(10)

One option is to simply choose 𝑁𝑘 energy values as
𝛾𝑘 = 𝜎𝛾 𝑏𝑘 . When 𝑁𝑘 is approaching to infinity, thesecond sum will approaching right value expressed insecond factor of equation (5). When 𝑁𝑘 is not large
enough, the error of second error is cannot be neglected.
But in reality, we need to decrease 𝑁𝑘 as small as possible
to save computation time; meanwhile, the 𝑁𝑘 energy
values must produce the second sum with acceptableerror.
In order to achieve the requirement listed above, wechoose the 𝑁𝑘 energy value as shown in (15).
𝛾𝑘 = 𝜎𝛾 𝑏𝑘 + 𝑐𝑘

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266

𝑐𝑘 = 0

(11)

1
𝑁𝑘

𝑒

𝑖𝑚

𝑑𝜃
𝛾
𝑑𝛾 𝑘 =

𝛾𝑘2 = 𝜎𝑘exp −(𝑚(12)𝑑𝜃𝜎 )2 /2𝑑𝛾 𝛾

With the restriction above, we can minimize the rms
value of 𝑐𝑘 . By minimize the rms value, we expect all 𝑐𝑘
values become zero when 𝑁𝑘 approches infinity.
Here we follow the procedure of Lagrangian multiplier
to seek the minimum of 𝑐𝑘2 with conditions in (15).
First we define a new function in (15) after introducing
new parameter 𝜆1 , 𝜆2 and 𝜆3 , where 𝑠2 is the right-handside constant of last equation in (12) .
𝑓 𝑐1 , ⋯ , 𝑐𝑁𝑘 , 𝜆1 , 𝜆2 , 𝜆3
=

𝑁𝑘
𝑘 =1

− 𝜆2
− 𝜆3 (

𝑐𝑘2 − 𝜆1
𝑁𝑘

𝑘=1
𝑁𝑘
𝑘 =1

𝑁𝑘
𝑘 =1

𝑐𝑘

𝛾𝑘2 − 𝜎𝑘

(13)

𝑑𝜃
𝑖𝑚 𝛾
𝑒 𝑑𝛾 𝑘 − 𝑠2 )Then we can write down 𝑁𝑘 equations from the newly
defined function as in (15). Combined with 3 equationsin (12), we can solve these 𝑁𝑘 + 3 equations with 𝑁𝑘 + 3
variables 𝑐1 , ⋯ , 𝑐𝑁𝑘 , 𝜆1 , 𝜆2 , 𝜆3 . By accomplishing all theprocedures we can get a deviated Gaussian distribution
with correct bunching factor in the simplified 1-D
analytical model.
𝜕𝑓(𝑐1 , ⋯ , 𝑐𝑁𝑘 , 𝜆1 , 𝜆2 , 𝜆3 )= 0, (𝑘 = 1 ⋯ 𝑁𝑘 )
𝑐𝑘

(14)

LIMITATION OF THE MODEL
There are limitations of this simplified model. The firstone comes from the fact that we ignore the dispersion in
the modulator.
When the modulator is long, thedispersion effect can’t be ignored, and equation (2) should
be replaced by a set of coupled equations.
Approximately, the dispersion of the modulator can be
represented as (15), where 𝑁𝑢 is the number of modulator
period. We can include it in to the chicane dispersion andperform the Lagrangian multiplier procedure.
𝑑𝜃
2𝜋𝑁𝑢
≅
𝑑𝛾 𝑚𝑜𝑑𝑢𝑙𝑎𝑡𝑜𝑟
𝛾0

(15)

The second limitation is the Lagrangian multiplierprocess only generates sequence that leads to correct
bunching factor at one specific position (the entrance ofradiator). Along the undulator the dispersions at eachProceedings of FEL 2007, Novosibirsk, Russia
point are different; there will be errors when other points
are calculated.

3-D SIMULATION
In one dimension model, we already had the 𝑁𝑗 × 𝑁𝑘
multi-particles. To extend it to 3D case, we need togenerate 𝑁𝑡 different transverse distribution (𝑥, 𝑦, 𝑝𝑥 , 𝑝𝑦 )sets for each one in 𝑁𝑗 × 𝑁𝑘 multi-particles. Totally the
number of particle in 3-D simulation is 𝑁𝑗 × 𝑁𝑘 × 𝑁𝑡 .
For the transverse distributions we can use Hammersley
pseudo random sequence to reduce fluctuation intransverse phase space distribution.
Here, as an example, we simulate the 2nd order HGHG
scheme in soft X-ray regime. Main parameter used insimulation is shown in Table 1. In this example, theenergy spread is larger than the energy modulation
amplitude; the beam is slight over bunched after
dispersion section. This leads the bunch factor at radiator
entrance to be small (around 0.012).
Table 1.. Simulation parameter
Beam energy (in electron mass)
8806
Energy spread
6e-4
Seed laser power (W)
1.0e8
0.171
Dispersion strength 𝑑𝜃/𝑑𝛾Modulator period (m)0.06Modulator length (m)4Radiator period (m)0.05
As the harmonic number is 2, 𝑁𝑗 is selected to be 16 forenough accuracy at given dispersion strength according to
Figure 1. For each phase value (θ, γ), we fill 𝑁𝑡 sets oftransverse Gaussian distribution using Hammersley
pseudo random sequence. Now the left variance is 𝑁𝑘 ,the number of gamma values. And the total number ofmacro particles is 𝑁𝑡 × 𝑁𝑘 × 16. 𝑁𝑘 needs to relatively
large because small number of 𝑁𝑘 will lead to large error
at the dispersion other than the optimized point. 𝑁𝑡 alsoneed a large number because the energy modulation varies
at different transverse location. Table 2 shows the choiceof each dimension
Table 2 .. Number of particle in each dimension

32, 64𝑁𝑘
16
𝑁𝑗
100, 200, 300, 400, 500
𝑁𝑡
We use our method to generate initial distribution ofabove HGHG FEL process and import the initial
distribution to Genesis 1.3. As comparison, we also use
the loading method of Genesis, which uses Hammersley
sequence for all 6 dimensions.
Figure 2 shows gain length in Radiator as function ofdifferent number of total macro particles. We can see thatthe result converges as macro particle number increases(both 𝑁𝑡 and 𝑁𝑘 increases). When 𝑁𝑘 is small, the gain
length calculation shows a small offset because the gain
length depends on the energy distribution.

TUPPH020

We can also compare this quiet start scheme with the 6D coordinate generated by Hammersley sequence. Using
quiet start scheme we can achieve accurate bunching
factor before entering radiator by utilizing small amountof macro-particles (Figure 3) The systematic error caused
by limitation stated in last section is small compare withthe signal (<1%).

Figure 2. Comparison of Gain Length in Radiator

Figure 3. Comparison of bunching factor before radiator

CONCLUSION
The quiet start scheme for HGHG FEL simulation ispromising and easy scheme to save more macro particle.
We generate the initial distribution of macro particles andimport to an existing FEL simulation code. The total
number of particle can be largely reduced by achieving
precise bunching factor in radiator in small modulation
case. But because we use some approximations in theanalysis, there is systematic error in the result, whichneeds more study to correct.

REFERENCES[1] L.H. Yu and S. Krinsky, Phys. Rev. A 35, 8 (1987)[2] L.H. Yu and, S. Krinsky, R.L. Gluckstern, Phys. Rev.
Lett. 64,3011 (1990)[3] L.H. Yu et al, Science 289, 932 (2000)[4] Y. Hao and L.H. Yu, Proceeding of 2007 Particle
Accelerator Conference, Albuquerque

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Proceedings of FEL 2007, Novosibirsk, Russia

FREE ELECTRON LASERS AND HIGH-ENERGY ELECTRON COOLING*
Vladimir N. Litvinenko, BNL, Upton, Long Island, NY, USA#
Yaroslav S. Derbenev, TJNAF, Newport News, VA, USA)
Abstract
Cooling intense high-energy hadron beams remains amajor challenge in modern accelerator physics.
Synchrotron radiation of such beams is too feeble toprovide significant cooling: even in the Large Hadron
Collider (LHC) with 7 TeV protons, the longitudinal
damping time is about thirteen hours. Two coolingmethods (or combination of them) – stochastic cooling(CS) based on broad-back RF feedback(s) and electron
cooling (EC) driven by energy recovery linac (ERL) – areunder development for cooling high energy hadroncolliders.
In this paper we focus on Coherent Electron Cooling(CEC), an unique technique which promising
significantly better efficiency that the above-mentioned
techniques, in a wide energy range. In the early 1980s,
CEC was suggested as a possibility for using various
microwave instabilities in an electron beam to enhance its
interaction with hadrons (i.e., cooling them). The
capabilities of present-day accelerator technology, ERLs,
and high-gain Free-Electron Lasers (FELs), finally caught
up with the idea and provided the all necessary€
ingredients for realizing such a process at energies typicalfor hadron colliders.
In this paper, we discuss the principles, and the main
limitations of the CEC process based on a high-gain FEL
driven by an ERL. We also present, and summarize in
Table 1, some numerical examples of CEC for ions andprotons in RHIC and the LHC.

INTRODUCTION
In contrast with electron- and positron-beams, hadronbeams in storage rings (colliders) do not have strong loss
mechanism (such as synchrotron radiation for electrons)
and, therefore, do not have a natural damping mechanism
to reduce their energy spreads and emittances.
There are several reasons why cooling high-energy
hadron beams, mostly at the top energy range of acollider, is strongly desirable.
First, any increases in the longitudinal- and transverseemittances of a hadron beam accumulated during multistage acceleration from a source to the store energy(collision) remain in the beam. Any instability causing the
growth of emittance (for example, that of the electron
cloud that is the limiting factor for most modern hadroncolliders) may entail the need to discard accelerated
beams and start the process again. In any case, presentday high-energy hadron colliders do not have control ofbeam emittances at the collision energy, and are forced touse beams as they are; this is not always the optimum
approach.
The main figure of merit of any collider is its average______________________________________________

luminosity, i.e., its average productivity for an appropriate
branch of physics. Cooling hadron beams at top energy
may further this productivity.
For a round beam, typical for hadron colliders, theluminosity is given by a simple expression:

L = fc268(1)where N1, N2 are the number of particles per bunch, fc istheir collision frequency, β* is the transverse β-function
at the collision point, ε is the transverse emittance of the€beam, σs is the bunch length, and h ≤ 1 is a coefficientaccounting for the so-called hourglass effect [1]:π 1/ x 2
h( x ) =e erfc(1/ x).
x
The hourglass effect is caused by variations in the beam’s
2

*

(

2

*2

)

size σ r = β ε 1+ s / βalong the length of thecollision€ region, which is defined by the bunch-length, σs.
Accordingly, for h >0.75, β* should be limited to valuesβ*≥σs. Hence, longitudinal cooling of hadron beam mayallow reduction of β * and increase the colliders’luminosity. Plans are to use a non-zero crossing angle atthe Large Hadron Collider (LHC) at CERN. In this case,reducing the bunch’s length would directly contribute toincreasing the luminosity and eliminating the necessity of
having a complicated crab-crossing system.
The effect of transverse emittance cooling on thecollider’s luminosity is less straightforward, but is also
important. For beams with limited intensities, theluminosity (1) grows as the transverse emittancedecreases. Furthermore, reduction of the beam emittance(in combination with bunch shortening) provide favorite
conditions for lowering β* using final focusing
quadrupoles with smaller aperture.
In many colliders luminosity is limited by beam-beameffects. In this case reduction of the transverse emittancewould require also proportional reduction of the bunch
intensities, N1 (and sometimes N2) in eq.(1), which may
cause reduction of luminosity per bunch. Possible
luminosity improvements in these cases are collider
specific.
In eRHIC – BNL’s plan for electron-hadron collider(EIC)- polarized electrons accelerated in an ERL will
collide with hadrons stored in the RHIC’s storage ring[2]. In this case, a reduction of the transverse emittance ofthe hadron beam engenders a proportional reduction of
the electron beam’s intensity while maintaining its
ultimate luminosity constant [3]. Reduction of theelectron beam’s current has multiple advantages: reducing
the strain on the polarized electron source, proportionallylowering synchrotron radiation (the main source of the* Work performed under the auspices of the U.S. Department of Energy.
# Corresponding author vl@bnl.gov

Storage Ring FELs

N1N 2  σ s ⋅ h 
4 πβ *ε  β * Proceedings of FEL 2007, Novosibirsk, Russia

TUCAU01

Table 1. Comparison of estimations for various cooling mechanisms in RHIC and LHC colliders.
The sign ∞ is used to indicate helplessly long damping times.
MachineSpecies
Energy GeV/n
Synchrotron radiation, hrs
Electron cooling, hrs
RHIC
Au
100
~1
20,961 ∞
RHIC
LHC
LHC

protons
protons
protons

250
450
7,000

40,246 ∞48,489 ∞13 (energy)/26 (transverse)> 30> 1,600∞∞

CEC, hrs
0.03
0.8
0.95
<2

To estimate electron cooling in LHC we used an energy scaling γ7/2 typical for RHIC’s electron cooler design [8,9], i.e., cooling
protons in LHC at 7 TeV is ~1010 harder that cooling antiprotons in the Fermilab recycler [7]. Hence, our usage of ∞∞ in an
appropriate column.

detector’s background); and, offering the possibility ofincreasing the electron beam’s energy.
ELIC - Jlab’s version of EIC – plans also to take fulladvantage of transverse cooling of hadron beam. This
plan calls for increase of the collision frequency to 1.5
Ghz to compensate for reduced number of particles per
bunch and to reduce β* to 0.5 cm [4].
Hence, high-energy cooling may play important role inincreasing the performance of high-energy hadron and
lepton-hadron colliders, including RHIC and eRHIC at
Brookhaven National Laboratory, BNL, ELIC at
Jefferson Laboratory, the Tevatron at Fermilab, andpotentially the LHC at CERN.
Electron cooling proved to be very efficient method ofcooling intense hadron- and ion-beams at low andmedium energies [6]. The electron cooler of 9 GeV
antiprotons in the Fermilab recycler represents state-ofthe-art technology [7], which already led to significant
increase in Tevatron’s luminosity. Development of the
ERL-based electron cooler at BNL promises effective
cooling of gold ions with energies of 100 GeV per
nucleon [8]. An advanced electron cooling scheme basedon ERL and circulator-ring is under consideration for
ELIC [5], promises to advance electron coolingtechniques even further. Nevertheless, the effectiveness ofelectron cooling is weaker for protons than it is for ions
(it scales with Z2/A, where Z is the change number of anion and A its atomic number, viz., Z2/A=1 for protons andZ2/A=31.7 for 197Au79). Efficiency of conventional
electron cooling scheme also falls sharply with thebeam’s energy (for RHIC it falls as γ 7/2 [9]). Hence,
traditional electron-cooling of protons with energies fromabout 100 GeV in RHIC to a few TeV in LHC withconventional techniques is hardly possible within therealm of present accelerator technology.
It was noted by earlier works [10], that potential of anelectron beam based cooling techniques may not be
exhausted by the classical electron cooling scheme. The
idea of coherent electron cooling (CEC) encompasses
various possibilities of using collective instabilities in theelectron beam to enhance the effectiveness of theinteraction between hadrons and electrons [11]. In thispaper, we focus on a specific case of using a high gain
FEL (driven by an ERL) for CEC. CEC combines theadvantages of electrostatic interaction with the broad bandof FEL-amplifiers: examples in this paper span from tensof THz to hundreds of PHz. Such systems are naturally fit
into a straight section of modern high-energy hadroncolliders. The proposed CEC method has following
differences compared with the concept of optical
stochastic cooling [12]:a) it may not entail significant modifications to the latticeof the hadron machine ;b) it uses electrostatic interaction instead of rather
inefficient radiation and interaction with TEM waves
by protons in a wiggler;c) it is not limited to few potential choices of laser
frequencies and their bandwidths in THz range.
Similar to other coherent cooling techniques, the CEC’s
cooling rate is limited by the cross-talk of neighboring
hadrons (and the short noise in the electron beam). Thus,
the cooling rate is limited by an effective number ofparticles in a coherent sample, which is inversely
proportional to the amplifier’s bandwidth. In the CEC
scheme, the FEL frequency can be chosen appropriately
to match the energy of the electron beam. Consequently,
for LHC energies the FEL wavelength naturally extends
into the soft-X-ray range (nm), where frequencies aremeasured in ExaHertzs (1018 Hz). Even a tiny fraction ofthis frequency extends far beyond the bandwidth of any
other amplifier.

PRINCIPLES OF HIGH ENERGYCOLLECTIVE ELECTRON COOLING
Figure 1 shows two (of many) possible layouts of alongitudinal coherent electron cooler. As in a regularelectron-cooling scheme, electrons and hadrons shouldhave the same relativistic factor in the CEC:

γ o = E e /me c 2 = E h /mh c 2 .

(2)The simplest (and most economical) version of the CEC
allows electrons and hadrons to co-propagate along thesame straight section. It has a small, weak chicane at the€end of the FEL section for adjusting the timing between
the electron-beam’s modulation and that of the hadron.
This scheme imposes limitations on the value of the
wiggler parameter, a w (see discussion in the following
sections). A more elaborate scheme (which also is more
flexible and complicated) separates the hadron- andelectron- beam so each can be individually manipulated.
For simplification, let us initially consider longitudinal(energy) cooling of the hadron beam. As shown in

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Proceedings of FEL 2007, Novosibirsk, Russia

Section 3, this cooling can be redistributed to include
transverse cooling. Otherwise, the principles of the FELbased coherent cooling remain the same. It has threeparts: The Modulator, the FEL Amplifier/ Dispersion, andthe Kicker.
Many processes discussed in this paper are easier todescribe in a co-moving (CMS) frame propagating withbeam velocity along the straight sections:

βo =

vo
−2
= 1− γ oc(3)For high-quality ultra-relativistic (γo>>1) hadron- andelectron-beams of interest for this paper, the motion of theparticles in the CMS frame usually is non-relativistic (v€ c is the speed of the light). In addition, the<< c, where
velocity distribution function is highly anisotropic withthe root-mean-square (RMS) velocity spread in thelongitudinal direction:

σ V //,CSM ≅ c ⋅ σδ(4)(where δ = E / E o −1 is the relative energy deviation ofa particle) that is much smaller compared with that in thetransverse direction

€

€

€

σ V⊥,CSM ≅ c ⋅ γ oσθ ,linear one, and density modulation on the ensemble of thehadrons is the direct superposition of density modulations
induced by individual hadrons. Because of the flat
velocity-distribution, the shape of the charge-density
modulation resembles that of a flat pancake, withlongitudinal extent significantly smaller that thetransverse size. When translated into the lab-frame, thelongitudinal extent of the pancake shrinks by a factor of γointo the nanometer range (see next sub-section). If thelength of modulator is chosen to allow a quarter of theplasma oscillation to occur within the electron beam,then, at the end of this section, the electron beam density
has a pancake-like distortion with a total excess charge of–Ze centered at the location of the hadron.
In a FEL-amplifier this modulation of charge density inthe electron beam is amplified via the well-known
mechanism of exponential FEL growth [13]. Maximum
gain in the optical power of such a FEL amplifier islimited by saturation [14,15] to about few millions. Thus,a linear FEL power gain of ≤ 1 06 and a corresponding
amplitude gain, GFEL ≤ 103, are conceivable. In this case,at the exit of the FEL, the individual charge pancake will
become a wave-packet (stack) of such pancakes separated
by the FEL’s resonant wavelength(5)

where σθ is the angular spread of electron beam in thelaboratory -frame.
Let us next consider the principle of CEC using this€ which is discussed in more detail in thesimple model,
following sections.

€

λo =

λw
(1+ aw2 ) ,
2
2γ o

(6)

(where λw and aw , respectively, are the wiggler period
and wiggler parameter), and, most importantly, with a
GFEL -times larger charge in the pancake. The duration of€such a wave-packet(i.e., the thickness of the individual
pancakestack)
isequal
to the coherence length of SASE€
FEL radiation [14,15], and can be as short as a few or a
few tens of FEL wavelengths (see the corresponding
section below). This pancake stack of charge-density
modulation will generate a periodic longitudinal
electrostatic field with period of the FEL wavelength:ko = 2π / λo ,(7)E(z) = E o ⋅ sin( k o z + ϕ ) .
Hadrons’ time of flight through the dispersion section
depends on the hadrons’ energy:€
Fig. 1. Schematic layout of the Coherent Electron Cooler
with three sections: a) A modulator, where the electron
beam is polarized (density modulated) by presence of
hadrons; b) an FEL, where density modulation in theelectron beam is amplified / longitudinal dispersion for
hadrons; c) a kicker, where the longitudinal electrostatic
field in the electron beam accelerates or decelerates
hadrons. The cooling mechanism is based uponlongitudinal dispersion in the hadron beam, i.e.,
dependence of the time-of-flight on their energy.
In the modulator, individual hadrons attract* electronsand create local density (and velocity) modulation centersat the position of individual hadrons. The process is a*

Repel, in the case of antiprotons or negatively charged ions

Storage Ring FELs€(t − t o ) v o = -D ⋅ δ ,€(8)where to is time of flight of a hadron with ideal energy
and longitudinal dispersion; in general cases, it is acombination of velocity dependence (in drifts) and passlength€(in chicanes) on the hadrons’ energy:

D = D free + Dchicane ;,L
D free = 2 ; Dchicane = lchicane ⋅ ϑ 2γ(9)where ϑ is the angle of trajectory in the chicane.
The pass-time of hadron with ideal energy should beequal
to that of the space-charge wave-packet. This crude€
synchronization can be achieved by properly choosing
their trajectories (or aw and small chicane for straight-

270€

Proceedings of FEL 2007, Novosibirsk, Russia
pass option – see details below). We note that chargedensity modulation induced by a hadron propagates withthe average longitudinal speed of the electron beam
everywhere except at the FEL. There, the wave-packet of
charge-modulation propagates with the group velocity of
the FEL’s optical wave-packet, which falls in between the
speed of light and the longitudinal velocity of electrons[16]: 1+ aw2 
v g ≅ c1−.
3γ o2 
€(10)Fine tuning the chicane provides for synchronization
between the space-charge wave-packet induced by ahadron in such away that the hadron with central energy,
arrives at the kicker section just on the top of theEo, €pancake of increased electron density (induced by thehadron)†, wherein the longitudinal electric field is zero.
Hadrons with higher energy will arrive at the kicker aheadof their respective pancake in the electron beam, and will
be pulled back (decelerated) by the coherent field of theelectron beam; we note that positively charged hadrons
are attracted to high-density pancakes of electrons.
Similarly, a hadron with lower energy falls behind and, asa result will be dragged forward (accelerated) by theclump of electron density. While propagating in a kicker
section of length, L2, the hadrons will experience anenergy kick of(11)
ΔE = −eZ ⋅ E o ⋅ L2 ⋅ sin{kDδ} ,where Ze is the hadron’s charge (Z=1 for protons and
Z=79 for Au ions). Thus, hadrons with energy deviation
within the δ < π /kD range will experience a coherent€ cooling, strength of which is proportional to FEL gain.
We dedicated the next section to calculations/estimationsof the CEC strength. In Section 4, we discuss the effect of€surrounding particles on the cooling mechanism.
Table 2: Main parameters of BNL’s ERL
Parameter

Units

Value

EnergyMeV

54.34

RF Frequency

MHz703.75Charge per bunchnC

5Normalized transverse
emittance

mm mrad3.2

Bunch length

DETAILS OF THE CEC MECHANISM
A complete and detailed theoretical description of CEC
is deeply embedded in early publications on CEC [10, 11,17] and extends well beyond the scope and size of thispaper. Here we focus on discussing a specific scheme of
CEC using the ERL-driven high-gain FEL.
For estimating the values we will adopt the parametersof the ERL’s electron beam designed at BNL for electron
cooling of RHIC [18,19], but scaled to the appropriate
energy of interest. Table 2 lists the main beam parametersof this ERL.

Modulator.
The modulator in the CEC scheme represents theeasiest, but all-important section, from where information
about the position and charge of each individual hadron(with charge Ze) is imprinted into the co-moving electron
beam. It is desirable to choose the length of the modulator
section equal ~ 1/4 of the electron-beam’s plasma
oscillation, which occurs with frequency ofω pe =

rD //,CSM ~ T1/ 4 ⋅ σ V //,CSM .

(12)

(13)

In the lab-frame, this dimension is Lorenz-contracted to

3.6 10-4cm

4 πn e e 2
γ o mewhere ne is the electron beam’s density in the laboratoryframe. After a quarter of a plasma oscillation [20], eachhadron will be surrounded by a cloud of electrons withtotal excess charge of –Ze ‡ It is important to note that€screening of the hadron is a dynamic process, i.e.,electron cloud screening of a hadron moving with avelocity vh with respect to the electron plasma also will
move with the same velocity, while individual electrons
will have very small drag velocity. The process is similar
to waves in the water, where the water molecules do not
move in average. It also is important to note that thehadron’s velocity will affect the size of its surrounding
electron cloud. Thus, the velocity spreads of both theelectrons and hadrons will determine the size of the
Debye ellipsoid. The longitudinal extent of the Debye
ellipsoid (electron cloud) in the CSM frame will be asimple product of the plasma’s period and the RMS
velocity spread:€

Relative energy spread

TUCAU01

rD //,lab ~

πc σδ
⋅ .
2ω p γ o(14)With ω p ~5 109 Hz being typical for the electron- beam’s

0.76

parameters, we plan to use for CEC (by keeping n e/ γ ~rD //,lab ~ 750 nm for 100 GeV/u Au ionsconst), €†Again, for negatively charged particle like antiprotons or
negatively charged ions, it will be low-density valley. The€
synchronization conditions are independent of the sign of thehadrons’ charge.

€

and rD //,lab ~ 170 nm for 250 GeV proton in RHIC. For 7

TeV protons in LHS, rD //,lab ~ 0.17 nm lies in the soft Xray range.

€ ‡for very cold electron plasma waiting 1/2 of the period will
make this value to be –2Ze, which is not very important€
improvement and which also diminishes in warm plasma.

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Proceedings of FEL 2007, Novosibirsk, Russia

Similarly, the transverse Debye radius will be given byπc⋅ γσθ ,
rD⊥ ~
2ω p

ρk =

(15)
which indicates

which is frame-independent and covers the range from 0.1
mm to 3 mm for the range of parameters we consider inthis paper.
Overall,€ there are no problems with assuming density
modulation in electron beam to be point-likelongitudinally and flat transversely, i.e., perfectly suited
for amplification in a high-gain short-wavelength FEL.
The only problem with the modulator length requiredfor 1/4 of the plasma oscillation that it is proportional to γ
because of the Lorenz time-contraction in the CMS frame(see Table 3). As a practical outcome from suchdependence, the length of the modulator for LHC energies
becomes impractical. Fortunately, it is possible to employ
velocity modulation of the electron along with a buncher
similar to that in an optical klystron [21] to effectively
modulate the electron beam’s density even for LHC€
energies.
Electronpeakcurrent, A

Length of 1/4
plasma oscillationin lab frame, m

RHIC, 40 GeV, Au

50

4.8

RHIC, 100 GeV, Au, p

50

8.5

RHIC, 250 GeV, p

100

30

LHC, 7 TeV, p

100

1325

2


δE
r L zz . (20)≅ −2Z e2 ⋅ 1 ⋅  −
a γ zE
a2 / γ 2 + z 2 

Propagating such electron distribution through a simple
buncher with longitudinal dispersion D = λo /2πσδ e[21] will create maximum density modulation with wavevector ko.
Vzrρ( z) = ∫∫ n˜ ( r )dxdy ,

(16)

(17)

€

€

€

2
e

∂ ρk
Zω
.
+ ω e2 ρ k =
2
∂t
2π

(18)

Equation (18) has a straightforward solution§

Obviously we are using CMS fame of electron beam.
Generalization
for a case of moving hadron is straightforward:
€

r r
∂2 n˜
+ ω e2 n˜ = Zω e2δ ( r − υt) and does not change physics of2∂t

the process in any significant manner€

Storage Ring FELs

272

γz/a

Buncherand, to be exact, in its spatial harmonic on FEL with kvector kcms = k o /2γβ z :
2

ρ

γz/a

For amplificationin the FEL, we are interested in€longitudinal density modulation€that initially the growth of density€

A detailed expansion of the theory of this process will
not fit into this short paper; hence, we consider thefollowing simple case where hydrodynamics equations
can be used, but which contain the most importantunderlying physics. Let us consider a hadron in rest§ incold, uniform electron plasma
and its density perturbationrcaused by the hadron n˜ ( r ,t) obeying the equation:r∂2 n˜+ ω e2 n˜ = Zω e2δ ( r ) .
2
∂t

(19)

modulation ~ (ω e t ) is very inefficient for ω e t << 1,i.e., for €a short modulator, as in the LHC case.
Fortunately, velocity modulation grows linearly and forthe case of t = L1 / γ o v o << 1/ω e , one can easily
calculatethe average longitudinal€CMS velocity field€
induced by presence of a hadron in electron beam with aradius a and the resulting energy modulation in the labframe:€

Table 3: Plasma oscillations in CEC’s modulator
Machine, Energy,
Hadrons, GeV/uZ(1− cosω e t ) ,
2π

-σδ

δ

δ

σδ

σδ
z

-σδ

z

Fig. 2. Longitudinal velocity map (left upper graph)and resulting density modulation (right upper cornergraph) after propagation through a simple 3-pole buncher(depicted in the middle). The simulations were done with
Mathematica [22].
The two pictures in the bottom of Fig. 2 illustrate theprocess in the case of a simple phase-space distribution:
an initial continuous electron beam (very long, comparedwith a a / γ o ), with energy spread ± σδ that experiences
energy modulation in the presence of a hadron (leftpicture). In a buncher, electrons with higher energies slip
forward and those with lower energies slip backwards tocreate density modulation€at the location of the velocity
rift. In short, proper use of buncher for electron beam**facilitates the generation of density modulation
proportional to first order of the phase of plasma
oscillations, ΔQ ~ −eZ ⋅ (ω e t ) . In the case CEC for 7
TeV LHC protons, the use of a short modulator section(by LHC standards) of 100 m and a buncher provides forvery short cooling times of less than one hour.

€**in kinematics terminology buncher is nothing else but a devise
reducing effective longitudinal mass and increasing electrons
mobility in z-directionProceedings of FEL 2007, Novosibirsk, Russia

FEL amplifier for electrons and the dispersion for
hadrons

LG 3D = LG1D (1+ Λ); LG1D =FEL amplifier: It is well known that initial modulation(and noise) in the electron beam density will be amplified.
The resulting TEM field, energy modulation, and density
modulation, all evolve together in FEL. If the FEL gain is€limited to below G~103 (to stay away from saturation),
the resulting amplitudes represent the simple linear
superposition of amplified signals from each hadron plus
noise from the electrons [14]. In particular, density
modulation in electron beam at the exit of FEL (and theentrance of the kicker section) can be expressed as(22)

Table 4: Main parameter of FELs for CEC

where KFEL is the Green function of FEL in response to a
δ-function charge perturbation, and T f is the time-of-flightof electron “wave-packet” from the end of modulator€ section to the beginning of the kicker section. The mainfeatures of the Green function are that it has carrying
frequency at FEL wavelength ω o = koc , has a durationof so-called correlation length (i.e., the number ofoscillation is ~ number of wiggler periods per FEL gain
length). The inverse duration of this “wave-packet”
defines the FEL amplifier’s
bandwidth.
€
In addition, this “wave-packet” propagates with thegroup velocity of FEL signal (10), i.e., the peak of its
amplitude moves forward with respect to electron beam.
2
As the result, for aw < 1/2 , the group velocity in FEL islarger that that of the hadron.
This situation affords an excellent opportunity to use
simple co-propagation of electrons and hadrons throughthe FEL€ with a small chicane to delay the electrons,
which are lighter and easier to manipulate. This delay€ for
few FEL wavelengths puts the hadron on the top of thecharge density “wave-packet” that it induces itself in themodulator.
In the case of aw2 > 1/2 , such simple scenario is not€applicable, and the electrons and hadrons should be
separated. The hadrons should be delayed for theequivalent of a few FEL wavelengths so to overlap withthe maximumof the “wave-packet”– the peak of KFEL.
€
In both cases, hadrons with designed energy should
finish in a zero electric field. This will require sub-FELwavelength adjustments, which do not interfere withlarge-scale timing. The process is similar to maximizing
gain in an optical klystron by tiny variation of€
longitudinal dispersion in its buncher [21].
We take a simple approach for estimating FEL
parameters. We assume that wiggler period of 5 cm withreasonable aw works for all cases, and that selected FEL
wavelength is significantly longer that rD //,lab . We use
analytical formulae derived by Ming Xie [23] to estimate
the lengths of the FEL gain,
Storage Ring FELs

λw;
4 πρ 3and the necessary FEL length for a desirable gain. Table 4
gives some resulting parameters.
The optimum longitudinal dispersion for hadrons canbe chosen from two considerations: a) Maximum coolingdecrement for the typical RMS energy spread δ :sin kDδ = 1 ; b) the requirements for cooling all
particles within the energy spread {-δmax,+δmax}:
sin kDδmax = 0 . Reasonable compromises can bechosen, viz., D = 1/kσδ , which we will use for ourfurther estimations.

 Z ∑ K ( t − t − T ) €hf
 hadrons FELρ = −k oe . € (21)
 + ∑ K FEL ( t − t e − Tf )
 electrons€

TUCAU01

Machine,Energy,€Hadrons, GeV/uλo

RHIC, 40 GeV/n, Au

FEL
Length, m

FEL Gain,

18 µm

6.5

100

RHIC, 100 GeV, Au, p

3 µm

9

200

RHIC, 250 GeV, p

500 nm

15

100

LHC, 7 TeV, p

10 nm

25

500

amplitude

Kicker section
In the kicker section, we have sinusoidal modulation of
the electron beam’s density, which, in the CMS frame isρ˜ =k GFEL ⋅ Z ⋅ e⋅ sin( kz /2γ o )
B
2γ o

(23)

where GFEL is the FEL amplification (for amplitude!) and
B = 2πβ ⊥εn / γ o is the beam’s transverse area, εn is thenormalized transverse emittance of electron beam, and β⊥€
is the transverse beta-function. In the CMS frame the field
is electrostaticand it is sufficient to solve a trivialr

divE = 4 πρ˜ to find it. Since the electron beam in the
ERL has close to a uniform distribution and the transverse
size of the beam is significantly larger the modulation
wavelength, the field near the beam’s axis ispredominantly longitudinal. Because Lorentz
transformation does not change the amplitude of alongitudinal field component, we have in the lab-frame:Ez ≅2GFEL ⋅ Ze
γ o ⋅ sin( k o ( z − v o t ) / β o ) . (24)β ⊥εnThis field will exist for about a quarter of the plasma’s
oscillation and, therefore, for a short kicker length, L2,
one can finally write the change of the hadron’s energy
22
per turn in CEC ( rp = e /m p c is the classical radius ofproton, and A is atomic number of hadron):r ⋅ L Z2
Δδ = −GFEL ⋅ p 2⋅ sin( kDδ ) . (25)β ⊥εn A€For the natural choice of dispersion D = 1/kσδ , thecooling decrement for small energy deviations per turnwill be

€

€

€

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Proceedings of FEL 2007, Novosibirsk, Russia

JCEC = 2G ⋅rp L2 Z 2⋅⋅.
σδ εn β ⊥ A(26)

It worth noting that this expression is energy independent,i.e., it promises to be effective in high-energy colliders
like the LHC.
using CEC is easier than cooling€ Cooling heavy ions
protons because of Z2/A >1 (factor 31.7 for 197Au78 ions in
RHIC). It is also important to point out that because ofsynchrotron oscillations, the value of the CEC decrement(26) should be divided by 2, i.e., the standard ratio for an
oscillator.
Table 5: Main parameter of kickers for CEC
Machine, Energy,
Hadrons, GeV/u

L2 ,m

Hardon bunch
length, nsec

σ s,e
σ s,h

RHIC, 40 GeV, Au

3

2.5

100

RHIC, 100 GeV, Au, p

5

1

RHIC, 250 GeV, p

10

1

100

LHC, 7 TeV, p

50

0.25

500

€

Δx = −η ⋅ eZ 2 ⋅ E o ⋅ L2 ⋅ kR26 x + .... (29)The typical decrement in horizontal cooling for such
system will be

Jx ~

€

σ s,e
σ s,h

(27)

These values, listed in Table 5, were used for calculating
the cooling times in Table 1.

ησεJCEC .
σx

Cooling of both transverse directions will require at least
local transverse coupling (see eqs. (29) and (30)) and nonzero projection of the dispersion vector on both eigen
vectors of€ the betatron modes. A detailed description ofsuch scheme goes beyond the scope of this paper.

COLLECTIVE EFFECTS AND
LIMITATIONS ON THE CEC
DECREMENT200

In practice, hadron bunches are usually much longer
than electron bunches. In this case, the decrement (26)should be multiplied by the ratio of the bunch lengths:

JCEC = JCEC ⋅The energy change causes a local change in the closed
orbit, and hence, a change in the horizontal betatrondisplacement that is proportional to horizontal dispersion
η: (sin in eq. (29) is linearized for simplicity)

As we discussed earlier, the electric field in the electron
beam is a linear superposition of “wave-packets” excitedby all hadrons and electrons, which carry information
about their origin, i.e., the position of each hadron andelectron in the beam (note that hadrons with a non-unit
charge have an additional Z in front of the identical fieldfunction, Eo).
Ez = Z ⋅∑ E (v t − z + z ) ⋅ sin k(v t − z + z )
o

o

i

o

i

i,hadrons€ TRANSVERSE COOLING−

Similarly to re-distribution of the damping incrementsof synchrotron radiation, it is possible to re-distributedecrements of CEC within the boundaries of the “sum of
decrement” theorem:

o

o

j

o

j

Hence, the energy kick for each hadron will contain kickfrom all hadron and electrons within the extent of the‘‘wave-packet”. The action of the self-induced field,€
J s + J x + J y = JCEC .
(28) which we already considered separately in the previous
section, is coherent and is repeated turn after turn. At the
One easy way of providing cooling of the horizontal same time, the relative phases of hadrons at an optical (µnemittance is to use a chromatic chicane, as shown in Fig.3 and nm) scale are completely random, and any
below. In a chromatic chicane, symplectic conditions correlations are completely eliminated after each turn€ arrival time of these wave fronts with the (similar to the storage ring in FELs [24]). Let us define
couple thetransverse coordinates and angles, which provides anN˜ = N˜ h + N˜ e /Z 2 , where Ñ h and Ñ e is the number ofenergy gain in the kicker’s dependence ofelectrons in the FEL coherence length†† L c=Ncλo, which
2“communicate with each other”. Writing the equation of
ΔE = −eZ ⋅ E o ⋅ L2 ⋅(29) evolution of RMS energy and averaging <sin2> of thesin k ( Dδ + R16 x ′ − R26 x + R36 y ′ + R46 y€) ;random phase, we get the standard equation for RMS
spread (analogous to stochastic cooling calculations):
where R nm are elements of transport matrix throughdσ E2
kD 2 1 2 ˜chicane (indexes 1,2,3,4,5,6 belong to canonical variables= −2Δ
σ E + Δ N ; Δ = eZ 2 ⋅ L2 ⋅ E o ,dnEo
2x,x’,y’y’, -ct and δ).

{€∑ E (v t − z + z ) ⋅ sin k(v t − z + z )j,electrons

}

R26≠0
Fig. 3 Chromatic chicane tilts the wave-fronts of€chargedensity modulation in an electron beam and couples theenergy kick with the horizontal position.

††

again, for simplicity of we used Nc=10 and 20 for numerical example
in this paper. There is a rigorous way of defining the correlating length
for a specific FEL by using correlation length of its Green function K:

Lc =Storage Ring FELs

274

€

∞

1
K max

2

2

∫ K(z) dz−∞

Proceedings of FEL 2007, Novosibirsk, Russia
with two important consequences. First is that maximum
cooling rate can not be larger that 1/Ñ per turn. This
limitation is taken into account by properly selecting the
FEL gain for cooling rates shown in Table 1.
Table 6: Other parameters for the CEC
Nh perMachine, Energy,
Nc
Lc,
bunch
Hadrons, GeV/uµm

and R&D ERL groups for being a test-bed for our initial
discussion of ideas used for the FEL-based CEC, and forgenerating several valuable suggestions.

REFERENCESÑ

RHIC, 40 GeV, Au

20

360

1 109

6 105

RHIC, 100 GeV, Au

20

60

2 109

5 105

RHIC, 250 GeV, p

10

52 1011

7 106

LHC, 7 TeV, p

10

0.2

1.15 1011

0.4 106

Second consequence is that the stationary (selfconsistent) energy spread is proportional to the number ofparticles in the coherence length (i.e., it is desirable tooperate the FEL at as short wavelength as possible!), andalso to the cooling rate:

1
Δ ˜
σ E2
=
⋅
⋅N
2
E o 4kD E o

TUCAU01(30)

Finally, we mention that throughout the entire suite ofnumerical examples used in this paper we ensured thatemittances of both the electron- and hadron- beams did
not exceed€ the FEL wavelength divided by 4π, Thisaction ensures the preservation of phase correlations at
the scale of the FEL wavelength.

CONCLUSIONSIn this paper, we showed that coherent electron cooling(CEC) can be very promising method of cooling beams in
high-energy hadron colliders. The CEC takes fulladvantage of high-gain FELs based on high brightness
ERLs. Cooling of 100 GeV/n ions and 250 GeV protons
in RHIC seems to be straightforward with this method.
Cooling protons in LCH at 7 TeV also seems to bepossible, but may require a slightly more elaborate
scheme (such as a buncher and separating the beams).
Proof-of-principle experiment to cool Au ions in RHIC
at ~ 40 GeV/n is feasible using the existing R&D ERL,
which is under construction in BNL’s ColliderAccelerator Department (C-AD). Commissioning thisERL is planned for early 2009. Moving this accelerator
into RHIC tunnel may take from two to three years.
In this paper we assumed standard statistical shot-noisein the electron beam and did not relied on any possible
noise suppression, which is being actively discussed by
the electron- cooling community.

[1] M. A. Furman, Proc. 1991 Particle Accelerator Conf.,
San Francisco, May 6-9, 1991, p. 422.
[2] V. Ptitsyn et al, http://www.bnl.gov/cad/eRhic/
Documents/AD_Position_Paper_2007.pdf[3] V.N. Litvinenko et al., Proc. PAC 2005
http://cern.ch/AccelConf/p05/PAPERS/TPPP043.PDF[4] Y. Derbenev et al., in Proc. of PAC 07[5] Y. Derbenev et al., in Proc. of COOL 07[6] I.Meshkov, Phys. Part. Nucl., 25, 6 (1994) 631[7] S.Nagaitsev et al., Phys. Rev. Lett. 96, 044801 (2006)[8] Ilan Ben-Zvi, et. al., NIM A532, 177, (2004)[9] A.V.Fedotov et al, New J. of Physics 8 (2006) 283.
[10] Ya. S. Derbenev, Proc. of 7th All-Union Conferenceon Charged Particle Accelerators, 14-16 October
1980, Dubna, USSR, p. 269 (in Russian);Ya. Derbenev, AIP Conf. Proc. No. 253, p.103 (1992)[11] Ya. Derbenev, in Proc. of Cool 07[12] A. Mikhalichenko, M. Zolotorev, Phys. Rev. Lett.,
71, p.4146 (1993).
[13] A.M.Kondratenko, E.L.Saldin, Part. Acc. 10 (1980)
207[14] E.L.Saldin, E.A.Schneidmiller, M.V.Yurkov, The
Physics of Free Electron Lasers, Springer, 1999[15] C.Pelegrinni, NIM A475, 177, (2001) p.1[16] see Ref. [14], page 365[17] Ya.S. Derbenev, Dissertation, Novosibirsk, 1978[18]http://www.bnl.gov/cad/ecooling/docs/PDF/
Electron_Cooling.pdf[19] D. Kayran et al., Proc. of PAC 2007 http://accelconf.
web.cern.ch/AccelConf/p07/PAPERS/THPAS096.PDF[20] see for example, C.L. Longmire, Elementary plasma
physics, Interscience publishers, 1963[21] N.A.Vinokurov, A.N.Skrinsky, Preprint of Instituteof Nuclear Physics, INP 77-67, 1977, Novosibirsk[22] Mathematica,  Wolfram Research, Inc[23] M. Xie, NIM A445, 59 (2000).
[24] V.N.Litvinenko et al, NIM A475, 177, (2001) p.65

ACKNOWLEDGEMENTS
We want to thank Ilan Ben Zvi and Thomas Roser(BNL) for encouraging discussions and well-pointed
questions and suggestions, which lead to some of thetechnical solutions presented in this paper. We are
grateful to Anatoly Kondratenko for his wiliness to share
his knowledge of processes in high-gain FELs. The firstauthor also would like to thank C-AD’s electron cooling
Storage Ring FELs

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COMMISSIONING RESULTS OF THE LCLS INJECTOR*
D. H. Dowell#, R. Akre, Y. Ding, P. Emma, J. Frisch, S. Gilevich, G. Hays, Ph. Hering, Z. Huang,
R. Iverson, C. Limborg-Deprey, H. Loos, A. Miahnahri, J. Schmerge, J. Turner, J. Welch,
W. White, J. Wu, SLAC, Stanford, CA 94309, USA,
L. Froelich, T. Limberg, E. Prat, DESY, Hamburg, Germany
Abstract
The Linac Coherent Light Source (LCLS) is a SASE xray Free-Electron Laser (FEL) project presently underconstruction at SLAC [1]. The injector section, fromdrive-laser and RF photocathode gun through first bunch
compressor chicane, was installed in fall 2006. Initialsystem commissioning with an electron beam has recently
been completed. The second phase of construction,
including second bunch compressor and full linac, isplanned for 2008. In this paper, we report experimental
results and experience gained during the first phase ofmachine commissioning. This includes the cathode, drive
laser, RF photocathode gun, linac booster section, S-band
and X-band RF systems, first bunch compressor, and thevarious beam diagnostics.

The LCLS injector begins with a photocathode RF gun
followed by two modified SLAC linac sections producing
a beam at 135 MeV, 100 amps peak current andtransverse normalized emittance of 1.2 microns for 1 nC
bunches. The cathode drive laser is located in areconstructed alcove above the RF gun. The 135-MeV
beam is deflected onto the main linac axis by a two-dipole
35 degree doubly achromatic bend or, with the first 17.5
degree dipole magnet turned off, the beam drifts to a 35
degree straight ahead spectrometer for energy and energy
spread measurements. Once on the axis of the main linac,
the electrons are accelerated to 250 MeV in three linac
structures before entering the first chicane bunch
compressor, BC1. Between the three linacs and BC1 is a
short x-band structure whose 4th harmonic straightens thebeam’s longitudinal phase space for linear compression.

INTRODUCTION
The months of April through August 2007 have beenspent commissioning the LCLS injector. This is the firstphase of machine commissioning, with the second phasestarting in Dec. 2007 after a 3-month downtime, and thefinal phase in Nov. 2008, culminating in FEL light in2009. First electrons from the new photocathode RF gun
were observed on April 5 and beam was quickly
established to the full (injector) energy of 250 MeV in themain SLAC linac on April 14, 2007 [2]. Over the next
five months all the injector systems were commissioned
and the beam accelerated to 15 GeV at the end of the
SLAC linac. The bunch charge (1 nC) and the measured
projected emittance of 1.2 microns meets the design
requirements of LCLS.

DESCRIPTION OF THE INJECTOR

THE DRIVE LASERThe RF gun’s copper cathode is illuminated by a UV
laser operating at 255 nm delivering up to 450
microjoules per pulse at 120 Hz. In addition to thewavelength and energy, the laser must meet stringent
stability and reliability requirements as well as strict
transverse and longitudinal shaping specifications. The
stability specifications were achieved with a pulsed
Ti:sapphire system pumped by two quasi-cw, diodepumped Nd:YAG lasers (Figure 2); however the shaping
requirements have not been met.
1.0mx1.5m breadboard

Measuring 150-200fs
phase stability from osc.

Femtolasers Synergy
Oscillator

119MHz>600mW

Stretcher>300ps
5 nm

4W

Figure 1 shows the major components of the LCLS
injector at the 2 kilometer point of the 3 kilometer SLAC
linac. The off-axis housing was built during the original
construction of the linac in 1962 [3], anticipating future
injection beamlines such as LCLS.

DAZZLER
Regen Amp

Spectra Physics
MILLENNIA Vs>1.5mJ, 120Hz

15mJ
120 HzJEDI #1
100 mJ,120 Hz

Pulse Picker
UV-diagnostics:
Streak camera
Spectrometer
Cross-correlator
TG-Frog…

>1mJ, 120Hz

Pre-Amp4-pass Bowtie 75mJ
>22mJ, 120Hz~12m to cathode

UVTransport
to Cathode>0.4mJ, 120Hz
255 nm

THG
>3mJ
120Hz

Compressor
>30mJ
120Hz

>40mJ
120Hz

120 HzAmplifier2-pass Bowtie 80mJ

JEDI #2
100 mJ,120 Hz

120 Hz
1.0mx1.5m breadboard

Figure 2: A block diagram of the RF gun drive laser
designed and built by Thales Lasers.

Figure 1: The injector for LCLS located in the off-axis
housing at Sector 20, at the 2/3-point along the linac.
___________________________________________* Work supported by US DOE contract DE-AC02-76SF00515.
#
dowell@SLAC.Stanford.edu

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The laser pulse shape is measured by combining a shortpulse from the oscillator with the UV pulse in a non-linear
crystal allowing back-conversion of the mixed signal to
the second harmonic. A cross correlation measurement of
the UV pulse sent to the cathode is shown in Figure 3.

Proceedings of FEL 2007, Novosibirsk, Russia

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Image of Laser Profile on Virtual Cathode Camera

Figure 5: A typical image of the laser transverse profileon the virtual cathode camera.
Figure 3: The laser pulse shape as measured in a crosscorrelator and fit with an n-order super Gaussian.
The short-term charge stability which results both fromthe laser’s energy and the laser-RF phase jitter is shown
for a measurement period of 53 seconds in Figure 4. The
charge was determined with a beam position monitor(BPM) located immediately after the gun anddemonstrates 1.1% (rms) charge stability, which easily
meets the 2% specification for stable operation of the
LCLS FEL. The long-term variation is controlled using a
feedback loop which varies the laser energy using an
adjustable wave-plate inside the IR to UV tripler.

1.1% charge stability, 2% is spec

Figure 4: The laser’s short-term energy stability of 1.1%(rms) is better than the design specification of 2%.
The laser transverse profile is monitored on the virtual
cathode camera (VCC) which views the light from a beam
splitter located just before the UV beam enters thebeamline vacuum. Figure 5 shows a typical VCC image
which is used in a feedback loop with a steering mirror tomaintain the laser beam at a fixed point on the cathode.
The details of this optical system have been described in
ref [4].

THE PHOTOCATHODE RF GUN
The LCLS photocathode RF gun has been described
elsewhere [5,6] and only its general features are
summarized here. The gun fields are fully rotationallysymmetric by incorporating dual feed (to eliminate thedipole fields) and a racetrack geometry (to cancel thequadrupole fields induced by the dual feed) for the fullcell into which the RF is coupled.
Since this gun is the sole electron source for the LCLS
user facility, it needs to operate reliably at the relatively
high repetition rate of 120 Hz as well as producing
exceptional quality beam. This was done by making
several changes to the BNL/SLAC/UCLA gun.
The LCLS gun was made more reliable by replacing thecommonly used azimuth angle RF coupling with muchlarger z-coupled ports running the full length of the fullcell. This approach combined with careful design of thecoupler-hole lip radii greatly reduced the pulsed heating
which otherwise would have limited the gun lifetime. In
addition, any field emission from the tuning slugs waseliminated with deformation tuners. These tuners where
found to be unnecessary during the tuning process. In
addition, the shape of the iris between the two cells was
modified to reduce its surface fields below that of thecathode. The resulting cathode surface field isapproximately 10% higher than the iris fields. With thesemodifications the gun was easily conditioned to 120
MV/m and 60 Hz repetition rate. Conditioning at 120 Hz
was limited to 107 MV/m due to excessive heating of the
gun probes, a limitation which will be corrected by the
installation of re-designed probes in 2008. Therefore to
reduce any risk of damaging the gun, it was decided tolimit the repetition rate to 30 Hz during the 2007
commissioning run. As a result, the gun operated
continuously at 30 Hz for more than 3 x 108 pulses during
the April 5, 2007 to August 24, 2007 commissioning
period.
Another important innovation of the gun which
improved its beam quality was to greatly increase thefrequency separation of the 0- and pi-modes. Previous sband guns had been built with 3.2 MHz separation
resulting in excitation of the undesired 0-mode by the low

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frequency components of RF envelope waveform,
allowing it to beat against the pi-mode. The presence of
the 0-mode increases the correlated energy spread andunbalances the fields between the two cells both duringtransient and in steady state [5,6]. Increasing the mode
separation to 15 MHz greatly reduces excitation of the 0mode, giving a pure pi-mode in the gun.

the laser fluence to the degree that vacuum activity in theform of low-level RF arcs were observed which cleaned
the cathode. The result has been a fortuitous, steady risein QE during the last three months of commissioning as
can be seen in Figure 7.

THE CATHODE

June 6, 2007
White light cathode image~9pC, June 2Electron beam image of cathodecopper grains

Figure 7: The quantum efficiency during the last two andone-half months of commissioning.
A mild laser cleaning of the cathode was also
performed. The fluence was deliberately kept low andonly one pass of the scan was done to limit any possible
damage to the cathode surface. The QE before and after
cleaning is shown in Figure 8, which was done in thepresence of low rf power of 1 MV rather than the nominal
6MV, equivalent beam energy. The laser-RF phase wasalso nominal at 30 degS from the zero crossing. The laser
fluence was approximately 360 microjoules per sq. mm in
a 0.67 mm diameter laser spot slowly moved over a 2 mm
x 2 mm area. The dwell time was 10 seconds at eachposition with a 100 micron step size. The initial and final
QE’s were 1.6x10-5 and 2.8x10-5, respectively.
QEScan-WPLT_LR20_111_LSR_ANGLE-2007-07-21-100028.mat
QEScan-WPLT_LR20_111_LSR_ANGLE-2007-07-21-143505.mat

1.2

1Emitted Charge (nC)

The cathode quantum efficiency was quite low for the
first two months of commissioning. To complicate theissue, the QE had the appearance of being even lower due
to incorrect Faraday cup measurements. Once the beam
was transported to the main linac, its charge was moreaccurately measured using known SLAC-standard charge
and beam position monitors. However this correction was
only a factor of 1.45, while the QE was initially almost
20-times lower than the design requirement.
In order to understand the poor cathode performance,
the cathode was imaged optically with white light and acamera in reflection geometry, and the emission
distribution imaged with the gun solenoid adjusted tocreate a point-to-point image of the cathode photoemission on the second YAG screen [7]. Illumination for
the white light image was done by directing light throughthe UV optics and vacuum window, and reflecting light
off the in-vacuum mirror onto the cathode. A digital
camera viewed the cathode with the opposing in-vacuum
mirror (installed for wakefield compensation) and vacuum
window.
The photo-emission imaging was done at
approximately 10pC bunch charge in order to minimize
space charge forces blurring of the image. A comparisonof these two methods of imaging is shown in Figure 6.
The resolution with both techniques is excellent and thecorrespondence between the white light features and theareas of high photo-emission is striking.

0.8

0.6

0.4

0.2

0

Feature observed at end ofhigh-power test

Figure 6: Images of the cathode taken using a white lightsource and a camera (left), and an electron emission
image on a YAG screen approximately 100 cm from thecathode. The gun solenoid is adjusted to image thecathode electrons on the 100 micron thick YAG screen.
The initial QE at the start of commissioning wasapproximately 2 to 3 x 10-6 which is 20-times lower thanthe design specification of 6 x 10-5. This very low QE
limited the maximum beam charge to 200pC during thefirst half of commissioning. However, reducing the laser
size on the cathode during the emittance studies increased
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0

50

100

150

200

250

300

350

Laser Energy (microJoules)

Figure 8: The measured charge vs. laser energy before(red) and after (blue) laser cleaning.
The QE history shown in Figure 7 is an approximation
based upon the charge emitted at the RF phase producing
the maximum cathode field (approximately 90 degS fromthe zero field phase), normalized to the laser energy. A
more precise measurement is given in Figure 9 where thecharge is given as a function of the laser energy at thelaser-RF phase of 30 degS from the RF zero crossing.
The linear portion at low laser energies gives the quantum
efficiency and the onset of the space charge limit isProceedings of FEL 2007, Novosibirsk, Russia

indicated by the roll-over of the curve from this linear
dependence. The space charge limit is quantified by aneffective transverse rms radius assuming a Gaussian
distribution [8,9]. The inserted image in Figure 9 shows
the actual transverse emission distribution as imaged on
the YAG screen as described above. This image
corresponds to the laser iris completely opened while thecharge vs. laser energy data was taken with the iris set to a
1.3 mm diameter cathode illumination.

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plot. The ellipses on the right represent the reference
phase space of the x- and y-planes at the OTR screen
location for the nominal quadrupole field. The straightlines represent the beam size at each quadrupole setting,transformed to the reference phase space.

Emission Image of
Cathode on YAG

Figure 10: Projected normalized emittance measured fora 1 nC bunch at 135 MeV (γεx = 1.14 μm, γεy = 1.06 μm).

Figure 9: The measured bunch charge vs. laser energy fit
with an analysis for the QE and the space charge limit.
The QE in this case was 3.7×10−5 and the effective
transverse radius 0.34 mm (rms). The inset shows theemission distribution with the laser iris fully open when
this data was taken. The scale corresponds to the beam
size on the YAG screen.

The electron bunch slice emittance is measured on thesame OTR screen with the transverse RF deflector
switched on, applying the same 5% area cut analysis
method to the data. A typical image with the deflector
switched on is shown in the center image of Figure 13. In
Figure 11, the bunch has been binned into 12 slices andthe horizontal emittance calculated for each slice.

MEASUREMENT AND ANALYSIS OF THE
TRANSVERSE EMITTANCE
The LCLS injector transverse emittance at 135 MV ismeasured using optical transition radiation (OTR) with a
1-micron thick aluminum foil. The images are acquiredwith a digital camera, background subtracted andanalyzed using a variety of methods to eliminate spurious
results due to long tails of the distribution. The on-line
software allows x- and y-plane projections of the images
to be analyzed for rms beam size based on several
methods, including: 1) rms of the entire profile, 2)
Gaussian fit, 3) asymmetric Gaussian fit, 4) 5% amplitude
cut, and 5) 5% area (charge) cut.
The results reported here use the 5% area cut technique.
In this method the background subtracted image is
integrated in the two transverse dimensions over theregion of interest (ROI) and the threshold level
corresponding to 5% of the area-integrated image isfound. The rms beam sizes for the projections above thisthreshold are used to compute the emittance.
The emittance results using the 5% area cut analysis are
given in Figure 10. The plots on the left show the rms
beam size as a function of the quadrupole field with fitted
curve overlaid. The beam emittance, Twiss and matchingparameters, as well as the goodness of fit are listed on the

Figure 11: The slice horizontal emittance for a 1-nC, 100ampere bunch at 135 MeV, with emittance values <1 μm
in the beam core.
Simulations of the beam emittance measurement were
performed using the IMPACT particle tracking code [10].
In these calculations the electron emission images shownin Figures 6 and 9 and the laser pulse shape given by thecross correlator were used for the starting particle
distributions at the cathode surface. Therefore both thetransverse and longitudinal asymmetries associated with
the initial conditions were included in the simulation.
This realistic electron beam distribution was accelerated
to 135 MeV and propagated to the OTR screen to

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simulate the quadrupole scan technique. The computed
transverse profiles were analyzed with the same area cut
method as done in the experiment to obtain the emittanceas a function of the area cut percentage.
The result of this analysis is summarized in Figure 12
where the transverse emittances are plotted as functions of
the percentage of area cut. The higher y-plane emittanceresults from the asymmetry of the initial electron
distribution and is typical of the emittance asymmetry
observed in the measurements.
Comparing the measured emittances of Figure 10 withthe curves in Figure 12, indicate that a percentage cut of 8
to 9% would result in good agreement with simulation.
Whereas the measurement technique described above
used 5% for the cut area, it is possible that a few per centof the measured distribution is lost in the camera noise or
there is a subtle difference between the measured andsimulated tails at the level of a few percent. In any case,this discrepancy is relatively small, and at worse would
imply the measured emittances are for 90 to 93% of thebeam charge rather than 95%.

The absolute bunch length after BC1 has beenmeasured using a 2.4-m long vertical RF deflecting cavity(LOLA) 900 m downstream of BC1, which acts as a
streak camera [11]. The bunch length measurements areshown in Fig. 14 at 1 nC, where the energy spreadinduced by the off-crest phase of the L1S and X-band RF
sections (see Fig. 2) is varied, producing the rms relative
energy spread on the horizontal axis of this plot. The
compression factor was also measured simultaneously byusing two beam phase monitor cavities, one up and one
downstream of BC1, to measure the ratio of phasevariations at each location as the phase of the drive laser
is scanned. This compression factor is multiplied by themeasured initial bunch length and plotted for easycomparison with the measured bunch length data. Thismeasurement is presently resolution limited by a phosphor
screen, which will be replaced during the fall 2007
installation period with a new OTR foil at 4.3 GeV. The
poor agreement of the data in the range σE/E > 4% may be
due to coherent synchrotron radiation in the compressor.
1.4
1.2

z

σ (mm)

1
0.8
0.6
0.4

Figure 12: Simulations of the emittance as a function of
the percentage area of the tails cut from the data.

0.2

BUNCH LENGTH COMPRESSION00

The LCLS injector includes a 4-dipole magnetic
chicane (BC1) at 250 MeV as the first bunch compression
stage. (The second compressor, BC2, will be located
350 m downstream at 4.3 GeV and installed in fall 2007.)
Nominally, the bunch is compressed by a factor of 4-5 in
BC1, but in the extreme, with X-band 4th harmonic RF
switched ‘ON’ to linearize the energy chirp (see Fig. 15),
the bunch can be compressed down to a few microns [11].
The chicane includes an OTR screen, adjustable
collimator, and a BPM at its center.
Deflector OFF

Deflector ON

Deflector ON
in Dispersion Region

Figure 13: OTR foil images with 1st RF-deflector cavity‘OFF’ (left), then cavity ‘ON’ to measure slice emittance(center), and again ‘ON’ with an OTR foil at highdispersion to measure longitudinal phase space (right).
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1

2

σ /E (%)

3

4

5

E

Figure 14: Bunch length after BC1 measured using the
RF deflector (red-circles), and initial bunch length times
compression factor (blue-diamonds) measured using two
beam phase monitor cavities up and downstream of BC1.
The calculated bunch length is also shown (green line).
The 2.4-m LOLA cavity will be relocated closer to theBC2 in fall ‘07, but is presently near the linac end at
14 GeV. A shorter transverse cavity is also locatedupstream of BC1 (Figs. 1 and 13) and used to measure theinitial bunch length and longitudinal distribution (Fig. 16,
left). The 14-GeV bunch was also compressed to 170
micron rms bunch length (Fig. 16, right), and smaller, butwith a resolution limit of about 100 μm rms, which will
be upgraded in 2007 with a new OTR foil at 4.3 GeV.
The BC1 dipole fields are unfortunately of poor quality,
including a significant sextupole field and linear field
gradient, which generates large horizontal dispersion andemittance growth beyond BC1. The linear dispersion has
been corrected using two small quadrupoles placed in
BC1 for this purpose, but the sextupole field limits theminimum horizontal emittance growth to about 40% (γεxProceedings of FEL 2007, Novosibirsk, Russia

from 1.2 μm before BC1 up to 1.7 μm after BC1). The
dipole magnets will be re-worked in the fall of 2007.
X-band OFF

X-band ON

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Detector
Imaging
Bend

ER
DR
SR

Figure 15: OTR screen in BC1 chicane with its horizontal
dispersion. The first RF deflector is ‘ON’ here, with the
X-band cavity ‘OFF” at left, and ‘ON’ at right,
demonstrating linearization of the energy chirp.

MirrorFigure 17: The radiation sources viewed by bunch length
monitor, BL11. The pyroelectric detector measures the
combined sources of synchrotron radiation (SR), edge
radiation (ER) and diffraction radiation (DR) reflected
into the detector by a mirror with a hole through which
the electron beam passes.

Further details of the BL11 bunch length monitor are
shown in Figure 18. The system splits the radiation into
two detectors each of which has two high-pass filters at
0.5 mm and 1.0mm which can be inserted for selecting
the wavelengths of interest. The responses of thesedetectors for the cases of no filter, and with the 0.5 mm
and 1.0 mm filters inserted as functions of the L1S phaseare plotted in Figure 19. Increasing L1S accelerator phaseincreases the bunch energy chirp resulting in stronger
compression in BC1.
Figure 16: Bunch length distribution measured using both
RF deflectors. The first measurement is at 135 MeV (left,
σz ≈ 1.1 mm, Ipk ≈ 97 A) and the second is at 14 GeV(right, σz ≈ 0.17 mm, Ipk ≈ 520 A), representing the bunch
length before and after BC1 compression at 1 nC.

Mesh Filter
Mesh Filter
Paraboloid
Paraboloid

BC1 BUNCH LENGTH MONITORSThe bunch length is monitored after BC1 using two
techniques. One, referred to as BL12, incorporates aceramic gap incorporated into the beam pipe downstreamof the compressor. The microwave radiation generated by
the short bunch’s wakefields is transmitted through theceramic and is detected by two fast, microwave detectors
which are sensitive to 100 and 300 GHz. Once calibrated
against the bunch length measurements using the LOLA
transverse deflecting cavity, these signals are used tofeedback the L1S RF phase and regulate the bunch length.
Another bunch length monitor located immediately
after the last BC1 dipole measures the coherent
synchrotron radiation, edge radiation and diffraction
radiation generated by the short bunch as it passes throughthe dipole and a holed mirror. A collection lens images
the diffraction radiation onto a pyroelectric detector. The
general layout is given schematically in Figure 17.

Beam Splitter
Beam Splitter
Pyro Detector
Pyro Detector

Beam
Beam

Edge Radiation
Edge Radiation
Figure 18: A computer generated drawing of the BL11
bunch length monitor system.

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BL11 Pyro Signal
BL11 Pyro Signal

6Phase Scan BL11x 10 6
Phase Scan BL11
14 x 1014
No filter
12
No filter
12 1mm High Pass
1mm High
High Pass
Pass
0.5mm
10
0.5mm High Pass
10

8
6
4
2

with a Gaussian shape, centered exactly at the setting
which makes the DL1 dipole-quadrupole-dipole bend
doubly achromatic.

8

Bunch Length Monitors

6

300 GHz

4
2

0

0
-2
-10
-2
-10

100 GHz
0

0

10
20
30
40
50
10
30 (degree)
40
50
Linac 20
L1 Phase
Li
L1 Ph
(d
)

60
60

70
70

Figure 19: The response of the pyroelectric detector as afunction of the phase of the linac section before the bunch
compressor. The signal is given for no wavelength filter,a 1mm high pass filter and a 0.5mm high pass filter.

UNEXPECTED PHYSICS
During the beam emittance studies after BC1, we beganobserving a strong enhancement of the optical signal fromthe OTR foils when the bunch was highly compressed.
The effect is illustrated in Figure 20 where the BL12
microwave detector signals and the OTR optical signal
obtained by integrating OTR image are given vs. the L1S
RF phase in a semi-log plot. Recall that increasing theL1S phase, decreases the electron bunch length where the
L1S phase for nominal LCLS operation is 25 degS. The
data show expected behavior for the two microwave
signals. The lower frequency 100 GHz signal is first to
respond, followed by the 300 GHz detector near 35 degS.
The 300 GHz signal saturates above 40 degS.
What is unexpected is the large increase in the OTR
optical signal, rising at least an order of magnitude above
the unbunched signal. This behavior of the optical signal
strength suggests there is micro-bunching of the electron
beam at optical wavelengths.
In addition to this large increase in the optical signal,
the beam image greatly varies from pulse to pulse. Thiscan be seen in the large error bars at high-compression
phases shown in Figure 20, which reflect the large shotto-shot variation. Similar variations are seen in the profile
projections given in Figure 21 for a sequence of beampulses. The images themselves are similarly striking,displaying chaotic patterns of random spots which can beorganized into a ring-like shape with the proper settings of
the upstream quadrupoles. This fascinating effect can beseen in Figure 22. And again, these phenomena indicate
the generation of coherent optical radiation due to microbunch instability.
Another indication of this interesting phenomenon isshown in Figure 23. In this study, the OTR optical signal
for the foil is shown, but in this case, BC1 is articulated tozero degrees so as to have zero R56. The quadrupole
singlet between the two 17.5 degree dipoles of DL1 (seeFig. 1) is varied and the optical intensity is found to vary
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OTR Optical Signal
RF Phase of L1S, relative to crest (degS)
Figure 20: The signals of the BL12 microwave detectors
at 100 (blue) and 300 (green) GHz, and the imageintegrated OTR optical signal (red) as seen by a digital
camera are plotted as functions of the L1S phase relative
the crest.
jFigure 21: Profile projections for five consecutive beampulses when the RF phase is set at 50 degS.
The data in Figure 22 can be explained by assuming thebunch has an energy modulation on the scale of optical
wavelengths before entering DL1. This modulation isconverted to current modulation by the 4 mm R56 of DL1
which then coherently radiates transition radiation at the
OTR foil. Varying the quadrupole from its design field
not only makes the bend dispersive but also results in
non-zero values for the R51 and R52 matrix elements which
can mix the bunches by tilting them in the transverse
direction, smearing the current modulation and reducing
the COTR signal. The coherent optical radiation (COTR)
is the strongest when the quadrupole is set for DL1
achromatic with R51 and R52 equal to zero. A possible
source of the initial energy modulation is shot-noise, as
the drive laser doesn’t have enough bandwidth to produce

Proceedings of FEL 2007, Novosibirsk, Russia

such optical scale modulations.
Experimental andtheoretical investigations are in progress.

Figure 22: An image of the COTR radiation obtained bycareful adjustment of the quadrupoles after the bunch
compressor.

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Table I: The design and measured beam properties.
Parameter
Final e− energy
Bunch charge
Init. bunch length (fwhm)
Fin. bunch length (fwhm)
Initial peak current
Projected norm emittanceSlice norm. emittanceSingle bunch rep. rate
RF gun field at cathodeLaser energy on cathodeLaser wavelength
Laser diameter on cath.
Cathode material
Cathode quantum eff.
Commissioning duration

sym
γmc2
Q
Δt0
Δtf
Ipk0

γεx,y
γεsx,y
f
Eg
ul

λl
2R
QE
-

dsgn
14
1
10
2.3
100
1.2
1.0
120
120
250
255
1.5
Cu
6
8

meas.
14
1
10
1.5-10100
1.1 - 1.2
0.7 - 1.0
10-30
115
300
255
1.3
Cu
3.5
5

unit
GeV
nC
ps
ps
A
μm
μm
Hz
MV/m
μJ
nm
mm
10−5
mo

REFERENCES

Figure 23: The integrated optical transition radiation
signal as a function of the quadrupole single between the17.5 degree bends. The optical signal is a maximum at
the quadrupole setting which makes the DL1 bend doubly
achromatic.

SUMMARY AND DISCUSSION
The design and beam properties measured during thefive month commissioning run are listed in Table I.
These results unambiguously show the injector meets all
the beam requirements for the LCLS.
The five month commissioning period not only
successfully validated the injector design and its
operation, but also observed strong coherent effects in the
beam diagnostics and transport on the optical scale.
These effects are yet another indication of excellent beam
brightness, and show we are now entering a new era ofbeam physics where coherence dominates not only with
the FEL interaction, but also during the production,
acceleration, transport and manipulation of these dense
electron bunches. The LCLS injector commissioning
additionally makes it clear that coherence and interference
effects will play a major role in future beam diagnostics.
Hence LCLS ushers in a new era not only of 4th
generation light sources, but also of bright electron beams
which coherently radiate all too easily.

[1] J. Arthur et al., SLAC-R-593, April 2002.
[2] R. Akre, et al., PAC’07, Albuquerque, NM, 2007.
[3] “The Stanford Two-Mile Accelerator,” R. B Neal,
Ed., W. A. Benjamin 1968, pp.1123-1124.
[4] D. H. Dowell, J. Castro, P. Emma, J. Frisch,
S.Gilevich, G. Hays, P. Hering, C. Limborg-Deprey,
H. Loos, A. Miahnahri and W. White, “LCLS Injector
Drive Laser,” PAC’07, Albuquerque, NM, 2007.
[5] C. Limborg-Deprey, D. Dowell, J. Schmerge, Z. Li
and L. Xiao, ”RF Design of the LCLS Gun” LCLSTN-05-3, Feb. 2005.
[6] L. Xiao, R.F. Boyce, D.H. Dowell, Z. Li, C. LimborgDeprey, and J.F. Schmerge, “Dual Feed RF Gun
Design for the LCLS”, SLAC-PUB-11213 andPAC’05, Knoxville, TN, 2005.
[7] D.H. Dowell, E. Jongewaard, C. Limborg-Deprey, J.
Schmerge and A. Vlieks, “Measurement and Analysisof Field Emission Electrons in the LCLS Gun,”
PAC’07, Albuquerque, NM, 2007.
[8] J. Rosenzweig et al., “Initial Measurements of the
UCLA RF PhotoInjector”, NIM A 341 (1994) 379385.
[9] J. L. Adamski et al., “Results of commissioning theinjector and construction progress of the Boeing one
kilowatt free-electron laser”, SPIE Vol. 2988, p158169.
[10] C. Limborg-Deprey, D. H. Dowell, P. Emma, R.
Iverson, J. Frisch, H. Loos, J. Turner, J. Schmerge, J.
Welch, J .Wu, Y. Ding, Z. Huang, J. Castro, G. Hays,
P. Hering, S. Gilevich, A. Miahnahri and W. White,“Simulations for the LCLS Injector,” These
Proceedings.
[11] P. Emma et al., PAC’07, Albuquerque, NM, 2007.
[12] R. Akre et al., PAC’01, Chicago, IL, June 2001.

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Proceedings of FEL 2007, Novosibirsk, Russia

DIRECT MEASUREMENT OF PHASE SPACE EVOLUTION IN THE
SPARC HIGH BRIGHTNESS PHOTOINJECTOR∗
E. Chiadronia† , D. Alesinia , A. Baccic , M. Bellavegliaa , R. Bonia , M. Boscoloa ,M. Castellanoa , L. Catanib , S. Cialdic , A. Cianchib , A. Clozzaa , L. Cultreraa , G. Di Pirroa ,A. Dragoa , A. Espositoa , M. Ferrarioa , L. Ficcadentie , D. Filippettoa , V. Fuscoa , A. Galloa ,G. Gattia , A. Ghigoa , L. Giannessid , M. Incurvatia , C. Ligia , M. Miglioratie , A. Mostaccie ,P. Musumecif , E. Pacea , L. Palumboe , L. Pellegrinoa , M. Petrarcag , M. Quattrominid ,R. Riccia , C. Ronsivalled , J. Rosenzweigf , A.R. Rossic , C. Sanellia , L. Serafinic , M. Serioa ,F. Sgammaa , B. Spataroa , F. Tazziolia , S. Tomassinia , C. Vaccarezzaa , S. Vescovia , C. Vicarioaab

INFN-LNF, via E. Fermi, 40 - 00044 Frascati, Rome, Italy

INFN-Roma “Tor Vergata”, via della Ricerca Scientifica, 1 - 00133 Rome, Italy
c
d

e
f

INFN-Milano, Via Celoria 16, 20133 Milan, Italy

ENEA C.R., via E. Fermi, 00044 Frascati, Rome, Italy

Università di Roma “La Sapienza”, Dip. Energetica, via A. Scarpa, 14 - 00161, Rome, Italy

UCLA - Dept. of Physics and Astronomy, 405 Hilgard Avenue, Los Angeles, California 90095, USAg

INFN-Roma I, p.le A. Moro 5, 00185 Roma, Italy

Abstract
The characterization of the transverse phase space forhigh charge density relativistic electron beams is a fundamental requirement in many particle accelerator facilities, in particular those devoted to fourth-generation synchrotron radiation sources, such as SASE FEL.
The main purpose of the SPARC initial phase was the commissioning of the RF photoinjector. At this regard, the evolution of the phase space has been fully characterized bymeans of the emittance meter diagnostics tool, placed in
the drift after the gun exit.
The large amount of collected data has allowed for the
first time a detailed reconstruction of the transverse phasespace evolution downstream the RF, giving evidences ofthe emittance compensation process as predicted by theory
and simulations.
In particular the peculiar behavior of a flat top longitudinal
electron distribution compared to a gaussian distribution
has been studied giving important insights for the correct
matching with the following linac whose working point isbased on the double emittance minimum effect.

INTRODUCTION
The SPARC project is an R&D activity oriented to thedevelopment of a high brightness photoinjector to drive
SASE FEL experiments [1]. In the first phase, the SPARC
layout (Fig.1) consisted of a 1.6 cell RF gun operated at
S-band (2.856 GHz, of the BNL/SLAC/UCLA type) andhigh peak field on the cathode ( 120 MV/m) with incorporated Copper photo-cathode, generating a 5.6 MeV energy∗ Work partially supported by the EU Commission in the sixth framework program, Contract No. 011935 EUROFEL-DS1 and from the MIUR
Progetti Strategici DD1834.
† enrica.chiadroni@lnf.infn.it

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beam. The first few meters of beam propagation, where
space charge effects and plasma oscillations dominate theelectron dynamics, have been studied by means of the movable emittance meter [2]. This device, based on the 1D

Figure 1: The SPARC photoinjector in the initial phase:from the right to the left, the RF gun with the solenoid,
the emittance meter, quadrupoles and dipole magnets, theenergy spectrometer and the beam dump.
pepper-pot technique, has allowed not only to measure thebeam size and emittance, but also to reconstruct the transverse phase space at different positions along the directionof motion. Due to the high sensitivity of this method, a very
precise emittance value can be calculated directly from thephase space analysis. For this reason, suitable data processing algorithms have been developed.
In the next phase of SPARC, which will start in Autumn,
the beam emerging from the gun will be focused andmatched into 3 accelerating sections of the SLAC type (Sband, TW), to boost the beam energy up to 155-200 MeV
and to drive a SASE FEL at 530 nm.

SYSTEM DESCRIPTION AND
OPTIMIZATIONTo reach its goal SPARC requires a temporally flat,pico-second laser source. This source [3] is based on a
Ti:sapphire oscillator that generates 100 fs pulses with aProceedings of FEL 2007, Novosibirsk, Russia
repetition rate of 79.33 MHz locked with the 36th subharmonic of the SPARC S-band master clock. The measured time jitter is within 1 ps. An acousto-optic dispersive filter, called DAZZLER, is placed between the oscillator and the amplifier to modify the spectral amplitude andphase function to obtain the target temporal profile [4]. The
amplifier delivers pulses at 800 nm with energy of 50 mJ
and a repetition rate of 10 Hz. The pulses go to the third
harmonic generator and UV pulses at 266 nm are produced.
At the end of the laser chain there is a grating stretcher tostretch the pulses temporally up to 8-12 ps [5]. After thatthe optical transfer line transports the laser beam at normal
incidence to the cathode with an energy between 50 and
100 µJ.
Since the uniformity of the transverse distribution strongly
influences the beam brightness, a dedicated laser cleaning
has been performed with 10 µJ and 100 µm spot size diameter, resulting in the increase of the mean quantum efficiency (QE) from 2.3 10−5 to 10−4 (Fig.2). An improvement of the emission uniformity has been found over a 4
mm square area, which allowed to get the nominal beam
parameters (1 nC electron beam charge, with 50 µJ laser
pulse energy at 120 MV/m peak field on the cathode).

Figure 2: Copper cathode quantum efficiency before (left)
and after (right) the laser cleaning.

The Emittance Meter
At the gun exit the beam is quasi-relativistic and conventional methods to measure the transverse emittance are notadequate due to the fact that internal collective forces playa fundamental role in the beam transport. For such spacecharge dominated beams, the most appropriate technique
to measure RMS (root mean square) transverse emittanceis the one based on the pepper pot method. This technique,which consists in splitting the beam into several beamlets
by means of a multislit mask intercepting the beam or, alternatively, a single slit moving across the beam spot, isimplemented in a device, called emittance meter, able toscan the 2 meters long region downstream the gun along
the beam line. The emittance can be measured in both x
and y planes at different positions along the direction ofbeam propagation in the range 1098 - 2100 mm following the emittance oscillations. In particular, due to the highmeasurement resolution, the entire distribution in space and

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angles can be precisely reconstructed from the sampling
in both directions, allowing the full characterization of thebeam transverse dynamics.
The complete knowledge of the beam parameters at different distances from the cathode is important also for defining the injector settings which optimize the emittance compensation process and for code validation.
Beyond a transverse diagnostics, the emittance meter allows also to get information on the beam longitudinal parameters. By selecting the central part of the beam witha slit, the evolution of the energy spread can be measured
at different z positions. The very good agreement between
measurements and PARMELA model, which does not take
into account the wake-fields effect, points out that the influence of the long emittance meter bellows is negligible(Fig.3).

Figure 3: Evolution of the energy spread versus z for two
different bunch charges compared with a PARMELA simulation.

DATA ANALYSIS
For the first time direct emittance evolution measurements and experimental studies of dynamical behavior
have been done.
Since the beam appears different during its propagation
along z, the estimation of the right beam halos and thepreservation of the same cut level at different locations are
critical issues to deal with. Indeed, conventional image processing tools might introduce artifacts which could coversmall fluctuations in the beam emittance dynamics.
Furthermore, the large amount of data collected has demanded the development of an automatic procedure fordata processing. At this purpose, three independent algorithms, based on different approaches, have been developed
for the emittance calculations: i) a single image analysis
and data extrapolation [6], ii) a trace space plot filtering [7]and iii) a genetic-based algorithm [8].

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Single Image Analysis and Data Extrapolation
The main program data flow is shown in Fig.4. It consists of four routines.

trace spaces.
Montecarlo simulations have demonstrated that this peak
appears in the transition between signal and noise, if thesignal-to-noise ratio and the speed of the signal increment
over the noisy background are high enough. Assuming thispoint to be 100% of the beam charge, it is possible to define
an emittance value depending on the charge cut level.

Genetic Algorithm

Figure 4: The analysis software data flow. The central column corresponds to the routine names, the left one shows
the input parameters while the right one the output parameters.
The first one is the core of the algorithm oriented to distinguish the signal from noise; it takes raw beamlets images as
input and after processing their profiles it calculates fromthem the moments of the beamlet charge distribution, i.e.
beamlet area, centroid and rms width along the direction
perpendicular to slit edges.
The second routine takes as input the files saved by the firstone, cleans data from bad values and calculates the emittance in two different ways: i) by averaging slit parameters and/or ii) by averaging different emittances calculated
from each single parameter. The third routine reconstructs
and saves the trace space for each single emittance measurement and the fourth one interpolates the trace space inorder to have more sampling along the abscissa and thencalculates the emittance from the trace space with the desired cut in charge.
This analysis procedure automatically operates a cut on the
charge effectively considered in the emittance computation,
whose level cannot be trivially retrieved. For this reason
and to validate and support the data analysis method, twomore algorithms have been developed, both starting fromthe transverse phase spaces.

The basic concept relies on the fact that a real beam canbe thought as composed by N sub-beams of different densities drawing concentric ellipses in the trace space, withdifferent slopes and covering areas of different intensities.
Starting from the interpolated phase space, the code generates an intensity distribution function from which the total intensity and the cut parameter are retrieved. Each ellipse is described by the three Twiss parameters and thetrace space centroid by two coordinates. A family of N solutions, called chromosomes, is generated, each of whichcorresponding to 2+3N parameters. Therefore the best setof ellipses is found by maximizing the Intensity/Area function, the area corresponding to the beam geometric emittance.
The code is optimized for N=8, but it can accept any number of ellipses. Fig.5 shows a very good agreement between
the genetic solution, given by the union of the eight analytical ellipses, and the projected distribution of the real bunch.

Phase Space Filtering
The goals of this code are the calculation of the emittance value directly from the phase space data and thequantification of the cut level introduced on the beam by
the previous algorithm.
The idea is to quantify the contribution of every pixel to thetotal emittance, retrieving the value of the x, x’ and using itin the Courant-Snyder invariant to calculate the emittance.
The emittance can then be used as sorting parameter, sothat pixels with the highest contribution on the emittancevalue, probably outside the beam core, are withdrawn.
Starting from these pixels the total charge and the second
derivative of the emittance with respect to the charge is calculated. A phenomenological evidence has shown a deep,
sharp peak in the second derivative in all the reconstructed
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Figure 5: Real beam sampled with 8 ellipses representing
the best chromosome.

Comparison
Many different emittance curves have been analyzed andhere is shown one of the most significant to compare all
the codes. Indeed, the small amplitude of the double minimum oscillation is an excellent candidate to check thatevery method is able to resolve it. Experimental data arecompared in Fig.6 to a numerical fit with the PARMELA
tracking code, showing a very good agreement [9].

Proceedings of FEL 2007, Novosibirsk, Russia

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The cutting level is 95% for the phase space algorithm and
97% for the genetic-based algorithm.

(a)Figure 6: Comparison between different algorithms and
PARMELA simulation.

RESULTS HIGHLIGHTS
Comparison between Gaussian and Flat-Top
Pulse

(b)

An accurate study, supported by PARMELA simulations(Fig.7), has been done to show how the beam dynamics
strongly depends on the laser pulse rise time. It is evident

Figure 8: a) Gaussian-like and flat-top-like pulse shapeswith the same FWHM = 8.7 ps. b) Measured emittanceevolution of Gaussian and flat top beams compared withPARMELA simulations.
Fig.8b. The comparison points out that the minimum emittance value is reduced from 2 to 1.5 mm-mrad by using aflat-top shape instead of a gaussian pulse, accordingly withPARMELA simulations.

High Brightness BeamA large number of runs were devoted to maximize thebrightness by minimizing the transverse emittance. The
best result, obtained with the flat-top longitudinal profile
shown in Fig.9, is presented in Fig.10 [10]. The minimum

Figure 7: PARMELA simulation of the emittance evolution
for pulses with different rise time.
that under the same conditions, the shortest rise time gives
not only the smallest emittance minimum, but it makes also
the double minimum oscillation more pronounced, whereas
at longer rise time it turns into a knee.
Experimentally we compared two different pulse shapeswith the same FWHM equals to 8.7 ps, but with different
rise time: 5 ps for the Gaussian-like pulse and about 2.5 ps
for the flat-top-like pulse (Fig.8a). The resulting emittanceevolution in the vertical plane, for a beam of 0.31 mm rms
spot size, 0.74 nC charge and 5.4 MeV energy, is shown in

Figure 9: Laser pulse longitudinal profile: FWHM = 9 ps,
rise time = 2.7 ps.

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emittance, for a beam with peak current of 92 A, is 1.6
mm-mrad, giving a peak brightness of 7 1013 A/mm2 . The
injection phase was set to -8 deg with respect to the maximum energy gain phase and the rms spot size was 360 µm.
The simulation made with PARMELA (solid line in the plotof Fig.10) reveals a very good agreement with the experimental data.

amplitude of the oscillation is about 0.3 µm which is above
the resolution of our measurement system.

Figure 12: Double minimum emittance oscillation withcorresponding PARMELA simulation.

Figure 10: Emittance as function of the longitudinal coordinate for high brightness beam.

Double Minimum Signature
The peculiar space charge regime which, in the flat
top pulse mode, gives rise to the emittance oscillation,observed up to now in numerical simulations only andon which photoinjectors worldwide have based the mostcommon compensation design, has been revealed [11] bystrongly reducing the rise time down to 1.5 ps (the longitudinal profile is shown in Fig.11) and moving the injection
phase of 12 degrees behind the phase of maximum energy
gain in order to increase the beam energy spread accordingly with the chromatic nature of the effect. The bunch

Figure 11: Laser pulse longitudinal profile: FWHM = 5 ps,
rise time = 1.5 ps.
charge was 0.5 nC in a 5 ps FWHM laser pulse length, corresponding to 100 A peak current. The beam energy was
5.5 MeV.
The evolution of the emittance along z, in very good agreement with PARMELA simulations, is shown in Fig.12. The
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Phase Space Analysis
Emittance oscillations have been explained as produced
by a beating between head and tail particles oscillating withdifferent plasma frequencies caused by correlated chromatic effects in the solenoid [12].
In the space charge dominated regime, simulations show across shape in the transverse phase space of a flat top distribution at its relative emittance maximum, corresponding
to the beam waist (Fig.13b), due to the fact that each slice,
which shapes the beam up, has the same weight in current. Thus, under laminar condition, the space charge dominated waist is reached at different positions by the head
and the tail of the bunch (Fig.13b, left picture), so that when
the bunch tail (green slice) is already diverging the bunchhead (red slice) is still converging, resulting in the observed
cross shaped transverse phase space.
In the Gaussian pulse case (Fig.13a), this effect is less pronounced since the amount of current at the bunch tails is
smaller, thus causing the bunch tails to go through a crossover and only the central slices through a waist [13], [14].
A comparison of the transverse phase space at the beam
waist as retrieved from beam measurements for both Gaussian and flat top distribution is reported in Fig.14. According to theory, experimental data show that a flat top
beam goes through a space charge dominated waist passing from convergent to divergent, resulting in the typicalcross shape in the reconstructed transverse phase space(Fig.14b), while it is absent in case of Gaussian beam
(Fig.14a).

CONCLUSIONS
The initial phase of the SPARC project is concluded
showing, for the first time experimentally and due to a movable diagnostics, the oscillation of the emittance in the region, downstream the RF gun, where the emittance com-

Proceedings of FEL 2007, Novosibirsk, Russia

WEAAU02(a) Gaussian beam(a) Gaussian beam(b) Flat top beam

Figure 13: PARMELA simulation of the transverse phasespace for a beam approaching its waist. Left pictures show
the ensemble of slices shaping the beam up: green is thebunch tail, light blue the center of the bunch and red thehead.
pensation process is predicted by theory. The high sensitivity of this diagnostics has allowed also to fully reconstruct
the beam transverse phase space from which, due to thevery high sampling rate, the emittance dynamics has been
reproduced in excellent agreement with the simulation.
The large amount of data collected has required the development of automatic tools for data processing which gives
a validation of measurement results, being all quantitatively
consistent with simulations and with each other.

ACKNOWLEDGMENTS
The authors wish to thank V. Lollo for his contribution
to the system mechanical design, engineering and bench
testing, F. Anelli and S. Fioravanti for their work on motor
controllers. Thanks also to A. Battisti, L. Cacciotti, L.A.
Rossi, R. Sorchetti and S. Strabioli.

REFERENCES[1] SPARC Project Team,Technical Design Report for the SPARC Advanced Photoinjector,
http://www.lnf.infn.it/acceleratori/sparc (2004)[2] L. Catani et al., Review of Scientific Instruments 77, (2006)
93301.
[3] C. Vicario et al., “Drive Laser System for SPARC Photoinjector”, Proceedings of the PAC’07, Albuquerque, NM,
USA, June 2007.

(b) Flat top beam

Figure 14: Reconstructed (left) transverse phase spaceat the beam waist compared with PARMELA simulation(right).
[5] S. Cialdi et al., Applied Optics 46, 22, (2007) 4959.
[6] D. Filippetto, “A robust algorithm for beam emittance andtrace space evolution reconstruction”, SPARC/EBD-07/002,
LNF-INFN, June 2007.
[7] A. Cianchi et al., “Accurate emittance calculation fromphase space analysis”, SPARC/EBD-07/003, LNF-INFN,
July 2007.
[8] A. Bacci et al., “A Genetic Code able to compute the emittance value of a real beam by a Multiple Ellipse Slice Analysis of the transversal phase-space image”, SPARC/EBD07/004, LNF-INFN, July 2007.
[9] C. Ronsivalle et al., “Comparison between SPARC emeter measurements and simulations”, Proceedings of the
PAC’07, Albuquerque, NM, USA, June 2007.
[10] A. Cianchi et al., “High brightness electron beam emittanceevolution measurements in SPARC RF photoinjector”, submitted to Phys. Rev., ST-AB.
[11] M. Ferrario et al., “Direct measurement of double emittance minimum in the SPARC high brightness photoinjector”, submitted to Physical Review Letters.
[12] M. Ferrario et al., “Recent Advances and Novel Ideas forHigh Brightness Electron Beam Production Based on PhotoInjectors”, The Physics and Application of High Brightness
Electron Beam (World Scientific Publishing Co. Pte. Ltd.,
2002).
[13] B.E. Carlsten, Nucl. Instrum. & Methods A 285, (1989) 313.
[14] L. Serafini, J.B. Rosenzweig, Phys. Rev. E 55 (1997) 7565.

[4] S. Cialdi et al., Optics Letters 31, (2006) 2885.
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Proceedings of FEL 2007, Novosibirsk, Russia

SUPERCONDUCTING PHOTOINJECTOR
Ilan Ben-Zvi, Andrew Burrill, Rama Calaga, Xiangyun Chang, Ranjan Grover, Ramesh Gupta,
Harald Hahn, Lee Hammons, Dmitry Kayran, Jorg Kewisch, Robert Lambiase, Vladimir N.
Litvinenko, Gary McIntyre, Damayanti Naik, David Pate, David Phillips, Eduard Pozdeyev, Triveni
Rao, John Smedley, Roberto Than, Robert J. Todd, Dan Weiss, Qiong Wu, Alex Zaltsman, BNL,
Upton, Long Island, New York
Michael Cole, Michael Falletta, Douglas Holmes, John Rathke, Tom Schultheiss, Robert Wong,
AES, Medford, New York
Alan Murray Melville Todd, AES, Princeton, New Jersey
Abstract
One of the frontiers in FEL science is that of highpower. In order to reach power in the megawatt range, one
requires a current of the order of one ampere with areasonably good emittance. The superconducting laserphotocathode RF gun with a high quantum efficiency
photocathode is the most natural candidate to provide thisperformance. The development of a 1/2 cellsuperconducting photoinjector designed to operate at up
to a current of 0.5 amperes and beam energy of 2 MeV
and its photocathode system are the subjects covered inthis paper. The main issues are the photocathode and its
insertion mechanism, the power coupling and High Order
Mode damping. This technology is being developed at
BNL for DOE nuclear physics applications such as
electron cooling at high energy and electron ion colliders..

INTRODUCTION
In the past few years we are witnessing the growth of a
new class of particle accelerators: high-power, highbrightness electron beams. This emerging technology isenabled by the combination of high-brightness electron
sources and high-current SRF Energy Recovery Linacs(ERL). While the current state-of-the-art is at about 10
mA current [1] (the Jefferson Laboratory FEL upgrade),
there is interest in much higher currents, in the range of
0.1 ampere to over 1 ampere CW, with emittances that areof the order of under 1 to a few 10’s microns normalized
rms, depending n the application, in particular on thebunch charge.
What are the applications driving this interest? First, as
the Jefferson Laboratory example suggests, high power
Free-Electron Laser (FEL) is one candidate. The highbrightness is required for the lasing conditions at UV or
shorter wavelength, and significantly higher currents aredesirable for high power FEL applications [2]. The energy
required for such applications is not very high, in therange of 100 MeV to less than 1 GeV for UV high-power
FELs.
The next application is also for the production ofelectromagnetic radiation, but for mostly spontaneousemission. This is the ERL based light sources [3,4]. For_______________________________________________________________________________________________________*Work done under the auspices of the US Department of Energy#
benzvi@bnl.gov

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290this application the current may be in the range of 100
mA, less for the extremely high brightness X-ray radiationor higher for flux dominant applications. The requiredenergy is between 3 and 10 GeV.
Another application is in an altogether different field,
electron ion colliders [5]. In this type of machine a currentof hundreds milliampere electrons or polarized electrons
is needed at energy of up to 10 or 20 GeV.
A somewhat specialized application is electron coolingof hadron storage rings, in particular heavy ion beams [6].
This application requires electron beams at currents of up
to 0.1 amperes but relatively low energies of under 100
MeV. Finally, there are a host of other applications thathave been demonstrated but are still under development:
X-ray sources via Thomson scattering of laser on theelectron beam and terahertz radiation a examples.
The electron gun and injector design is arguably themost critical part of the ERL. It is here that the ultimate
performance of the ERL is determined: What will be its
current, its bunch structure, and its transverse andlongitudinal emittances. These parameters can only be
degraded in subsequent parts of the ERL, never improved.
The gun and injector are also the most dynamic elements,
with rapid progress being made. It has some of the mostintractable problems, in particular the issue of providing agood photocathode and dealing with severe space-chargeinteraction and limited space. The flip side of this is that
any improvement made in this relatively small element
affects the performance of the complete ERL and caneasily lead to dramatic improvements.
In this paper we will look at the technology andchallenges confronting the development of high-current,
high-brightness electron sources and describe theapproach taken by the few laboratories which are actively
developing this technology: Brookhaven National
Laboratory and Advanced Energy Systems, KF
Rossendorf, the University of Peking and DESY.

THE CURRENT STATUS OF SRF GUNSThe first pioneering experimental work on asuperconducting RF gun took place about 15 years ago in
Wuppertal by Michalke [7]. The activity in the area of
SRF guns around the world is growing steadily.
Successful milestone operation of a SRF gun with asuperconducting half-cell cavity were carried out in 2002

Proceedings of FEL 2007, Novosibirsk, Russia
at the Forschungszentrum Rossendorf [8], and a new SRF
photoinjector for CW operation at the ELBE linac isunder development [9]. The conclusion from thesuccessful operation of the half-cell SRF injector cavity at
Rossendorf is addressing the crucial question if thephotocathode inside the superconducting cavity reduces
the quality factor due to particle pollution. During about
200 hours operation time, such an effect was not seenusing CsTe2 cathodes. It also demonstrates convincinglythat a reliable mechanism for inserting a normalconducting cathode stem into a superconducting cavity
does not affect the good performance of the SRF cavity.
Following this initial success the Rossendorf groupembarked on the design and production of a 3 ½ cell gun
which has also various other improvements for getting thesmallest emittance out of the device, including carefulshape optimization, bunch focusing by a high-order RF
mode, symmetrized input coupler and improved tuner
system [9]. Other SRF guns have been built and operated.
An all niobium RF gun developed by BNL, AES and JLabdemonstrated large charge (10 nC) in a short (~10 ns)
bunch train [10,11]. The University of Peking started very
early on a novel hybrid pulsed DC - a half cell niobium
gun [12]. The team at Beijing is now proceeding with a 3½ cell gun [13, 14]. Superconducting photocathodes in asuperconducting RF gun are pursued by a DESY-JLabBNL collaboration [15], where good SRF performancehas been combined in proof-of-principle ½ cell gun andphotoemission has been measured. This led to a new 1 ½
cells gun with sophisticated RF design [16]. Following
early successes, a new generation of guns is emerging,where multi-cell guns with improved geometries, focusing
and coupling aim at a small emittance at higher average
currents, 1 to 10 mA, as called by UV or x-ray FELs.

THE BNL – AES SRF GUN
The main feature of the BNL-AES gun, seen in Figure
1., is the design for a very high current, up to 0.5 ampere,
for a variety of applications as described above, inparticular for electron cooling and electron-ion colliders.
Table 1 shows the parameters of the BNL-AES SRF gun.
It has been optimized [17] to obtain a small emittance at alarge charge by shaping the gun cavity, selection of its
frequency and field.

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The gun design is dictated by the objective of a highcurrent but at a limited (1 MW) CW klystron power. Thusa single cell design is used, which allows for a highaccelerating field at a limited total voltage of 2 MV.
The choice of frequency was dictated by the need tomaintain the frequency a harmonic of the RHIC frequency
with 360 bunch pattern of 28.15 MHz, lower thefrequency to a value where beam breakup thresholdcurrent in the ERL will be large and, finally, a frequency
where CW MW klystrons are available. That led to the
choice of 703.75 MHz.
This SRF gun is equipped with a demountable
photocathode capable of being inserted and retracted
while maintaining the vacuum integrity and cleanliness ofthe photoinjector. A schematic of the photoinjector andassociated helium vessel is shown in figure 1.
The cavity iris had to be made small for beam dynamics
reasons (reduction of effective length of the cavity). That
precluded damping all HOMs through the beam pipe.
HOM damping is an important issue. It was found thatthe beam pipe diameter could be kept at 10 cm, the same
dimension as the iris of the cavity and still adequately
propagate most of the HOMs. Other benefits of having
reduced beam pipe size is simplification of strong
coupling of the 1 MW RF power to the beam, as well as
reduction of the size of the gate valve needed at the end of
the beam pipe, a tremendous weight and cost savings.
Table 1: BNL-AES SRF Gun Specifications
Parameter

Units

Value

Frequency

MHz703.75

Iris radiuscm

5Equator Diameter

cm

37.9

Cavity lengthcm

25

Beam kinetic energy

MeV

2

Peak electric field

MV/m

35.7

Peak magnetic field

A/m

58740

Stored energy

Joule

8.37

QRs (geometry factor)

Ω

3.52

R/Q

Ω

96

Qe (external Q)

Fig. 1. The BNL-AES SRF electron gun.

37000

Power input

MW

1

Maximum current

mA

500

Emittance at 1.4 nC

μm rms normalized

1.4

Cathode recessmm1

Cathode spot size

mm diameter5

Emission phase

Degrees25

Longitudinal loss factor

V/pC

0.7

Transverse loss factor

V/pC/m32

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Additionally, a focusing solenoid, constructed from ahigh temperature superconductor, will be inserted justinside the gate valve in order to help decrease the beamemittance. This will be much easier with the reduced
beam pipe size as it will significantly reduce the amountof material needed to make the solenoid, significantly
reducing the power needed to drive the solenoid andsubsequently the heat generated during its operation.
The gun propagates all but 3 of the HOMs down the
beam pipe to be strongly absorbed by a ferrite HOM
absorber at room temperature. The three trapped modes
can be easily missed by harmonics of the beam repetition
frequency and detailed calculations have shown that theeffect of long range wake fields can be neglected if thebeam amplitude and phase noise are under a reasonable
limit. It is expected that the strong coupling of thefundamental power couplers will damp some or all ofthese modes. Work is in progress on this question.
The gun design accommodates a load-lock cathodeinsertion mechanism, which is introduced through adouble quarter-wave choke joint which accepts a UHV
cathode transporter. The photocathode will be extended
approximately 1 meter into the photoinjector andpositioned at the exact location for operation.
The cathode transporter, in turn, couples to a UHV
cathode preparation chamber. The locking mechanism has
been designed with UHV requirements and introductionof minimal particulate matter into the cavity. The quarterwave choke joint is much easier to fabricate than thealternative proven design, presently used by Rossendorf,
which incorporates a more complex arrangement
including an additional, detuned cavity. The quarter wave
choke joint concept has undergone preliminary testing andwill be subsequently tested using a fully SRF 1.3 GHz
photoinjector presently in place at BNL.

PHOTOCATHODE ISSUES
The photocathode is the single most difficult issue for ahigh-current electron gun.
What are the requirements for a high-current
photocathode suitable for this gun?
1. Avoid contamination of the SRF gun.
2. Provide high quantum efficiency.
3. Long life.
4. Prompt emission.
5. Ideally, allow exposure to air to simplify installation.
6. Provide a low thermal emittance.
The initial choice of a cathode for this gun is the multialkali photocathode. As described above, there is aprovision for inserting an independently cooled,electrically isolated photocathode into the photoinjector.
The cathode insertion device is a complicatedarrangement that must satisfy a number of different
criteria. It must be electrically and thermally isolated
from the cavity in order to avoid additional heat loads tothe cryogenic system due to the fact that the cathode ismaintained at an elevated temperature relative to thecavity and because of the high average current being
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extracted from the photocathode. It must also be designed
such that when inserted there is a means of avoiding
multipacting or other RF losses through the insertion
mechanism. This is being addressed using the quarterwave choke joint mentioned above.
The photocathode we have pursued is CsK2Sb [18], andwas selected based on its high quantum efficiency andconvenient operational wavelengths. (QE of 2-14% at 532
nm and 10-30% at 355 nm) The fabrication of thephotocathode is a process that is highly dependent on theexact deposition system configuration, thus making it
difficult to directly import a recipe from another source.
The general technique, obtained through our collaboration
with David Dowell at SLAC, formerly at Boeing, is todeposit ~200 Å of antimony followed by the deposition of~150 Å of potassium and then deposition of cesium while
monitoring the QE. The cesium deposition is terminatedwhen the QE reaches a maximum.
The technological challenges presented by using a
CsK2Sb photocathode in a SRF photoinjector revolvearound the vacuum conditions to which the photocathodeis exposed. All the multi-alkali photocathodes require
extremely good vacuum conditions, 10-10 Torr or better, inorder to maintain their designed QE for a reasonable
length of time. At BNL we demonstrated over 2 months
storage of CsK2Sb photocathodes in 2x10-10 Torr vacuum.
Vacuum degradation during operation in the gun should
not be a problem in an SRF photoinjector as it ismaintained at 2K.
The temperature of the photocathode in the gun is
reduced to bellow room temperature. The operation of
the CsK2Sb photocathode has been tested down to 170 K
and has seen only a 10% decrease in QE.
Another possible approach to photocathodes has been
proposed and is under investigation [19. The idea is to“amplify” the emission from a photocathode. A thin (ofthe order of 30 micrometers) diamond window is
positioned between the photocathode and the gun. The
diamond has a thin metal coating facing the photocathode,and a monolayer hydrogen facing the gun. A DC voltage
is applied between the metal layer on the diamond and thephotocathode. The primary electrons are generated in thephotocathode by a laser, accelerated in the gap between
the photocathode and the diamond and strike the diamondwith 5 to 10 KeV. The primary electrons produce a large
shower of secondary electrons and holes (using about 13
eV of primary energy per electron-hole pair). The
electrons and holes are separated quickly by the field in
the diamond (produced by the RF gun). The holes areabsorbed into the metal layer. The electrons drift throughthe diamond, thermalizing to a small fraction of anelectron volt in the process, and exit the diamond to thegun. A critical element here is endowing the diamond side
facing the gun with a negative electron affinity, by
bonding hydrogen to the diamond’s dangling bonds.
The emission is prompt and has very low thermalenergy. The diamond properties are such that the heatgenerated by the various processes (mainly the primaryenergy deposition, RF heating of the metal layer and theProceedings of FEL 2007, Novosibirsk, Russia
heat generated by the transport of the electrons throughthe diamond) is conducted efficiently to the walls with an
insignificant temperature gradient. In addition, themechanical strength of the diamond promises that thecapsule may hold atmospheric pressure for transporting
the evacuated photocathode. The hydrogenated diamondsurface is very robust, and can be carried through air for
installation without losing its negative electron affinity.
The main difficulty with the diamond amplification
process is trapping of electrons in the surface boundary
layer, either a hydrogenised diamond facing an anode(emission measurement) or a metal coating on the
diamond, serving as an anode (transmission
measurement).
In the work done so far we demonstrated that the
expected gain of about 77 secondary electrons per 1 keVof a single primary electron’s energy can be achieved intransmission measurements by removing trappedelectrons either by the transmission of holes (while thefield in the diamond is reversed) or by a small amount oflight (such as a laser pointer). This can be seen in Figure
2, where gain (defined as the ratio between the collected
anode current and primary current) is shown as a functionof the field in the diamond for various primary electronenergies. The loss in the metal layer is measured to be 3.5
keV. At every primary energy we see the gain curve for“single pulse”, which avoids the accumulation of trappedcharge, and a curve for continuous operation using a few
milliwatts of green laser for de-trapping.
Work is in progress on hydrogenised diamond, in which
the trapping is deeper.

Fig. 2. Gain in transmission with trapping eliminated.

REFERENCES[1] S. Benson, D. Douglas, P. Evtuschenko, K. Jordan, G.
Neil, and T. Powers, “Operational Aspects of HighPower Energy Recovery Linacs”, Proceedings LINAC
2006, Knoxville, Tennessee, August 20-25, 2006.
[2] V. Litvinenko, I. Ben-Zvi “Potential Use of eRHIC’s
ERL for FELs and Light Sources”, Proceedings, 2004
International FEL Conference, Trieste, Italy, August29-September 3, 2004.

WEAAU04[3] C. Sinclair, “ERL Based Synchrotron Radiation Light
Sources”, Proceedings ERL’05 workshop, Newport
News, VA, March 20-23, 2005.
[4] I. Ben-Zvi and S. Krinsky, “Future Light Sources
Based upon Photo-injected Energy Recovery Linac”,
Synchrotron Radiation News 14, 20 (2001),[5] I. Ben-Zvi, et. al., “ERLs in High Energy and Nuclear
Physics”, Proceedings ERL’05 workshop, Newport
News, VA, March 20-23, 2005.
[6] Ilan Ben-Zvi, et. al., “R&D towards cooling of the
RHIC Collider”, 2003. Nuclear Instruments andMethods in Physics Research A532, 177, (2004)[7] A. Michalke, “Feasibility of a photoemission sourcewith superconducting RF cavity”, AIP Conference
Proceedings 279, 761, (1993).
[8] D.Janssen et al., “First operation of a superconducting
RF-gun”, NIM A, 507 (2003) pp 314-317.
[9] A. Arnold et al, “Development of a superconducting
radio frequency photoelectron injector”, NIM A 577(2007) 440–454[10] H. Bluem, M.D. Cole, A.M.M. Todd, I. Ben-Zvi, T.
Srinivasan-Rao, J. Schill, “Photocathode Electron
Source Development at Advanced Energy Systems”,
Proceedings EPAC 2000, June 2000.
[11] T. Rao, I. Ben-Zvi, A. Burrill, H. Hahn, D. Kayran, Y.
Zhao, P. Kneisel, M. Cole, “Photoemission Studies on
BNL/AES/JLab All Niobium, Superconducting RF
Injector”, Proceedings PAC 2005, Knoxville,
Tennessee, May 16-20, 2005.
[12] C. E. Chen, R. L. Geng, J. H. Song, L. F. Wang, J.
Yu, B. C. Zhang, K. Zhao, “A Hybrid Laser-driven Ebeam Injector Using Photo-cathode Electron Gun andsuperconducting Cavity”, Proceedings EPAC 1996,
Sitges, Spain, June 10-14, 1996.
[13] Kui Zhao, Private communication, August 2007.
[14] S. Huang et al, “Beam Loading Tests on DC-SC
Photoinjector at Peking University”, Proceedings 2004
FEL Conference,
Trieste, Italy, August 29 –September 3, 2004.
[15] J. Sekutowicz et al, Nb-Pb Superconducting RF-Gun,
Proceedings EPAC’06, Edinburgh, Scotland, June 2630, 2006.
[16] Jacek Sekutowicz, Private communication, August
2007[17] R. Calaga, I. Ben-Zvi, M. Blaskiewicz, X. Chang, D.
Kayran and V. Litvinenko, “High current
superconducting gun at 703.75 MHz”, Physica C:
Superconductivity, 441, 159, (2006)[18] A. Burrill, I. Ben-Zvi, T. Rao, D. Pate, Z. Segalov, D.
Dowell, “Multi-Alkali Photocathode Development at
Brookhaven National Lab for Application inSuperconducting Photoinjectors”, Proceedings PAC
2005, Knoxville, Tennessee, May 16-20, 2005.
[19] T. Rao, I. Abdel, I. Ben-Zvi, X. Chang, J. Grimes, R.
Grover, J. Smedley, R. Todd, J. Warren, Q. Wu, J.
Bohon, D. Fischer, D. Dimitrov, “Status of Diamond
Secondary Emission Enhanced Photocathode”,
Proceedings 2007 ERL Workshop, Daresbury,
England, May 21-25, 2007.

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Proceedings of FEL 2007, Novosibirsk, Russia

A COMPACT ELECTRON SPECTROMETER FOR AN LWFA*
A.H. Lumpkin**, R. Crowell, Y. Li, and K. NemethArgonne Accelerator Institute, Argonne National Laboratory, Argonne, IL 60439, U.S.A
Abstract

EXPERIMENTAL BACKGROUND

The use of a laser wakefield accelerator (LWFA) beam
as a driver for a compact free-electron laser (FEL) has
been proposed recently. A project is underway at Argonne
National Laboratory (ANL) to operate an LWFA in the
bubble regime and to use the quasi-monoenergetic
electron beam as a driver for a 3-m-long undulator for
generation of sub-ps UV radiation. The Terawatt Ultrafast
High Field Facility (TUHFF) in the Chemistry Division
provides the 20-TW peak power laser. A compact electron
spectrometer whose initial fields of 0.45 T provide energy
coverage of 30-200 MeV has been selected to characterize
the electron beams. The system is based on the Ecole
Polytechnique design used for their LWFA andincorporates the 5-cm-long permanent magnet dipole, the
LANEX scintillator screen located at the dispersive plane,a Roper Scientific 16-bit MCP-intensified CCD camera,
and a Bergoz ICT for complementary charge
measurements. Test results on the magnets, the 16-bit
camera, and the ICT will be described, and initial electron
beam data will be presented as available. Other challenges
will also be addressed.

The 20-TW laser at TUHFF consists of a three-stage
chirped-pulse amplified Ti:Sapphire laser system runningat 10 Hz. The 15-fs (FWHM) seed pulse train from theoscillator is stretched to 440 ps in a double-pass single
grating stretcher, and then a Pockels cell pulse picker isused to lower the repetition rate to 10 Hz. The beam
passes through a three-stage amplifier and then is directed
into a two-grating pulse compressor resulting in a 600-mJ,
30-fs (FWHM) pulse of 20 TW. A schematic is shown in
Fig. 1. A more detailed description of the laser system canbe found elsewhere [6]. The compressed laser beam isthen directed into the interaction chamber and focused toabout 30 µm size onto the 1.2-mm-diameter supersonicHe gas jet. Electron pulses of relativistic energies are
generated and pass through a rotating Cu disk that blocks
the laser beam, but transmits the electrons to a sample or
the electron spectrometer or other diagnostics.

INTRODUCTION
One of the challenges of the laser wakefield accelerator(LWFA) project is generation of robust, quasimonoenergetic electron beams. At the AAC06 Workshop
a number of laboratories reported observation of such
beams ranging in energies from 10s of MeV to 1 GeV
with charges ranging from 10 s to 100 s of pC [1]. The
Chemistry Division is currently using and developing an
LWFA within their Terawatt Ultrafast High Field Facility(TUHFF) [2]. Although pulsed radiolysis chemistry
experiments are the primary objective, an initiative todemonstrate an LWFA operating in the bubble regime [3]with quasi-monoenergetic beams is being driven by
Strategic LDRD funds. A long-range goal of this projectis to use the beam to drive an undulator for generation ofultrafast spontaneous radiation. Other laboratories havetargeted the possible driving of a free-electron laser (FEL)[4]. As part of the present ANL project, characterizationof the electron beams generated is a critical aspect.
Towards this end an electron beam spectrometer is needed
to measure the electron beam spectrum to look for theenergy peak and energy spread. This is in addition to abasic charge measurement and a beam divergencemeasurement. The compact spectrometer design is basedon that reported by Glinec et al. [5].
______________________*Work supported by the U.S. Department of Energy, Office of
Science, Office of Basic Energy Sciences, under Contract No.
DE-AC02-06CH11357.
**
lumpkin@aps.anl.gov
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Figure 1: Schematic of the TUHFF with the Ti:Sapphireoscillator, pulse stretcher, three amplifiers, pulse
compressor, and the interaction chamber.

Compact Electron Spectrometer
The major components of a compact electron
spectrometer based on the Ecole Polytechnique University
LOA design [3,5] are the permanent magnet dipole; thescintillator screen at the dispersive plane; the 16-bit CCD
camera with optics, which views the screen; and an
integrating current transformer (ICT) for complementarycharge measurements.
Permanent Magnet Dipole: The two NdFeB magnets
are 5 cm long by 2.5 cm wide by 1.2 cm thick. Magnet
characterization was performed by the APS Magnetic

Proceedings of FEL 2007, Novosibirsk, Russia
Devices Group in their ID magnet measurement facility.
Both magnets were characterized and their reference files
generated. This was requested in case there is subsequent
radiation damage to the magnets from energetic electrons
in the LWFA. A collimator may be appropriate before themagnets. The one magnet field strength vs. z plot wasdetermined. A gap was selected to replicate the 0.45 T
values of the LOA magnets [4]. That gap is 12 mm fortwo magnets, although there is an end effect that may
reduce the effective dispersion. This provides coveragefor 20-, 50-, 100-, and 200-MeV electrons with varying
dispersion resulting in energy resolutions of 6, 14, 27, and53%, respectively [5]. In addition, effective energy
resolution can be limited by the natural divergence andbeam size at the scintillator screen.
With the completion of the magnet holder assembly, thetwo magnets were positioned with a 12-mm gap, and the
combined fields in this configuration were measured in
the APS magnet measurement facility. The plot of fieldstrength versus z is shown in Fig. 2. The total field isabout 0.46 T as expected with some end effects again thatwill reduce the effective dispersion 5-10%.

WEAAU05

and minimally process images. Other programs are used
for profile analysis.
The ICCD was taken to the APS S35 optics lab for
calibration and resolution tests. We also simulated aworking configuration of the PCs being 100 ft away inanother lab from the camera control unit and camera head.
This is basically how it would run in the LWFA lab.
The camera was mounted on a rail with carriers so the105-mm F-mount Nikon zoom lens could be used at
different working distances. The calibration lab has aplatform holding a filter wheel that includes a backilluminated 15-µm diameter pinhole as a resolution test
object and a grid pattern for spatial calibrations. The
platform can be moved in three dimensions for centering
the source or scanning the field of view and for precise zmotion relative to the camera lens distance to optimize
focus. A photograph of the setup is shown in Fig. 3.

Field (T)
0.5

0.4

0.3

0.2

Series1

0.1

0
0

50

100

150

200

250

-0.1

z (mm)
Figure 2: Map of the field strength along the z axis fortwo 5-cm long magnets with a 12-mm gap. The horizontal
axis is in mm (courtesy of Isaac Vasserman, APS).
LANEX Scintillator: Extensive tests have been done
previously with the Kodak x-ray screen called LANEX[4]. This is essentially a Gd2O2S:Tb inorganic scintillator
with efficient conversion of both x-ray and electron
incident energies. It has been reported to give similarenergy absorption per electron for electron energies from
10 MeV to 500 MeV so it is a good candidate for theconverter screen in the spectrometer [4]. These emit in theblue-green with a strong component at 548 nm, which is agood wavelength match to CCD quantum efficiency
curves.
16-bit ICCD Camera: A Roper Scientific 16-bit
camera was selected for use as the readout of the energy
information displayed on the screen. The camera is
Peltier-cooled and has a 1024 × 1024 array with 13-µmsquare pixels. It has a PCI card that includes the digitizers
to provide 16-bit deep images. The microchannel plate(MCP) intensifier tube is of a high quality with 6-µmdiameter channels for the 18-mm-diameter tube. There isa Roper software package loadable on the PC to display

Figure 3: Photograph of the ICCD camera on the S35
optical calibration table. Calibration factors and resolution
tests were done for various lens distances.
The tests were initially done at working distances of 14
cm, 17.3 cm, and 29 cm. The grid pattern was used toobtain the calibration factor in each case. A bright square,
10 mm on each side, was used as the main reference. Fine
features in the pattern were used for initial focus
adjustments. We then selected the pinhole source andscanned the z direction over several mm. An example ofthe preliminary depth-of-focus results for a working
distance of 17.3 cm is shown in Fig. 4, where the FWHM
resolution is 2.5 ch or 50 µm. These data show that forthis lens setting, resolution can be degraded if the z
position is off by 3 mm from the center of the focus curve.
A separate Air Force line-pair pattern was used as well at
this working distance.
Additional working distances were used at 40, 50, 60,
and 70 cm, but the resolution test was not done because
we had consistently obtained the 2.5-ch FWHM result,just with different calibration factors. The calibration
factors and expected field-of view (FOV) are shown in
Table 1. With our LWFA geometry we will view thescintillator back at the 40-70 cm working distance withthe camera located outside the chamber looking throughthe port. A pumpout port was moved, and we installed awindow in the port more directly downstream of the

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Proceedings of FEL 2007, Novosibirsk, Russia

10

3.0

z-position(mm) vs FWHM (ch)ICT Integated Signal (nV-s)

Image FWHM (Ch)

6

4

2

2.0

1.5

1.0

0.5

0

0.0

56

58

60

62

64

66

Figure 4: Depth-of-focus scan for a working distance of
17.3 cm for the 105-mm lens. The 2.5 ch (FWHM)
resolution would be 50 µm for this calibration factor.
interaction zone for viewing images on the back of thescintillator.
Table 1: Summary of the Calibration Factors and FOVs
for 105-mm Zoom Lens Working Distances
Working Distance
(cm)
14.0
17.3
29.0
40.0
50.0
60.0
70.0

Calibration Factor(µm/pixel)
13.7
19.6
36.9
50.0
62.5
74.0
89.3

FOV
(cm)
1.4
2.0
3.8
5.1
6.3
7.6
9.1

ICT: A Bergoz ICT is expected to be used in vacuumwith a return loop added to provide complementarycharge measurements (although the LOA experiments
indicated background issues and gave a large error bar on
absolute measurements [5]). Initially the existing Faraday
cup will be used for experiments.
The ICT was tested using an HP 8114A pulse
generator. With the pulse width set at 10 ns, one could set
the level to 1 V to have 10 nV·s injected on a wire passing
through the center of the ICT. This corresponded to 0.2
nC into a 50-ohm test load. The voltage level was
adjusted to vary the injected charge, and the results areshown in Fig. 5. The integrated ICT signal output wasdetermined using the Agilent Infinium 54854A
oscilloscope operating in the “integrate mode.” The scope
trace had ~16 mV peak with 30 ns (FWHM) for the 0.2nC input. This means that a low-noise environment isneeded for seeing 10 s of pC pulses in the LWFA.

Proposed Layout
The LWFA main chamber is ~1.3 m in diameter; however
the location of the gas jet nozzle is on one side of a 30cm-diameter pumpout port centered in the chamber floor
and is ~35 cm from the chamber wall. This latter distanceis a constraint for installing hardware downstream of the
FEL Technology I

0.0

0.2

0.4

0.6

0.8

1.0

1.2

Equivalent Charge (nC)Z-position (mm)296

Equiv. Charge(nC) vs int.of ICT(nV-s)

2.5

8

Figure 5: Test results for the Bergoz ICT showing theequivalent charge input and the signal response output(integrated) of the ICT in nV·s.
nozzle. First the rotating copper disk is put in, whichblocks the intense laser beam and transmits generated
electrons. A 6.2-cm lead collimator with a 10-mmdiameter hole at beam centerline may be needed. The
magnets are 5 cm long with a 12-mm gap, and the
LANEX screen is positioned 17 cm downstream from theentrance edge of the magnets. The LANEX is fronted by athin Aluminum foil to block laser light leakage if there isany. The screen is about 10 cm wide by 2.5 cm high. The
ICCD camera with lens has been positioned at the port toview the back of the LANEX at a working distance TBD,
but on the order of 40-70 cm to give the FOV in energy.
Two mirrors in the optical path outside the chamber
redirect the scintillator light to the lead-shielded camera
location. The camera is mounted on a Newport rail
supported by a small optical breadboard. The small
Faraday cup will initially be positioned for charge
measurements. Installation is nearly completed except for
final alignment and electrical signal connections.
An initial experiment will be done with no magnets tolook for low divergence beams at the LANEX with the
FC and camera behind the LANEX. If there is a lowdivergence electron beam, there should be quasimonoenergetic beam as well based on our interpretationof the literature [3]. Also, we can check for the calculated
beam size asymmetry with the larger size in the directionof the incident laser polarization as reported by Nemeth etal. [7]. Since the polarization is horizontal in the ANL
LWFA, we may need to rotate the spectrometer plane.
With enough charge and signal, the complementary OTR
experiments from the disk downstream side and a thin foil
could be pursued. If there is any microbunching of thebeam at blue-shifted wavelengths of the fundamental laser
wavelength, the signature should be confirmable with avisible light spectrometer.

EXPERIMENTAL AND ANALYTICALRESULTS
As mentioned in the previous section, the ANL results
are only in an early phase although prompt electrons weregenerated and used for photolysis experiments in the pastProceedings of FEL 2007, Novosibirsk, Russia

(

y (m)

x (m)

[2]. Simulations were done at ANL using the code
VORPAL to evaluate the expected performance of thepresent LWFA [7,8]. Beam energies of the order of 100
MeV are expected with a plasma density of ~5 × 1018
e/cm3 and the properly focused laser spot (1018 W/cm2) atthe gas jet. As shown in Fig. 6, the e-beam should actuallyexhibit some longitudinal structure which is analogous to
SASE-induced microbunching in an FEL. In this case it is
the structure impressed by the co-propagating laser fields
as the trapped electrons are accelerated though theplasma. Coherent OTR would be generated when such
beams transit a dielectric boundary. Such an effect has
been reported in the last year by Glinec et al. [9]. In
another development, the use of colliding laser beams to
produce a more controlled injection of electrons into the
LWFA process has resulted in tunable beam energies andmore reproducible performance as reported by J. Faure etal. [10]. The longer range goal to use an LWFA beam todrive undulator radiation is schematically shown in Fig. 7.
As techniques improve one can expect continued progressin beam quality in regards to energy, energy spread,charge, and emittance. It is difficult to predict theevolution time at this point, but generation of 10-GeV
beam by the time of ACC08 is the community target [1]with 1 GeV already demonstrated [11].

1.800

1.806

1.800

z (mm)

1.806

z (mm)

Figure 6: Simulation of the LWFA bubble regime for x-z
polarization plane (left) and y-z plane (right) displays of
microbunching.
e–dipoleFigure 7: A schematic of the LWFA beam generating
spontaneous emission radiation in an undulator.

SUMMARY
In summary, the ANL LWFA project is on the verge ofgenerating electrons again, and a compact electron
spectrometer has been installed to look for quasi-

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monoenergetic beam behavior. The challenge ofgenerating enough charge (100s of pC) with low
emittance and energy spread will have to be met before
serious work with an undulator would be feasible. The
initial ultrafast pulse lengths of the laser can betransferred to the trapped electrons in the bubble regime
so generation of short-pulse radiation from an undulator is
feasible.

ACKNOWLEDGMENTS
The authors acknowledge the support of R.Gerig and
K.-J Kim of the Argonne Accelerator Institute and theassistance of I. Vasserman, B. Yang, J. Power, A. Brill,
and T. Pietryla on component testing and of S.
Chemerisov for LWFA interaction chamber setup.

REFERENCES[1] Proceedings of the AAC06, M. Conde and C.
Eyberger (Eds.), July 15-22, 2006, Lake Geneva, WI,
AIP Conf. Proc. 877 (2006) and references therein.
[2] D.A. Oulianov et al., “Ultrafast Pulse Radiolysis
Using a Terawatt Laser Wakefield Accelerator,”
submitted to J. Appl. Phys. (2006).
[3] V. Malka et al., “Monoenergetic Electron Beam
Optimization in the Bubble Regime,” Phys. of
Plasmas 12, 056702 (2005).
[4] C.B. Schroeder et al., “Design of an XUV FELDriven by the Laser Plasma Accelerator at the LBNLLOASIS Facility,” Proc. of FEL06, Berlin, Germany,pp. 455-458 (2006); http://www.jacow.org.
[5] Y. Glinec et al., “Broadrange Single Shot Electron
Spectrometer,” Ecole Polytechnique report dated July
6, 2006.
[6] R.A. Crowell et al., Radiat. Phys. Chem. 70, 501(2004).
[7] Karoly Nemeth et al., “Laser driven coherent betatronoscillation in a laser-wakefield cavity,” submitted to
PRL 2007.
[8] Yuelin Li, private communication, February 14, 2007.
[9] Y. Glinec et al., “Observation of Fine Structures in
Laser-Driven Electron Beams Using Coherent
Transition Radiation,” Phys. Rev. Lett. 98(19),194801 (May 2007).
[10] J. Faure et al., Nature 444, 737 (2006).
[11] W. Leemans et al., “GeV electron beams from a
centimeter-scale accelerator,” Nature Physics 2, 696699 (01 October 2006); Anthony Gonsalves et al.,“Experimental Demonstration of 1 GeV Energy Gainin a Laser Wakefield Accelerator,” Proc. of PAC07,
Albuquerque, NM, June 25-29, pp. 1911-1915(2007).

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ADAPTIVE 3-D UV-LASER PULSE SHAPING SYSTEM TO MINIMIZEEMITTANCE FOR PHOTOCATHODE RF GUN AND NEW LASERINCIDENCE SYSTEM
H. Tomizawa, H. Dewa, T. Taniuchi, A. Mizuno, T. Asaka, K. Yanagida, S. Suzuki, T. Kobayashi,
H. Hanaki, Accelerator Division, Japan Synchrotron Radiation Research Institute (JASRI/SPring-8),
Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan
F. Matsui, Creative & Advanced Research Department, Industrial Technology Center of Fukui
Prefecture, 61 Kawaiwashitsuka-cho, Fukui City 910-0102, Japan.
Abstract
We developed an adaptive 3-D shaping (both temporal(1D) and spatial (2D)) short pulse (80 fs~40 ps) UV-laser
system as an ideal light source for yearlong stable
generation of a low-emittance electron beam with a highcharge (1~2 nC/pulse). In its current form, the laser’s
pulse-energy stability has been improved to 0.2~0.3%(rms; 10 pps, 0.4 TW in femtosecond operation) at thefundamental wavelength and 0.7~1.4% at the thirdharmonic generation. Such improvement reflects anability to stabilize the laser system in a humiditycontrolled clean room. The pulse-energy stability of amode-locked femtosecond oscillator has been
continuously held to 0.3% (p-p) for 4.5 months (1% for
10 months), 24 hours a day. In addition, the ideal spatial
and temporal profiles of a shot-by-shot single UV-laser
pulse are essential to suppress emittance growth in an RF
gun. We apply a deformable mirror that automaticallyshapes the spatial UV-laser profile with a feedback
routine, based on a genetic algorithm, and a pulse stacker
for temporal shaping at the same time. The 3D shape ofthe laser pulse is spatially top-hat (flattop) andtemporally a square stacked chirped pulse. Using a 3Dshaped laser pulse with a diameter of 0.8 mm on thecathode and pulse duration of 10 ps (FWHM), we obtaina minimum normalized emittance of 1.4 π mm mrad witha beam energy of 26 MeV. We found that the last mirror
in the vacuum to make normal incidence is an obstacle
for the electron beam. Therefore, we developed theoptical elements for a new hollow laser incidence with anaxicon final focusing. We fixed temporal parameterswith the present mechanical pulse stacker and prepared a
new UV-pulse stacking system (fixed parameters)
consisting of three birefringence α-BBO crystal rods.

INTRODUCTION
We have been developing a stable and highly
effective UV-laser pulse as the light source of a photocathode RF gun [1] that in turn provides a highbrightness electron beam source to achieve future X-ray
light sources (FEL (free electron laser), Compton backscattering, etc.) since 1996 at SPring-8 (Synchrotron
Radiation Research Group). The electron source forseveral X-ray FEL projects [2-4] requires a very-lowemittance (high-brightness) electron beam as low as 1 π
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mm mrad. One of the most reliable candidates for thishigh-brightness electron source is a photocathode RF gun.
This type of gun generates an electron beam pulse from a
photocathode illuminated by a laser pulse. Ourdevelopment of this gun is oriented toward a yearlong
stable system for user experiments. It is necessary for thecopper cathode of this RF gun to have a UV-laser pulse
with a pulse width of ~10 ps and a photon energy of ~4
eV. Since we started to develop the laser test facility, twoissues related to the laser light source have arisen. One isthe energy stability of the UV-laser light source.
Therefore, we have stabilized the third-harmonic
generation (THG) of a CPA (chirped pulse amplification)
Ti:Sapphire terawatt laser system (Figure 1) as the laser
light source for the SPring-8 RF gun.
The other problem concerns the spatial and temporallaser profiles. To minimize the beam emittance of aphotocathode RF gun, the laser pulse shape should be
optimized three-dimensionally. Over the past six years at
SPring-8’s test facility for the photocathode laser lightsource, several 3-D shaping systems have beendeveloped from combinations of spatial (transverse: x-,y-axes) and temporal (longitudinal: z-axis) pulse shaping
methods (Figure 1). The spatial profile has to bemodified with a microlens array [5] or a deformablemirror (DM) [6]. In addition, the temporal profile has tobe modified with a spatial light modulator (SLM) [6-7]or the pulse stacker described in this paper. One of thecandidates for a reliable 3-D laser pulse shape has been
the cylindrical shape (spatially top-hat and temporally
square pulse). With a square-shaped 9-ps laser pulse, thelowest beam emittance of 1.2 π mm mrad at 1.0 nC/pulse
has already been achieved by J. Yang et al [7]. Previously,
we have demonstrated a UV-laser spatial profile shaped
as a quasi top-hat (flattop) with a deformable mirror used
to automatically optimize it with a feedback routine
based on a genetic algorithm. Using this top-hat laser
pulse (diameter of 1.0 mm on the cathode) with a pulse
duration of 5 ps (note: temporally, not square), we could
obtain low-emittance beam generation of 1.7 π mm mrad
[6] at a net electron charge of 0.1 nC/pulse. However, thebeam emittance at high charge was much larger. This
indicates that a 5-ps laser pulse is too short for the laser
spot diameter of 1 mm. (The charge density is too high.)

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Figure 1: Laser pulse growth and three-dimensional (spatially (2D) and temporally (1D)) shaping process: the pulse
duration of THG (263 nm) depends on the group delay dispersion (GDD) introduced by AO-modulator (DAZZLER:FASTLITE) after the stretcher (790 nm). To obtain a 20-ps pulse by stacking eight micro chirped pulses (three stages ofpulse stackers), micro chirped pulse duration should be optimized to 2.5 ps at the cathode by changing GDD withDAZZLER (also possible with shifting compressor length).
Therefore, we prepared longer square laser pulses of
10 and 20 ps generated by stacking equivalently split
2.5-ps Gaussian chirped pulses to obtain lower emittancein a higher-charge region. Three stages of pulse stacking
can generate a 20-ps pulse from eight 2.5-ps micro
chirped pulses. The purpose of introducing longer laser
pulses is to make the laser spot size on the cathodesmaller while still decreasing the charge density. The
small beam size helps to decrease the initial (thermal)
emittance, and the small charge density suppresses thespace charge effect. A 3-D particle tracking simulation
predicted that smaller beam emittance could be obtainedwith a laser pulse length of about 20 ps at 1.0 nC/pulse[8]. This simulation result implies an important
prediction, i.e. that electron pulse length can be
maintained around 10 ps with both 10- and even 20-ps
laser pulse lengths, due to electron bunch compression
during its acceleration in the RF cavity.

DEVELOPMENT OF YEARLONGSTABLE LASER LIGHT SOURCEWe chose the THG of a CPA Ti:Sapphire terawatt
laser system (repetition rate of 10 Hz) as the laser lightsource for the SPring-8 RF gun. At THG (central
wavelength: 263 nm), the femtosecond UV-laser pulse
energy is up to 2.5 mJ/pulse. In its current form, thelaser’s pulse energy stability has been improved to
0.2~0.3% (rms; 10 pps, 0.4 TW in femtosecond
operation) at the fundamental and 0.7~1.4% at the THG.
At the first stage of development, this stability had been
held for 1.5 months continuously, 24 hours a day. The
improvements we had passively implemented were tostabilize the laser system as well as the environmental
conditions. We introduced a humidity-control systemthat maintained humidity at 55% (fluctuating by less than
2% (p-p)) in a clean room to reduce electrostatic charge
on the optics. This system keeps dust particles awayfrom the optics and thus avoids burn-out damage. The
temperature was kept constant at 21±0.3˚C (p-p),
monitored on the laser table. The improvement in THG
stability results from the ability to stabilize the laser
pumping sources (Q-switched YAG) of the amplifierswith a temperature-controlled base plate in this humiditycontrolled clean room. This base plate for YAG
stabilization maintained temperature at 25˚C (fluctuatingby less than 0.1˚C % (p-p)). In addition, we are testing a
feedback system to control the long-term drift of the
YAG laser due to the lifetime of the flash lamp, which is
now limited to continuous operation of around fivemonths (in our record, 119,380,846 shots at max.) while
maintaining the high stability of the laser’s pulse energy
as mentioned above.

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800

800

700
Oscillator output (mW)Central Wavelength (nm)Spectral Bandwidth (nm)600

Oscillator Output (mW)
Spectral Bandwidth (nm)Central Wavelength (nm)

Oscillator Output (mW)
Spectral Bandwidth (nm)Central Wavelength (nm)

700

500
400

Oscillator Output (mW)

300

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400
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100

100

0

0

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5

10

15

20

25

Elapsed Time (day)Central Wavelength (nm)

600

0

20

40

60

80

100

120

140

Elapsed Time (day)Figure 2: Improvement in laser oscillator’s long-term stability (left: just passive, right: full-active, Femto-align &Femto-lock): With full-active feed-backing, the mode-locking and spectral distribution has been kept constant.
Aside from long-term drift of the pumping source
YAG, the long-term stability of the total laser system (inTHG) depends only on the stability of mode-locking at
the oscillator laser. A new oscillator laser (Femtosource
Synergy; Femtolasers Produktions GmbH) was installedin our system in April 2005. This oscillator was passively
stabilized with a temperature-controlled base plate(21±0.1˚C (p-p)). In the first long-term continuous
operation test run, its mode-locking was kept stablewithout any active stabilization for one month (left figureof Figure 2). However, laser parameters did not remain
constant. This indicates that pointing of the pumping
laser or laser self-focusing in the crystal (due to change
in cavity length) causes drift in the long term (1~2
weeks). When the geometrical configuration of the laser
cavity changes with these drifts, its mode-locking
becomes unstable. Therefore, for the second test run, we
introduced two active feedback systems (Femto-alignand Femto-lock; Femtolasers Produktions GmbH) tolock the geometrical configuration of the laser cavity.
Femto-align is designed to compensate for long-term
instabilities caused by environmental sources ofinterference such as thermal deformations or pumppointing drift. It avoids mode-locking failures andreduces unexpected fluctuations. It monitors the output
power and optimizes operations whenever deviations
occur. The active controlling mirror can compensate forlong-term instabilities of the total laser system. On theother hand, Femto-lock is a sub-ps-jitter synchronization
for the oscillators. It allows locking the round-trip
frequency of the oscillator pulses to a given reference
RF-source (ROHDE & SCHWARZ GmbH & Co. KG:
SMHU). The system comprises a fast piezo translator(PZT) in combination with a wide-range translation stage.
This arrangement allows the unit to compensate for fast

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fluctuations (~kHz) as well as for slow long-term drifts(e.g. mechanical deformations due to temperature drifts).
This combination of feedback guarantees drift-free
yearlong operation.
In the second long-term continuous operation test run,the oscillator was actively stabilized by utilizing both
Femto-align and Femto-lock, and it was operated at thelocked repetition rate of 89.25 MHz. This long-term
stability test had to be stopped for maintenance of theinfrastructure. The pulse energy stability of the modelocked femtosecond oscillator with a temperaturecontrolled base plate (21±0.1˚C (p-p)) was held at 0.3%(p-p) for 4.5 months continuously, 24 hours a day (rightfigure of Figure 2). Except for momentary line drop due
to natural disasters (thunderbolts, etc.) or infrastructure
maintenance, this oscillator has continuous yearlong
operation while maintaining constant laser parameters(pulse energy, pulse duration, spectral distribution, etc.)
The laser parameters have been kept constant without
any sign of instability. This indicates that the drifting
deformations of the laser’s geometrical configuration
could have been locked within the stable region of modelocking.

3D SHAPING EXPERIMENT WITH UVLASER PULSE
The 3D UV-laser pulse shaping system combined witha deformable mirror (transverse: 2D) and a chirped pulse
stacker (longitudinal: 1D) is shown in Figure 3. Utilizing
the long-term stable UV-laser source described above,
this system can generate a 3D cylindrical laser pulse.
Note that the original micro chirped pulse is optimized inits shape and pulse duration with DAZZLER (AOmodulator) at the fundamental. We explain both shaping
techniques in the following.

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Figure 3: Three-dimensional (spatially (2D) and temporally (1D)) UV-laser pulse shaping system: the 3D shaping
system consists of a deformable mirror (DM) and a chirped pulse stacker. These two shaping techniques can be
optimized independently because there is no interference between them. The schematic drawing of pulse stacking
shows 10-ps pulse generation by stacking four 2.5-ps micro chirped pulses (two stages of pulse stackers).

Top-hat spatial profile optimization withcomputer-aided deformable mirror
We used a computer-aided deformable mirror (topright photo in Figure 3) as a spatial shaper. This
deformable mirror consists of an aluminium-coated,
multilayer silicon nitride membrane and 59 small mirror
actuators behind the reflective membrane with a centerto-center distance of 1.75 mm between the actuators. The
outermost layer of the reflective membrane is protectedwith an MgF2 coating to maintain reflectivity at about~80% in the ultraviolet region. Adjusting voltages
between the control electrodes on the boundary actuators
results in fine adjustment of each mirror actuator; theadjustable region of the control voltages is between 0 and
255 V in steps of 1 V, making it possible to shapearbitrary spatial profiles in a total of 25659(~10141)
forming possibilities. However, such high adjustability
makes manual as well as simple algorithm adjustment
impossible.

Closed loop system for spatial shaping
A closed loop system is essential for a deformablemirror to optimize the laser’s spatial profile
automatically. We use a PC to control the electrodevoltage of the deformable mirror and to measure thespatial profile with a laser profile monitor (Spiricon, Inc.:
LBA300-PC). Laser light is reflected with deformationby the deformable mirror and monitored with the profile
monitor, whose analyzing program can provide many
parameters to evaluate the characteristics of beamprofiles. The program is remotely controlled by Active-X[9] control (Object Linking and Embedding), so we
could control the deformable mirror while monitoring thelaser beam parameters.

Algorithm for automatic control
This spatial shaping method with adaptive optics
requires a sophisticated algorithm. We developed
software based on a genetic algorithm (GA) toautomatically optimize the deformation of thedeformable mirror (DM). The set of voltages of wholeDM-electrodes are treated as chromosomes in theirapplication. At first, we prepared 50 chromosomes as theinitial population and used the MGG (Minimal
Generation Gap) method to select the surviving
chromosomes. The 59 DM-electrode voltages are applied
independently in the range of 0 to 255 V, and these werecoded to 59 elements in a chromosome.

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In this type of deformable mirror (electrostatic
actuator), the displacement in the central region of themembrane is proportional to the square of the electrodevoltage. In the initial population, applied electrodevoltages (chromosome element values) were randomly
selected from the set of discreet voltages (0, 42, 70, 93,
113, 131, 147, 162, 176, 189, 201, 213, 225, 236, 250 V)
to linearly change the displacement. In this procedure,chromosomes are treated as follows.
(1) Make a Family consisting of four chromosomes:
Two chromosomes are selected randomly from theinitial population to make the family, and thesechromosomes are placed as “Parents.” Then, theother two chromosomes as “Children” are generated
through the crossover of the chromosomes of the“Parents.” In our program, we prepared threedifferent methods of crossover: random crossover(in our case “58-point crossover”), one-pointcrossover, and two-point crossover. Thus, fourchromosomes are prepared and treated as “Family,”which is called “Generation” in GA. The mutation
rate was set 1% of the total number of generations.
(2) Drive the deformable mirror and obtain results of thelaser parameters from measurements of the laser’s

spatial profile. In the MGG method, the four chosen
chromosomes in the family are compared, and thetwo best chromosomes survive as superior. Drive thedeformable mirror by setting the chromosomes offour members of the “Family” (in the order“Father,” “Mother,” two “Children”) and obtaineach result of beam parameters calculated from theanalysis program of the laser profile monitor. The
beam parameters of the laser’s spatial profile are
obtained for evaluation in the following step.
(3) Evaluate the resulting parameters using a fitness
function. These results are scored by a fitness
function defined by top-hat beam shaping. The
fitness function is a linear combination of the nineparameters shown in Table 1 with each coefficient
as weight. If a chromosome is more highly scored in
the evaluation of the fitness function for top-hat, it
will be promoted to a higher position in the ranking
of “Family.” Thus, in this ranking, the chromosomes
are ordered by comparing values of the fitness
function.
(4) The two best chromosomes are selected as superior
and then returned to the population. This proceduremakes one generation step forward, and the
population is renewed to initiate the next generation.

Figure 4: Closed control system for experiment: With evaluation of top-hat (flattop) profiles on laser profiler (LBA300PC), the deformable mirror (DM) is automatically controlled to optimize the spatial profile toward the top-hat as atarget profile.
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Fitness function for genetic algorithm tooptimize spatial profile through evaluation ofbeam parameters
We chose nine useful parameters [6] to evaluate the
top-hat profiles. These parameters for top-hat shaping
and their functions are shown in Table 1. A fitness
function is made of the linear combination of theseparameters. The fitness function is used as an index forthe sophisticated program-based genetic algorithm. The
more the laser profile is closed to the target profile (tophat), the higher the value of the fitness function is. Thisis calculated for the spatial profile corresponding to eachchromosome to evaluate the spatial profile, spot-size
diameter, and centre position of the profile. Maximizing
the value of the fitness function with the GA-program,the computer-aided deformable mirror optimizes the
profile toward a target spatial profile such as the top-hat.
The most representative parameter is the Top Hat Factor(THF) [10], where THF is defined as an integral functionof the energy fraction as shown in Figure 5. After 2500
generation steps, an inhomogeneous spatial profile was
improved to the quasi-top-hat profile shown in Figure 6.

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Table 1: Parameters and their uses in fitness function toevaluate spatial profile optimization

Parameters of fitness function for top-hat (flattop)
shaping with deformable mirror
BeamCentreMinimise the difference from the initialcentre position (x, y)

THF

Maximise the Top Hat Factor (0~ 1)(Top-hat: THF=1.0; Gaussian: THF =0.5)

Effective
Area

Maximise the integrated energy within
the set circle area

Effective
Diameter

Minimise the difference
diameter of set circle

Flatness

Minimise the standard deviation divided
by the average in a top-hat area

Peak-topeak

Minimise the difference between themax. and min. in a top-hat area

Beam
Diameter

Minimise the difference from the set
diameter

Hot Spot

Minimise the max. in a top-hat area

Dark Spot

Maximise the min. in a top-hat area

from

the

SQUARE TEMPORAL PROFILE
GENERATION (UV-PULSE STACKER)
Principle and configuration of chirped pulse
stacker that is not affected by interference

Figure 5: Top Hat Factor (THF) [10] for evaluation ofTop-hat profiles: In the top figure, curve A is a Top-hat
beam with THF of 1.0, curve C a Gaussian (conoidal)
beam, and curve B is beam profile between Top-hat andGaussian.

Figure 6: Result of spatial profile optimized to Top-hat
with a deformable mirror (Laser profile monitor:
LBA300-PC). The figures are normalised with the peakintensity to avoid saturation of laser profiler pixels.

A pulse stacker is composed of sets of half-wave plates
and polarizing beam splitter cubes. One stage of thepulse stacker consists of a pair of a splitter and a halfwave plate. The full s-polarization is rotated to a 45degree polarization with a half-wave plate. It is thendivided into an s-polarized pulse and a p-polarized one
with the first polarizing beam splitter at each stage. The
p-polarized pulse is delayed with an optical delay line
and then combined with the s-polarized pulse after using
the next polarized beam splitter at each stage. Finally, as
shown in Figure 7, the chirped laser pulse of 2.5 ps isstacked with optical delay at each stage to generate alonger square pulse. By stacking eight micro chirped
pulses in three stages, we can obtain a 20-ps squarecombined pulse. The polarizing beam splitter cubes are
the optical contact type (Showa Optronics Co., Ltd.),
considering the high power density of the UV-laser pulse.
The diagram of the optical system and timing chart of thepulse stacker with a three-stage configuration are shownin Figure 8. At every stage of this pulse stacker, the spolarization pulse at the first splitter is always the originof the optical timing delay (see timing chart of Figure 8).
This makes it possible to keep the same origin of any

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timing delay, even if a 5-, 10- or 20-ps squarely
combined pulse is generated by masking a p-polarization
pulse at each corresponding stage.

Figure 7: Principle of chirped-pulse stacking (8 pulses:
three stages): Avoiding interference, the s- and ppolarized micro chirped pulses are alternatively stacked
with the optical delay as long as the micro pulse duration.

the delay line such that the s- and p-polarized pulses
reach the cathode at the same time. The procedure
determines the origin by utilizing the electron beampulse generated at the photocathode as follows [8]. Theenergy of the electron pulse is measured for two laser
pulses divided by each stage of the pulse stacker. Theenergy of the electron beam is measured as beam
positions on a florescence profile monitor after a bending
magnet downstream of the RF-gun cavity. To eliminate
the positioning jitter and short time drift, the beam
positions are measured 5000 times. The micrometer
position of the p-polarized pulse is tuned as these twoelectron beam pulses come to the same position on the
profile monitor after several iterations. The timing
precision of the origin was about 0.5 ps, estimated fromthe position jitter distribution. After this procedure, withDAZZLER, micro chirped pulse duration is optimized tomake the beam profile at the dispersion section
homogeneous.

NEW FIXED 3D-SHAPING SYSTEM
WITH HOLLOW LASER INCIDENCE
Through optimization with computer-aided DM andadjustable mechanical pulse stacker, we could improve
the laser’s 3D profiles and obtain their optimal
parameters to minimize emittance. Using a 3D-shaped
laser pulse with a diameter of 0.8 mm on the cathode andpulse duration of 10 ps (FWHM), we obtain a minimum
horizontal normalized emittance of 1.4 π mm mrad witha beam energy of 26 MeV, holding its net charge to a 0.4
nC/pulse. At a higher net charge of 1.0 nC/pulse, theminimum beam emittance is 2.0 π mm mrad withequivalent diameter and a longer pulse duration of 20-ps(FWHM). However, vertical normalized emittance isaround 1.5 times greater than horizontal. Considering theasymmetry of electrical field in the first coupler of thefirst accelerator tube, we rotated it 90 degrees to checkthe cause of the difference between x- and y- emittances.
Consequently, the vertical emittance was greater than theother, as the emittance difference before the experimentwith rotation of accelerator tube.

Figure 8: Optical system (upper) and timing chart(lower) of UV-laser pulse stacker: The drawings areshown in the case of three stages (pairs of polarizing UVlaser beam splitter cubes) of pulse stacker. The initial
UV-laser pulse duration is set to 2.5 ps for generating a~20-ps combined macro pulse. The pulse stacker kit iscommercially available (http://www.luminex.co.jp/)
under license from SPring8 /JASRI.

Finding the origins of optical delay lines
To generate a long pulse without any timing gap oroverlap, the origins of the optical delay lines must be
determined with a precision of less than 0.5 ps. The
origin is defined here as the micrometer-level position in
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Figure 9: The present normal incident system (left) andnew type of incidence with hollow optics (right): thefinal focusing axicon lens makes the spatial profile of the
top-hat at its ray crossing (focus) point (top-right).

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Then, we strongly doubt that the normal incident
mirror can be the cause of the emittance difference. In
particular, the higher charge the electron bunch is, themore significant the difference. Therefore, we developed
a new hollow laser incidence system as shown in Figure
9. The hollow inside-out Gaussian laser beam isgenerated by an axicon lens pair, and then reflected at thehollow mirror for normal incidence through the hollow
lens focusing to the photocathode.
In this new incidence system, the strategy for
generating top-hat spatial shaping has to change. Up tonow, we have obtained enough parameters to optimize
the 3D laser pulse shape. There seems to be no difficultyin generating top-hat or homogeneous profiles with fixed(not-adaptive) optics. As shown in the upper right of
Figure 9, using the axicon final focusing lens, there is aquasi-flattop region in the depth of a focus (ray crossing).
On the other hand, we fixed temporal parameters withthe present mechanical pulse stacker and prepared a new
UV-pulse stacking system (fixed parameters) consistingof three birefringence α-BBO crystal rods (Figure 10).
When the incident ray injects with an angle to the opticalaxis, the extraordinary ray delays to an ordinary ray in abirefringence crystal. We utilize this delay in the samemanner of the mentioned pulse stacker to generate a 20ps square stacked chirped pulse. In this method, we
rotate the crystal rods on the laser propagation axis
independently to control polarisations and compensate
angle of rotation, instead of using waveplates.

Figure 10: UV-laser pulse stacking rods: The angle ofrotation of each rod is shown.

SUMMARY & FUTURE
DEVELOPMENTS
For the shot-by-shot optimization of each laser-pulse
profile, the laser system should be passively stabilized
through environmental controls. At present, if theoscillator is stable without mode-locking failure, theoverall laser system can remain stable for yearlong
operation with the energy stability described in this paper.
During this potentially continuous yearlong operation,
every laser parameter was kept constant without any
signs of instability.
We demonstrate a 3D shaping (both temporal (1D) andspatial (2D)) short pulse (5~20 ps) laser beam as an ideal
light source for yearlong stable generation of a lowemittance electron beam with a high charge. At present,
we apply a deformable mirror that automatically shapes
the spatial UV-laser profile with a feedback routine,
based on a genetic algorithm, and a pulse stacker for
temporal shaping at the same time. The 3D shape of thelaser pulse is spatially top-hat (flattop) and temporally a

WEBAU01square stacked pulse. Using this 3D-shaped laser pulse(diameter: 0.8 mm; 10-ps pulse), we obtain a minimum
horizontal normalized emittance of 1.4 π mm mrad.
This high-brightness electron source has maintained
almost enough low emittance for X-ray FEL
requirements during yearlong continuous operation.
However, the vertical emittance is around 1.5 times
greater than the other. To solve this, we developed a newincidence method with a hollow laser generator. We havealready developed whole hollow optics. For thisrequirement of renewing 3D-laser pulse shaping, wehave developed the hollow axicon final focus lens for
spatial top-hat and UV-laser pulse stacking birefringencecrystal rods for square macro pulse up to 20 ps.
Precisely optimizing the 3D-shape of the laser pulse,
we are striving to generate a further high brightness
beam with an emittance as low as possible. Recently,
another candidate for a reliable 3D-pulse shape wasproposed for even lower emittance [11], which is anellipsoidal with equivalent fluence along the temporalaxis. In this case, a microlens array or deformable mirror
cannot help to generate such a three-dimensionallyellipsoidal distribution. A method using a fibre bundle isone solution to avoid the difficulty of adjusting different
optical paths [12]. The fibre bundle is a practical system
to shape both spatial and temporal profiles at the sametime during laser-pulse transportation. The principle ofthis shaping method involves, in practice, thousands ofpulse stackings in defusing the 3-D volume. However, it
is difficult to make a smaller laser spot size of ~ 1 mm on
the cathode for a realistic working distance of ~1 m inconventional cathode illumination. Therefore, we
proposed this shaping technique for only a backward
cathode illumination system to shorten the working
distance. For this purpose, we are developing atransparent cathode with several materials [13].

REFERENCES[1] T. Taniuchi et al., Proc. of FEL’96, 1996, p. 137.
[2] “TESLA Technical Design Report, PART V, The XRay Free Electron Laser”, ed. G. Materlik and Th.
Tschentscher, March 2001.
[3] “Linac Coherent Light Source (LCLS) Conceptual
Design Report”, SLAC-R-593, April 2002.
[4] J. Rivers, “SCSS X-FEL Conceptual Design Report”,
RIKEN, May 2005.
[5] H. Tomizawa et al., Proc. of EPAC02, 2002, p. 1819.
[6] H. Tomizawa et al., Proc. FEL05, 2005, p. 138.
[7] J. Yang et al., J. Appl. Phys. Vol. 92, 2003, p. 1608.
[8] H. Dewa et al., FEL06, 2006, p. 649.
[9] Operator’s Manual, Model LBA PC Series, Version
2.50, Spiricon, Inc.: Chapter 9, “ActiveX”.
[10] Operator’s Manual, Model LBA PC Series, Version
2.50, Spiricon, Inc.: Chapter 6.19, “Top Hat Factor”.
[11] C. Limborg-Deprey et al., NIMA 557, 2006, p. 106.
[12] H. Tomizawa et al., NIMA 557, 2006, p. 117.
[13] Japan Patent Application No. 2005-267593.

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Proceedings of FEL 2007, Novosibirsk, Russia

PERFORMANCE TESTS OF THE PHOTON MONOCHROMATOR FOR
SELF-SEEDING AT FLASH ∗R. Treusch, U. Hahn, J. Viefhaus, DESY, Hamburg, Germany
H.K. Bechtold, J. Hartvig, H. Juul, V. Toft, Aarhus University, Aarhus, Denmark
S.V. Hoffmann ISA, Aarhus, Denmark
C. Knöchel, LBNL, Berkeley, California, U.S.A.
R. Reininger, Scientific Answers & Solutions, Madison, Wisconsin, U.S.A.
R. Follath, G. Reichardt, F. Senf, F. Siewert, BESSY GmbH, Berlin, Germany
Abstract
A single pass FEL amplifier can produce extremely intense and fully coherent radiation at short wavelengths if it
is seeded by a coherent light beam resonant with the magnetic structure and collinear with the electron beam. Sinceat the present time a single pass SASE1 FEL is the only
source of sufficiently intense, tunable radiation in the soft
X-ray region, it has been proposed to use such a sourcein combination with a narrow-band monochromator forseeding an FEL amplifier [1]. By means of such a ”SelfSeeding”, the soft X-ray free electron laser FLASH [2] at
DESY will be modified so that it can provide coherent radiation in space and time in a wavelength range from about
60–6 nm (≈ 20–200 eV).
Here, we will focus on the performance of the photon monochromator beamline for the seeding which was
set up and tested at the synchrotron radiation storage ring
ASTRID in Aarhus. The optical and mechanical design
will be described along with results on the resolving powerof the monochromator which have been obtained scanning
across rare gas resonance lines at various energies.

INTRODUCTION
Since August 2005 FLASH is providing SASE radiation
for users, presently tunable from about 47–13 nm and soonfrom 60 down to 6 nm. The pulses possess a pulse length ofa few 10 fs, almost full transverse coherence, limited longitudinal (temporal) coherence and pulse energies from about
10–100 µJ. By means of the Self-Seeding (or Seeding Option) FLASH will be modified in a way that it can provide
fully longitudinally coherent, narrow-bandwidth radiation.
The output radiation will then exhibit all the characteristic
properties of conventional optical lasers but at much shorter
wavelengths and with a continuous tunability between 6
and 60 nm. The enhanced beam properties will extend therange of possible applications, particularly for high resolution spectroscopy and for all experiments which need fulllongitudinal coherence.
The Self-Seeding consists of an additional undulator section, a bypass for electrons and a photon monochromator
beamline. R&D in undulator design, FEL theory and elec∗ Work funded through HGF-Strategiefonds (01SF9935/1)
1 Self-Amplified Spontaneous Emission

FEL Technology II

306tron beam dynamics, as well as on photon beam propagation and optical components were important parts of the
project. The photon monochromator beamline aspect will
be detailed here. More details, also on all the other components can be found in [3].
The general layout of the Self-Seeding is sketched infigure 1. The first undulator operates in the SASE mode

Figure 1: Schematic setup (side view) of the Self-Seeding
for FLASH. Behind the first undulator, FEL radiation andelectrons are separated. While the electrons travel throughthe bypass represented by the four blue dipole magnets inthe upper part of the figure, the photons propagate acrossthe photon monochromator beamline below in order to provide a narrow-bandwidth seed that is overlayed with theelectrons again at the entrance of the second undulator.
in the “linear” (= exponential gain) regime, about 2–3 orders of magnitude below saturation. It produces intense,but structured light pulses as shown in the left part offigure 2. Subsequently electrons and photons are separated. Before they are overlayed again in the second undulator, the electrons travel through a magnetic chicanethat is used to remove the longitudinal density modulation (“micro-bunching”) of the electron beam which was
induced by the FEL process in the first undulator. For thephotons, a high resolution grating monochromator together
with some matching optics is used as a narrow-band filter
to provide the coherent radiation seed which is amplified
to saturation in the second undulator section. The resulting
spectral distribution is given in the right part of figure 2.
The requirements for the final seeding radiation pulse
are obvious: its photon wavelength has to be within thegain bandwidth of the FEL amplifier, the photon bandwidth
has to be narrow enough to provide a coherence length aslong as the electron bunch length, and the intensity of theProceedings of FEL 2007, Novosibirsk, Russia
50

dW/d(∆ω/ω) (mJ/%)dW/d(∆ω/ω) (µJ/%)

80

60

40

20

0
-1.0

sures that the seed pulse delivered by the monochromator
clearly dominates the shot noise in the second undulator
and is amplified to saturation. Figure 3 depicts the layoutof the beamline, while table 1 summarizes the parametersof the optical elements.

60

100

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40
30
20
10

-0.5

0.0

∆ω/ω0 (%)

0.5

1.0

0
-1.0

-0.5

0.0

0.5

1.0

∆ω/ω0 (%)

M5

M1
Und. 1cylindricalcylindrical

M3

Und. 2plane

Figure 2: Simulated typical frequency spectrum of a single FEL pulse (from [1]). Left: behind the 1st undulator(SASE, 2 orders of magnitude below saturation). Right: atthe exit of the 2nd undulator (seeded FEL in saturation).
seeding radiation has to be much larger than that of theshot noise2 coming from density fluctuations in the electron beam. Successful seeding then yields a spectral brilliance of FLASH that is up to a factor of 100 higher, i.e. theoutput power of the seeded FEL is concentrated in a single line which is about a hundred times narrower than the
spectrum of the conventional SASE FEL while the pulse
energy at saturation remains approximately unchanged. In
addition, the pulse now attains full longitudinal coherence.

PHOTON MONOCHROMATOR
BEAMLINE
The optical design of the photon beamline was performed applying computer programs that were partly developed for the Self-Seeding at FLASH [4, 5]. The programs combine standard ray tracing with a wavefront propagation of the simulated FEL beam from the end of the first
undulator section across the optical elements of the beamline. The output wavefront was used as input for FEL simulations calculating the amplification process in the second
undulator. This finally yielded numbers for the efficiencyof the seeding process, i.e. the quality of the coupling of
the seed pulse with the electron bunch.
In the final, optimized layout, the beamline consists ofthe monochromator, containing a premirror and a variedline spacing (VLS) spherical grating, and a pair of focusing
mirrors at each side of the monochromator. To minimize
the number of elements in the beamline, all the reflections
and the diffraction are in the same plane. Beside the desired
monochromator resolving power of E/∆E ≈ 10000 −
20000, the optical system was designed such that it produces a 1:1 image of the (complex conjugated) wavefront
at the entrance of the second undulator section. This way,
the optimum coupling, i.e. best longitudinal and transverse
overlap between the seed pulse and the electron bunch isachieved [1, 6]. The beamline optics were optimized forthe short wavelength end at 6.4 nm and will work satisfactorily up to about 60 nm [7]. The calculated efficiency ofthe beamline in the wavelength range from 5.8 to 77 nm
is better than 10% with carbon coated optics [8]. This en2 = spontaneous undulator emission along the first few gain lengths

M2
spherical
entranceslit

M4

VLS grating

spherical

spherical

exit
slit

Figure 3: Layout of the photon monochromator beamlineof the Seeding Option (side view). M1 to M5 denotes themirrors. For better visibility, the mirror angles and vertical displacements are greatly exaggerated. The distance
between undulator 1 and undulator 2 is 22 m, whereas the
maximum vertical distance to the straight line (for the grating and M4) is about 135 mm only (cf. table 1).
Table 1: Parameters of the photon monochromator beamline for the Self-Seeding [7]. Horizontal position means
left to right in fig. 3. Incidence angles are given with respect to the surface normal. Positions/angles for M3 andGrating are listed for both ends of the design scan range.
Component
M1: cylindricalM2: spherical
Entrance Slit
M3: plane
Grating: VLS,
spherical
Exit Slit
M4: spherical
M5: cylindrical
Start Und. 2:

Position (Hor./Vert.)[mm,mm]4500/
05844.86/-117.666844.86/-117.66
8879.75/-117.668946.89/-117.66
9020.75/-134.66
15552.1
16502.1
17500
22000

/
/
/
/

-134.66-134.6600Radius[mm]345.50 (sagittal)
41.360 × 103

Angle[Degree]
87.50
87.50

6.0457×106

86.56
83.52
88.28
86.77

25.70×103
530.75 (sagittal)

86.16
86.16

Layout of the mirror chambers
Due to the tight space, the mirror chamber design had tobe very compact. It was decided to have all movements ofthe mirrors outside the vacuum chamber, in order to avoid
a production of particles in the vacuum arising from friction of moving parts inside the chamber. From the stringent requirements of positioning accuracy in the µm andsub-mrad range it followed that one needs a very good resolution of the individual movements, in particular the adjustment of beam incidence angle (pitch), and a good reproducibility of the position settings. All, at most six, degrees
of freedom had to be “orthogonal”, i.e. decoupled. This
demanded high precision bearings, translation slides etc.,
a precise mounting and a robust construction. In the final
design, all movements were realized with a twofold suspension, as symmetric to the center of the mirror as possible.
Figure 4 shows an exploded view of the mirror chamber for
mirror M1. The four mirror chambers for M1, M2, M4 andM5 are, apart from minor differences regarding the mirror
holder, almost identical and based on a tested prototype.

FEL Technology II

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WEBAU03

Proceedings of FEL 2007, Novosibirsk, Russiazwhich are rotated via external movers that push/pull the respective lever arm of each cradle (Figure 5). High precision
radial bearings4 are employed for the suspension to guarantee the precision and rigidity of the rotational axes.

beam

Grating

roll

pitch

Angle
encoderyaw
xPitch GratingyFigure 4: Exploded view of the setup for mirror manipulation used for M1, M2, M4 and M5, including the vacuum
chamber. In the lower half one sees stacked tables for x-,
y- and yaw-movements which move the complete vacuum
chamber, including the mirror. The upper half shows nestedroll, pitch and z-movements that manipulate the mirror inside the vacuum chamber through a feedthrough connectedwith bellows.

Layout of the monochromator
The monochromator is the most crucial component of
the beamline with respect to alignment accuracy and desired resolution of the movements [3]. In particular, therequired precision and resolution of the pitch of the premirror M3 and the grating made it necessary to put these
two rotations inside the vacuum chamber and to attach stateof the art angle encoders with sub-µrad resolution3 rightat the corresponding axes, similar to some commerciallyavailable designs. The basic principle for the movementsof the monochromator was adopted from a patented layout [9] that has been applied for high resolution plane grating monochromators. Among its several advantages, thisdesign has a wavelength independent magnification along
the dispersion direction. The optical principles of the current monochromator are however, different. The focusing
and higher order aberration corrections are achieved with
only two elements, the plane mirror (M3) and the variable line spacing spherical grating (a more detailed discussion of the basic principles of the monochromator can befound in refs. [10, 11]). The mechanics for changing themonochromator wavelength setting consist of two nested
but separately suspended “cradles” for the grating and M3
3 Heidenhain RON905 UHV

FEL Technology II

308

Pitch M3

Figure 5: Drawing of the monochromator mechanics showing both, the in vacuum pitch movements via bellowcoupled linear feedthroughs as well as the external stacked
tables for x-,y- and yaw-movements. The vacuum chamber
mounted on the uppermost table has been omitted.
In order to span the wavelength range from 6-60 nmwith proper imaging properties and resolving power including some overlap, one needs three gratings with
800 lines/mm (≈ 4.5–16 nm), 356 lines/mm (10–36.5 nm)
and 160 lines/mm (from about 22 to even 83 nm). In contrast to the usual approach with three gratings on independent substrates, we decided to go with three holographically produced gratings side by side on a common spherical Si substrate. That way, the manufacturer (Zeiss) could
already – and much better than with individually aligned
gratings – ascertain that all gratings are nicely parallel to
one another and have all the same incidence (pitch) angle
as well as the same roll angle. The perfect optical qualityof the gratings regarding parameters such as slope errors,
radius of curvature and groove density variation – without
and also within the grating holder – was verified at BESSY
with the latest generation of nanometrology devices [12].

MONOCHROMATOR PERFORMANCE
In order to test the monochromator performance, inparticular its resolving power, the beamline was set up at
ASTRID from M1 down to the exit slit (without M4 andM5). A photoionization chamber (gas cell) was put justbehind the exit slit to measure the energy dependent ionization of rare gases by monitoring the ion current. Scanning
across resonances with linewidths of 1 meV and below– as in the case of doubly excited Helium around 64 eV –directly reveals the resolving power of the monochromator [13]. Other rare gas resonances, e.g. from
4 custom-made by Mahr, Göttingen, GermanyProceedings of FEL 2007, Novosibirsk, Russia
3

HEG
MEG

10 x 10

3

20 µm

9
8

exit slit:

7
6

LEG

40 µm

5
4

100 µm

3
20

30

40

50

60

70

80 90

200

100

Photon Energy (eV)Figure 7: Summary of the measured resolving power.
Filled squares: data from resonance measurements, empty
squares: simulation results [14] incl. lines to guide theeye. HEG / MEG / LEG=high / medium / low energy grating (800 / 356 / 160 lines/mm), respectively.

n=2+

30
Gas Cell current [pA]

20 x 10"Resolving Power"

Argon (around 244–250 eV) and Krypton (91–95 eV) withwidths of few ten to more than one hundred meV only
allow to estimate a lower limit of the resolving power atthese energies while still being very useful for accurateenergy calibration.
Figure 6 shows a scan across the He resonances after proper alignment and optimization of the beamline
at ASTRID. The width of the narrow resonances (e.g.
n=7+,8+) of only (3.5 ±0.5) meV yields a resolving powerof E/∆E ≃ 19.000 and is in very good agreement with therespective simulations [14]. Some more results are summarized in figure 7 in comparison to the simulations. Even
without a final optimization of all the beamline settings –which would have required a more detailed survey of alldegrees of freedom – we reached 90 % of the expected values and surpassed the requirements for the seeding at theseenergies by about a factor of two already. In addition, the

WEBAU03from the HASYLAB(DESY) experiment controls and vacuum groups and all the colleagues in the ISA workshopsthat manufactured most of the beamline mechanics and thevacuum chambers.

n=3+

n=4+
n=5+
n=6+ ...

20
n=3−
n=4−

REFERENCES
10

60

61

62

63

64

[1] J. Feldhaus et al., Opt. Commun. 140, 341-352 (1997)

65

Photon Energy [eV][2] W. Ackermann et al., Nature Photonics 1, 336-342 (2007)[3] R. Treusch, The Seeding Option for the VUV Free Electron
Laser at DESY, Final Report, DESY, Hamburg (2003), available on request (rolf.treusch@desy.de)n=7+

Gas Cell current [pA]

3.2

[4] R. Reininger et al., AIP Conf. Proc. 521, 458-462 (1999)

n=8+
n=9+

3.0

[5] R. Reininger et al., Nucl. Instr. and Meth. A 467-468, 38-41(2001)

n=10+
n=11+ ... 16+
2.8[6] E.L. Saldin et al., Nucl. Instr. and Meth. A 445, 178-182(2000)

2.6

2.4

65.1

65.2

[7] R. Reininger, Optics parameters of the beamline for theseeded FEL, Internal Project Report (2001), Ref. B7 on the
CD-ROM of Ref.[3]65.3

Photon Energy [eV]

1 0

Figure 6: Photoionization yield scan across the He P
resonances (raw data without further normalization). The
lower figure is a zoom into the tail of the Rydberg-series(n=7+ to continuum) of the upper figure.
aforementioned common grating substrate very much simplified alignment and operation, as expected. When, e.g. ,changing after proper energy calibration from one grating
to another, the relative energy setting on the new grating
was typically 0.2–0.5 ‰ (some 10 meV) off.
Based on our results we conclude that the monochromator beamline is mechanically very stable, precise, reproducible and fully within its specifications with resolving
powers between 10000 and 20000, i.e. bandwidths of a few
meV only. It meets all requirements for the Self-Seeding.
We would like to acknowledge the technical support[8] R. Reininger, VLS grating efficiencies and gratings specifications for the seeded FEL beamline, Internal Project Report (2002), Ref. B9 on CD-ROM of Ref.[3][9] German patent No. 3045931, U.S. patent 4,490,041, see als:H. Petersen et al., Rev. Sci. Instrum. 66(1), 1-14 (1995)[10] R. Reininger, A study of possible PGM beamlines for theseeded SASE free electron laser, Internal Project Report(1999), Ref. B2 on CD-ROM of Ref.[3][11] R. Reininger, A varied line-spacing spherical grating
monochromator for the seeded SASE FEL, Internal Project
Report (1999), Ref. B3 on CD-ROM of Ref.[3][12] F. Siewert et al., AIP Conf. Proc. 879,Part 1, 667-670 (2006)[13] M. Domke et al., Physical Review A 53, 1424-1438 (1996)
and refs. therein[14] R. Reininger, Expected performance of the seeding beamline at ASTRID, Internal Project Report (2003), available on
request (R.T.)

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Proceedings of FEL 2007, Novosibirsk, Russia

SINGLE-SHOT LONGITUDINAL BUNCH PROFILE MEASUREMENTS
AT FLASH USING ELECTRO-OPTIC DETECTION: EXPERIMENT,SIMULATION, AND VALIDATION.
B. Steffen∗ , E.-A. Knabbe, H. Schlarb, B. Schmidt, P. Schmüser, DESY, Hamburg, Germany
W.A. Gillespie, P.J. Phillips, Dundee University, Dundee, UK
S.P. Jamison, ASTEC, Daresbury Laboratory, STFC, UK
G. Berden, A.F.G. van der Meer, FELIX / FOM Insitute ’Rijnhuizen’, Nieuwegein, NL
A.M. MacLeod, Abertay University, Dundee, UK
Abstract
At the superconducting linac of FLASH at DESY, wehave installed an electro-optic (EO) experiment for singleshot, non-destructive measurements of the longitudinal
electric charge distribution of individual electron bunches.
The time profile of the electric bunch field is electrooptically encoded onto a chirped titanium-sapphire laser
pulse. In the decoding step, the profile is retrieved either from a cross-correlation of the encoded pulse with a
30 fs laser pulse, obtained from the same laser (electrooptic temporal decoding, EOTD), or from the spectral intensity of the transmitted probe pulse (electro-optic spectral decoding, EOSD). At FLASH, the longitudinally compressed electron bunches have been measured during FEL
operation with a resolution of better than 50 fs. The electrooptic process in gallium phosphide was numerically simulated using as input data the bunch shapes determined witha transverse-deflecting RF structure. In this contribution,
we present electro-optically measured bunch profiles andcompare them with the simulation.

SINGLE-SHOT ELECTRO-OPTIC
DETECTION
Precise measurements of the temporal profile of extremely short electron bunches are essential for a detailed
understanding of the bunch compression and lasing mechanisms in a SASE FEL. Single-shot electro-optic (EO) detection techniques are ideally suited for this purpose since
they are non-destructive and permit correlation studies between the time profile of electron bunches and the properties of FEL pulses produced by the same bunches.
The transverse electric field of a relativistic electron
bunch passing close to an electro-optic crystal corresponds
to a THz pulse traveling through the crystal. This THz
pulse induces a transient birefringence in the EO crystal
which can be sampled by a linearly polarized optical laser
pulse. In this experiment we use gallium-phosphide (GaP)
instead of the more common zinc telluride (ZnTe) as it offers a factor of two better time resolution. The electro-optic
temporal decoding (EOTD) technique was applied [1, 2]∗ email: bernd.steffen@desy.de

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310

fixed
delay

λ

/4 λ/2 AP

fs laseropticalstretcher

CCD
BBO

GaP

Figure 1: (color) Schematic drawing of the electro-optic
temporal-decoding (EOTD) experiment at the FLASH
linac. For details see text.
yielding the best time resolution of the single-shot EO detection methods.
The schematic setup is shown in Fig. 1. The titaniumsapphire (Ti:Sa) laser amplifier (pulse length 30 fs FWHM,
central wavelength 795 nm, pulse energy 0.8 mJ, repetition
rate 1 kHz) is synchronized to the 1.3 GHz accelerator RF.
The laser beam is split into two beams: the probe beamand the gate beam. The probe beam is stretched to 20 pswith a grating-pair optical stretcher and guided through apolarizer P to set the polarization parallel to the [-1,1,0]
axis of the EO crystal. It is then injected into the linac vacuum chamber and passes through the GaP crystal placed at
a distance of 4-5 mm from the electron beam. The birefringence induced by the Coulomb field of the passing electron
bunch is translated into a time-dependent elliptical polarization of the stretched probe beam. This in turn is converted into an intensity modulation with a half wave plate
and an analyzer A that is orthogonal to the polarizer P. Any
residual birefringence is removed by a quarter wave plate.
The EO-induced intensity modulation of the probe pulse
is measured through cross-correlation of probe and gate
pulse in a frequency-doubling BBO crystal. By overlapping the two pulses non-collinearly, a spatially dependent
time delay is introduced between the pulses. The BBO light(λ ≈ 400 nm) is imaged by an intensified CCD camera, andthe temporal profile of the electron bunch is derived fromthe light intensity as a function of position. The intrinsic
time resolution of the optical cross-correlator is σ = 25 fs(rms).
The electric field of the bunch is also arranged to be parallel to the crystallographic [-1,1,0] axis (aligned in horizontal direction), so that the main axis of the refractive

Proceedings of FEL 2007, Novosibirsk, Russia

SIMULATION OF THE ELECTRO-OPTIC
PROCESSI probe /I laser
0.03

0.02

0.01

-0.2

signalθ=2°

backgroundθ=2°
signal θ=0
0
0.1
0.2
Γ in rad-0.1

Figure 2: Normalized intensity of the probe beam as a function of the phase retardation Γ for θ = 0, and θ = 2◦ .

For ideal electro-optic sampling conditions the THz
pulse and the laser pulse should propagate through the EO
crystal at the same speed. In reality the THz phase velocity vph ( f ) is frequency dependent and differs from thegroup velocity vg of the optical laser. A numerical simulation code for the EO process was written [4] to account for
the velocity mismatch and to take also into consideration
the frequency dependencies of the electro-optic coefficientr41 ( f ) and of the THz amplitude transmission coefficient atthe vacuum-crystal interface
Atr ( f ) =◦index ellipsoid encloses an angle of 45 with the horizontal
axis and hence 45◦ to the laser polarization. When passing through the birefringent GaP crystal its two polarization components along the main optical axes of the crystal
acquire a relative phase retardation:Γ=

2π d 3n r41 ETHz
λ0 0

(1)

Here λ0 is the optical wavelength, d the thickness of thecrystal, n0 = n(λ0 ) the optical refractive index of GaP in
the absence of an electric field, r41 the electro-optic coefficient, and ETHz the amplitude of the THz field. Formula (1)is based on the simplifying assumption that THz and laser
pulse have the same propagation velocity in the GaP crystal.
Note that in electro-optic sampling (EOS) experiments
the delay between THz and probe laser pulse is varied infine steps and the THz time profile is obtained by averaging over many THz pulses. This scanning method isinadequate at FLASH because the time jitter between theelectron bunches and the Ti:Sa laser pulses is too large(> 100 fs). Therefore, single-shot methods are required,the best one being the EOTD technique described above.
The half wave plate shown in Fig. 1 can be used to obtainan EO signal that is either linear or quadratic in the THz
field. The intensity of the laser probe pulse impinging on
the BBO crystal depends on the phase retardation Γ and theorientation angle θ of the half wave plate in the form [3]Iprobe (θ, Γ) =WEBAU04

Ilaser[1 − cos(Γ + 4θ)]
2

(2)

2
1 + n( f ) + iκ( f )Here n( f ) + iκ( f ) is the complex index of refraction. In
the code the EO crystal is subdivided into thin slices ofthickness δd = d/N (typically N = 10 slices for a crystal
thickness of d = 100 µm), and both the THz pulse andthe laser pulse are propagated as wave packets through the
crystal. Pulse spreading and attenuation are explicitly taken
into account. In each slice the contribution δΓ to the phaseretardation is computed applying Eqn. (1) with the properdelay between the two wave packets in the respective slice.
The overall phase retardation Γ is obtained by summation
over all slices.
An alternative method is based on the so-called electrooptic response function:
"
!#
Z d
1
1
r41 ( f ) Atr ( f )−exp i 2π f zdz
G( f, d) =dvph ( f ) vg
0(4)
The phase retardation parameter can be computed from G
by inverse Fourier transformation. Figure 3 shows the absolute magnitude of the EO response function of gallium
phosphide calculated from published material data [5, 6, 7].
The strong oscillations are caused by the excitation of
the lowest transverse-optical lattice resonance of GaP at
11 THz. The vanishing response at about 8 THz is dueto the zero-crossing of r41 at this frequency. From thesecurves it is obvious that strong shape distortions will arise
if the THz pulse has significant Fourier components in theresonance region of GaP. Moreover, the GaP crystal thickness must be less than 100 µm if one aims for excellent
time resolution.
d=65 µm
175 µm300 µm|G(f)| [pV/m]

0.2

Here Ilaser is the intensity of the incident laser beam. EO
detection is frequently made at crossed polarization, corresponding to θ = 0. For small values of Γ the EO signal
is then proportional to Γ2 , see the black curve in Fig. 2.
Hence the EO signal is quadratic in the THz field. Rotating
the half wave plate by a few degrees leads to a larger EO
signal that is almost linear in ETHz , however, there is a nonvanishing background in the absence of an electron bunch(red curve in Fig. 2).

(3)

0.1

0
0

5

10
frequency [THz]15

20

Figure 3: The EO response function of GaP for a crystal
thickness of d = 65 µm, 175 µm, and 300 µm, respectively.

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Proceedings of FEL 2007, Novosibirsk, Russia

For benchmarking the EO process and determining its
performance limitations we have carried out simultaneous
measurements with the EOTD system and a transversedeflecting rf structure (TDS), featuring excellent time resolution. The TDS was developed at SLAC [8] and was
installed and commissioned at FLASH in cooperation withSLAC [9]. In the TDS, the temporal profile of the electron
bunch is transferred to a spatial profile on a view screen by
a rapidly varying electromagnetic field, analogous to thesawtooth voltage in conventional oscilloscope tubes. The
TDS at FLASH is a 3.6 m long traveling wave structure operating at 2.856 GHz. The bunches pass the structure nearzero crossing of the RF field and receive no net deflection
but are streaked in the transverse direction. A single bunchout of a train can be streaked. With a fast kicker, this bunchis deflected toward view screen that is imaged by a CCD
camera. The other electron bunches are not affected. The
time resolution of the TDS for the measurements presented
here is about 20 fs (rms).
An EOTD measurement on a longitudinally compressed
electron bunch, such as needed for SASE FEL operation, ispresented in Fig. 4. The TDS measurement on the adjacentbunch is also shown. The superior time resolution of the
TDS is evident. EOTD signals as short as 55 fs (rms) could
be measured using a 65 µm thick GaP crystal. The TDS
signal shape was used as an input for the numerical simulation of the EO process. The predicted EO signal shape is
as is shown in Fig. 4. Its main peak is in excellent agreement with the measured signal. Even the absolute normalization, not shown in the figure, agrees to within 20% to

26 fs

THz pulse

-0.2

-0.5

1 -0.50
0.5
time [ps]

43 fs
0.02
T DS trace
E T Hz, eff

2

0
0.2
time [ps]0.4

E O s imulated- bg

1.5

[t]

1
0.5

Figure 4: Steps in the comparison between TDS and EOTD
signal shapes using a 65 µm thick GaP crystal at an angle θ = 2◦ of the half wave plate. Left: From top to bottom: TDS signal, equivalent THz pulse at EO crystal, simulated EO signal. Right: Comparison between simulationand EOTD measurement. The simulated and the measured
signals are normalized to the same peak height. The widths
correspond to the rms values of the fitted Gaussian pulse
shapes.
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1simulation
2.5

0.4 -0.2

0
0.5
time [ps]30%, which is well within the expected fluctuations and theuncertainties of the EO material properties. The measured
signal shows a higher tail than the predicted one, which canbe attributed to wakefields trailing the electron bunch.
The observed broadening from σ ≈ 20 fs in the TDS datato σ ≈ 55 fs in the EO data is mainly due to the limitations
caused by the lattice resonance in GaP. For sufficiently longelectron bunches (σ ≥ 90 fs) the time profile as measured
by the TDS is faithfully reproduced by the EOTD signal,see Fig. 5.
In another measurement, we employed the simpler
EOSD method [10] which does not require a laser amplifier but has the drawback of an inferior time resolution. A
GaP crystal of 175 µm thickness was used. From Fig. 3,
we infer that frequencies above 5 THz are strongly suppressed in such a thick crystal. As a result both the simulated and the measured EO signals are significantly longer
than the real bunch, but both are in perfect agreement. The
TDS measurement is shown in the left part of figure 6. The
frequency dependent response function of the GaP crystal
leads to a significantly stretched equivalent THz pulse inside the EO crystal. In spite of the stretching the THz pulse
is still too short to be accurately reproduced by spectrally
resolved detection with a Ti:Sa laser pulse chirped to 1.5 ps(rms). Frequency mixing of the effective THz pulse and thelaser probe pulse leads to an additional broadening of thepredicted EO signal (green curves in fig 6). In the rightEO signal
simulation

0
0.2
time [ps]TDS

Figure 5: TDS and EOTD signals of bunches showing adouble peak structure due to a detuned compression system. The simulated EO signal is shown as a green curve inthe left panel.

arb. units

43 fs

55 fs
measurement

EOTD

EOSD signal I/I laser

TDS signal

EOTD signal

20 fs

EOTD signal

EXPERIMENTAL RESULTS

TDS signal

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simulation
measurements

0.01

0
-1

- 0.5

0

0.5

1

time [ps]

1.5

2

2.5

0

0

2
time [ps]4

Figure 6: Left: TDS measurement, simulated effective THz
pulse and simulated EO signal. Right: EOSD measurements of five consecutive compressed bunches in comparison with the simulated EO signal. Data were taken atθ = 2◦ using a 175 µm thick GaP crystal. The laser pulses
were stretched by chirping to σ = 1.5 ps.

Proceedings of FEL 2007, Novosibirsk, Russia

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part of figure 6 the predicted EO signal is compared to five
EOSD electron bunch measurements. Excellent agreement
is observed both in shape and amplitude. This indicates thatthe published GaP material properties and the resulting response function are correct. The comparison between thesimulated effective THz pulse and the EOSD signal showsthat in this case the signal width is not limited by the response function of the EO crystal but by frequency mixing
between chirped laser pulse and THz pulse.

CONCLUSION
The temporal electro-optic decoding method has been
benchmarked with a transverse-deflecting RF structure.
Simulations based on published EO material data, and using the measured TDS electron bunch profiles as input data,
are consistent in shape and amplitude with the EO measurements. Electron bunch profiles with a width of 55 fs (rms)are close to the resolution limit set by the GaP material
properties. New electro-optic materials [11] with a broader
frequency response than GaP will be needed to improve thetemporal resolution.

REFERENCES[1] G. Berden et al., Electro-optic technique with improved
time resolution for real-time, nondestructive, single-shotmeasurements of femtosecond electron bunch profiles, Phys.
Rev. Lett., 93:114802, 2004.
[2] S. P. Jamison et al., Temporally resolved electro-optic effect,
Opt. Lett., 31:1753, 2006.
[3] B. Steffen. Electro-optic methods for longitudinal bunch
diagnostics at FLASH, PhD thesis, University of Hamburg,
2007. DESY-THESIS-2007-020.
[4] S. Casalbuoni et al., Numerical Studies on the Electro-Optic
Sampling of Relativistic Electron Bunches, TESLA Report
2005-01 (2005).
[5] D. A. Kleinman and W.G. Spitzer, Infrared lattice absorption of GaP, Phys. Rev., 118:110, 1960.
[6] Q. Wu and X.-C. Zhang, Seven terahertz broadband GaP
electro-optic sensor, Appl. Phys. Lett., 70:14, 1997.
[7] W.L. Faust and C.H. Henry, Mixing of visible and nearresonance infrared light in GaP, Phys. Rev. Lett., 17:1265,
1966.
[8] O. H. Altenmueller, R. R. Larson, and G. A. Loew, Investigations of traveling-wave seperators for the stanford twomile linear accelerator, Rev. Sci. Instrum., 35:438, 1964.
[9] M. Hüning et al., Observation of femtosecond bunch length
using a transverse deflecting structure, Proceedings of the
FEL 2005, Palo Alto, CA, USA, 2005.
[10] I. Wilke et al., Single-shot electron-beam bunch length measurements, Phys. Rev. Lett., 88:124801, 2002.
[11] X. Zheng et al., Broadband and gap-free response of a terahertz system based on a poled polymer emitter-sensor pair,Appl. Phys. Lett., 87: 081115, 2005.

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Proceedings of FEL 2007, Novosibirsk, Russia

MAGNETIC MEASUREMENTS, TUNING AND FIDUCIALIZATION OF
LCLS UNDULATORS AT SLAC*
Y. Levashov, V. Kaplunenko, A. Weidemann, Z. Wolf
SLAC, Menlo Park, CA 94025, USA
A new Magnetic Measurement Facility (MMF) has
been built at Stanford Linear Accelerator Center (SLAC)
to measure, tune and fiducialize LCLS undulators. The
climate controlled MMF utilizes two magnetic
measurement benches and a large Coordinate
Measurement Machine (CMM) to provide a throughput of
one undulator per week. Magnetic measurement, tuning
and fiducialization processes are presented and firsttuning results are discussed.

INTRODUCTION
The Linac Coherent Light Source (LCLS) based on a
Self-Amplified Spontaneous Emission Free-Electron
Laser (SASE-FEL), is being built at Stanford Linear
Accelerator Center (SLAC) by a collaboration of four USDOE laboratories. A new injector and a part of theexisting SLAC linac will be used as an electron source atenergy of 13.64 GeV. The 120 m long LCLS undulator
line consists of 33 segments. Each segment is a fixed-gap
planar undulator assembled of permanent NdFeB magnets
and canted poles. The undulator period is 3cm, gap at thebeam line is 6.8mm, effective K value varies from 3.500
to 3.485 to account for beam energy loss, and theradiation wavelength will be 1.5A. A prototype of thesegment and the first two undulators have been measured
and tuned at the Advanced Photon Source (APS) in
Argonne National Laboratory (ANL) [1],[2].
Requirements for LCLS undulator tuning andfiducialization are specified in a Physics Requirement
Document [3]. The requirements must be met for all beam
positions within ±2 mm horizontally and ±200µm
vertically of the nominal beam axis. Trajectory excursions
for one segment should be less than 2μm, r.m.s. phaseerrors and particle-wave slippage <10°, first field integrals<40×10⁻⁶Tm, second field integrals <50×10⁻⁶Tm², and K
should be set to 1.5×10⁻⁴. The position of the undulator
magnetic axis, and the beam trajectory at the nominal K
value should be known relative to external mechanicalreferences to 50μm horizontally and 40μm vertically.
Because of their low electrical noise and small planar
Hall effects, Sentron XZM12-3-0.6-2T Hall probes areused to sample magnetic fields along an undulator for
beam trajectories and K calculations. Field integrals aremeasured by 3.6m long coils. Additional measurements
are made with one period long λ -coils.

*

Work supported by US Department of Energy contract DEAC02-76SF00515.

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The semi-automated process of LCLS undulator tuning
allows for a throughput of one undulator per week, whichis required to meet the tight project schedule.

MAGNETIC MEASUREMENTLABORATORY
The main concern taken into consideration during
construction of the MMF was the temperature. The
remnant field of permanent magnet material typicallychanges by about 0.1% per degree Celsius, which requires
the temperature to be constant at ±0.1C° level to meet thetolerance on the K. A high quality air conditioning system
keeps the air temperature in the MMF within tolerance, as
shown in figure1.
T e m p e ra tu re (C )Abstract*

20.1
20.05
20
19.95
19.9
20-Jul-07 22-Jul-07 24-Jul-07 26-Jul-07 28-Jul-07 30-Jul-07 1-Aug-07
Date

Figure 1. Ambient temperature in MMF
Each undulator stays inside the temperature controlled
room for one week prior to the start of measurements toreach thermal equilibrium with the room temperature.
During magnetic measurements and tuning, the undulator
temperature is monitored by 5 sensors distributed along
the length of the device. The difference between the
background magnetic field in the laboratory and themagnetic field in the undulator hall at different LCLS
tunnel locations was measured to be 0.1G. Many othermetal objects, which could affect the ambient magnetic
field components, should be taken into account during thetuning process. For that reason all undulators are coveredby a μ-metal shield, shown in figure 2, which reduces theambient magnetic field by a factor of 6. Also they are set
in the same orientation in which the segments will be
installed in the tunnel, and measured on the same steel
support structure.
Initialmechanicalacceptancechecksandfiducialization measurements of an undulator are made on
the 4 meter long CMM. Undulators are tuned on two
separate magnetic measurement benches, which allow
work to proceed in parallel. The measurement devices aremounted on precision x, y, z - stages with Heidenhain
scales and encoders. The instruments are triggered by a
National Instruments FPGA in a PXI-1031 chassis. Probe
positioning accuracy w.r.t. reference indexes on the scales

Proceedings of FEL 2007, Novosibirsk, Russia
is better than 5 micrometers. The benches are equippedwith cam mover and capacitive sensor systems, whichallow alignment of an undulator to the bench in 5 degrees
of freedom, with the remaining longitudinal position
being only measured. The process of alignment to thebench is completed in approximately 15 minutes to a few
micrometers/microradians.

WEBAU05

trajectories, phases, K adjustments and checks to be
performed. The undulator support has a steel girder andsteel pedestals as will be used in the tunnel to simulate thetunnel conditions. After completion of the tuning process,a final dataset of measurements is made. The
fiducialization process also begins on the fine tuning
bench and is completed on the CMM.

Gap adjustment screws

Tuning trajectories, phases and Kµ - shield

Tapered Shim

Tapered ShimGap adjustment screws

Figure 2. Each undulator is wrapped in a mu-shield,
which reduces the ambient magnetic field effect by afactor of 6.
Hall probes are calibrated periodically relative to a
Metrolab PT2025 NMR teslameter on a calibration stand.
The calibration stand has a special chiller set to 20°C tokeep the Hall probe at the same temperature it will havewhen in use. This increases the accuracy and repeatabilityof the calibration to 0.3G. The difference between two
calibrations is shown in figure 3.

Difference (G)

0
-0.05
-0.1
-0.15
-0.2
-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Field (T)

Figure 3. A polynomial fit is made for each Hall probe
calibration. The polynomial coefficients are applied tomeasured data to calculate the corrected field. The
difference between two Hall probe calibrations is shown.
Additionally, measurements of a 3.7kG reference magnet
are made periodically, right before taking a final set ofmeasurements, to check if the probe calibration haschanged.

UNDULATOR TUNING
Undulator tuning is performed in accordance with aplan, in which all steps of tuning and fiducialization are
enumerated. On the 4.5m long "rough tuning" bench,
trajectories, phases, and K are set to the tolerances. Then amagnetic shield is installed and the undulator is moved tothe 7.5m long "fine tuning" bench where a more extensive
set of equipment allows field integral measurements, final

The tuning procedure starts with alignment of a Hall
probe to the undulator. Horizontal and vertical scans are
made at poles periodically down the undulator. The
symmetry point horizontally and the minimum fieldvertically define the magnetic center at each pole. A fit to
the magnetic centers is made to find the axis location.
Any magnetic pitch and yaw angles are corrected using
the cam mover system. Upon finishing the alignment,
scans of the magnetic field, sampling the field every
0.2mm, are made. The Hall probe is moving along theundulator at high speed (80mm/s) which reduces theeffect of the probe zero drift. Only a single measurement
is required for reproducibility of 2⋅10⁻⁵ which is enoughto set K and tune trajectories to better than 1μm. EachHall probe measurement starts and ends inside zero fieldchambers located at both ends of the bench. The probe
zero offsets and zero drifts are calculated and corrections
are made to the measurements. The Hall probe is not used
to measure field integrals, since a small DC offset fromthe probe, when integrated over the segment length, canexceed the required tolerances.
Beam trajectories, phase errors and K are calculatedusing a special computer program, which also specifies
locations and strengths of the shims to be applied to maketrajectories straight and to bring phases and K within thetolerances.
Since the magnetic shield blocks access to the gap
adjustment screws, as shown in figure 2, an undulator is
tuned on the "rough tuning" bench without it andcorrections anticipating the shield are made to themeasurements. Beam trajectories and phases are tuned byapplying special shims, developed at ANL [1]. The K
value is set by changing the gap size. All gap adjustment
screws should be torqued to the same value to obtain gap
adjustment accuracy better than 2μm. After beam
trajectories and phases are corrected and K is set, theshield is installed and the undulator is moved onto the"fine tuning" bench.

Measuring and tuning field integrals
Accurate measurements of the small field integrals are
made by a 3.6m long integrating coil with 150 turns,
wound on a G10 strongback and aligned straight to±0.1mm. It allows measurement of field integrals in both
directions in a small gap by the same coil. The
measurements are challenging because the coil is only
allowed to move by a half a millimeter due to a small gap,
and to minimize averaging over a significant volume of

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Proceedings of FEL 2007, Novosibirsk, Russia

100

100

80

80

60

60

40

40

20

20

0

0

-20

-20

-40

-40

-60

-60

-80

-80

-100

Second integral (*10-6 Tm**2)

First integral (*10-6 Tm)

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-100
-8

-6

-4

-2

0

2

4

6

8

X (mm)- First X-field integral- Second Y-field integral- Second X-field integral- First Y-field integral

Tolerance

Figure 4. An example of X-dependence of horizontal and vertical field integrals measured by the moving coil. The
polynomial fit is of fifth order.
field. Offsets are dealt with by measuring as the coilmoves both forward and back. The first integral ismeasured by fixing return path wires of the coil on thegirder and translating both ends of the coil parallel toitself inside the gap by stages. The voltage induced in thecoil is sent to a Metrolab PDI-5025 integrator.
The second field integral is measured by holding theexit end of the coil fixed and moving the entrance end, as
proposed by P.Vobly [4]. The second field integral has aweighing factor equal to the distance to the end point of
the integration.
Heavy filtering is applied to the coil output signal toreduce the electrical noise. The X -dependence of the firstand second field integrals in both horizontal and verticaldirections is measured and corrected to the tolerances, as
shown in figure 4, by applying different types of shims,
developed at ANL.
Special tests were done to check the sensitivity andaccuracy of the field integral measurement system. Thelong coil measurements of the small background field
integrals were compared to field integrals calculated fromfluxgate measurements and to the known field integrals ofsmall magnets placed at various positions. The magnet’s
strengths were measured by independent means. The tests
showed a good 10% agreement between the coil and thefluxgate and 6% level of accuracy in measuring the firstand second field integrals by the coil.

applied to the Hall probe measurements to match the field
integrals measured by the long coil.
During the LCLS operation, it is planned to roll an
undulator out of the beam line by 80mm. Field integrals
are measured by the coil and the magnetic fields are
sampled by the Hall probe at the undulator retracted
position to have data for future beam trajectory
corrections. Since it is outside the magnetic shield, thebackground field components are measured and taken into
account.
To check repeatability of the measurements, a reference
undulator is sent through the laboratory for measurements
after every 4-th undulator. Results of the reference magnet
measurements are shown in table 1.
Table 1
Reference undulator measurement results
May
June
July
2007
2007
2007
+30
+20
+44
I1x (10-6 T⋅m)
2
-6
2
-20
+4
-20
I x (10 T⋅m )
1
-6
+16
+19
+8
I y (10 T⋅m)
2
-6
2
+15
+21
+20
I y (10 T⋅m )Phase
Errors (°)

Final dataset
When all the measurements are made and the undulator
is tuned within the tolerances, the shims are glued inplace. Then, the trajectories and the K value are checked
and a final dataset of results is made. A map of field
integrals is measured in a range of ±6mm with 1mm steps
horizontally and ±0.2mm with 0.1mm steps vertically. In
addition, Hall probe scans are made in the horizontal
direction ±6mm from the magnetic axis location with astep size of 1mm. Small corrections of order of 0.1G are
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r.m.s.

3.7

3.7

3.7

Entr.

-1.0

-1.5

-1.3

Exit

-4.4

-4.4

-4.3

Cell

-5.3

-5.9

-6.0

3.498635

3.498567

3.498483

Kcorrected(∆K/Knom)
1

2⋅10

-5

-2⋅10

-5

-4⋅10-5

2

I x,y – first field integrals; I x,y – second field integrals; Kcorrected –effective K, corrected for different magnetic axis x-positions; ∆K/Knom –relative K error w.r.t. nominal.

FIDUCIALIZATION
Fiducialization is the process of finding how the ideal
beam axis, determined magnetically, relates to tangible

Proceedings of FEL 2007, Novosibirsk, Russia
objects on an undulator, in our case tooling balls. Special
pointed magnets (PM) are used as an intermediatereference [5]. These magnets have a well defined field
pattern. The location of the PM centers w.r.t. the PM
tooling balls have been found in advance from acalibration. Upon completion of undulator tuning, twomagnets are bolted to each end of the undulator and Hall
probe scans are made to locate their centers, as shown infigure 5. Horizontal and vertical offsets of the undulator
magnetic axis w.r.t. the PM tooling balls are calculated.
Then the undulator with the PMs attached to it is moved
to the CMM. On the CMM distances between all toolingballs are measured and the fiducialization data calculated.
A number of additional measurements are made tocheck fiducialization data for possible errors. Two extra
PMs are fixed permanently on pedestals next to the bench
and measured as references. Horizontal and verticaldistances between all tooling balls are measured by
optical tools and compared with the CMM data.
Additionally, a direct optical measurement of the Hall
probe enclosure is made. The accuracy of the opticalmeasurements is about 50μm, but it is a good check of
fiducialization data for large errors.

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ASKNOWLEDGMENT
Many thanks to Isaac Vasserman (ANL) for pricelesshelp and tutoring and to Heinz-Deiter Nuhn (SLAC) for
valuable discussions.

REFERENCES[1] I. Vasserman et al., “Magnetic measurements andtuning of the LCLS prototype undulator”, Nucl. Instr.
and Meth. A 507 (2003) 191.
[2] E. Trakhtenberg et al., “Undulator for the LCLS
project--from the prototype to the full-scale
manufacturing”, Nucl. Instr. and Meth. A 543 (2005)
42.
[3] H.D. Nuhn et al., “General Undulator System
Requirements”, LCLS Physics Requirements
Document, 1.4-001.
[4]. E.I.Antokhin, A.M.Batrakov, P.D.Vobly, N.I.Zubkov,
Yu.M.Kolokolnikov,
E.G.Miginsky,
A.V.Utkin,
V.M.Tsukanov, “System for measuring 1 and 2
integrals of the undulator magnetic fields”, Preprint
BINP, 2002-046, Novosibirsk, 2002.
[5] I.Vasserman “Quadrupole magnetic center definition
using the hall probe measurement technique.” APSPub. LS-285, Argonne, 2004.

Figure 5. Pointed magnets are attached to the undulator
segment for fiducialization.

CONCLUSION
By August 2007, 11 undulator segments have beensuccessfully measured and tuned to specifications in the
new climate controlled laboratory at SLAC. All
measurement systems are thoroughly calibrated andtested. LCLS undulator measurement and tuning
techniques and procedures proved to be adequate to meetthe strict tuning requirements. All tuning steps are well
documented in a number of technical notes and available
online.† Raw data and analysis results are saved in a
directory structure and available from the SLAC web
site‡.
†LCLS Technical Notes are available at wwwssrl.slac.stanford.edu/lcls/technotes.
‡
At www-group.slac.stanford.edu/met/MagMeas/MAGDATA/LCLS/Undulator/.

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Proceedings of FEL 2007, Novosibirsk, Russia

MAGNETIC MEASUREMENTS OF THE FLASH INFRARED UNDULATOR
N.Morozov*, A.Chesnov, E.Matyushevsky, D.Petrov, E.Syresin, JINR, Dubna, Russia,
O. Grimm, J. Rossbach, University of Hamburg, Germany,
Y.Holler, DESY, Hamburg, Germany

Abstract
The FLASH free-electron laser at DESY, Hamburg, hasrecently been equipped with an infrared electromagnetic
undulator, providing radiation in the range 1-200 μm. It
will be used both for electron beam diagnostics purposes
and as a powerful source synchronized to the VUV andsoft X-ray pulses of the FEL. The undulator wasconstructed at the Joint Institute of Nuclear Research(JINR). This paper summarizes the extensive magnetic
measurements that where performed both at JINR andDESY prior to installation of the undulator.

INTRODUCTION
An important feature of the beam formation system of
FLASH is the possibility to produce ultra-short (below 50μm) electron bunches. Such short bunches produce
powerful coherent radiation with multi-megawatt power
level. Generation of two-colors by a single electron bunch
reveals unique possibility to perform pump-probe
experiments with VUV and IR radiation pulses [1,4].
Coherent radiation produced by the electron beam in the
IR undulator strongly depends on the bunch profile, thus
allowing the use of the device for longitudinal profile
diagnostics

UNDULATOR MAGNET DESIGNThe undulator (Figure 1) magnetic system [2,3] consistsof two ferromagnetic girders with 22 poles each. The
exciting coils are set on poles. The coils of the top andbottom girders are connected sequentially and powered bya single electrical supply. Each main coil consists of four
layers, and each layer consists of 16 turns. The windings
are made of a square-shape copper pipe (8.5x8.5 mm2)with a cooling channel of 5.3 mm diameter. The
maximum current in the winding is 435 A (current density
8.7 A/mm2). Each regular coil has an additionalcorrection winding to provide fine regulation of themagnetic field. The number of turns in the correction
winding is 270, and wire diameter is 1 mm. The corrector
winding allows to regulate the number of Amper·turns
within 2% of maximum value of the main winding. The
correction coils permit to compensate a perturbation of
the magnetic field related to an imperfection of magnetic
system at its construction. The coils of two end poles
differ from the coils of regular periods, and consist of 8
and 36 turns for the first and the second pole,
respectively. End-pole coils have also a correcting
winding for fine adjustment of the magnetic field.
____________________________________________*Corresponding author, email: morozov@nusun.jinr.ru

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Figure 1: View of the infrared undulator on the DESY
magnetic field measurement bench

SCOPES OF THE MAGNETIC FIELD
SHAPING
Undulator magnetic field measurements and correction
were provided at the first stage in JINR (Dubna) andfinally in DESY (Hamburg). At both sites a Hall probemagnetometer was used for the field measurement. The
probe head was moved and controlled in three dimensions
by stepping motors and a high accuracy linear encoder (~some μm). The magnetic field monitoring was realized
by reference Hall or NMR probe. During the magnetic
field measurement campaign the following goals wererealized:• the first and second total integrals are
I1<200 G·cm and I2<200 kG·cm2;• the first integral in each regular undulator period
is I1<200 G·cm;• magnetic field reproducibility and long timestability for the first and second total integrals
are I1=±50 G·cm and I2=±5 kG·cm2;• flat beam orbit;• using one power supply for regular correction
coils and as few as possible power supplies forthe edge correcting coils.
The above undulator requirements have to be fulfilled in
the range of the main coil excitation currents Io = 0(remanent field) – 435 A (Bo=11000 G).
To achieve those goals, a large amount of simulation
work was done at the initial stage of the project design bydifferent codes (POISSON, ANSYS, TOSCA, RADIA)[2]. Those simulations have resulted in a flexible
magnetic system with the possibilities to achieve thedesign goals.

Proceedings of FEL 2007, Novosibirsk, Russia

The measured magnetization curve (central field, pole4) has shown full correlation of this data with thesimulation results by the TOSCA code (Figure 2).
To achieve a minimal first field integral in the regularundulator periods we have realized an iterative correctionof the field integral by tuning the values of the correction
coils shunt resistors. All regular undulator pole correctors(3-20) were excited by one power supply. The best
correction was done first for the main coil current Io=200
A (Figure 3). For other main coil currents the correction
was done by tuning the corrector current value. The
initial value of the first field integral in the regular periods
has achieved 1500 G·cm. The results of the regularperiods first integral tuning are shown in Figure 4.

Second integral distributions along the undulator axis areshown in Figure 8 for the maximal main coil excitation
currents.

Io=390 A
Io=350 A
Io=275 A
Io=200 A
Io=130 A
Io=78 A
Io=50 A
Io=30 A

700
600
500
400
300

Int.1 (G*cm)

UNDULATOR MAGNETIC FIELD AND
ITS CORRECTIONWEPPH003

200
100
0
-100
-200
-300
-400
-500
1

2

3

4

5

6

7

8

9

Nperiod

12000

Figure 4: Distribution of the first field integral in theregular undulator periods for some excitation currents

experiment
TOSCA simulation

11000
10000

600

9000

500

7000
400

6000
5000

300

Int.1 (G*cm)

Bpole 4 (G)

8000

4000
3000
2000

200
100

1000

0

0
0

50

100

150

200

250

300

350

400

450

-100

Io (A)
-200
0

50

100

150

200

250

300

350

400

Io (A)

Figure 2: Undulator magnetization curve

Figure 5: Final first field integral as function of the main
coil excitation current
Io=200 A
before correction
correction coils turn on

2000

50

1500

0

500
2

Int.2 (kG*cm )Int.1 (G*cm)

1000

0
1
-500

2

3

4

5

6

7

8

9

N period

-1000

-50

-100

-150

-1500
-200
0

Figure 3: Distribution of the first field integral in theregular undulator periods (Io=200 A) before and after
correction
The task of the total first and second field integral
correction and minimization was successfully solved bycareful tuning of the correctors currents for the pole 1, 2,
21, 22. The maximal correction current is 8 A for thesepoles. The final first and second field integral is presented
in Figure 5 and 6. The corrector coils settings depending
from the main coil current are presented in Figure 7.

50

100

150

200

250

300

350

400

Io (A)

Figure 6: Final second field integral as function of themain coil excitation current
To investigate temperature effects of the undulator, aFluke Ti45 thermography camera was used. Figure 9shows an example of such thermographic images. The
emissivity for calculating temperatures was taken as 0.95.
From a series of such measurement, the coils are in
equilibrium after about 30 minutes. The thermal coupling

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WEPPH003

Proceedings of FEL 2007, Novosibirsk, Russiaof the coils to the massive iron yoke and the support
structure is weak, however, and a 6 hour time constant isfound for the magnetic field.
The results of the reproducibility for the first and second
field integral at some test runs are presented in Figure 10
and 11. The study of the undulator magnetic field
variation during a 27 hour run at the maximum excitation
current Io=435 A has shown that the undulator magnetic
field integrals have reached equilibrium some minutes
after the working regime setting. The results of the longterm measurements are shown in Figure 12.

run 1 during tuning
run 2
run 3
run 4
run 5

150
100
50

Integ. 1 (G*cm)

0
-50
-100
-150
-200
-250
-300
0

50

100

150

200

250

300

350

400

450

Figure 10: Reproducibility of the first field integral

left main periodright main period
N1
N 22
N2
N 21

10
9
8
7
6
5
4
3
2
1
0
-1
-2
-3
-4
-5
-6
-7
-8
-9
-10

run 1 during tuning
run 2
run 3
run 4
run 5

50

0

2

Integ. 2 (kG*cm )Icorrectors(A)

Io(A)

0

50

100

150

200

250

300

350

400

450

500

Imain(A)

-50

-100

-150

Figure 7: Correctors coils settings
-200
0

50

100

150

150000

200

250

300

350

400

450

Io(A)
Io=435 A

100000Figure 11: Reproducibility of the second field integral

50000

2

Int.2 (G*cm )0-50000200-100000-ΔB
Int.1- Int.2-150000

0

50

100

150

200

250

300

350

400

450

500

550

Z(cm)

Figure 8: Magnetic field second integral for Io=435 A-1-300000

150

2-Δ(Bref.-Bref.t=0)*10 (G)-250000

Int.1 (G*cm), -Int.2 (G*cm )*10

3

-200000

100

50

0
0

5

10

15

20

25

30

t (h)

Figure 12: Data from the long test run of the undulator

Figure 9: Thermographic image of the infrared undulator
60 minutes after switching on at 435 A current

FEL Technology I

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CONCLUSION
The undulator magnetic field measurement and shaping
campaign has approved the technical solution for themagnetic system design. The undulator has shown goodstability and reproducibility of the basic magnetic fieldcharacteristics.
We would like to thank M. Yurkov, V. Akkuratov,
O. Brovko, V. Borisov and A. Shabunov who participatedin the undulator design, manufacturing and magnetic fieldmeasurements.

WEPPH003

REFERENCES
[1]
[2]
[3]
[4]

B. Faatz et al., NIM A 475 (2001) 363.
E. A. Matyushevsky et al., JINR E9-2005-168,
2005.
V.Borisov et al, Proceedings of EPAC 2006,
Edinburg, Scotland, THPLS133, p.3595-3597.
O.Grimm et al, Proceedings of the 27th
International Free-electron laser conference FEL
2005, Stanford, USA, p.183-186.

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Proceedings of FEL 2007, Novosibirsk, Russia

NUMERICAL CALCULATIONS OF THE RADIATION EMITTED FROM
THE FLASH INFRARED UNDULATOR
O. Grimm∗ , J. Rossbach, University of Hamburg
V. Kocharyan, DESY, Hamburg, Germany
Abstract
The VUV and soft X-ray free-electron laser FLASH at
DESY, Hamburg, has been complemented with an infraredundulator working in the wavelength range of 1 to 200 µm,
providing pulses naturally synchronized with the FEL radiation. The results from the magnetic measurements prior to
installation are used here as input for calculations of the expected radiation spectrum. Especially the behavior at small
excitation currents is important for beam diagnostics using
coherent radiation.

INTRODUCTION
Complementing the FLASH facility at DESY, Hamburg,with an undulator working in the mid- and far-infrared
regime was first proposed in [1]. There is a strong interest in using such an undulator delivering up to 10 MW
peak power in the THz-regime as a radiation source, allowing pump-probe experiments with high temporal resolution. Another equally important application lies withinlongitudinal bunch shape diagnostics [2, 3]. More details
on the undulator have been reported in [4, 5].
The device has been build and installed in the FLASH
accelerator, with first beam passing through expected in
September 2007. In [6] results of the magnetic measurements that were performed prior to installation are reported. These are used for detailed numerical calculationsof the radiation characteristics, some of which are reported
in this paper. Such calculations are necessary input to optics codes to quantitatively analyze the transmission characteristics of the infrared beam line.

NUMERICAL CODES
Several numerical codes have been used to perform calculations of the radiation characteristics. Comparisons between the results from different codes are mandatory to get
confidence about their validity.
Many calculations are performed with a custom-madecode written in Matlab called SynchroSim. The code implements a full time-domain calculation based on using thegeneral Liénard-Wiechert fields from an accelerated charge[7] and a subsequent Fourier transformation to get the spectrum. There are no approximations involved, however the
calculation speed is low. Alternatively, a direct calculation in frequency-domain can be done using the paraxial∗ Corresponding author. E-Mail: oliver.grimm@desy.de

FEL Technology I

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approximation of synchrotron radiation emission [8], giving much higher speed.
The Synchrotron Radiation Workshop (SRW) code has
also been used extensively [9]. Some cross-checks were
performed with the SPECTRA code [10].
Perfect agreement was found for on-axis spectra calculated with SRW, SPECTRA and SynchroSim. The transverse intensity distribution at 61 µm wavelength and 1 GeV
energy is compared between SRW and SynchroSim in
Fig. 1. Also here very good agreement is found.
The horizontally asymmetric distribution and interference fringes result mainly from the undulator end poles.
Some contribution results also from the inclusion of the dipole magnet that is installed downstream of the undulator.
It has a field of about 0.45 T at 500 MeV and is used todump the electron beam. It should be noted that further
along the infrared beam line the relative contribution of thedipole will reduce, as the optics is optimized for the radiation contribution from the undulator.
Further comparisons confirmed the good agreement between different codes, thus calculations in the following
were performed with the most convenient program.

SPECTRUM CALCULATIONSThe spectrum calculated for 200 A excitation currentof the undulator at 511 MeV electron energy is shown in
Fig. 2. On-axis a typical resonance spectrum is obtained
containing only odd harmonics. When integrating over atransverse area of 60×60 mm 2 (corresponding to the beamline acceptance at that position), the spectrum acquires aclear baseline. This is an indication of the fact that onlya small fraction of the total energy emitted by an electron
ends up within the harmonics, see the estimation in the lastsection.
This effect becomes more pronounced at smaller excitation currents, as Fig. 3 shows for 30 A. This is due to the
reduced opening angle of the harmonics at smaller K value,
and thus larger contribution of non-resonant radiation when
the acceptance aperture is fixed.

TRANSVERSE INTENSITYCALCULATIONS
The transverse distributions of the total radiation intensity (summed over both polarizations) with the undulator
current set to the maximum value of 435 A is shown in
Fig. 4 for the first and third harmonic (192 µm and 64 µm
at 511 MeV, respectively). The 60 mm diameter aperture ofProceedings of FEL 2007, Novosibirsk, Russia

WEPPH004

40

Vertical Position

20

400
Phot/nC/0.1%bw/mm

2

0

-20

-40mm

-40mm

-20

0
Horizontal Position

20

300

200

100

0

40

0.05

0.10
Photon Energy

0.15

0.20eV

0.15

0.20

50
40
30

10

400x100Phot/nC/0.1%bw

Vertical position (mm)

20

−10
−20
−30

300

200

100

−40
−50
−50

3

−40

−30

−20

−10
0
10
Horizontal position (mm)

20

30

40

50

Figure 1: Transverse intensity distribution 9 m behind theundulator centre at 61 µm wavelength and 1 GeV energy.
Top: SRW, bottom: SynchroSim.
the beam transport line at that position clips the first harmonic. This reduction of the harmonic amplitude has to betaken this into account for beam diagnostics, as the coherent amplification due to the form factor of the longitudinalcharge distribution is imprinted on the relative height of theharmonics.
These plots were calculated at a single wavelength exactly on resonance. Any measurement will integrated overa certain range. Fig. 5 shows the intensity distributionof the first harmonic at 30 A excitation current both fora wavelength on resonance and when integrated over the
10% harmonic bandwidth.
Fig. 6 finally shows the transverse intensity distribution
for both polarizations at 30 A when integrated over the fullbandwidth of Fig. 3.

TOTAL EMITTED ENERGY
At high K parameter, the spectrum is wiggler-like, consisting of a large number of harmonics. This can be easily understood qualitatively by approximating the undulator for that case as a series of 18 bending magnets of opposite polarity (as the undulator has 9 full periods), sep-

0.05

0.10
Photon Energy

Figure 2: Spectrum at 200 A excitation current and an energy of 511 MeV. On-axis spectrum (top) and integration
over a transverse area of 60×60 mm 2 . The first harmonicis at 92 µm.
arated by half a fundamental wavelength. The spectrum
emitted by one bend (approximated as that from circularmotion synchrotron radiation) will then be modified into aline spectrum, as Fig. 7 shows.
This approach allows to deduce a scaling of the pulse
energy within a given harmonic n. From [11], the bandwidth for an undulator with N periods and fundamental
frequency ν 0 isΔν/ν ≈ 1/(N n),

ν = nν0 ,and the solid angle subtended by the central cone for the
relativistic gamma factor γΩ≈π

1 + K 2 /2 K1 πK 2.
≈
2γ 2 N n
4γ 2 N n

The envelope E of the harmonics amplitude in Fig. 7 follows from the low-frequency expression of the synchrotron
radiation intensity on axis [7]. It scales for a given magnetic field as ν 2/3 . The scaling of the energy E within one
harmonic can thus be estimated as
E ∼ E · Δν · Ω ∼ n−1/3 .

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Proceedings of FEL 2007, Novosibirsk, Russia

The ratio becomes, by approximately evaluating the Bessel
function expression,

Phot/nC/0.1%bw/mm

2

5000
4000

K 4N
Wr
≈ 3K 3 /8
.
Wh
6
n−1/3

3000

n=1

2000

For K = 42, corresponding to a first harmonic at 192 µm
for 511 MeV, and N = 9 this results in W r /Wh ≈ 3400.

1000
0
0.5

1.0

1.5

2.0
2.5
Photon Energy

3.0

3.5

4.0eV
−33

x 10
100
4.5
80
4
60

1.6x103.5

640

y (mm)

Phot/nC/0.1%bw

3

20

1.4
1.2

2.5

0
−20

2

−40

1.5

0.8

−60

1

0.6

−80

0.5

1.0

0.5

1.0

1.5

2.0
2.5
Photon Energy

3.0

3.5

−100
−100

4.0

−50

0

50

100

x (mm)−33

x 10

Figure 3: As Fig. 2, but for 30 A excitation current. The
first harmonic is at 2.8 µm.

100
9
80
8
60
7

40

3K 3 /8Wh ≈
4πe2 γ 2(J0 (1/2) − J1 (1/2))2 ·n−1/3 ,
2
0 λu K
n=1

where λu is the undulator period. The total energy W r radiated by a single electron when passing through an undulator with sinusoidal field can be obtained by integration of
the instantaneous power, giving
Wr ≈FEL Technology I324

πe2 γ 2 K 2 N.
30 λu620
y (mm)

This scaling holds for n much smaller than the harmoniccorresponding to the critical frequency: n  3K 3 /8.
The total energy W h in all harmonics can be roughly estimated as summing them up to this critical harmonic. Using
the expression for the first harmonic energy from [11], thisresults in

0

5

−20

4

−40

3

−60

2

−80

1

−100
−100

−50

0
x (mm)

50

100

Figure 4: Transverse intensity distribution 10 m behind theundulator centre, at 192 µm (1 st harmonic, top) and 64 µm(3rd harmonic, bottom) wavelength. The colour intensity
scale is in J/(m2 Hz).
Only a very small fraction of the energy lost by an electron
actually ends up in one of the harmonics.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH004

−32

1.2

30

3000
0

2000

-10

1000

-20

0

-30mm
-20

-10

0
10
Horizontal Position

20

30

0

20

-10

10

-20

0

0

3

10

-30
-10

0
Horizontal position

10

20

Figure 5: Transverse intensity distribution 10 m behindthe undulator centre, on resonance of the first harmonic(2.8 µm, top) and integrated over its 10% bandwidth (bottom). Units of the colour scale are photons/(nC mm 2 0.1%
BW) (top) and photons/(nC mm 2 ) (bottom).

140

20

120
100

0

80

3

10

x10

Vertical position (mm)

0.4

0.2

40

-20

0.6

30

20

-30

0.8

60
-10

40

5

10

15
20
25
Frequency (THz)

30

35

40

Figure 7: Comparison of the on-axis spectrum 9 m behindthe undulator centre as calculated with SRW for the actual undulator field to the effect of interference of circularmotion synchrotron radiation from the individual undulator
poles.

CONCLUSIONSExemplary calculations of the single-electron radiation
generated by the FLASH infrared undulator are presented
in this paper. Good agreement is found between different numerical codes. Such calculations allow incorporating a realistic source into Fourier optics codes to evaluate beam line performance and to interpret quantitatively
spectral and intensity measurement results. The resultspresented suggest that angular filtering is needed to obtainwell-defined resonance spectra.

REFERENCES[1] B. Faatz et al., Nucl. Instr. Meth. A475, 363 (2001)

20

-20

0

x10

Vertical position-30mm[2] G. Geloni et al., DESY 03-031 (March 2003)-30[3] O. Grimm, P. Schmüser, TESLA FEL 2006-03 (2006)
-30

-20

-10
0
10
Horizontal position (mm)20[4] O. Grimm et al., Proc. of FEL 2005, Stanford, 21-26 August
2005, p. 183

20

40

10

30

[5] V. Borisov et al., Proc. of EPAC 2006, Edinburgh, 26-30
June 2006, p.3596

020[6] N. Morozov et al., these proceedings

-10

10

-20

0

3

x10

Vertical position (mm)Interference of circular−motion synchrotron radiation
SRW calculation

1

4000
10
Intensity (J/(Hz m2))

Vertical Position

20

x 10

-30
-30

-20

-10
0
10
Horizontal position (mm)20Figure 6: Transverse intensity distribution at 30 A excitation current, 10 m behind the undulator centre, integrated
from 300 nm to 3 µm (the range of Fig. 3). Horizontal polarization (top), vertical polarization (bottom). Units of thecolour scale are photons/(nC mm 2 ).

[7] J. D. Jackson, Classical Electrodynamics, John Wiley &Sons, New York (1975)[8] G. Geloni et al., DESY 05-032 (February 2005)[9] O. Chubar, P. Elleaume, Proc. of the EPAC 1998, Stockholm, 22-26 June 1998, p.1177
http://www.esrf.eu/Accelerators/Groups/
InsertionDevices/Software/SRW[10] http://radiant.harima.riken.go.jp/spectra[11] H. Wiedemann, Particle Accelerator Physics II, Springer,
Berlin (1995)

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Proceedings of FEL 2007, Novosibirsk, Russia

MAGNET SORTING FOR THE XFEL HYBRIDUNDULATOR—COMPARING STUDY
Yuhui Li, Bart Faatz and Joachim Pflueger
Deutsches Elektronen Synchrotron (DESY), Hamburg, Germany
Abstract
Current permanent magnet material quality is insufficient to obtain field qualities in undulators, which satisfy
FEL requirements. Therefore position and orientation ofmagnets have to be carefully chosen in order to obtain mutual cancellation of field errors. In this paper we compare
two different sorting schemes, simulated annealing and astraight forward paring method. They are applied to a 5m
prototype structure built for the European XFEL facility.
The algorithms of these two methods are described in detail and the sorting results and the expected field qualities
are carefully compared.
Key words: undulator, sorting, annealing, pairing

INTRODUCTION
The European XFEL will be a user facility in the wavelength range from 0.1 to 1.6 nm [1]. It will use the so-called
Self Amplified Spontaneous Emission (SASE) scheme toreach saturation in a single pass [2, 3]. The XFEL will
use a technology similar to FLASH [4]. The electron beam
is generated in an RF photo cathode gun, accelerated andcompressed twice before it reaches its final nominal energy of 17.5 GeV. After acceleration and collimation, thebeam will be distributed among several SASE undulators
and wigglers for spontaneous emission. The radiation is
distributed among 10 user stations. The wavelength canbe changed by changing the electron beam energy or bychanging the undulator gap.
Studies for FLASH have shown that the transverse overlap between radiation and electron beam has to be better than 20% of the beam size in order not to have a toolarge reduction in gain and therefore a too large increasein needed undulator length [5]. A similar criterion holds
for keeping the resonance condition, i.e. keeping the phaseshake within reasonable values. A typical rms deviation
here is a few degrees. The undulator magnet quality needed
to provide this overlap and phase shake without additional
effort does not exist. Therefore, additional methods have to
be used in order to guarantee a sufficiently good undulator
quality.
Given the quality of the individual magnets, several
methods can be used to obtain the appropriate undulator
quality. One such method is magnet sorting, i.e. measuring the magnetic properties of the individual magnets andputting them into the structure such that errors in the magnet blocks cancel each other [6]. Another method which
can be applied to correct the main field component of thestructures that are discussed in this paper is pole-height adjustment [7]. This procedure, which has to take place in
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any case, is outside of the scope of this report and can only
be applied to the main field. Therefore, our main aim is
to correct the transverse field components that cannot becorrected by this method.
The structure for which the magnets are sorted is shownin Fig. 1. It consists of magnets separated by iron poles that
focus the flux lines resulting in the main magnetic field. Of
each magnet, several parameters have been measured: themagnetization in all three directions (M x , My , Mz ) and the(n)(s)
main magnetic field at a given distance (B z , Bz ), thus
giving the north-south inhomogeneous field. For a perfect(n)(s)
magnet, Mx = My = 0 and Bz = Bz . In order touniquely identify the orientation of the magnet, each ofthem is marked as in Fig. 1. Therefore, the direction of the
field components is known independent of the orientationof the magnet.
Permanent magnet

Reference surface

Iron pole
Upper girder

By
Bx
Bz

Lower girder
Magnet pair
Magnet pair No. (i=) 1

2

3

4

5

Mz

Bz(s)

Mx

My

Bz(n)

…

Figure 1: Coordinate system for the undulator and the magnet blocks. The red dot is used to determine the orientationof the magnet under any transformation that may be applied
inside the magnetic structure. The arrangement shown here
is referred to as the normal state.
With the magnet transverse flux M x , My , the transverse
undulator field can be evaluated by:
Bx,i ∝ (Fl,i Mx,l,i + Fu,i Mx,u,i )(−1)i
By,i ∝ Fl,i My,l,i − Fu,i Mx,u,i(1)

The subscript l refers to magnets on the lower girder, u
to magnets on the upper girder, i means pole position, F
stands for a possible flip of magnet at a certain position,with F = 1 the magnet in its normal state and F = −1
in its flipped state. Bx,i and By,i are undulator transverse
fields on each magnet pair, one in the upper girder, anotherin the lower girder (see Fig. 1).
In this paper, we will sort the magnets using two different methods, namely simulated annealing and pairing ofmagnets based on the magnetic measurements.

Proceedings of FEL 2007, Novosibirsk, Russia

ALGORITHMS DESCRIPTION OF
SIMULATED ANNEALING AND PAIRING
The method of simulated annealing [8, 9, 10] is a technique that has been used for optimization problems. Its
main purpose is to avoid getting trapped in a local optimum. Because of the the analogy with the slow cooling
down of liquids this process is called (simulated) annealing. In the case of sorting magnets, the magnet positionand orientations are changed and the magnetic field forthis magnet distribution is calculated. It is quite possible that any single change makes the field quality worse,
whereas a combination of changes improves the quality.
Simulated annealing offers the possibility to move througha state which is worse to a state which has a better undulator
quality needing several magnet permutations in a row. The
simulated annealing algorithm can be divided into several
steps:
1. Find all possible magnet permutations
2. Find a generator of random changes in this configuration

WEPPH005

so Bx,2i−1 + Bx,2i , By,2i−1 + By,2i , i = 1, 2, 3... represents the transverse field in i−th period and these twoelements are also included in the cost function. The firstand second magnetic field integral of the transverse fields
Bx,i and By,i determine the electron beam angle and distance from axis, so the first integral of the transverse field
is included too. Consequently six elements are included in
the cost function, three in each plane:• Rms value of transverse field of each magnet pair
• Rms value of transverse field of each undulator period• Rms value of first integral transverse field on eachmagnet pair along undulator
So the value of the cost function E is
E = w1 A + w2 B + w3 C + w4 D + w5 E + w6 F , (2)with w1 , w2 , w3 , . . . the weights for these six elements,
which need to be given each time the annealing programis executed.

3. Define a cost function E (analog of energy) whose
minimization is the goal of the procedure.

Algorithm of pairing magnets

4. Change the system configuration randomly; depending on the values of the cost function before and after
changing (E1 , E2 ), calculate the value p :Sorting work can also be done by pairing of magnets. It
is divided into two steps: first list all magnets in increasing order of their flux, secondly pairing the magnet withsmallest flux to the one with largest flux one by one. The
algorithm is:

p = exp[−(E2 − E1 )/T = exp[−ΔE/T ]If E2 < E1 , the change is accepted; if E 2 > E1 ,randomly generate a number m in the range of [0, 1].
If m < p, then this change will still be accepted, if
m > p , this change will be refused.
5. Control the parameter T (analog of temperature) decreasing during the process. This annealing scheduletells how the T value is lowered, e.g., when and by
what amount T is decreased.
A simulated annealing program controls the main annealing progress: first the undulator’s configuration is randomly rearranged for 20000 times to determine the rangeof values of ΔE that will be encountered from move to
move, by this the average value ΔE can be obtained.
Depending on ΔE a starting value for the parameter T
is chosen which is considerably larger than the largest ΔE
which is normally encountered. Then after I 1 times accepted changes or I 2 times refused changes (I 2 is normallylarger than I1 ), the parameter T decreases by a certain
amount. If three times in a row T decreases because ofrefused changes, the program will be terminated by a last‘quenched’ sorting, in which only the change of ΔE < 0is accepted.
If the undulator is ideal, the field B x,i and By,i should be
zero, so the cost function includes these two elements. Twoneighbouring magnet pairs construct one undulator period,

1. Calculate the absolute transverse field value |M x | and|My | for each magnet, then store them as ascendingorder in two arrays;
2. Choose another magnet to match the magnet whose
absolute value is largest. First step we choose themagnet whose |M x | and |My | is closest to the onethat has to be matched. This includes the possibility that by flipping the magnet the sign of M x and My
changes at the same time. If matching both cannot besatisfied, then flipping the magnet to make the sign of
Mx different has priority.
3. After pairing the magnets, we pair the pairs. Because
the x-direction of the field had higher priority during
the previous step, the y-direction is considered firstduring this step. After this treatment, as shown in
Fig. 3, the spikes appear by couples and the sign isdifferent, so the integral field can be decreased.
4. After pairing the pairs, we pair double pairs. This time
it considers x-direction field more (the result of thisstep is shown in Fig. 3). Then we pair four pairs by
y-direction field, and then eight pairs by x-direction
field, and so on.
From the algorithm described above, one can see that thepairing method, unlike to the annealing method, does not

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randomly rearrange of the undulator magnet configurationand is therefore less computer intensive. The result of thepairing method and the annealing method will be comparedin next section.

SORTING RESULTS OF SIMULATEDANNEALING AND PAIRING
Magnet sorting by simulated annealing
It is known that suitable weight of the elements includedin the cost function must be set before running the program. One reasonable method to determine the weight isthat first randomly setting the undulator configuration formany times and then observing how much the deviation ofeach element’s contribution to the cost function is. Theneach of element weight is set depending on this deviation[11]. The random setting time is 20000. We set as weightof each element the inverse of the deviation of its contribution to the cost function. Table 1 illustrates the different
weights. As can be seen, the weight of the field integral
is much smaller than the others and in fact can be nearlyneglected in the cost function. If the field integral is notneglected, the value of cost function is mainly determinedby it.

Table 1: Weight for the rms value of each element for costfunction
Elements for the cost function
weightBx on each magnet pair35971
By on each magnet pair
89365
First integral of Bx on each magnet pair
1.513
First integral of By on each magnet pair
4.0816Bx (i) + Bx (i + 1) on each undulator period 13210
By (i) + By (i + 1) on each undulator period 33333

Sorting for the 5 m long undulator by pairingAs described earlier, the pairing method is divided into
many steps: pairing magnets, pairing magnet pairs, paring
double magnet pairs and so on. The result of the different steps on the field at different length scales is shown in
Fig. 3.

Figure 3: Improvement of the field integral after each stepof optimization, pairing of magnets (black curve), pairingof pairs (red curve) and pairing of double pairs (blue curve).
The field integral before pairing is the same as in Fig. 2 andtherefore not shown.
Figure 2: Sorting result by annealing with different element weight listed in Table 1. Both of the field integrals
are decreased by two orders of magnitude.
Fig. 2 illustrates the result. One can see that the field
integrals decrease by an order of magnitude.
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It illustrates how the field integral depends on the subsequent sorting steps. Because in the first step the magnets
are paired, attempting to improve both B x and By , both ofthe corresponding field integrals improve by about an orderof magnitude (black curves in Fig. 3 compared to the original integrals in Fig. 2). Pairing of magnet pairs results ina correlation for B y such that on the scale of an undulator

Proceedings of FEL 2007, Novosibirsk, Russia
period, the errors in B y compensate each other, resulting ina reduced field integral in this plane after the second step
(red curve). Because in this step B x is not considered, thisfield integral is changed but not improved. The last stepin Fig. 3 shows how sorting magnets on a scale of two undulator periods results in further correlations, now also on
Bx which was taken into account in this (final) sorting step
(blue curve showing an improvement in teh x-direction).

Comparison of Annealing and Pairing

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whereas this is more difficult with the pairing method. Thisis illustrated in Ref. [12].

SUMMARY
In order to reach saturation in an FEL the overlap between electron and photon beam has to be guaranteed. To
this aim individual magnets are measured and put into theundulator structure in a special order. The two methods discussed in this paper are simulated annealing and pairing ofmagnets. Only the transverse field components have beencorrected.
As has been shown, both methods can greatly improve
the transverse undulator field. The pairing method is morestraightforward and gives a better field than the annealing
method. The field integral is about a factor of 2 better for
pairing, which would result in a better overlap. However,both methods meet and even exceed the required field accuracy.

REFERENCES[1] Massimo Altarelli et.al., The European X-Ray FreeElectron Laser Technical Design Report, ISBN 3-93570217-5[2] A. M. Kondratenko and E. L. Saldin, Part. Accel. 10, 207(1980)[3] R. Bonifacio, C. Pellegrini, and L. M. Narducci, Opt. Commum. 50, 373 (1984)[4] S. Schreiber, Proceedings of the 27th International Free
Electron Laser Conference pp, 12-18, 2005, Stanford, California, USA[5] B. Faatz, J. Pflueger, Y. M. Nikitina, Nucl.Instr. and Meth.
A 393 (1997) 380[6] B. Faatz and J. Pflueger, Magnet Sorting for the TTF-FEL
Undulator using Simulated Annealing, TESLA FEL Report
1999-01

Figure 4: Comparing the transverse field integrals after
sorting by annealing and pairing. One can see that for bothof transverse field integrals the pairing method gives a factor of 2 smaller errors because the errors are compensated
immediately and errors cannot build up to large deviations
The comparison of pairing and annealing is illustrated inFig. 4. One can see that field integrals are clearly smaller incase of the pairing method. The reason for this is that errors
are corrected locally. The results so far show that magnet
pairing is much less computer intensive and gives slightly
better results. As a consequence, one might say that there
is no reason to use simulated annealing. However, in casesome magnets have to be exchanged after part of the undulator magnets have already been assembled, the annealing
method has the clear advantage that one can resort the remaining part of the undulator with magnets still available,[7] J. Pflueger, H. Lu and T. Teichmann, Field fine tuning bypole height adjusting for the undulator of the TTF-FEL, Presented at the 20th International FEL conference, August 1721, 1998, Williamsburg, USA[8] Kirkpatrick, S., Gelatt, C.D and Vecchi, M.P. 1983, Science,Vol. 220, pp.671-680[9] Kirkpatrick, S. 1984, Journal of Statistical Physics, Vol. 34,
pp. 975-986[10] Numerical Recipes, William H. Press, Saul A. Teukolsky,
William T. Vetterling and Brian P. Flannery, Cambridge
University Press, pp. 436[11] Duncan Scott, An Introduction to Monte-Carlo Methods for
Magnet Block Sorting An APPLE-II Type Helical Undulator, ASTEC-ID-024, 2004[12] Y. Li, B. Faatz and J. Pflueger, Magnet Sorting for the XFEL
Hybrid Undulator — Comparing Study, TESLA-FEL report
2007-06, DESY, Hamburg, Germany

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STUDY OF UNDULATOR TOLERANCES FOR THE EUROPEAN XFEL
Yuhui Li, Bart Faatz and Joachim Pflueger
Deutsches Elektronen Synchrotron (DESY), Hamburg, Germany
Abstract
For an X-ray FEL facility, error tolerance simulations
for undulator systems are necessary. Previous work mainly
took into account random errors for each pole and then simulate their impact. However, some errors, for instance thegirder deformation, are not random but periodic. In thispaper both random and periodic errors as well as a combination are studied. The results are limited to non-steering
errors, i.e. a reduction in overlap between electrons andphoton beam has been avoided throughout this study.
Key words: tolerance, undulator, XFEL

Some papers investigating the impact of undulator fielderrors show that beam wander and phase shake are the key
reasons for the increase of gain length [8, 9]. Beam wander
reduces the transverse overlap between electron beam andradiation. Phase shake indicates an electron ponderomotive phase variation and therefore a reduction in bunching.
In this paper only the impact of phase shake is taken into
account.
The FEL simulation code Genesis 1.3 is used for our
simulations [10].

DESCRIPTION OF BASIC ERROR TYPESINTRODUCTION

Girder support point(a)

In the European XFEL project, photons will be generated in the X-ray range of 3.1 keV to 12.4 keV [1]. Highpower radiation will be generated using Self-Amplified
Spontaneous Emission (SASE). Saturation will be rezchedwithin a typical length of 100 to 150 m [2, 3]. Undulator
errors unavoidably exist in this long undulator system. A
first estimate for an upper limit on these errors is related to
the SASE-FEL bandwidth ρ:
Δλs
2ΔK
<ρ
≈
λs
K

(1)

With the value of ρ of the order of 10 −4 for the European
XFEL project, undulator gap variation should smaller than
1 μm and the temperature variation should be smaller than
0.08o C [4]. If Eq. (1) could be satisfied, the power degradation and saturation length increase would be minimal.
Because this is far from trivial and a mayor cost driving
factor, a more detailed study is neccessary.
The European XFEL facility will supply 0.1 nm to
0.4 nm radiation. Wavelength tuning can be achieved bychanging the undulator gap or the electron beam energy.
Even though the tolerance level for different modes is different, their behaviour is similar. Therefore in this paper weonly list the result of SASE1 with 0.1 nm mode which has
the tighest tolerance requirement. A more complete study
can be found in [5].
Two kinds of undulator field errors can be distinguished.
One kind is random error on each undulator pole. This kindof error can be caused for example by the inhomogeneous
field of magnet blocks [6]. Another kind of error changes
along undulator as periodic or semi-periodic function. Thiskind of error exists for instance because of the girder deformation or gap tilt [7]. The previous tolerance simulation
work concentrated mainly on the first kind of error. Thus
this report only studies the latter one.
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Girder support point

(b)

K

K
ǻK

ǻK

K0

K0

Z

Z
Ȝį

Ȝį

(c)

(d)
g1

K0

Ȝį

Z

g3

K
ǻK

K
ǻK

g2

K0

Z
Ȝį

Figure 1: The induced undulator error by girder deformation and gap tilt (a) sinus, (b) sawtooth, (c) triangle and (d)constant
The periodic errors are divided into four basic types: sinus, triangle, sawtooth and (stepwise) constant. The sinus
error is used to approximate undulator girder deformation
due to the magnetic forces which can be compensated for
one gap setting only. Fig. 1 (a) shows this effect. For theEuropean XFEL, a four point support structure is used inorder to minimize this effect. A periodic error can also be
generated by the inhomogeneous movement of the undulator driving motors. Fig. 1 (b), (c) and (d) illustrate so
generated three kinds of periodic errors (sawtooth, triangle
and constant). The movement accuracy is assumed to be
1 μm.
Finite motor movement accuracy results some in residual
random errors of which the importance has to be quantified.
For this purpose, the same error model as shown in Fig. 1
is used, but in this case the resulting amplitude variation
ΔK is random. In contrast to this, the undulator girder
deformation is always homogeneous and thus a periodic
error can always be expected. Therefore, in this paper thesimulation of random sinus errors is not investigated. Fig 2
illustrates this random error.

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Figure 2: The random error for the three error types. The
error amplitude randomly changes from error period to error period.

PHASE SHAKE CALCULATIONS WITHPERIODIC ERRORSAs already mentioned, phase shake is an important reason for radiation power degradation. For the periodic error
considered in this paper, the phase shake can be analyticallycalculated. The undulator parameter K can be written as
K(z) = K0 + ΔK · f (z)(2)

where K0 is the nominal undulator parameter, ΔK ·f (z) denotes the undulator error. ΔK expresses
the error strength and f (z) (f (z) = 0, f 2 (z) = 1) the error
shape.
It can be shown that the RMS phase shake for a periodic
error (f (z) = f (z + λδ ) with λδ the error period) can beapproximated by:
ku K02
ΔK
·α
λδ ,
σΔϕ =
1 + K02
K0(3)

where α is a coefficient dependingon√√the error√ shape.
The
coefficientvalues
are
1/
2π,
1/
30,
1/
45 and
√1/ 12 respectively for the sinus, triangle, sawtooth andconstant error.
It is important that the RMS phase shake is proportional
to the product of ΔK/K 0 times the error period λ δ . To
illustrate this more clearly, Fig. 3 shows simulation resultswith a periodic sinus field error. One can see that the ΔKof black the sinus error is five times larger than the red error, whereas the error period λ δ of the black error is ten
time shorter than the red error. From Eq. (3) the red error
therefore has a larger RMS phase shake. Consequently, thepower growth along the undulator with the black error is
expected to be closer to the ideal than the red one. This isindeed confirmed by the blue dotted line in the bottom plotof Fig. 3, which is the power growth for the ideal undulator.

ERROR SIMULATION FOR SASE1
In this section we introduce the method of our error tolerance calculation and the results for SASE1, 0.1 nm mode.

Simulation method
As mentioned for each operation mode four error types(sinus, sawtooth, triangle, constant) are simulated. For
each error type, the simulation is divided into two steps:

Figure 3: Two sinus error’s with different amplitude andperiod and its impact on the power growth. The ΔK ofthe black line is larger but because of its shorter λ δ its
rms phase shake is smaller. Thus its power degradationis smaller thanthat of the red curve.
first simulating the periodic error and then the random error. The error models for different types are shown in
Fig. 1.
First we calculate the periodic error impact. From Eq. (3)we know that the the RMS phase shake can be changed
either by adjusting the error strength ΔK/K 0 or the error period λ δ . Because the power degradation is determined by the RMS phase shake, any product of ΔK/K 0
and λδ with the same phase shake corresponds to a certain
power degradation. Therefore first we have taken 9 different error strengths: ΔK/K 0 = 0.1%, 0.15%, . . . , 0.5%.
For each ΔK/K0 , 30 different error periods λ δ /λu =10, 20, . . . , 300 are chosen. Thus the power growth withtotally 270 combinations of ΔK/K 0 and λδ is calculated.
So far the simulation for periodic error is done. Then the
random error is simulated. We choose three points (combination of ΔK/K 0 and λδ ) where 10%, 20%, 30% power
degradation can be expected. Thus totally 9 points are chosen. For each point, we fix the λ δ and set a suitable κthat if ΔKi /K0 (i denotes the random error strength in ith
period) randomly varies in the range of [−κ, κ], the RMS
phase shake is close to the value of the periodic error. For
each combination 100 random simulations are performed

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and totally 900 random errors are calculated.

Simulation result for random error

Simulation result for periodic error

Fig. 5 shows the correlation between the power degradation and the RMS phase shake for the random sawtooth
error. Comparing to the correlation of periodic error, forthe random error the power degradation still correlates to
the RMS phase shake. The mean power value for a certain RMS phase shake is similar for random and periodic
distributions, but the spread for random errors is larger.

Figure 4: The power degradation versus RMS phase shakeat a fixed point inside the undulator before saturation isreached. There is a perfect correlation between power andphase shake, independent of what error shape has beenused.
It is interesting to illustrate the power degradation withdifferent RMS phase shake values and different error types.
Fig. 4 shows the result. The correlation between the power
degradation and the RMS phase shake is good and same
RMS phase shake generated by different error types resultsin the same radiation power. Based on this result we canimagine that for any kind of error type which is not included in our simulation, the power degradation can also
be evaluated by the RMS phase shake.

Figure 5: Power versus phase shake in case of a sawtooth
error. The back squares show the results of random sawtooth amplitude and length scale. The red circles show theperiodic sawtooth errors that are already shown in Fig. 4.

COMBINED ERRORS ANDTEMPERATURE COMPENSATION
Combination of different errors

Table 1: Summary of results of tolerance simulations for
SASE1, 0.1 nm mode. The numbers quoted here correspond to a power reduction of 10%.
Type
RMS phase λδ
ΔK/K0 Δg
shake
(mm)
sinus
0.146
1.2m 0.366%
0.030
triangle
0.156
10m 0.058%
0.005
sawtooth 0.1655m
0.148%
0.013
constant 0.183
10m 0.043%
0.004
Table 1 shows the tolerance result for SASE1, 0.1 nm
mode with a 10% power reduction. From this table one cansee that a sinus girder deformation as large as 30 μm canbe tolerated which is considerably larger than the estimatebased on the Pierce parameter ρ. On the other hand a λ δ of
10 to 12 m still requires gap control in the μm level. This,hoever, is technically no problem.
the from all of the error types, the girder deformation or
the gap movement accuracy can relax to a value larger than
1 μm, which is evaluated by the Perice parameter ρ. On
the other hand, the longer periodic length λ δ brings tighter
error strength ΔK/K 0 .
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In the sections before, the impact of four different error
types have been illustrated separately. Because in practicethese errors are combined it is also necessary to study the
impact of this kind of combined error.
In principal the sinusoidal girder deformation can be assumed to be always periodic. While the triangle, sawtoothand constant error are all generated because of the inaccuracy of motor movement, they are random. 20 μm of girder
deformation, 2 μm motor movement accuracy and 10 μm
of girder deformation, 1 μm motor movement accuracy are
simulated.
The power degradation and the RMS phase shake areshown in the Fig. 6. One can see that the larger error values bring larger RMS phase shake and therefore the power
degradation is larger. The largest power degradation value
is about 40%. In addition, the large variation in power ismainly due to the random error, as was already shown in
Fig. 5. This means that even though the girder deformation is an order of magnitude larger than the random gap
error, the power degradation is not dominated by it, which
confirms the result shown in Table 1.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH006

tive way of compensating this effect is to locally correct theundulator gap according to the local temperature. This requires a precise local temperature measurement and a precision temperature sensor on each undulator segment. The
local gap is adjusted if a threshold set by the accuracy of thesensor is exceeded. We assume 0.1 o C, which is demanding on an absolute scale. The red points in Fig. 7 show theresults. The power loss can be recovered completely.
In terms of Eq. (3) the product ΔK/K 0 · λδ is 0.14
for 1o C, ΔK/K0 = 10−3 , 140 m error length versus
1.8 × 10−4 for ΔK/K0 = 3.57 × 10−5 and 5 m the lengthof an undulator segment, which is an alternative way of explaining the above result. As shown in Fig. 7 temperature
variations as much as 5 o C can be compensated completely.
Figure 6: The power reduction due to the combined periodic sinus and random sawtooth/constant error.

Linear temperature gradient and compensation
by adjusting the undulator gap

SUMMARY
Error tolerances for the undulator system of the European XFEL are analyzed in this paper. It has been shownthat for non steering errors, the RMS phase shake is a goodnumber to predict the power reduction in an undulator system. For periodic errors the phase shake can be calculated analytically by the product ΔK/K 0 · λδ times a constant depending only on the error shape. Thus for small
error period length comparatively large errors can be tolerated, whereas for large error periods the error level are verysmall. Local temperature measurement and local gap correction was shown to effectively compensate power losses
caused by global temperature variation. This method canbe effectively used to reduce requirements on temperaturestabilization.

REFERENCES[1] Massimo Altarelli et.al., The European X-Ray FreeElectron Laser Technical Design Report, ISBN 3-93570217-5[2] A.M. Kondratenko and E.L. Saldin, Part. Accel. 10, 207(1980)

Figure 7: Power reduction due to a temperature gradientover the entire undulatorlength of up to 5 o C and the compensation by an appropriate adjustment of the undulator
gap. The gap has been adjusted by 1 μm as soon as themeasured temperature exceeds 0.1 o C.
Over the length of the undulator system the temperature may differ. These effects were investigated. From
Eq. (1) 0.08 oC are estimated for total temperature variation. This requires a sophisticated air conditioning systemwith demanding properties. As a simple rule, due to thereversible temperature coefficient of the permanent magnet material 0.1o C temperature variation corresponds toΔK/K0 = 10−3 . The effect of the linear temperature variation over the whole undulator system is plotted against theradiation power in Fig. 7, black points. It is seen that a 1 o Cvariation reduces the power by more than 50%. For 2 o C
and above there is no radiated power anymore. An effec-[3] R. Bonifacio, C. Pellegrini, and L.M. Narducci, Opt. Commum. 50, 373 (1984)[4] J. Pflueger, Undulator Systems and Photon Diagnostics for
the European XFEL Project, Proceedings of the 27th International Free Electron Laser Conference (2005) 378-382[5] Y. Li, B. Faatz and J. Pflueger, Sutdy of Undulator Tolerances for the European XFEL, TESLA-FEL report 2007-07,
DESY, Hamburg.
[6] Y. Li, B. Faatz and J. Pflueger, Magnet Sorting for the XFEL
Hybrid Undulator — Comparing Study, presented at thisconference[7] J. Pflueger, M. Tischer, Nucl. Instr. and Meth. A483 (1999)
388-393[8] B. Faatz, J. Pflueger, Y.M. Nikitina, Nucl. Instr. and Meth.
A393 (1997) 380-384[9] B.L. Bobbs et.al, Nucl. Instr. and Meth. A296 (1990) 574578[10] S. Reiche, Nucl. Instr. and Meth. A429 (1999) 243-248

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Proceedings of FEL 2007, Novosibirsk, Russia

MCP-BASED PHOTON DETECTOR WITH EXTENDED WAVELENGTH
RANGE FOR FLASHL. Bittner, J. Feldhaus, U. Hahn, M. Hesse, U. Jastrow, V. Kocharyan, P. Radcliffe, E.L. Saldin,
E.A. Schneidmiller, K. Tiedtke, B. Timmann, R. Treusch, N. von Bargen, M.V. Yurkov
Deutsches Elektronen-Synchrotron (DESY), Hamburg, Germany
O.I. Brovko, D. Kharlamov, V.I. Lokhmatov, E.A. Matyushevskiy, A.V. Shabunov, E.M. Syresin
Joint Institute for Nuclear Research (JINR), Dubna, Moscow Region, Russia
Abstract
cation and further fine tuning of the machine parameters
Experimental experience gained at the extreme ultraviolet SASE FEL FLASH (DESY, Hamburg) has shown thatsuccessful operation of the facility strongly depends on thequality of the radiation detectors. Here key issues are: wide
wavelength range (6 to 100 nm for FLASH), wide dynamic
range (from the level of spontaneous emission to the saturation level), and high relative accuracy of measurements
which is crucial for detection of a signature of amplification and characterization of statistical properties of the radiation. In this report we describe MCP-based radiation detector for FLASH which meets these requirements. Key element of the detector is wide dynamic range micro-channel
plate (MCP) which detects scattered radiation from a target. With four different targets and MCPs in combination
with optical attenuators present detector covers operating
wavelength range from 6 to 100 nm, and dynamic rangeof the radiation intensities, from the level of spontaneousemission up to the saturation level of SASE FEL.

INTRODUCTION
The free electron laser FLASH is in operation at DESY
since the year 2000 [1–5]. Several upgrades of the facility
have been performed, and after an upgrade of 2007 FLASH
will cover a wavelength range from 6 to 100 nm. Instrumentation for photon beam characterization has been developed as well [6–11]. An important piece of the photon diagnostics are detectors for measurements of the pulse
energy. Originally FLASH has been equipped with PtSiphotodiodes and thermopiles based on YBCO High-Tcsuperconductors (HTSCs) [6, 7]. These detectors helped to
fix the first signature of light amplification at FLASH [1],but it has been realized soon that they have rather limited
possibilities. The first one refers to limited dynamic range,
and the other one relates to the physics of interaction of
powerful, ultrashort VUV radiation pulses with the detector. In fact, nonlinearities and saturation effects started tooccur in PtSi-photodiodes much earlier with respect to calibrations performed with conventional lasers. To solve theproblem of limited dynamic range and saturation effects
we launched development of MCP-based radiation detector [8], and pretty soon succeeded to tune FLASH to saturation in 2001 [2,3]. An important feature of MCP-detector
is high relative accuracy of intensity measurements. Thisis crucial for detecting the first signature of light amplifiFEL Technology I

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for increasing the gain. MCP detector is used for measurement of statistical properties of the radiation allowing todetermine the pulse length and mode contents of the radiation [12]. In 2004 the energy of FLASH accelerator has
been increased to 700 MeV, and a new MCP detector optimized for wavelength down to 10 nm has been installed,
and became the primary tool for searching amplification,
tuning the gain, and for statistical measurements [4, 5, 9].
In this paper we describe 3rd generation MCP detector at
FLASH optimized for the measurement of SASE radiation
with the wavelength down to 6 nm.

CURRENT EXPERIENCE WITH
MCP-BASED DETECTOR AT FLASH
Photon detectors at FLASH are installed in a beamline
downstream the undulator. The most critical step of tuning
lasing process is to find the signature of light amplification.
The problem relates to a strong background of incoherent
radiation produced by the whole bunch (charge 0.5-1 nC)
MCP4

MCP3

Target unit #2

Target unit #1

MCP2

MCP1

CeYaG crystal

Figure 1: Top: layout of MCP-detector operated at FLASHin 2004-2007 [9]. Detector consists of two identical units
for detection of radiation at fixed angles. The targets aresemi-transparent gold mesh and gold wire. On-line tuning with this detector allows to have simultaneously quantitative data and visual observation of the photon beam on
CeYaG crystal.

Proceedings of FEL 2007, Novosibirsk, Russia

100

1

(a)
10 deg-2

10<Erad>[µJ]

10
Reflectivity

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-4

10

Au

90 deg

-6

0.1

Cu

10

1

Fe

0.01

-8

5

10

l

15

20

0

5

10

[nm]

Figure 2: Reflectivies of Au, Cu and Fe versus wavelength
for angles of 10 and 90 degrees. Surface roughness is 1
nm [13].

15
z [m]

(b)

0.8

p(Erad)

10

20

25

30

σ = 72%
M = 1.9

0.6
0.4

10

0.2

106

0.0

0

1

4

10

102
1

2
3
Erad/<Erad>4(c)

σ = 18%2
3
Erad/<Erad>

4

2

1600

1800

2000

2200

2400

U [V]

p(Erad)MCP gain

851Figure 3: MCP gain versus applied voltage.
0

passing through the whole undulator length (27 m). In thepresent experimental conditions, at the energy of electronsof 700 MeV and bunch charge of 0.7 nC the pulse energyof the spontaneous emission is about 40 nJ within the 10mm aperture of the detector located 18.5 m downstreamof the undulator. Thus, it becomes crucial to have highprecision photon detectors permitting the detection of small
increases in the radiation intensity. For this purpose a radiation detector equipped with a microchannel plate (MCP)
is used [9]. Schematic layout of the detector is shown in
Fig. 1. It consists of two identical units, each of them
contains removable targets (gold wire of 250 µm diameter and gold mesh with wire of 60 µm diameter, open area65%) and two MCPs detecting photons at large and smallreflection angles. Figure 2 shows reflectivity of the gold forlarge and small reflection angles. Geometrical positions of
MCPs have been chosen such that acceptances of photons(given by convolution of the reflectivity with geometricalfactors: reflecting area and angular acceptance) differ bya factor about 300, but overlap at some intermediate lightintensity. MCPs detecting backward scattered radiation are

0

1

5

Figure 4: Measured average energy in the radiation pulse
versus undulator length (up) showing exponential growthand saturation [5]. Center and lowest panels, probability
distributions for the energy in the radiation pulses. Center
plot: end of the regime of exponential growth where theaverage pulse energy is equal to 1 µJ. Lowest plot: saturation regime where the average pulse energy is equal to
40 µJ. Radiation wavelength is 13.7 nm. Solid line on thecenter plot represents a gamma distribution with the parameter M = 1.9. The solid line on the right plot represents
simulations with the code FAST [14].

placed very close to the target and accept more photons
despite less reflection coefficient. Inspecting the amplification curve of MCP (see Fig. 3) one can wonder why wecomplicated setup with two different MCPs: one MCP has

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very large dynamic range of six orders of magnitude. The
choice of such a geometry has been mainly dictated by thefollowing reasons. In the real experimental conditions there
is always gamma background originated from the accelerator beamline. In the case of FLASH this background becomes to be significant when high voltage applied to MCP
exceeds 1900 V. When light intensity is high, applied voltage needs to be reduced, and below 1400 V space charge
effects in MCP channels start to play significant role. Thus,
practical operating range of the MCP gain is about threeorders of magnitude only, less than the dynamic range of
SASE intensity.
The electronics of the MCP-detector itself has low noise,
about 1 mV at a level of signal of 100 mV (1% relative
measurement accuracy). Another source of disturbances ofmeasurements were fluctuations of the bunch charge. To
exclude the influence of bunch charge fluctuations we perform on-line normalization of the radiation energy to thebunch charge. This technique gave us the possibility to detect reliably SASE gain at a 2% level above spontaneousemission. Once amplification is detected, output energy
can be easily increased to the level of about ten µJ, theonset of the saturation regime. This occurs due to the exponential dependence of the output signal on a change inany important parameter of the electron beam. Tuning of
the radiation energy in the saturation regime above 10 µJ
is a delicate procedure, and requires perfect alignment of
the orbit in the undulator (on a scale of ten micrometers),
and the rf phases of the gun and the first three accelerating
modules with relative accuracy of about 0.1 degree.
Absolute calibration of MCP has been performed withspontaneous emission at one operating boundary (nanojoule range of pulse energies), and with gas monitor detector [11] at another operating boundary (from a few to
70 microjoules pulse energies). During experimental runof 2004-2007 years MCP detector demonstrated excellent
performance and served as the main tool for SASE search,tuning, intensity characterization and statistical measurements in the wavelength range from 45 to 13 nm (see Fig. 4
from [5]).
We should note that the target of MCP detector (mesh orwire) always produces diffraction pattern resulting in an inhomogeneous intensity distribution at the sample position.
Thus, MCP-detector can not be used for online monitoringof the intensity while operating with specific user experiments requiring undisturbed radiation pulse. Gas detector
is used in this case [11].

MCP-DETECTOR WITH EXTENDEDWAVELENGTH RANGE (MCP07)
For the planned upgrade of the FLASH for operation at 6
nm we also designed and manufactured a new MCP detector. The reason for a new installation is obvious from analysis of reflectivity curve versus the wavelength (see Fig:2).
While gold target is perfect for use in the wavelength range
above 10 nm, its reflectivity falls dramatically for shorter
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MCP5

Target unit

MCP3

MCP1

MCP2

MCP4

MirrorFigure 5: Layout of MCP detector with extended wavelength range installed at FLASH in 2007 (MCP07). Detection of backward reflected radiation is performed withstationary mounted MCP1 a nd MCP2. MCP3 and MCP4
are movable. When positioned off-axis they measure small
angle reflected radiation. Measurements of direct photon
beam is also possible when positioning MCPs on axis.
MCP5 detects radiation reflected by Fe mirror. Target unit
contains four grids of different materials (Au, Cu, Fe), andlight attenuator.

1
-1

10
Reflectivity

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-2

10

-3

10

-4

10

rms 1 nm

-5

10

10

20

l

30

40

[nm]

Figure 6: Reflectivies of Fe versus wavelength for anglesof 30 and 45 degrees. Surface roughness is 1 nm [13].
wavelengths, and different targets and geometry of the detector should be used. General layout of the new detector(MCP07) is shown in Fig. 5. We conserved small/large angle reflection geometry of MCPs which demonstrated to bereliable solution for detection of the radiation above 10 nm.

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WEPPH007

Keeping gold mesh, we added three more targets: two ironmeshes (88% and 79% open area), and one copper mesh
(60% open area). This will help to operate the detector
in some range below 10 nm. For tuning SASE at very
short wavelengths we assume to use movable MCPs directly facing photon beam. Reduction of the light intensity(if required) will be provided with mechanical attenuatorof light (perforated Ni foil located in the target unit, 2%
open area). To have full control on light intensity in thewide range we installed side MCP which detects radiationreflected by iron mirror. Mirror serves for two purposes.
The first one is to deflect the photon beam off-axis whichallows to place MCP in better background conditions. The
second function of the mirror is calibrated attenuation of
the light (see Fig. 6). With two fixed angles of the mirror(30 and 45 degrees) and with mechanical attenuator we canchange the light intensity on MCP in the range of several
orders of magnitude. This will allow us to overlap all therange of radiation intensities, from the level of spontaneousemission to the saturation level.

REFERENCES[1] J. Andruszkow et al., Phys. Rev. Lett. 85(2000)3825.
[2] V. Ayvazyan et al., Phys. Rev. Lett. 88(2002)104802.
[3] V. Ayvazyan et al., Eur. Phys. J. D 20(2002)149.
[4] V. Ayvazyan et al., Eur. Phys. J. D 37(2006)297.
[5] W. Ackermann et al., Nature Photonics, 1 (2007)336.
[6] R. Treusch, HASYLAB Annual Report, DESY,
Hamburg, 2005, p.159-164 (see also http://wwwhasylab.desy.de/science/annual reports/2005 report/index.html).
[7] K. Tiedtke et al., AIP Conf. Proc. 705 (2004)588.
[8] B. Faatz et al., Nucl. Instr. and Meth. A 483(2002)412.
[9] A. Bytchkov et al., Nucl. Instrum. and Methods A
528(2004)254.
[10] M. Richter et al., Verfahren und Monitordetektor zur Bestimmung der Intensitat von gepulster VUV- oder EUVStrahlung sowie Verwendung eines derartigen Monitordetektors (Deutsches Patent- und Markenamt, No. 102 44
303.3, Munchen)(2002).
[11] M. Richter et al., Appl. Phys. Lett. 83 (2003)2970.
[12] V. Ayvazyan et al.,A507(2003)368.

Nucl. Instrum. and Methods[13] Data taken from LBL database
http://henke.lbl.gov/optical_constants[14] E.L. Saldin, E.A. Schneidmiller, and M.V. Yurkov, Nucl. Instrum. and Methods A 429(1999)233.

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MEASUREMENTS OF PROJECTED EMITTANCE AT FLASHK. Honkavaara∗ , Hamburg University, 22761 Hamburg, Germany
F. Löhl, E. Prat, DESY, 22603 Hamburg, Germany

Abstract
FLASH is a SASE FEL user facility at DESY operating with photon wavelengths in the range from vacuum ultraviolet to soft x-rays. Although the slice emittance is amore appropriate parameter to characterize the SASE process, the projected emittance provides a useful measure of
the electron beam quality. At FLASH, the projected emittance is measured at three locations along the linac: in theinjector (130 MeV), after the collimator, and in the undulator section. The emittance is determined by using a multimonitor method with OTR monitors and wire scanners. In
this paper we describe the measurement set-up and procedure, and report recent results.

INTRODUCTION
FLASH is a SASE FEL user facility at DESY (Hamburg,
Germany). It produces short (in order of 10 fs) laser likepulses in the wavelength range from the vacuum ultraviolet
to the soft X-ray [1].
Figure 1 shows a schematic layout of the FLASH linac
as operated in 2006 and the first half of 2007. Electron
bunch trains with up to 800 bunches are generated by alaser-driven RF gun. The macro-pulse repetition rate is
5 Hz, and the bunch frequency 1 MHz. During the measurements reported here, the linac is operated with one or
two bunches per bunch train. The bunch charge is 1 nC.
Five accelerating modules, with eight 9-cell superconducting TESLA cavities each, provide electron beam energies up to ∼730 MeV. The electron bunch is compressedby two magnetic chicane bunch compressors. At the location of the first bunch compressor, the beam energy is∼130 MeV, and at the second one ∼370 MeV. During themeasurements reported here, the total beam energy after
acceleration is ∼500 MeV. The SASE radiation is producedby six undulator modules with length of 4.5 m each.
The SASE process requires a high quality electron beamin terms of transverse emittance, peak current and energy
spread. In the characterization of this process, the slice parameters are the appropriate parameters to consider. However, also the projected emittance, which is relatively easy
to measure compared to the slice emittance, provides animportant measure of the electron beam quality. In addition to be able to produce a small emittance beam at the
injector, it is important to conserve this small emittance up
to the undulator, where the SASE radiation is produced.
∗ katja.honkavaara@desy.de

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In this we paper describe the emittance measurements
performed at three location along the FLASH linac: at the
injector, after the collimation section and at the undulator.
These measurements are also discussed in [2].

EXPERIMENTAL SET-UP
We measure the transverse projected emittance using a
multi-monitor method. This method is based on measurements of the transverse beam distribution (shape and size)
at several locations with fixed beam optics.
There are two diagnostic sections dedicated to emittancemeasurements along the FLASH linac (see Fig. 1). The
first one is located downstream of the first bunch compressor. This section has four OTR (optical transition radiation) monitors combined with wire scanners mounted into a
FODO lattice of six quadrupoles with a periodic beta function. Below, we refer this section as the ’BC section’. A
second FODO lattice with four OTR monitors is locatedupstream of the undulator, referred here as the ’SEED section’. A fifth OTR monitor placed upstream of the FODO
lattice is used as an additional monitor in the measurements. Along the undulator, the emittance is measured using wire scanners located in front of each undulator module. A seventh wire scanner station is downstream of theundulator.

OTR monitors
OTR monitors are based on detection of backward optical transition radiation. The OTR light is emitted when theelectron beam passes through an aluminium coated silicon
screen inserted at an angle of 45 ◦ with respect to the beam
trajectory. The ligth is deflected downwards into an optical
set-up consisting of three achromat doublet lenses, threeneutral density filters, and a digital CCD camera. Each lensprovides a fixed magnification, and can be remotely moved
in and out of the optical axis. For accurate measurements
we use the lens with the highest magnification (1:1). With
this lens the measured resolution is 11 μm rms.
The digital CCD cameras with a firewire interface areconnected to a PC in the accelerator tunnel. The PC is connected via local Ethernet to an “image server” in the control
room. The read-out system, using a LabView based control
software, provides beam images for the on-line visualization and for different applications.
More details of the OTR monitor system are in [3, 4].

Proceedings of FEL 2007, Novosibirsk, Russia
ddd

Laser

4 OTR monitors and wirescanners
in 3 cell FODO latticedRF−GunAccelerating modules
1st bunch
2nd bunchcompressor
compressor

WEPPH008
ddd

By−pass line
4 OTR monitorsin 3 cell FODO lattice
Undulator
Collimator

7 wirescanners
DumpdddFigure 1: Layout of the FLASH linac (not to scale). Beam direction is from left to right, and the total length is about
250 m. Locations of OTR monitors and wire scanners, used for the emittance measurements, are indicated.

Combined OTR and wire scanner monitors
The OTR monitors in the BC section are combined withwire scanners. Each scanner has a fork with three tungsten
wires with a diameter of 18 μm. The wires are oriented
such that one of them scans horizontally and another one
vertically; the third wire provides information of the coupling between the two planes. The wire scanner is mounted
into a common vacuum chamber with an OTR screen, located 5 mm downstream of it. The read-out system, consisting of scintillator panels and photomultipliers, detects
secondary particles emitted when the wire passes the electron beam.
In the emittance measurements reported here, we used
the OTR monitors only. However, a cross check between
profiles measured by the OTR monitors and the wire scanners have been performed showing a good agreement [5].

Undulator wire scanners
Seven wire scanner stations are mounted along the undulator. Each of these stations has two individual wire scanners: one scanning in horizontal direction, and the otherone in the vertical. Each scanner has three wires: a 10 μm
thick carbon wire, and two tungsten wires with diametersof 10 μm and 50 μm . The read-out is based on detectionof secondary emission particles measured with scintillator
panels and photomultipliers. More technical details of theundulator wire scanners are in [6].

In the case of wire scanners, the beam profile is recorded
over several macro-pulses (one point per macro-pulse), andonly one profile is used when determining the beam size.
The rms size of the entire beam is used in the emittancecalculations.
The transverse emittance is determined from the measured beam sizes and the transport matrices between themonitors using a least square fitting. A second method isa tomographic reconstruction of the phase space using the
maximum entropy algorithm. The results obtained by bothmethods agree well [7]. Since the fitting technique is faster,
we use it in our measurements.

EXPERIMENTAL RESULTS
The projected emittance in the BC section has been routinely measured since early 2005. The emittance measurement procedure is well understood, and we have performed
systematic studies on the dependence of the emittance on
different machine parameters. A detailed description ofthese measurements, results and error analysis is in [8].
In the two other sections accurate emittance measurements have been possible only since the beginning of 2007.
Table 1 shows the measured projected emittance at threelocations along the FLASH linac. All of the three measurements have been performed within a few hours withthe same machine conditions. The second column (Day 2)

MEASUREMENTS AND ANALYSIS
During an emittance measurement with OTR monitors,
we record 20 beam and background images for each OTR
screen. The averaged background is subtracted from eachbeam image. After that, a sophisticated image analysis procedure is applied to each image [7].
Not only the emittance of the entire beam, but also theemittance of the high density core is of interest. We determine this core by cutting away 10% (an arbitrary choice)of particles in the tails of the two dimensional transverse
beam distribution. After that, the horizontal and verticalrms beam sizes of the entire beam and of the 90% core arecalculated. These rms sizes are used to calculate the emittance.

Location
BC
SEED
Undulator

Day 1
x
y
3.7
3.2
(2.0) (2.0)
3.7
4.7(2.2) (3.2)
4.4
4.1

Day 2
x
y
3.7
3.8
(2.4) (2.5)
2.7
3.0(2.0) (2.2)
4.3
4.4

Table 1: Projected emittances measured at three locations
along the FLASH linac in two different days. The presented values are normalized rms emittances in units of
mm mrad. The value in the bracket is the rms emittanceof the 90% beam core. Estimated error of the measured
emittances is 0.5 mm mrad.

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shows the same measurements repeated 4 weeks later. The
presented values are normalized rms emittances of the entire beam. In the BC and SEED sections, where the measurements have been performed using OTR monitors, therms emittance of the 90% beam core is presented as well.
In all the cases, the electron beam charge is 1 nC and theelectron beam is accelerated on-crest through the accelerating modules.
The error analysis, taking into account errors in the measured beam size, in the beam energy, and in the transverse
matrices, leads to an error estimation of 0.5 mm mrad forthe measured emittance values.
No substantial change in the projected emittance can beobserved along the linac (Table 1). Similar results havebeen obtained also on other days, when the linac has beenwell-tuned.
During these measurements, our goal was not to optimize the emittance but to study the emittance transport.
In well optimized conditions, a projected emittance below
2 mm mrad in the BC section has been measured [8].

We have also observed that the matching to the undulator
works better, when we use the sigma of a Gaussian fit instead of the rms beam size as input for the Twiss parameter
calculation.
Saturation of the photomultiplier signal has been another problem when measuring the emittance in the undulator. The photon shower generated by the electron
beam is squarely proportional both to the wire diameterand to the atomic number of the wire material. As a consequence, when using a 50 μm tungsten wire the amount oflight input to the photomultiplieris much larger than with a
10 μm carbon wire. The used photomultiplier has a nonlinear behavior when the light input is too large. This
causes an increase of the measured beam size, which leads
to an increase of the measured emittance. In order to avoid
this artificial increase, the measurements presented here are
performed by using the carbon wire only. During the shutdown, filters with an attenuation factor of 32 have been
mounted in front of each photomultiplier. This should allow us to use the tungsten wires as well.

TECHNICAL ISSUESSUMMARY AND OUTLOOKThe last OTR screen in the SEED section is locatedonly a few meters upstream of the undulator. Losses created when the beam passes through the screen are so highthat they may cause degradation of the permanent undulator magnets. Recently, this problem has been solved by
mounting a deflecting magnet and a lead shield after thelast screen.
At high electron beam energies, the emitted OTR light isconcentrated in a very narrow cone. As a consequence, thealignment of the OTR monitors becomes critical. During
the measurements in the SEED section, we have observed
low beam spot intensities on some of the screens. Especially when the beam is not well-optimized, the intensity
depends on the position of the spot on the screen. This indicates a misalignment of the system. During the shutdown
in spring 2007, the OTR monitors have been replaced by
combined OTR and wire scanners monitors (similar to theones in the BC section). In addition, the OTR monitors
have been realigned.
Matching of the beam to the FODO lattice is important
for accurate emittance measurements [8]. In the BC andSEED sections matching works well. In the undulator section, however, it is difficult due to the fact that the so-called
transfer matrix condition number is large, an order of magnitude larger than in the BC section. As a consequence, asmall error in the measured beam size may lead to a large
error in the calculated emittance and Twiss parameters. An
additional complication is caused by the small undulator
aperture. The beam tube inside the undulator has a diameter of about 10 mm only. In order to avoid losses due to toolarge beam sizes or missteering of the the beam, matchingmust be done carefully. Matching has been improved byusing more quadrupoles with less changes in the currents,
and by cycling the magnets after each matching iteration.

The projected emittance along the FLASH linac has beenmeasured at three locations. No substantial change of theemittance has been observed.
During the shutdown in spring and summer 2007, a sixth
accelerating module has been installed in the FLASH linac.
This, together with the upgrades of the other accelerating
modules, will provide beam energies up to 1 GeV in thenear future. We have improved our measurement system in
the SEED and undulator sections. In the SEED section, theOTR monitors have been replaced by the combined OTR
and wire scanner monitors. In the undulator, attenuators
are installed in front of the wire scanner photomultipliers.
Studies on the emittance transport will continue in autumn 2007.

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ACKNOWLEDGMENT
We thank the colleagues and the technical staff of DESY
(Hamburg and Zeuthen), and of INFN (LNF and Roma Tor
Vergata) contributing in the realization and maintenance of
the OTR and wire scanner systems. Special thanks are due
to M. Sachwitz, A. Wipprecht, P. Castro and L. Fröhlich forstudies on the undulator wire scanners, especially concerning the saturation problems. We like to thank V. Balandin
and N. Golubeva for their work on the beam optic tools andfruitful discussions on matching problematic in the undulator section. Thanks are also due to W. Decking, T. Limberg
and S. Schreiber for many interesting discussions and useful suggestions.

REFERENCES[1] W. Ackermann et al., “Operation of a free-electron laserfrom the extreme ultraviolet to the water window”, Nature
Photonics 1 (2007) 336-342

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH008[2] E. Prat et al., “Beam profile measurements and analysis at
FLASH”, PAC 2007, Albuquerque, New Mexico, June 2529, 2007
[3] 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
[4] L. Catani et al., “A large distributed digital camera system
for accelerator beam diagnostics”, Review of Scientific Instruments 76, 073303 (2005)[5] K. Honkavaara et al., “Transverse electron beam diagnostics
at the VUV-FEL at DESY”, FEL 2005, Stanford, California,
August 21-26, 2005
[6] M. Sachwitz et al., “Wire scanners in the undulator sectionof the VUV-FEL at DESY”, DIPAC 2005, Lyon, France, 6-8
June, 2005
[7] F. Löhl, “Measurements of the transverse emittance atthe VUV-FEL”, DESY-THESIS 2005-014 and TESLA-FEL
2005-03, Diploma Thesis, Hamburg University, 2005
[8] F. Löhl et al., “Measurements of the transverse emittance atthe FLASH injector at DESY”, Phys. Rev. ST Accel. Beams
9, 092802 (2006)

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RECENT MEASUREMENTS OF THE LONGITUDINAL PHASE SPACE AT
THE PHOTO INJECTOR TEST FACILITY AT DESY IN ZEUTHEN (PITZ)∗
J. Rönsch† , J. Rossbach, Hamburg University, 22761 Hamburg, Germany
G. Asova‡ , J.Bähr, C. Boulware, H. J. Grabosch, M. Hänel, Y. Ivanisenko§ , S. Khodyachykh,
S. Korepanov, M. Krasilnikov, S. Lederer, B. Petrosyan, A. Shapovalov¶, T.Scholz, L. Staykov,
R. Spesyvtsevk , F. Stephan, DESY, 15738 Zeuthen, Germany
D. Richter, BESSY, 12487 Berlin, Germany
K. Rosbach, Humboldt University Berlin, 12489 Berlin, Germany
L. Hakobyan, YerPhI, Yerevan, Armenia
A. Onuchin, Budker Institut of Nuclear Physics, Novosibirsk 630090, Russia

The Photo Injector Test facility at DESY in Zeuthen(PITZ) was built to test and optimize electron guns for
short wavelength Free-Electron Lasers (FELs) like FLASHand XFEL at DESY in Hamburg. For a detailed analysis of the behaviour of the electron bunch, the longitudinal
phase space and its projections can be measured behind thegun cavity. The electric field at the photo cathode was increased from 40 MV/m to 60 MV/m to optimize the transverse emittance. The momentum distributions for different gradients and gun phases will be presented. In orderto study emittance conservation, a booster cavity and additional diagnostics were installed. The evolution of thelongitudinal phase space in the booster cavity will be investigated. Measurements of the momentum distribution
and longitudinal distribution behind the booster cavity will
be discussed.

ditioning and the first run period at high gradient are presented in [4, 5]. In this paper the influence of the higher
gradient on the momentum distribution will be discussed.

MOMENTUM
In order to understand the behaviour of the gun forhigher gradients at the cathode, measurements and simulations for different gradients were done. Figure 1 shows
measurements and simulations of the maximum mean momentum reached for different powers in the gun. The trend<p> (MeV/c)

Abstract

8
7
6
5
4

INTRODUCTION
The main goal of PITZ is to test and to optimize L-Band
RF photo injectors for Free-Electron Lasers. The requirements on such a photo injector are small transverse emittances, charge of about 1 nC, short bunches (FWHM of
about 20 ps) and the possibility of long bunch trains of 800
pulses emitted with a frequency of 1 MHz. The heart of
PITZ is a copper gun cavity with a solenoid magnet that isused to focus the beam. Detailed analyses of the gun cavity
at a gradient of 40-45 MV/m were presented in [1, 2, 3].
In order to decrease the effects of space charge forces andthus decrease the transverse emittance, the gradient at thecathode was increased to 60 MV/m. Experience of the con∗ This work has partly been supported by the European Community,
contract numbers RII3-CT-2004-506008 and 011935, and by the ’Impulsund Vernetzungsfonds’ of the Helmholtz Association, contract number
VH-FZ-005.
† jroensch@ifh.de‡ On leave from INRNE, Sofia, Bulgaria§ On leave from IERT, Kharkov, Ukraine¶ On leave from MEPHI, Moscow, Russia
k On leave from NSCIM, Kharkov, Ukraine

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3
2
1
0
0

1

2

3

4

5
6
7
power (MW)Figure 1: Measured mean momentum as a function of thepower in the gun (red dots). the black curve describes the
expectation, it is fitted with the square root of the power.
of the measured mean momentum fits to the expectations
up to a power in the gun of about 3.5 MW. For higher
powers the mean momentum stays below the expectation.
The power in the gun cannot be measured directly in the
gun and the error of the power measurement is quite large( ± 0.5 MW). One possible explanation would be that themeasurement of power the is not correct, it is for example
possible, that it measures higher order modes or the cavity
is misshapen and field balance could change. Another possibility is, that we are loosing power between the point ofProceedings of FEL 2007, Novosibirsk, Russia

WEPPH009<p> (MeV/c)

power measurement and the gun, for example in the coupler due to misalignment.
6.55
6.5

6.45
6.4
6.35

measured

6.3

corrected

6.25

simulated

6.2

p rms (keV/c)-20 -15 -10
90
80

-5
0
5
10
relative phase (deg)measuredsimulated

70
60
50
40
30
20
10
-20 -15 -10

-5
0
5
10
relative phase (deg)Figure 2: Mean momentum (top) and momentum spread(bottom) as a function of the gun phase.
The maximum mean momentum reached in the gun was
about 6.5 MeV/c. Figure 2 shows a measurement and thecorresponding simulation of the mean momentum (top) andmomentum spread (bottom) as a function of the gun phase.
The phase with maximum mean momentum gain was defined as zero for both measurement and simulation. Simulation and measurement of mean momentum fit not completely. The measured momentum spread is larger than thesimulation, one reason for the large error bars that the subtraction of the background (dark current), whose momentum is very close to the one of the beam, is not perfect.
Another point is that the phase of the minimum is different for measurement and simulation. Due to the large error
bars this effect is not so clear in this graph and has to beinvestigated in more detail.
For the gun phase with maximum momentum gain of
6.4 MeV/c, the momentum was measured after the booster
cavity for different booster phases and settings. Figure
3 shows the measured mean momentum and momentum
spread of the electron beam as a function of the booster
phase for different power (0.6 and 1.9 MW) in the booster.
The phase with the smallest momentum spread is in bothcases: phase with maximum energy gain - 5 deg. There is a

Figure 3: Mean momentum and momentum spread asa function of the booster phase for about 0.6 (top) and
1.9 MW (bottom) in the booster.
strong difference in the value of the momentum spread forthe two cases. This might be due to some incorrect settingof the camera or wrong focusing. It was also seen that the
YAG-screen, which were used for the measurements wereburned, this could falsify the results. More detailed studies
have to be performed.

LONGITUDINAL DISTRIBUTION
A screen station (HIGH1.Scr2) for the measurement of
the longitudinal distribution of the electron bunch was installed about 1.4 m downstream the exit of the booster cavity (about 5 m downstream the cathode). For the measurement of the bunch length aerogel (n = 1.008), an optical transmission line and a streak camera is used. It
was designed such that bunch length measurements canbe done with booster cavity turned on and off, i.e. a momentum range from 5 to 40 MeV/c is covered [6]. First
measurements were done in the summer of this year withand without booster cavity. Figure 4 shows the measured
and simulated rms bunch length done without booster atan energy of about 6 MeV/c for a charge of about 0.6 nC
within the measurement range. The phase with the highest
momentum gain was determined using dipole magnet andis set to zero in the graph. Unfortunately, it was not possi-

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arrival time (ps)

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35
30
25

measuredsimulated

20
15
10
5
0
-40 -30 -20 -10 0 10 20 30
relative phase (deg)Figure 6: Relative arrival time of the bunch at the streak
camera.

ble to make comparable measurements at screen station forbunch length measurement before the booster (about 1.7 m
downstream the cathode) due to radiation damage of somecomponents. The rms value is increasing with the phase.
The full width half maximum (FWHM) behaves differently. The FWHM is large around the phase with the highest momentum gain (-7 deg to 2 deg), while the rms value
is medium range. A large FWHM can be found for higher
phases as well, but the rms value of the bunch length is also
large. Figure shows the longitudinal distribution for threecases for a better understanding of curve. For the phase

Figure 7 shows the measured and simulated rms bunch
length at an energy of about 16 MeV/c, for the gun phasewith the highest energy, as a function of the booster phase.
The booster phase with the maximum momentum gain was
defined as 0 deg. The measurement cover a large phaserange (120 deg). The rms bunch length stays almost con-

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with maximum momentum gain (0 deg) the FWHM and therms values is larger than for -30 deg. This leads to a higher
peak current for -30 deg. For 20 deg the FWHM is large,
but the rms values as well, due some long tail of the distribution. So cases with large FWHM and and small rmsvalues is favourable, since the charge is distributed morehomogeneous and the influence of space charge forces canbe reduced.
The arrival time of the bunches as a function of the gun
phase in plotted in figure 6. Here one can see a difference inthe arrival time between simulation and measurement. Thisdifference in phase between measurement and simulation iscomparable to the one we see in the curve of the momentum
spread (Fig. 2). This could be a hint for a systematical error
in the set up, but this could be also cause by a shift in thephase during the measurement.
344

16
14
FWHM

12
10

rms measured

8

rms simulated

6

Figure 5: Longitudinal distribution of the electron bunch
for phase with maximum mean momentum gain -30 deg+0 deg and 20 deg

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4

2
60

bunch length (ps)Figure 4: Measurements and simulations of the electron
bunch length as a function of the gun phase20-80 -60 -40 -20 0 20 40 60 80
relative phase (deg)Figure 7: Measurements and simulations of the electron
bunch length as a function of the booster phasestant over a large range around the phase with the maximum momentum gain. For an off-crest the bunch lengthchanges stronger. Figure 8 shows the arrival time of thebunch for the same measurement. Measurement and simulation fit well within the range of -60 to 10 deg. Starting for
10 deg the measurement shows an unexpected behaviour,
but the values in the plot of the bunch length seems to bereasonable. It seems to be a measurement artefact, maybe
there was a jump in the delay of the streak camera.

SUMMARY
The measurement of mean momentum, momentum
spread upstream and downstream the booster was presented. Observed problems and inconsistencies were de-arrival time (ps)Proceedings of FEL 2007, Novosibirsk, Russia
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measuredsimulated-80 -60 -40 -20 0 20 40
relative phase (deg)Figure 8: Relative arrival time of the photon pulse produce
by the electron bunch at the streak camera as a function of
the booster phase. This is assumed to be equal with arrival
time of the electron bunch at the screen station
scried and have to be analysed further to understand indetail the problems of this gun and to avoid them in future. A new screen station for the measurement of bunch
lengths was put into operation successfully, first measurements were presented and discussed.

REFERENCES[1] V. Miltchev et al., “Transverse emittance measurements at thephoto injector test facility at DESY Zeuthen”, FEL’04, Elettra, Triestre, Italy, 2004.
[2] D. Lipka, “Investigations about the longitudinal phase spaceat a photo injector for minimized emittance”, PhD Thesis
2004 Humboldt University Berlin[3] M. Krasilnikov et al., “Characterization of the electron sourceat the photo injector test facility at DESY Zeuthen”, NIM A
528(2004)360-365.
[4] S. Lederer et al., “Conditioning of a new Gun Cavity Towards
60 MV/m at PITZ”, PAC’07, Albuquerque, NM, USA, 2007.
[5] S. Rimjeam et al., “Status and Perspectives of the PITZ Facility Upgrade”, FEL’07, Budker Institut of Nuclear Physics,
Novosibisk, Russia, 2007.
[6] J. Rönsch et al., “Investigations of the Longitudinal Beam
Properties at the Photoinjector Test Facility in Zeuthen”,
FEL’06, BESSY, Berlin, Germany, 2006.

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PHOTOCATHODE LASER PULSE DIAGNOSTICS AT PITZ*
M. Hänel#, J. Bähr, Y. Ivanisenko+, S. Korepanov, M. Krasilnikov, F. Stephan,
DESY Zeuthen, Germany
Abstract
The main objective of the Photo Injector Test facility at
DESY in Zeuthen (PITZ) is the development of electron
sources that meet the requirements for existing and future
FELs such as FLASH or the European XFEL. The goal is
the minimization of the transverse emittance of the
produced electron bunches. In this respect one of the key
issues is the cathode laser system, which should provide
longitudinal and transversal flat-top pulses with anexcellent long-term stability. In this work we present thefull system of laser diagnostics that is currently used at
PITZ to monitor the laser pulse parameters.

measurements of the streak camera can be evaluated usinga Matlab script which provides key parameters of thepulse from a fit procedure, i.e. the FWHM, rise- and falltimes as well as the depth of the modulations on the flattop. Long-term observations show that this method of
pulse-shaping is very robust due to its simplicity.

INTRODUCTION
Laser systems of photo injectors play a crucial role forgenerating electron bunches with optimum transverse
emittance. In our case the laser must produce pulse trains
with a repetition rate of 10Hz consisting of up to 800 micro pulses with 1MHz repetition rate. The laser pulses
wavelength is 262nm and they have a temporal flat-top
shape (FWHM 20ps, rise-/fall-times 6-8ps) as well as atransverse flat-top profile. To extract the required chargeof 1nC from the photocathode (Cs2Te) the laser must provide pulses with an energy of at least 1μJ (for 0.5% quantum efficiency). For further details on the laser system
which was developed by the Max Born institute Berlin see[1].
In this paper we present the diagnostics system that isused to monitor the key laser parameters accompanied byrecent results.

TEMPORAL LASER PROFILE
The currently used laser system is able to produce flattop pulses (FWHM 20ps, rise-/fall-times 6-8ps) in the UV
utilizing a pulse shaper which consists mainly of a grating
stretcher and two birefringent crystals. The effects of thepulse shaper, the subsequent amplification stages, and theconversion of the infrared light into the UV combine togenerate flat-top pulses. For tuning the temporal laser
shape one can adjust the rotation angles of the birefringent
crystals as well as their temperatures. For a detailed description on this pulse shaping technique see [2].
To measure the temporal profile of the laser pulses, astreak camera is used which has a temporal resolution of
about 2ps in the UV (Hamamatsu C5680). In addition the____________________________________________*This work has partly been funded by the European Community, contract no. RII3-CT-2004-506008 and 011935 and by the 'Impuls- undVernetzungsfonds' of the Helmholtz Association, contract no. VH-FZ005.
#
marc.haenel@desy.de+on leave from IERT Kharkiv, Ukraine

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Figure 1: Typical temporal laser pulse shape used during 2007 run period evaluated by the mentioned Matlab
scriptSPATIAL LASER PROFILE
The spatial flat-top shape of the laser pulses is generated by cutting out a round spot from the center of thewidened Gaussian intensity distribution which is produced by the laser. To provide various spot sizes a platewith several apertures of different diameters is mounted
on a motorized stage which is remotely controllable. This
almost flat-top distribution is then relay imaged onto thephotocathode.
For monitoring the transverse profile three different virtual cathodes are used each having the same optical path
length as the pulses to the real cathodes have. Two ofthese virtual cathodes are cameras with a rest-sensitivity
in the UV so that the pulses can be shone directly onto the
CCD chip. These cameras can be used in different intensity regimes due to different attenuations. The third virtual
cathode consist of a Ce:YAG plate which converts theultraviolet light to visible light. This virtual cathode wasintroduced recently to develop a method of measurement
which does not rely on the rest-sensitivity of the CCD
cameras in the UV. Experience shows that this sensitivity
rapidly becomes inhomogeneous across the CCD chip.
The method using Ce:YAG plates is described in a separate section.
In figure 2a one can see a typical image of the transverse laser profile shown in false colors. Figure 2b displays the same profile in a more intuitive 3Drepresentation. These images were taken using the direct
measurement by shining the laser on the CCD chip. Thismethod has a great disadvantage. Using standard settings
for the shutter speed (1/60s) results in smear out effect forthe profile. Instead of the one shown in figure 2 one meas-

Proceedings of FEL 2007, Novosibirsk, Russia
ures a profile with less structure and a big halo around thecenter spot which makes it hard to determine the correct
beam size. The reasons for this behavior are not clear andwill be investigated.
Because the smear out effect appears to be a slow process the shown profile was measured using a shutter speedof 2μs and the timing was set such that only the first pulseof the train is captured. The shown image is the averageover 100 frames.
For this measurement an aperture of 1.2mm diameter
was used. The RMS values for x and y differ due to thenon symmetric distribution and are slightly higher than
the real one because of the position jitter (see corresponding paragraph). The RMS of the flat-top intensity distribution is 7.5%.

Figure 2a (upper): Transverse laser profile as seen by
one of the virtual cathodes.
Figure 2b (lower): The same profile in 3D-view
values on the x and y axes are in mm, z axis is arbitrary
intensity.

Measurements with Ce:YAG - plate
The optical scheme for measuring the transverse profileof the laser pulses using the fluorescence properties of
Ce:YAG is depicted in figure 3. The laser is directed onto
the plate and a part of the ultraviolet light is converted toa broadband signal in the yellow-green wavelength region. The profile in the Ce:YAG plate is imaged onto a
CCD-chip by use of a commercial objective. The remaining ultraviolet light is absorbed by the lenses of the objective (BK7).

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Laser pulse 262nm
Ce:YAG – platewith mounting

Broadband fluorescenceof Ce:YAG in the green

mirror
CCD-camera Imaging optics

Figure 3: optical setup for the measurement of thetransverse laser shape using Ce:YAG
The measurements were performed with three Ce:YAG
plates all having the same geometric shape. The surfaces
were uncoated. In figure 4 transverse profiles for different
plates and positions on the plates are displayed. On every
picture pronounced interference structures are visible.
These structures vary with position and are different forevery Ce:YAG plate. From these pictures one can conclude that it is not possible to get reliable information
about the transverse pulse shape by use of this method.

a)

b)

c)

d)

Figure 4: images of the transverse profile for two
Ce:YAG - plates and different positions on the platea) 1.8mm aperture, 1st plate, pronounced horizontal interference stripes are visible due to non parallel surfacesb) - d) 1.2mm aperture, 2nd plate, same conditions of thelaser but different positions on the plate
The next step is to provide the Ce:YAG plates with anantireflective coating on each surface for further investigation.

LASER PULSE ENERGY JITTER
Besides possibilities to measure the laser pulses energies at the laser output it is more important to know how
much energy is actually impinging on the photo cathode.
This energy is less than 20% of what the laser produces
due to the losses in the beam line which are mainly introduced by the beam shaping apertures. Therefore a photomultiplier tube is used which measures a strongly attenuated part of the beam that is coupled out before thelaser enters the vacuum of the gun. Photomultiplier tubes
have several advantages. They can provide a linear re-

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sponse over a large range of laser pulse energies, they areable to measure at 1MHz repetition rate and by changing
the drive voltage the actual amplification can be chosenfrom several orders of magnitude.
To be able to calibrate the signal of the photomultiplieranother measurement device is used. This is based on acommercially available UV sensitive photo diode together
with an energy-meter which are externally calibrated andcan be read out remotely via RS232 connection (Ophir
NOVA II, PD10-pJ-SH-V2). This photo diode is only capable of measuring a repetition rate of 10kHz at maximum. Therefore it cannot be used directly to measure thelaser pulse energies within the train. Averaging the signalsof both devices for one pulse per train gives the calibration factor.
In Figure 5 the laser pulse energy distribution within apulse train consisting of 40 pulses is displayed. Every data
point represents the averaged energy for the corresponding pulse. The mean value is 54.34 in this case arbitrary
units.
As a general criterion for the energy stability one canLaser energy stability

50
40
30
20
10

LASER POSITION JITTER
Another key parameter of the laser system is the position of the spot on the real cathode. While positionchanges in the order of 0.5mm can be easily measured
using the virtual cathodes small scale movements must be
monitored by a more sophisticated method. For this reason a procedure was developed which uses a fast quadrant
diode. Knowing the transverse laser profile and the signals of the quadrant diode one can extract the actual position of each single laser pulse within the pulse train [3].
Figure 7 shows the measured x- and y-positions within a
train of 40 pulses. The position of every pulse is averaged
over 200 pulse trains and one can see that there is no significant systematic movement of the pulse position within
one train. The error bars are the RMS values for the position of every single pulse. The overall jitter for all pulses
in all trains is xrms = 35μm and yrms = 39μm.
There are different possible explanations for this rather

0
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calculate the overall RMS for all pulses in all measured
trains. This turns out to be 1.46 and corresponds to 2.7%
pulse energy jitter but contains also a possible slope
within the trains. Therefore the average RMS jitter for asingle pulse is smaller and was calculated to be 2%.
The RMS of the mean values is 1.3%.

2,76

X position, mm

Figure 5: Laser pulse energy for every single pulse in a
train of 40 pulses evaluated over 50 trains. The dotsshow the mean value and the error bars represent theRMS value of the energy for each single pulse.

3,44
2,72
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2,68

3,36
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Laser pulse energy, a.u.

60

The laser pulse energy is directly linked to a key parameter of the machine, i.e. the extracted charge. The
measurement of the charge jitter using an ICT reveals avalue of 1.62% (see Figure 6). For this measurement the
charge of the first pulse in each train was determined.
At this charge level the slope of the charge vs. laser energy curve is 0.444pC/nJ and therefore a charge stability
jitter of 1.62% translates to a laser energy jitter of 2.8%
which is in good agreement with the measured one of 2%
taking into account that besides the laser energy jitter also
other sources exist for the charge jitter.

3,32
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Pulse number in train
Hybrid Detector: Quadrant diode + CCD matrix

averaged over 200 trains

Figure 7: Analysis of the position jittercharge stability

1380
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1340

mean: 1250,6pC
rmscharge: 22,07pC

1320

rms: 20,3pC (1,62%)high value. The main reason is vibrations of the opticalelements in the tunnel. One can estimate that for an optical path length of about 7m in the tunnel the first mirror
only needs to turn by 5nrad to introduce 35μm movementon the cathode.

charge in pC

rmsbkg: 8,7pC
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Figure 6: Charge stability measurement
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SUMMARY
In this paper the key parameters of the used photo cathodelaser system for the 2007 run period were presented.
The temporal profile of the laser pulses are in agreementwith the design parameters (20ps FWHM, 6-8ps rise-/falltimes) and show a good long-term stability. The transverse profile has steep edges and exhibits a structure with
an RMS of 7.5% on the top. A new system consisting of a
Ce:YAG – plate as converter from the UV to visible light
was tested and it was found out that this system currently
does not meet the demands for this kind of measurement.
The laser pulse energy fluctuations were characterized
and the value of 2% is in good agreement with the charge
stability. Finally the position jitter of the laser pulses on
the cathode was determined and shows that the mean position within a pulse train is almost constant but the RMSvalues of xrms = 35μm and yrms = 39μm are rather high.

REFERENCES[1] I. Will, G. Koss, I. Templin, “The upgraded photocathode laser of the TESLA Test Facility”, Nuclear Instruments and Methods in Physics Research A 541(2005), 467–477[2] M. Krasilnikov, J. Baehr, M. Hänel, F. Stephan, I.Will,“Experimental Optimization of the Cathode Laser
Temporal Profile”, Proceedings of DIPAC 2007, Venice, Mestre, Italy 2007
[3] Ye. Ivanisenko et al., “Photo injector cathode laser
beam intensity and pointing position diagnostics andinfluence on the electron beam emittance measurements”, Proceedings of DIPAC 2007, Venice, Mestre,
Italy 2007

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INVESTIGATIONS ON THE THERMAL EMITTANCE OF Cs2Te
PHOTOCATHODES AT PITZ∗
S. Lederer† , G. Asova‡ , J.W. Baehr, K. Boyanov‡ , C. Boulware, H-J. Grabosch, M. Haenel,Y. Ivanisenko§ , S. Khodyachykh, S. Korepanov, M. Krasilnikov, B. Petrosyan, S.Rimjaem, T.Scholz,
R. Spesyvtsev¶, L. Staykov, F. Stephan (DESY, Zeuthen, Germany)
L. Hakobyan (YerPhI, Yerevan, Armenia),
D. Richter (BESSY GmbH, Berlin, Germany)
J. Roensch (University of Hamburg, Hamburg, Germany)

Abstract
The main objective of the Photo Injector Test facility
at DESY in Zeuthen (PITZ) is the production of electron
beams with minimal transverse emittance. The lower limitof this property of electron beams produced with a photocathode in an RF-gun is determined by the thermal emittance. To understand this crucial parameter for high performance FEL’s, measurements under RF operation conditions for cesium telluride (Cs 2 Te) photocathodes are done.
Results for various accelerating gradients and the dependence on the laser spot size in the cathode plane are presented and discussed in this work.

INTRODUCTION
The thermal emittance determines the lower limit of thenormalized emittance of electron beams in injectors. Cesium telluride (Cs2 Te) photocathodes are used at PITZ as
sources for electron beams because of their high quantum
efficiency (QE) and their ability to release high charge electron bunches in a high gradient RF-gun. In the past several
theoretical and experimental studies on the thermal emittance of semiconductor photocathodes like Cs 2 Te were performed [1, 2, 3, 4].
In Figure 1 a simplified overview of PITZ is given. The
1.5 cell L-band RF-gun is surrounded by a main and bucking solenoid for compensation of emittance growth due tospace charge forces. Under normal operation conditions
electrons are emitted from the Cs 2 Te cathode by illumination with flat-top laser pulses with temporal FWHM ≈20 ps and λ = 262 nm wavelength. A 10 MW klystronprovides gradients of about 60 MV/m at the cathode. This
gradient is a necessary step toward achieving the required
emittance for the European XFEL [5]. More details on the
PITZ set-up can be found elsewhere [6].
∗ This work has partly been supported by the European Community,
contracts RII3-CT-2004-506008 and 011935, and by the ’Impuls- undVernetzungsfonds’ of the Helmholtz Association, contract VH-FZ-005.
† sven.lederer@desy.de‡ on leave from INRNE, Sofia, Bulgaria§ on leave from IERT, Kharkiv, Ukraine¶ on leave from NSCIM, Kharkiv, Ukraine

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Figure 1: Simplified overview first part of PITZAt PITZ it is not possible to measure the thermal emittance directly at the cathode. In order to estimate a thermal emittance, a normalized beam emittance has been measured for very low bunch charge and short laser pulses at
the first emittance measurement system (EMSY1) 4.3 m
downstream (Fig. 1) by the slit scanning technique [7].
In this contribution results from the emittance measurements performed at PITZ are presented for different rms
laser spot sizes on the cathode and different accelerating
gradients between 30 and 60 MV/m.

THEORETICAL ESTIMATIONS ON THE
THERMAL EMITTANCE
The photoemission from semiconductors can be described by a three step model [8]. In the first step anelectron from the valence band (VB) is excited to the conduction band (CB) by photon absorption. Due to the energy gap between the conduction and the valence band of
Eg = 3.3 eV for Cs2 Te, the photon energy must be larger
than 3.3 eV [8]. At PITZ a laser with a wavelength of
λ = 262 nm (Eph ≈ 4.72 eV) is used for the electron
excitation into the first density of states maximum in theCB, located 4.05 eV above the VB maximum [8]. The second step involves the electron transport to the surface. In
the last step the electron is emitted into vacuum. For theemission process the electron has to overcome the potential barrier at the surface, which for semiconductors can be
described by the electron affinity E A (difference between

Proceedings of FEL 2007, Novosibirsk, Russia
the vacuum level and the minimum of the CB). For Cs 2 Te
EA is in the order of 0.2 eV [8]. So the threshold photon
energy for electron emission is E thr = Eg + EA = 3.5 eV.
For PITZ and the above given photon energy this leads toan average kinetic energy of E kin = 0.55 eV after emission. It is important to mention, that these results only holdfor pure photoemission (i.e. no electric fields at the cathode) and for fresh Cs 2 Te cathodes. If the cathodes are used
in a photo-injector under operational conditions the electron affinity could be reduced by the high electric field at
the cathode. On the other hand changes in the chemicalcomposition of the cathode during operation can result inchanged emission conditions (i.e. changed work function)[9].
Based on the argumentation given in [1], the kinetic energy of the emitted electrons can be determined by measuring the thermal emittance. Assuming an isotropic emission
into the half sphere in front of the cathode surface the thermal emittance can be written in terms of the rms laser spot
size σl at the cathode and E kin .

2Ekin
(1)
th = σl
3m0 c2OPERATIONAL PARAMETERS
The thermal emittance  th adds quadratically to otheremittance terms forming the measured transverse emittancemeas .
meas ≈

2th + 2SC + 2RF

(2)This relation has to be taken into account to adjust theoperation conditions of the injector to perform thermal
emittance measurements. The emittance growth caused by
space charge forces reduces with smaller bunch charge. As
compromise between small space charge and good signal
to noise ratio during measurements, bunch charges of maximum 6 pC were used. The influence of the RF-field at
the cathode during the emission on the emittance can be
reduced by short gaussian laser pulses instead of flat-top
temporal profiles, used for normal operation. The shortest pulses currently producible by the laser system at PITZ
have a sigma of 3-4 ps. During measurements the gun RFphase was adjusted to the phase of maximum mean momentum gain Φ m . If not commented the data in this paper were obtained with the above mentioned operational
conditions and the booster operating at maximal momentum gain. Usually slits of 10 μm width were used at the
EMSY1.

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Figure 2: Results from emittance measurements as functionof laser spot size for E 0 = 30 MV/m for cathode #83.3;
symbols: data, lines: linear fit.
slope (dth /σl ) of a linear fit and considering equation 3,
which results from the differentiation of equation 1.
Ekin =

3m 0 c2
2



dth
dσl

2
(3)

The variation of the rms laser spot size at the cathodes wasachieved by apertures of different diameters put into thelaser beam line [10].
In Figure 2 measured emittances of Cs 2 Te cathode #83.3
for an accelerating gradient of E 0 = 30 MV/m are presented. The field on the cathode during the emission process was determined by E = E 0 sin (Φm − Φ0 ). The
phase Φ0 was estimated from the rising edge of the chargescan vs. RF-phase. For the current case this results in
E = 17.2 MV/m. In addition to the experimental data,
the linear fits are shown. The resulting kinetic energies forthis and the other measured gradients are summarized in
Figure 7.

EXPERIMENTAL RESULTS
The aim of the emittance measurements presented in thiscontribution, is to give an estimate on the kinetic energiesof the emitted electrons for different RF-gradients at thecathode.
From the measured emittances as function of σ l one canestimate the kinetic energy right after the emission from the

Figure 3: Results from emittance measurements as functionof laser spot size for E 0 = 35 MV/m for cathode #83.3;
symbols: data, lines: linear fit.
Figure 3 shows measured emittances together with thelinear fits for an accelerating gradient of E 0 = 35 MV/m.

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Although for both gradients the measured data can be described by a linear dependence from the rms laser size,
deviations to the fits are not small, i.e for the smallest
σl . A possible reason for the latter one can be the increased charge density of the electron bunch and therefore
increased space charge forces. Also neither the data nor
the fit end in zero emittance for σ l = 0 mm, which could
be caused by the accelerating RF-field, also at short laser
pulses, and/or by a systematic error during the measurements.

Figure 4: Results from emittance measurements as function of laser spot size for E 0 = 40 MV/m; blue and red
symbols: data for cathode #83.3, green and magenta symbols: data for cathode #90.1
Figure 4 presents the emittances measured at E 0 =40 MV/m for cathode #83.3 and #90.1. Identical measurements for E0 = 60 MV/m are presented in Figure 6.
The datasets were measured with the same operational conditions in the gun section, but the emittances of cathode#90.1 were obtained without booster and with a slit width at
EMSY1 of 50 μm. Before the thermal emittance measurements on cathode #90.1, this cathode was used intenselywith σl = 0.36 mm, and bunch charges of 1 nC wereextracted during the whole period. A QE-map taken in
the beginning of the thermal emittance measurements at
E0 = 60 MV/m (Fig. 5 right) clearly shows an area inthe center region of the cathode with strongly reduced QE.
The active area at the right plot in Figure 5 corresponds tothe center of the photograph on the left side.

Figure 5: Photograph (left) and QE-map (right) of cathode#90.1
To avoid a mixing of regions with different QE during
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the emittance measurements, for cathode #90.1 data were
only taken for σ l < 0.36 mm. The fits in Figure 4 clearlyshow a different slope obtained from both cathodes, resulting in higher kinetic electron energies for cathode #90.1(see Fig. 7). In contrary to that, in Figure 6 the slopes forboth cathodes are comparable.

Figure 6: Results from emittance measurements as function of laser spot size for E 0 = 60 MV/m; blue and red
symbols: data for cathode #83.3, green and magenta symbols: data for cathode #90.1
The kinetic energies obtained from the slopes of the linear fits to the data described above are summarized in Figure 7. Since there is no physical reason for different energies in X and Y direction after the emission, in the figure the geometrical averages of the kinetic energies in bothtransverse planes are presented. The plot clearly shows
the influence of the electric field at the cathode on the
kinetic energies, which already was observed for lower
gradients [4]. For an accelerating gradient of 60 MV/m
(E = 43.2 MV/m during emission) we find for both cathodes kinetic electron energies slightly above 1.2 eV. Despite the big uncertainties, this preliminary value is a factor of two higher than for the absence of the electric field(0.55 eV).

Figure 7: Kinectic electron energies as function of the fieldat the cathode; blue: cathode #83.3, red: cathode #90.1

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SUMMARYREFERENCES

In this contribution measured transverse emittances fordifferent rms laser spot sizes at the photocathode and different gradients are presented. For this measurements the
charge was kept to values about 6 pC, and short laser pulses
were used. From the thermal emittances the kinetic energies were estimated for two Cs 2 Te cathodes. An increaseof the kinetic electron energies after the emission with increasing electric field at the cathode was observed. For thehighest acceleration gradient available we found kinetic energies of slightly above 1.2 eV. For better understanding of
the measured data (i.e. why  th (σl = 0) = 0), a more detailed analysis and a comparison with simulations is necessary.

[1] K. Floettmann, ”Note on the Thermal Emittance of Electrons
Emitted by Cesium Telluride Photo Cathodes”, TESLA-FEL
report 1997-01, DESY, 1997.
[2] J.E. Clendenin et al., ”Reduction of thermal emittance of rfguns”, SLACPUB- 8284, SLAC, 1999.
[3] P. Michelato et al., ”Thermal emittance estimation using atime-of-flight spectrometer”, Proceedings of the European
Particle Accelerator Conference 2000,, Vienna, Austria.
[4] V. Miltchev, et al., ”Measurements of thermal emittance for
cesium telluride photocathodes at PITZ”, Proceedings of theFree Electron Laser Conference 2005, Stanford, USA.
[5] M. Altarelli, et al. (eds.), ”The Technical Design Report of
the European XFEL”, Chapter 4: XFEL accelerator. DESY
2006-097, July 2006, p. 80.
[6] S. Rimjaem, et al., ”Status and perspectives of the PITZ Facility Upgrade”, to be published in Proceedings of the Free
Electron Laser Conference 2007, Novosibirsk, Russia.
[7] L. Staykov et al.”Commissioning of a New Emittance Measurement System at PITZ”, Proceedings of the Free Electron
Laser Conference 2006, Berlin, Germany.
[8] R.A. Powell, W.E. Spicer, G.B. Fisher, and P. Gregory, Phys.
Rev. B, 8 3987 (1973).
[9] S. Lederer, et al., ”XPS studies of Cs2 Te photocathodes”, tobe published in Proceedings of the Free Electron Laser Conference 2007, Novosibirsk, Russia.
[10] J. Baehr et al., ”Upgrades of the Laser Beam-line at PITZ”,
Proceedings of the Free Electron Laser Conference 2005,
Stanford, USA.

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STATUS AND PERSPECTIVES OF THE PITZ FACILITY UPGRADE∗
S. Rimjaem† , G. Asova‡ , J.Bähr, C. Boulware, K. Boyanov‡ , H.J. Grabosch, M. Hänel,
Y. Ivanisenko§ , S. Khodyachykh, S. Korepanov, M. Krasilnikov, S. Lederer, A. Oppelt¶,
B. Petrosyan, S. Riemann, A. Shapovalovk , T.Scholz, L. Staykov, R. Spesyvtsev∗∗, F. Stephan,
DESY, 15738 Zeuthen, Germany
K. Flöttmann, DESY, 22603 Hamburg, Germany
L. Hakobyan, YerPhI, Yerevan, Armenia
D. Richter, BESSY, 12487 Berlin, Germany
J. Rönsch, University of Hamburg, 22761 Hamburg, Germany
K. Rosbach, Humboldt University, 12489 Berlin, Germany
Abstract
The Photo Injector Test facility at DESY in Zeuthen(PITZ) has been established to develop and optimize electron sources that cover requirements of Free Electron
Lasers (FELs) facilities such as FLASH and the European
X-ray Free Electron Lasers (XFEL). A major upgrade of
the facility is ongoing in steps, in parallel to the commissioning of the extended setup and first experiments. The
new setup towards the final design mainly includes a photo
cathode RF gun, a post acceleration booster cavity and several diagnostic systems. In order to fulfill the characterization of the high brightness electron source, the diagnostic
systems will consist of three emittance measurement systems, two high-energy dispersive arms, an RF deflecting
cavity and a phase space tomography module as well asbunch length diagnostics. In this paper, results of the commissioning of the new RF gun, which has been installed
and conditioned at PITZ in spring and summer of 2007, thecurrent PITZ status and details of the future facility upgrade
will be presented.

INTRODUCTION
Source and injector development has been realized as
one of the most important challenges in electron accelerator technology since several accelerators, e.g. FELs,
XFEL or Linear Collider, demand excellent beam conditions right from the source. The main requirement for anelectron injector is its capability to produce a high brightness beams. PITZ has been designed and built to serve thispurpose in order to produce intense electron beams withvery small transverse emittance and reasonably small longitudinal emittance. The main objective at PITZ is to generate a reliable electron beam, with transverse emittance of∗ This work has partly been funded by the European Community, contract no. RII3-CT-2004-506008 and 011935 and by the ’Impuls- und Vernetzungsfonds’ of the Helmholtz Association, contract no. VH-FZ-005.
† sakhorn.rimjaem@desy.de‡ On leave from INRNE, Sofia, Bulgaria§ On leave from IERT, Kharkov, Ukraine¶ Presently at PSI, Villigen, Switzerland
k On leave from MEPHI, Moscow, Russia∗∗On leave from NSCIM, Kharkov, Ukraine

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about 1 mm mrad with a bunch charge of 1 nC and an energy spread smaller than 1%. The possibility to achievesmall beam emittance has been demonstrated during the
successful commission of the facility in the first phase(PITZ1) [1] and intermediate upgraded phase (PITZ1.5)[2].
Further upgrade of the facility towards the final design
PITZ2 has been continued to extend the ability to achievea smaller beam emittance. The so called PITZ1.6 has been
finalized and was taken into operation in 2006. PITZ1.6
has completed its tasks with characterization of two new
gun cavities (prototype 3.1 and 3.2). Recent commissioning and experimental results from PITZ1.6 with gun 3.2
will be discussed in this paper. Furthermore, the facility
upgrade towards the next phases will be described.

PITZ1.6 SETUP WITH RF GUNPROTOTYPE 3.2
The current PITZ setup (PITZ1.6) consists of a 1.5 cellnormal conducting RF gun with a Cs2 Te photocathode anda Nd:YLF laser system, a normal conducting booster cavity for post acceleration and diagnostic systems upstream
and downstream of the booster cavity. The RF gun andbooster cavity are operated with separated L-band (1.3
GHz) RF power systems. The diagnostic sections include
devices for characterize the electron beam, e.g. beam size,
bunch charge, its position, transverse emittance, longitudinal phase space distribution, electron bunch length, beam
momentum and momentum spread. The main upgradefrom PITZ1.5 to PITZ1.6 comprises installation of three
new emittance measurement systems [3] and a new screen
station after the booster for bunch length measurements atelectron energies between 4 and 40 MeV [4]. Gun prototype 3.1 was installed and operated up to the maximum
requirements of FLASH with maximum peak power of 3.5
MW, resulting in ∼40 MV/m gun gradient at the cathode,with RF pulse length of 900 µs at 10 Hz repetition rate [5].
Gun prototype 3.2 was installed in the PITZ1.6 beam line
and was taken into operation in April 2006. A main goal for
its operation is to study and optimize its properties in thepresence of a high accelerating gradient of up to 60 MV/m.

Proceedings of FEL 2007, Novosibirsk, Russia

normallized E-field

1.2
after tuning
before tuning

1.0
0.8
0.6
0.4
0.2
0.0
0

40

80
120
160
relative position, z [mm]

200

240

Figure 1: Electric field profile in Gun 3.2 cavity before andafter tuning process.
parameterfπ [GHz]fπ−0 [MHz]Q0πbefore1.30135.0-

after
1.30035.1
21316

at PITZ
1.3007
5.0
23853

Table 1: RF measurement results of Gun 3.2 before tuning,
after tuning and after installation at PITZ.

Conditioning and Dark current Measurements
After the brazing, the tuning and the cleaning process
finished, the gun has been installed and commissioned at

60

600

40

400
shut
down

20

200

01.18E+0 1.18E+0 1.18E+0 1.18E+0 1.18E+0 1.18E+0 1.18E+0 1.18E+0
Apr
109
9

9

9

May93099RF pulse length (µs)

In October 2006, frequency measurements of the gun
cavity have been performed and the results showed a detuning from 1.3 GHz of 746 kHz at an expected operation temperature of 55o C. The field profile of the gun 3.2 cavity wasmeasured by using the bead-pull technique and the fieldat the cathode was about 18% higher than in the full cell.
Since a preferable value of the field balance from simulation in order to compromise between high momentum gain
and a maximum gradient at the cathode for space charge
compensation is about 5-10%, the gun was mechanicallytuned by using a convenient tuning device to slightly deform the cavity walls at the cathode plat and at the couplerfacing wall of the iris [5].
The gun was tuned to reach a desired resonant frequencyof 1.3 GHz at an operating temperature of 56o C with thefield balance between the half and the full cell of 1.03 or thefield at the cathode is 3% higher than that in the middle ofthe full cell. The field distribution before and after the tuning are shown in Fig. 1. Prior to installation at PITZ, waterto-air leak of a cooling channel was found. After the leak
was repaired, the frequencies and the quality factor of the
gun were re-measured resulted in a higher frequency corresponding to an operating temperature of 64o C. Field profile
was not re-measured. RF measurement results of gun 3.2
before and after the tuning process as well as when it was
installed at PITZ are summarized in Table 1. The quantities fπ , Q0π and fπ−0 stand for the resonant frequency, theunloaded quality factor of π-mode and the mode separation
between π- and 0-mode, respectively.

PITZ from April to August 2007. It has been conditioned
up to a maximum gun gradient of about 60 MV/m at maximum power of 6.9 MW and the stable operation can beachieved with the RF pulse length up to 200 µs. Further,
the RF pulse length was increased to 700 µs but only forthe short time period because of high level of dark current.
Then, the gun cavity conditioning has been continued at
RF pulse length of 400 µs for about two weeks before thenominal experiments started. History of the gun gradientand RF pulse length during the conditioning (April-June2007) is shown in Fig.2. In nominal experiments, the gun
has been operated mostly for RF pulses of 140 µs (with100 µs flat-top) at 10 Hz repetition rate. The nominal peak
power in the gun cavity was 6.7 MW corresponding to theaverage power of 9.4 kW for 140 µs RF pulses.
gradient in gun (MV/m)

Tuning of Gun 3.2

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0

Jul 6

9

Figure 2: Gun gradient and RF pulse length history of gun
3.2 at PITZ. Maximum gradient (red line) is the highest
gradient reached in the cavity, average gradient (green dot)is the average accelerating gradient over operating time period of one hour and the RF pulse length is represented by
the blue line.
Cesium telluride (Cs2 Te) photo cathodes are used at
PITZ for standard operation, whereas molybdenum (Mo)cathodes have been applied for the conditioning. Dark current measurements have been performed at various gun
powers with different cathodes for both Mo and Cs2 Te
types. The results are shown in Fig.3, where the maximum dark current is the highest current value measured asa function of the main solenoid currents. One of the measurements is shown in Fig.4 for Cs2 Te cathode no. 109.1.
From Fig.3, one can see that the dark current level was improved from conditioning and operation for both Mo andCs2 Te cathodes except the Mo cathode no. 32.2, which
was used at the beginning of the conditioning and a serious
damage on its surface has been observed. Another remarkable observation for the Mo electro-polished cathode (no.
55.3) demonstrated lower level of the dark current. These
dark current measurements show the progress of conditioning, but the overall dark current level was still high.
Possible reasons may be because of the fabrication errorof the area around the cathode plug during the assembling,
the bad vacuum condition due the several dismounts (3times) of the coupler which had vacuum leak after the bakeout or the bad condition of the cathode after experiencing
high accelerating field. Presumably, the high level of the

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Proceedings of FEL 2007, Novosibirsk, Russia

max. dark current [mA]18
Mo #32.2 (18.05.07)

15

Mo #31.4 (04.06.07)
Mo #55.3 (14.05.07)

12

Cs2Te #34.6 (30.05.07)
Cs2Te #109.1 (31.05.07)

9

Cs2Te #42.4 (05.08.07)

6
3
0
1

2

3

4
5
gun power [MW]6

7

Figure 3: Maximum dark current as a function of gun
power for different cathodes of gun 3.2.

FUTURE STAGES AT PITZ

Dark current [mA]

3.2

2.4

5.5 MW
5.0 MW
4.5 MW
4.0 MW
3.5 MW
3.0 MW
2.5 MW

1.6

0.8

0.0
0

100

200

300

400

500

Main solenoid magnet current [A]Figure 4: Dark current measurements as a function of themain solenoid magnet current for cathode no.109.1 performing on May 31, 2007.
dark current is responsible for the measured outgassing rateof some parts in double diagnostics cross (DDC, at ∼0.78
m from the photo cathode). Several Teflon parts were foundmelted during DDC reparation, what explains bad vacuum
conditions also in the gun cavity. Moreover, this high darkcurrent has caused a severe radiation level in the accelerator tunnel which damaged several electronic components
in the radiation effecting area. More details of the conditioning of gun 3.2 at PITZ and effects of high dark current
level to delay the commissioning and experiment at PITZ
are described in the reference [6].

Recent Experimental Results
Momentum and longitudinal phase space have beenmeasured at two locations: low energy (LEDA) andhigh energy dispersive arms (HEDA). Experimental results
show that the highest momentum value achieved from gun
3.2 was ∼6.5 MeV/c with an energy spread of about 40
keV/c at gun power of 6.7 MW [9]. This momentum value
is lower than the expectation from simulation for the gun
gradient of 60 MV/m, which should be about 6.92 MeV/m
for the field balance of 1.03. For the post acceleration measurement, the highest momentum measured at HEDA was∼16 MeV/c with 30 keV/c momentum spread. In fact, thebooster can be operated with higher acceleration, but due
to a limitation of the dipole current it was not possible tomeasure the momentum higher than 16 MeV/c.
Projected emittance measurements for gun 3.2 have been
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performed using the slit mask technique at the emittancemeasurement station (EMSY1) located ∼0.7 m downstream of the booster exit. The results show that the minimum transverse emittance measured during the commissioning period of gun 3.2 was 1.54 ± 0.15 mm mrad forthe gun gradient of 40 MV/m and 1.26 ± 0.18 mm mradfor ∼60 MV/m [10]. Moreover, thermal emittance fromthe cathode has been investigated and the results reveal thatphotoelectrons with kinetic energies of 1.4 ± 0.2 eV were
emitted from the cathode at the gun gradient ∼60 MV/m[11]. This value is a factor of two larger than the theoretical model.

Upgrade to PITZ1.7
In mid of August 2007, an upgrade to the intermediatephase PITZ1.7 was started. Main upgrades from PITZ1.6
to PITZ1.7 comprise a modification of the low energy diagnostics section and installation of a new high energy dispersive arm (HEDA1).
• Upgrade of low energy diagnostics section
The dipole at the present low energy dispersive arm(LEDA) at PITZ is a copy of the former injector section at
FLASH which was not optimized for PITZ. The solenoid
currents necessary for good focusing of the beam downstream of the booster cavity lead to the too large beam sizeat the dipole chamber. Modification of the pole shoes andvacuum chamber will be performed to increase the vacuum
chamber aperture from 12mm to 27mm. In addition, thedouble diagnostic cross (DDC) in front of the dipole will
be upgraded in order to improve the situation of vacuum
and wake fields. The new DDC will include a slit which
will be used to improve the resolution of the momentum
measurements at LEDA.
• The first high energy dispersive arm (HEDA1)
HEDA1 is designed to be a multipurpose system. It will be
used as spectrometer to measure momentum, a device tocharacterize the longitudinal phase space and a system tomeasure transverse slice emittance. This system includes
a 180o dipole magnet which simplify the reconstruction of
the momentum measurement, a slit at the exit of the dipole,a quadrupole magnet and two screen stations. One station will be used for momentum measurements for electron energies up to 40 MeV and the other one, equippedwith an optical read-out for streak camera, to investigate
longitudinal phase space by using off crest acceleration in
the booster and the slit exit of the dipole. HEDA1 can beused to measure the transverse slice emittance at difference
longitudinal positions along the bunch.

Upgrade to PITZ2In order to fulfill the characterization of high brightness electron beam, new diagnostic systems will be in-Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH013

Figure 5: Schematic layout of the future PITZ2 beam line.
stalled at PITZ towards the final design (PITZ2). ThePITZ2 setup includes a photocathode RF gun, a post acceleration booster cavity and several diagnostic systems including three emittance measurement systems, two highenergy dispersive arms, an RF deflecting cavity and a phasespace tomography module as well as bunch length diagnostics (see Fig.5). The primary goal of PITZ2 is to study
the conservation of small emittance beams along the beamline after the booster acceleration. The key parameters forthis emittance conservation is the replacement of an existing TESLA booster cavity with a new Cut Disk Structure(CDS) booster, which can provide higher energy gain up
to ∼24 MeV with the limited RF power and does not degrade the beam quality. An improvement of the laser system is required in order to provide rise/fall time of 2 pslaser pulses with FWHM of 20 ps. Furthermore, additional new diagnostics will be installed in the high energy
section downstream of the booster to extend the ability offacility to study more details about the beam properties. An
RF deflecting cavity and a phase space tomography module
will be included for analysis of the phase space distribution.
At the end of the beam line, a third spectrometer will be
installed in combination with diagnostics to measure momentum and momentum spread, slice emittance and longitudinal phase space using a Cherenkov radiator and streak
camera or the RF-deflector. More details about the beamdiagnostics upgrade for PITZ2 can be found in reference[8].

CONCLUSION
The gun 3.2 has been conditioned and taken into operation at PITZ for roughly 4 months in spring and summerof 2007. It has fulfilled the goal to operate at a gun gradient of ∼60 MV/m with 140 µs RF pulses length and 10 Hz

repetition rate. Several results from the conditioning andexperiments of this RF gun with the present PITZ1.6 beamline have been presented in this paper. Further upgrade of
the facility to the next phase PITZ1.7 has started in mid ofAugust 2007. After the upgrade is finished next operation
period will start in winter 2007/2008.

REFERENCES[1] F. Stephan et al., “Recent Results and Perspective of the Low
Emittance Photo Injector at PITZ”, FEL 2004, Trieste, Italy.
[2] A. Oppelt et al., “Status and First Results from the Upgraded
PITZ Facility”, FEL 2005, Stanford, CA, USA.
[3] L. Staykov, “Commissioning of a New Emittance Measurement System at PITZ”, FEL 2006, Berlin, Germany.
[4] J. Rönsch et al., “Investigations of the Longitudinal Beam
Properties at the Photoinjector Test Facility in Zeuthen”,
FEL 2006, Berlin, Germany, 2006.
[5] A. Oppelt et al., “Tuning, Conditioning, and Dark Current
Measurements of a New Gun Cavity at PITZ”, FEL 2006,
Berlin, Germany.
[6] S. Lederer at al., “Conditioning of a new gun cavity towards
60 MV/m at PITZ”, PAC 2007, Albuquerque, NM, USA.
[7] K. Flöttmann, A Space Charge Tracking Algorithm (ASTRA), http://www.desy.de/mpyflo.
[8] S. Khodyachykh at al., “New Beam Diagnostic Developments at the Photo-injector Test Facility PITZ”, PAC 2007,
Albuquerque, NM, USA.
[9] J. Rönsch at al. “Recet Measurements of the Longitudinal
Phase Space at PITZ”, FEL 2007, Novosibirsk, Russia.
[10] L. Staykov at al. “Measurements of the projected normalized transverse emittance at PITZ”, FEL 2007, Novosibirsk,
Russia.
[11] S. Lederer at al. “Investigation on the Thermal Emittanceof Cs2 Te Photocathode at PITZ”, FEL 2007, Novosibirsk,
Russia.

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Proceedings of FEL 2007, Novosibirsk, Russia

PERFORMANCE OF THE FERMI FEL PHOTOINJECTOR LASER*
M. B.Danailov, A.Demidovich, R.Ivanov, I.Nikolov, P.Sigalotti
ELETTRA, 34012 Trieste, Italy
Abstract
The photoinjector laser system for the FERMI FEL has
been installed at the ELETTRA laser laboratory. It isbased on a completely CW diode pumping technology
and features an all-CW-diode-pumped Ti:Sapphire
amplifier system, a two stage pulse shaping system, atime-plate type third harmonic generation scheme andaspheric shaper based beam shaping. The paper will
present experimental results describing the overall
performance of the system. The data demonstrates that
all the initially set parameters were met and some largely
exceeded. We present what is to our knowledge the first
direct measurement of the timing jitter added by a
Ti:Sapphire amplifier system and show that for our case it
is below 10 fs.

INTRODUCTION
The photoinjector laser (PIL) is known to be one of thevery important sub-systems for all single-pass UV and Xray FELs. The charge and quality of the electron bunch
created at the photoinjector (PI) affect dramatically theoperation of the FEL and can be a strong limitation in
obtaining the expected FEL performance. This isespecially true for the challenging projects that are now inconstruction phase (like LCLS, SLAC, European XFEL).
A lot of attention has thus been devoted previously forstudying the optimum parameters of the PIL. It is now
well accepted that the UV beam should have a nearly flat
top spatial profile, while the optimum longitudinal(temporal) shape may vary [1-3]. In addition, laserparameters like energy and beam pointing that may seemeasier to control, have also to be very carefully optimised.
The overall system design appears to be more difficult in
the case of copper photocathode, because of the requiredvery high UV energy (~0.5 mJ for extracting 1 nC). The
implementation of beam and pulse shaping techniques atthese energy levels in UV is quite challenging. In thispaper we describe the schemes and technologic solutions
developed at Elettra for the FERMI PIL. As it will beseen the system fully meets and in some aspects exceeds
the requirements.

MAIN SYSTEM DESIGNAs it has already been discussed in earlier papers [4],the only laser technology that can meet all the PIL
parameters requested for copper photocathode, and isenough mature and reliable, is the one based on
Ti:Sapphire as an active material and regenerative
amplifier/multipass chirped-pulse amplifier design. The___________________________________________∗ This work has been partially supported by the EU Commission in the

Sixth Framework Program, Contract No. 011935 EUROFELFEL Technology I

358

amplifier system described here is a custom systemconstructed by Coherent Inc. This is in fact the first
amplifier system of this type, reaching an energy level
above 18 mJ in the infrared, with the use of entirely CW
diode pumping technology, which is the base for theextremely high UV energy stability reported below. The
amplifier design is shown on Figure 1.
As it is seen, the seed coming from a Ti:Sapphireoscillator (Mira), is stretched and amplified to a mJ levelin a regenerative cavity, after which it is further amplified
in two two-pass amplifier stages. Each of these is pumped
by up to 45 mJ from two Evolution HE Nd:YLF Qswitched pump lasers. As mentioned above, they are
pumped by diodes in CW. Table 1 summarizes some of
the main laser parameters.
Parameter
IR output energy

Specs> 18 mJ

Pulse duration (Gauss.fit)
Center WL<100 fs
780+/-5nm
M2x,y<1.5

M2 value
UV energy before shaping
Short term energy stability
UV (500 shots), RMS
Long term energy stability
UV (8 hours), RMS
Beam pointing stability
Timing jitter (10 Hz-10MHz),RMS

Measured> 18 mJ(~15 mJ in
operation)~90 fs~783 nm>2 mJ<3%

M2x~1.27,
M2y<1.17>2.3 mJ
<0.6%

<3%

<0.8%

<10 μrad<350 fs<5 μrad<180 fs

Table 1: Main laser parameters , left- specified, rightmeasured
We note that the system is capable of delivering >18 mJ
energy per pulse in IR, however the reported 2.3 mJ of
UV energy is obtained at ~15 mJ in the IR. This regime ispreferred for everyday operation because of lower diodecurrent (~19A) and also lower load on the opticalcomponents. Conversion efficiency to third harmonic(261 nm) is about 15% and has been fixed after carefulbalancing of spot-size and pulse duration. Bothinterferometer like and ‘time-plate’ designs of the THG
unit have been tested with similar results. However, in thelatter we have observed a deterioration of the calcite plate
which pre-compensates the group velocity mismatch, so
at present the interferometric version is in operation.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH014

Figure 1: Amplifier design.

The concept chosen for our time-shaping system has
been already described previously [4]. In brief, it
implements a two-step hybrid shaping system in which apreliminary shaping is performed in IR by an
acoustooptic dispersive filter (DAZZLER , Fastlite), andthe final shape and duration of the pulse are done in the
UV in a Fourie system. In principle the DAZZLER allows
both amplitude and phase modulation [5]. We note thatthe amplitude shaping done by the DAZZLER is partiallylost in the amplification process due to the strong ‘red’
shift of the amplified spectrum with respect to the seeding
one. For this reason the DAZZLER alone is not sufficientfor producing the required pulse shapes. .
The main temporal shaping is thus performed in UV by
the 4-f system shown on Fig.2. The UV pulse comingfrom the harmonic generation system enters a Fouriershaping scheme consisting of the grating G1, folding
mirror M1, lens L, deformable mirror (DM) and retroreflecting mirror M2. The modulation
is mostly
performed by the DM (OKO Technologies). The
particular mirror used is a custom made dielectric plate(HR at 260 nm) glued on a 20 piezo transducers (2lines of10), each of them can be moved by up to 10 micron. As it
is seen from the figure we use a configuration where themirror is used at a large angle, thus increasing the numberof useful actuators and the induced phase difference. In
alternative configuration, a longer focal distance lens andDM at normal incidence can be used. The DM is used forproviding mostly the high order dispersion terms, while
half of the large second order dispersion term giving thefinal (several ps range) pulse lengthening is given by the

G2

IN

TIME SHAPING

G1

Δ

f

M1

DM
Δ

L

f
OUT

M2

Figure 2: UV pulse shaping optical scheme (up) andphoto of the setup (down).

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Proceedings of FEL 2007, Novosibirsk, Russia

off-focus distance Δ of the grating with respect to thefront Fourier plane. The second half of the required groupvelocity dispersion (GVD) is provided by the double
passage through the grating G2, which is also used tocancel the residual spatial chirp introduced by the shaper.
The pulse length can be changed by changing Δ in boththe shaper and stretcher and respectively adjusting theshape of the DM.
1,0

rms=4.5%0,90,8system. Typical results at the output of the shaper andafter a Relay imaging is shown on Fig.5, left and right,
respectively.
1,0

INTENSITY (a.u)

WEPPH014

a.u.

0,7

0,8
0,6
0,4
0,2

0,6
0,5

0,0
18

0,4

14

12

10

a.

0,3
0,2

8

6

4

2

0

TIME (ps)

1,0

0,1
0,0

16

0,9

0

2

4

6

8

10

12

0,8

14

0,7

ps

rms=3.2%

a.u.

0,9

a.u.

0,6

1,0

0,5
0,4

0,8

0,3

0,7

0,2

0,6

0,1
0,0

0,5

b.

0,4

0

2

4

6

8

0,3
0,2

1,0

0,1

0,9

0,0

0

2

4

6

8

10

12

14

0,7

ps

14

16

0,6
a.u.

Figure 3: Flat-top pulses with duration of 6 and 10 ps
produced using phase modulation by the DM.

12compr.=0 cm
compr.=1 cm
compr.=2 cm

0,8

16

10

ps

0,5
0,4
0,3

Typical examples of the commonly requested flat-top
type temporal profile are shown on Figs5. The flat-top
duration could be made even longer, up to 15 ps, with theexpense of increased modulation (~7% RMS) and falltime (~ 2ps).
As mentioned above, in the case of FERMI a nearlyquadratically increasing ramp, as shown on Fig.4 a, isrequired [3], so the system has at present been optimized
for generating such a profile. Fig. 4b presents typicalpulse profile measured by cross-correlating the UV pulse
with an IR pulse using down-conversion in a 250 micron
thick BBO crystal. It was possible to change the durationof the ramp by adjusting the UV stretcher length. For
small duration changes the pulse shape was not strongly
affected, so no other adjustments were needed. For larger(i.e. more than 2 ps) duration changes, an additional
adjustment of the piezo-mirror was necessary.
The transverse shaping of the UV beam is performed by
a commercial asperic beam shaper (Moltech). After aproper adjustment of the input Gaussian beam dimension
the shaper produces a flat-top distribution which then isrelay-imaged on the cathode by the beam transport
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0,2
0,1
0,0

c.

0

2

4

6

8

10 12 14 16 18 20
ps

Figure 4: Increasing ramp pulse shapes, a-plot of therequired pulse shape; b- cross-correlation trace of theobtained UV pulse; c- pulses of variable duration
obtained by adjusting the compressor

Figure 5: Images of flat-top UV beam after beam shaper(left), and after Relay imaging (right)

Proceedings of FEL 2007, Novosibirsk, Russia

The initially requested timing jitter for the FERMI PIL
was initially set conservatively at 350 fs RMS , taking
into account simulations that were performed at Elettra, as
well as the best specs of commercial Ti:Sapphireoscillators. It was expected that the actual system
performance will exceed the specs and this was confirmedby the measurements. First, the phase noise of theoscillator locked to an external low noise RF generator
was measured. Integrating this curve in the range 10Hz10MHz an RMS timing jitter of about 180 fs was
obtained (blue curve on Fig.6). The red curve on the samegraph shows the result of the same type of measurement
done using a commercial fibre laser (Menlo Systems). It
is seen that, if needed, jitter could be reduced by a factorof two if the latter (after frequency doubling) is used forseeding our amplifier system. At present, however, thejitter performance of the Ti:sapphire oscillator isconsidered satisfactory for the photoinjector laser.

typical 10 min record is shown on Figure 7. The jitter
value extracted from this measurement was 9.8 fs. At
longer time scale, the cross-correlation signal was
exhibiting slow drifts, which indicates the need of
implementing a beam-path stabilization of the beamtransport when the system will be installed at thephotoinjector.
B

600
500
CC. Signal [a.u.]

TIMING JITTERWEPPH014

400

Mean 500.05
std +_ 9.8 ~ 2fs
calibration 0.2fs/a.u.
Min-Max = 63*0.2 = 12fs

300
200
100
0

0

100 200 300 400 500 600 700
Time [s]200

Figure 7. Typical cross-correlation signal by the jittermeasurement

Menlo
Coherent

180
160
140
J itter - fs

120
100

CONCLUSIONS

80
60
40
20
0
1
10

2

10

10

3

4

10
Hz

10

5

6

10

10

7

Figure 6. Timing jitter of the Ti:sapphire oscillator(blue) and an Er-doped fibre laser (red)A question which arises naturally and to our knowledge
has not been so far addressed in literature is how muchjitter is added by the amplifier system. To clarify thispoint we pe4rformed a measurement of this jitter bymonitoring the cross-correlation signal generated in a thin
nonlinear crystal (BBO) by samples of the pulses before
and after the amplifier. After measuring the crosscorrelation (about 150 fs long nearly Gaussian ), the delay
was fixed at half-maximum level, so as to have maximum
range where the measured fluctuation of the crosscorrelation signal was linearly proportional to the timing
jitter. A calibration was performed by measuring thesignal change by controlled delays. The signal wasmeasured at the rep rate of the amplifier (50 Hz). A

This paper presents details on the exact setup andperformance of the laser system developed for the FERMI
photoinjector. The obtained results show that theimplemented solutions for amplification, harmonic
generation and shaping schemes were correct and allow toguarantee all the required parameters. In particular, wedemonstrate for the first time the generation of theprescribed for FERMI increasing ramp UV pulse shape.
We also present a first measurement of the timing jitter
added by a high energy Ti:sapphire amplifier.

REFERENCES[1] C. Limborg-Deprey, Proc.27th FEL Conf.(2005), 418.
[2] O.J. Luiten, M.J. Van der Wiel, 27th FEL
Conf.(2005) ,paper WEOB003.
[3] G.Penco et al, Proc.FEL 2006, Berlin, Germany,
p.625.
[4] M.B.Danailov et al, Proc.FEL 2006, Berlin,
Germany, p.617.
[5] P. Tournois,
Opt. Comm. 140 (1997), p.245.

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A LASER HEATER FOR FERMI@ELETTRA
S.Spampinati, S. Di Mitri, B Diviacco, Sincrotrone Trieste, Italy.
Abstract
To cure the microbunching instability in the
FERMI@elettra FEL a laser heater is proposed. The
one-dimensional model of the instability predicts alarge energy modulation cumulating as the electron
beam travels along the linac. According to analyticalstudies and simulations the longitudinal Landau
damping provided by the laser heater is expected tohelp in suppressing the formation of such a
modulation. The efficiency of the beam heating isstudied as function of the transverse laser-electron
beam mismatch in the laser heater undulator in case ofa realistic transverse beam profile.

INTRODUCTION
The FERMI@elettra [1] project will upgrade theElettra linac with the installation of a photoinjector, alaser heater, an X-band cavity and two magnetic bunch
compressors. The linac will then be able to provide thehigh current, low emittance and low energy spread(high brightness) electron beam needed by the singlepass Free Electron Laser (FEL). In this paper we
describe the laser heater.

LASER HEATER
The laser heater is planned to be installed in the linac
at a point where the electron beam energy is roughly
100 MeV. This device will provide a controlled
increase of the uncorrelated energy spread. According
to analytical and numerical studies, the beam heating is
expected to help in suppressing the microbunching
instability through longitudinal Landau damping [2].
The laser heater layout is shown in Figure 1.
The laser heater consists of an undulator locatedwithin a small magnetic chicane that allows an externallaser to seed the electron beam. There is space forfurther diagnostic devices beyond the exit of the laser
heater undulator.

corresponding density modulation is negligible;
however, the induced energy/position correlation issmeared by the transverse motion in the chicane. As aresult, the laser/electron interaction leads to aneffective heating of the beam. The main laser heaterparameters are listed in the Table 1.
The laser used for the heater will be split from themain beam of the Ti:Sa laser used for the photoinjector
laser
system. The maximum peak laser power
available in the undulator is 10 MW. The IR laser will
be stretched to reach a pulse duration of 20 ps. The
pulse energy needed is <1mJ, therefore only a smallpart of the infrared light energy available (for laser
heater and photocathode, >18mJ) will be needed forthe laser heater. The induced energy spread must be in
the rage 10 – 20 keV RMS [3].
Table 1: Mean laser heater parameters
Parameter

value

Undulator period

4 cm

Number of periods

12

Bending angle

3.5 degrees

Bending length

20 cm

Drift between bending

30 cm

Drift before undulator

20 cm

Drift after undulator

218 cmTotal length

418 cmNeglecting changes in the laser and beam transverse
dimensions during the interaction, the provided energy
modulation for a “hard edge” undulator filed [4] isgiven by equation.(1):
r2

2
⎛ K
⎞⎤ − 4σ r2
P K LU ⎡ ⎛ K 2 ⎞⎟ ⋅e⎟ − J1⎜Δγ L (r ) = L⎢J 0 ⎜
2 ⎟2 ⎟⎥⎜⎜P0 γ 0 σ r ⎣ ⎝ 4 + 2K ⎠⎝ 4 + 2 K ⎠⎦

νsin( 0 )
2

ν0
2

with:

ν 0 = 2πN(λ − λ r )λ(2)PL is the laser peak power, P0 = 8.7GW , r is theaverage radius of the electron beam transverse size,
σ r is the RMS laser spot size in the undulator andFigure 1: Schematic of the laser heater layout.
The particles interact with the laser in the short
undulator and they gain an energy modulation with aperiodicity on the scale of the optical wavelength. The
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γ 0 mc 2 is the average total energy of the electron
beam. J0 and J1 are the Bessel functions, K is theundulator parameter, Lu is the undulator length, λu isthe undulator period, N is the number of periods of theProceedings of FEL 2007, Novosibirsk, Russia

WEPPH015

undulator, I is the laser intensity, γ is the Lorentz
factor, λr is the resonance wavelength of thelaser/electron interaction and λis the laser
wavelength.
The ratio R between the energy modulation ΔγL andthe energy spread σγ depends on the transverse
parameter B defined as:

B=

σr
σx

(3)

where σ x is the rms horizontal size of the electronbeam.
R is 2 for B=1 and it is <2 for B>1. As the Landau
damping is less effective for B<1, it is possible toestimate the needed laser power by using R=2 that is:Δγ (0)σγ = L
2(4)

UNDULATOR
The laser heater undulator is a simple planar
permanent magnetic structure. It is designed to beresonant at the 780 nm nominal wavelength of theTi:Sa photocathode laser for an average beam energy
ranging from 85 MeV to 105 MeV. The resonantcondition is:

λ ⎛ K2 ⎞⎟λ 0 = u2 ⎜⎜1 +
2 ⎟⎠
2γ ⎝

(5)

The undulator period determines the minimum
energy at which the undulator is resonant and theminimum gap needed. The undulator is not resonant
at a beam energy of 85 MeV for a periods longer than
4.3 cm given the minimum gap required is too tight fora period shorter than 4.0 cm. These considerations are
made explicit in Figure 2. A period 4 cm long has been
therefore chosen.
The number of periods has to be limited in order tohave a large energy acceptance. Figure 3 shows thevariation of energy spread as a function of the laser
detuning for various number of undulator periods.

Figure 3: Energy spread percentage variation vs. laser
wavelength detuning from the resonance condition.
The present undulator design includes 12 periods (810 effective periods) for a total length of 48 cm. The
terminations are designed to have no residual
dispersion and to provide no orbit displacement. The
gap range is 24 – 38 mm for a maximum peak field in
the range 0.312 T – 0.102 T.
According to the undulator parameters discussed sofar, eq. (4) predicts a peak power of 0.5 MW to induce
an energy spread of 20 keV rms.

CHICANE DYNAMICS
The effects of the laser heater chicane on the beam
have been analysed. The particle longitudinalcoordinate along the bunch (i.e., referred to the beam
centre of mass) when the beam reaches the centre of
the chicane can be evaluated through the 2nd ordertransport matrices at the same location and the initialenergy and transverse coordinates:
2

δ
⎛δ ⎞
z(f ) = z(i) + R 51x + R 52x + R 56 γ + T566 ⎜⎜ γ ⎟⎟ (6)γ0⎝ γ0 ⎠'For a symmetric achromatic chicane, R 51 = 0m .
The energy/position correlation induced by theinteraction is smeared if the following relation issatisfied [5]:λR 52 σ x ' > L
(7)

2π

For

FERMI, R 52 = 0.031m ,β ≈ 2.5m andσ x' = ε x β x ≈ 55μm . Thus, the correlation isefficiently smeared for a finite emittance beam asshown in Figure 4.

Figure 2: Resonance energy in MeV vs. undulator gap.
The undulator tunability has been evaluated for
different undulator period lengths.

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Proceedings of FEL 2007, Novosibirsk, Russia

Figure 4: Longitudinal phase space (energy spread in
KeV vs. bunch length in m) out of the laser heater
chicane. A finite transverse normalized emittance of 1
mm mrad is sufficient to smear the energy/position
correlation induced by the laser/electron interaction.
For comparison, we show that the smearing effect does
not happen for a null emittance, i.e. the correlation
persists.
Exiting the photoinjector, the bunch head as at ahigher energy respect to the bunch tail, therefore eq.(6)describes a beam lengthening. Given the design
parameters reported in Table 1 and the known beamenergy chirp provided by running off-crest in the
upstream linac (the photoinjector accelerates
approximately on crest), the laser heater chicane
produces an increase of the beam length of about 2%.
This effect is not critical for the subsequent
compression.
Moreover, as the energy spread increases in thedispersive region, the heating can lead to an emittance
dilution by additionally induced betatron motion. The
relative emittance growth can be estimated by [5]:Δε x 1 ⎛ σ γ η ⎞
⎟
= ⎜⎜
εx
2 ⎝ γ 0σ x ⎟⎠Figure 5: Energy profile of the beam out of the photoinjector.
According to the energy distribution shown in Figure
5, the dispersive motion in the laser heater chicane
generates a different transverse displacement of thebeam longitudinal slices with respect to the undulator
axis (see, Figure 6).
The different overlap of each slice with the seedinglaser, together with the variation of the slice transverse
dimension also shown in Figure 6, leads to a nonuniform beam heating.

2

For FERMI this effect is negligible since

(8)
Δε x
= 1.5 ⋅ 10 −5εx

PARTICLE TRACKING

Figure 6: Mean transverse (x) position and transverse(x, y) rms dimensions of the beam in the chicane.

Using the tracking code elegant [x], particle tracking
has been performed on a 6 dimensional Gaussian
electron beam with elegant code. The energy
distribution of the electron beam generated by thephoto-cathode has been reproduced in elegant and isshown in Figures 5.

Different runs have been performed by changing thelaser waist from 480 m (B=2 for the flat part of thebeam) to 240 m (B=1 for the flat part of he beam) toobtain a more uniform beam heating. Accordingly, thelaser power has been changed (see, eq.(1)) to induce
always the same uncorrelated energy spread. Results
are shown in Figures 7 and 8.

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Proceedings of FEL 2007, Novosibirsk, Russia

Figure 7: Rms uncorrelated energy spread along thebunch. Laser waist is 240 m (B=1 for the flat part ofthe beam). Laser peak power is 0.130 MW.

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Figure 10: Longitudinal phase space (relative energy
spread vs. bunch duration) at the linac end,
corresponding to the beam heating in Figure 8.
Simulations predict that an rms uncorrelated energy
spread of 10 keV can be induced uniformly over about
60% of the bunch duration with a laser waist of 480
m and a peak power of 0.165 MW. Preliminary
calculations indicate that 37 keV energy spread can bereached in the bunch core with a the maximum peak
power of 10 MW at a beam energy of 85 MeV.

CONCLUSIONS
Figure 8: Rms uncorrelated energy spread along thebunch. Laser waist is 480 m (B=2 for the flat part ofthe beam). Laser peak power is 0.165 MW.
The resulting beam was then propagated through therest of the linac. The longitudinal phase space at theend of the linac is shown in Figure 9 and in Figure 10,
corresponding to Figure 7 and Figure 8, respectively.

The parameters of the laser heater main components(undulator and magnetic chicane) have been explored.
Analytical calculations and particle tracking
demonstrate that the peak power by the Ti:Sa photocathode laser is sufficient for the required beam
heating.

[1] FERMI@elettra CDR, to be published.
[2] E.L. Saldin, E.A. Schnaidmiller, M.V. Yurkov,
Nuclear Instruments and Methods A 429 (1999) 233.
[3] A.Zolents et al., Fermi Tecnical Note 06/15 (2006).
[4] G.Dattoli, A.Renieri, Laser Handbook Vol.4(1984).
[5] Z.Huang et al., Phys Rev ST-AB 7 074401 (2004).
[6] M.Borland, APS LS-287 (2000).

Figure 9: Longitudinal phase space (relative energy
spread vs. bunch duration) at the linac end,
corresponding to the beam heating in Figure 7.

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Proceedings of FEL 2007, Novosibirsk, Russia

UV PERFORMANCES OF PULSED LASER DEPOSITION GROWN MG
PHOTOCATHODES*
L. Cultrera, G. Gatti, F. Tazzioli (INFN/LNF, Frascati (Roma)), C. Ristoscu (INFLPR, Bucharest Magurele), P. Miglietta, A. Perrone (INFN-Lecce, Lecce)
Abstract
We report a detailed description of the laser cleaning
procedure and emission performance measurement on a
Pulsed Laser Deposited Mg film. During the tests
performed after the end of each cleaning operation we
have evidenced an increase of Quantum Efficiency (QE)in time. Then the QE apparently stabilizes at a remarkably
higher value. The study of this phenomenon is importantbecause it determines both the working QE value and thelifetime of the cathode. Moreover, the stability of the QE
has been revealed for a time scale of several days after
each laser cleaning process, in our vacuum conditions.

films deposition of several
materials [9, 10]. The
PLD apparatus used to deposit thin films is shown infigure 1. During the deposition the vacuum chamber was
filled with pure He at a pressure of 5 Pa to reach theplume confinement regime leading to an increase of thedeposition rate [11].

INTRODUCTION
The electron injectors for the advanced projects offourth generation X-ray sources, as SASE-FELs [1], andfor future linear colliders [2], are mostly based on laser
excited photocathodes. Metals have order of femtosecond response and they are rugged in handling. Amongthem, Mg has premium QE, in the order of 10-3 at near
UV wavelength (266 nm). However, bulk Mg cathodes
have shown poor emission uniformity and failures in thehigh electric fields environment of RF guns. Moreover,the QE value degrades in time even in the UHV vacuumof RF guns.As an alternative, Mg films on copper
substrates have been proposed and tested on the basis of
their presumed better purity and uniformity [3]. Previous
reports on Mg films grown by Pulsed Laser Deposition
showed promising results in particular with respect touniformity of emission, quantum yield, and adhesion to
the substrate [4-6].
In order to reach the utmost QE value is necessary to
remove the inevitable oxide layer that forms on the film
surface. Only two techniques were used to perform suchoperation: laser cleaning and ionic etching [7]. The laser
cleaning operation must be performed with particular caredue to the limited thickness of the film and to avoid
inducing surface roughness. It was evidenced that thecleaning irradiation may determine a variation of the film
surface morphology [8].
The aim of this paper is to describe the film deposition
conditions, the laser cleaning procedure and to evidence
the performance of Mg films from photoemission point ofview.

EXPERIMENTAL
Cathode preparation
The PLD technique is a well-known method for thin___________________________________________* This work has been partially supported by the EUcommission in the sixth framework program, contract no.
011935 EUROFEL and by MIUR, Progetti Strategici, DD
1834, December 4, 2002.
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Figure 1: PLD experimental setup.
With the aim to clean the target surface, a preirradiation treatment was applied with 5,000 laser pulses.
During this laser cleaning, the Cu substrate was shieldedfrom the initial ablated material, which could contain
impurities. Several films were prepared to optimize thedeposition process. The deposition parameters of thetested sample are shown in table 1.
Table 1: Mg film deposition parameters.
TargetMg
Substrate
Cu
Target-Substrate distance
3.5 cmLaser spot size
1.0 mm2
Base pressure
5 x 10-6 Pa
Laser pulses
5000• Cleaning (5 x 10-6 Pa)
50000• Deposition (in He at 5 Pa)
Laser fluence
10 J/cm2
Film thickness
2.5 μmFilm diameter
12 mm
Vacuum diode cell
The QE measurements were performed in aphotodiode cell under UHV condition. The cathode andthe anode separated at a distance of 3 mm were placed
inside the photodiode cell (fig. 2). The Mg film occupied
the cathode position and was electrically grounded. The
anode plate was biased with high DC voltages up to 5 kV
thus allowing the generation inside the gap of an intenseelectric field of about 1.7 MVolt/m.

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 2: Laser cleaning and QE measurement setup.
In order to illuminate the cathode and for precisealignment of UV laser beam on cathode surface the anodeplate was machined with two symmetric holes. They havea diameter of 4 mm and form an angle of 72° with respect
to the normal of the cathode surface. This particulargeometry was chosen for two main reasons:• The first was to avoid the use of a metallic grid
usually present in such experiments. Our previous
experimental results clearly indicated that the light
distribution on the cathode surface, in presence of ametallic grid, was affected by diffraction structuresand hampered uniform illumination of the cathodesurface [6];• Secondarily, the angle of 72° was chosen in order toperform experiments with the same geometricalconfiguration used in the last generation of the
BNL/SLAC/UCLA 1.6 cells S-Band RF gun [12].
The vacuum chamber in which the photodiode cell
was inserted was evacuated at a base pressure of about
2x10-7 Pa by means of an ionic pump. The quality of thevacuum was controlled by a quadrupole mass
spectrometer.

Laser cleaning and QE measurements
Laser cleaning and QE measurements of the Mg films
were performed using the UV radiation of the 4th
harmonic of a Q-switch, mode-locked Nd:YAG laser(QUANTEL YG-501) able to deliver up to 300 μJoule at
266 nm with a pulse duration of 30 ps. The laser energy
measurements were performed by integrating the signal of
the calibrated fast photodiode, while the charge
measurements were done using a charge integrator.
The laser cleaning procedure was performed byscanning the focused laser beam over an area of about
2.4x2.4 mm2. The laser beam had a diameter on thecathode surface of about 300 μm and energy of about 25
μJoule per pulse (power density and laser fluence wereabout 3 GW/cm2 and 35 mJ/cm2 per pulse respectively).
Such value of the power density was experimentally
determined during preliminary tests as being the thresholdfor the ablation of the oxidized layers. The power density
threshold value for the ablation was deduced looking at
the vacuum level of the UHV chamber: we observed thatonce such value was reached, the vacuum level inside thechamber slightly worsened indicating that material
ablation was occurring.

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The scanning scheme was chosen in such way thatlaser shots focused over consecutive horizontal path lines
slightly overlap in order to make sure that all parts of thesurface were exposed to the laser beam. Typically during
the laser cleaning the laser repetition rate was set at 5 Hz
and the scanning speed of the laser spot was on the orderof 10-3 m/s.
After each laser cleaning procedure the focusing lens
was removed and the laser beam was directed to thecentral part of the irradiated area of the cathode tomeasure the QE. In order to perform measurements far
from space charge saturation, the laser energy wasdecreased by means of calibrated neutral density filters.

RESULTSThe first emission measurement was performed before
any laser cleaning treatment. It revealed a very poor QE
of about 2x10-6. Just after the first laser cleaning
procedure, performed as above described, the QE
measured value rose of about 2 orders of magnitude
reaching the noticeable value of 5x10-4, very close to thevalue reported in literature for bulk pure Mg [13].

Figure 3: QE measurement vs. time after laser cleaning.
In order to study the stability of emission we
performed QE measurements vs. time for several hours(fig. 3). The measurement after the first laser cleaning
was performed for about 1.5 hours. We detected a slightincrease of the QE value during this time from the initialvalue (just after the cleaning) of about 5x10-4 up to
6.5x10-4. After about 12 hours, we carried out a new laser
cleaning of the cathode surface. The QE value wasmonitored again for about 2.5 hours. After the 2nd
cleaning, the measured QE was slightly lower than thelast measured value, but also in this case its value
increased from 5.5x10-4 of up to about 8.0x10-4. About 12
hours later, we executed a 3rd cleaning and measured the
QE continuously. We observed again that after an initial
decrease just after the laser cleaning (from 8.0x10-4 to
7.5x10-4), the QE value increased up to 1.2x10-3 during
the next 6 hours. The 4th cleaning procedure wasaccomplished about 12 hours before the last QE
measurements. In this case, the single raster scheme was
performed 5 times. After the laser cleaning we detected astrong decrease of the QE that lowered to an initial value

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of 7.5x10-4. During the next 6.5 hours we continuously
measured the QE value, observing a continuous increase
up to a value of about 1.4x10-3. The 5th and final laser
cleaning, carried out using a single raster scheme, resulted
in an initial QE value of 10-3 that rose up to 1.4x10-3
during next 4 hours. It is evident the strong variation, up
to a factor two, during each measurement.
The sample was kept under vacuum at a base pressureof 2x10-7 Pa during the next two days. After this time we
performed new measurements without additional laser
cleaning procedure. We observed that the QE value was
the same with that measured two days before, i.e. 1.4x103. This value was preserved also after the irradiation of thesurface with about 5 μJoule for about 1 hour with arepetition rate of 5 Hz. The aim of the test was to verify
the ability of such cathode to maintain its emission
performances also during irradiation with laser energy
slightly exceeding that required to extract electron
bunches of 1 nC charge.
Additionally the QE map of the irradiated area wasdrawn. In order to perform such measurement the laser
energy was lowered to few nJ by means of neutral density
filters. The laser was focused on the cathode surface by a
30 cm focal length fused silica lens. The truncatedgaussian laser spot was then moved in succession over a
grid of 9x9 points on the laser-cleaned area. The average
QE on each irradiated area of about 300 μm diameter isevaluated from the slope of emission curves, i.e. collectedcharge vs. laser energy, far from space charge saturation
regime. The 300 μm diameter is the minimum compatible
with the sensitivity of our charge detector apparatus toremain below the extractable charge limit. Naturally thisentails a limit on the spatial resolution which cannot beless than about twice the value of the laser spot diameter.
The QE map of the sample collected 72 hours after the
5th and last laser cleaning process is reported in figure 4.
With the limitations due to the size of the laser spot
during such measurements the emission seems to bereasonably uniform inside a circle of about 500 μm ofradius centred in the most intense emitting area.

Figure 4: QE map after 5th laser cleaning.

DISCUSSION
QE values for Mg reported by now in literature, either
for bulk or film, are scattered in a range within 2.5x10-4
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and 3x10-3 for an exciting wavelength of 266 nm. The
reason of this spread can be the different experimental
conditions, as e.g. vacuum base pressure and electric field
intensities [14-16].
Theoretical prediction for the QE value for Mg at 266
nm indicates a value of about 5x10-4. Higher values
cannot be predicted assuming a work function of 3.66 eV.
A decrease of such value by means of the formation ofsome electric dipole on the surface due to the gas
absorption may be the key to explain such highphotoemission performance from this material.
The very gradual laser cleaning procedure described
before should remove only the uppermost deeply oxidized
layer. It has the typical rock-salt structure of the MgO andwas formed by exposing the film surface to air during thetime between the deposition procedure and emission
characterization, both performed in UHV environment.
Ref. 3 reports that successive laser cleaning procedures
resulted in an increase of the QE. This is also clearlyobserved also in our previous [4-6] and present
experiments, demonstrating that pure Mg metal surface
has been obtained with the removal of surface oxidized
layers. Nevertheless, a continuous monitoring of theemission yield of the Mg film during a time interval ofseveral hours after each laser cleaning clearly indicatesthat some other processes influenced the electron surface
emission properties. Few years ago the effects of oxygen
adsorption on the quantum yield of Mg films have beenreported by Q. Yuan et al. [17]. They showed that asignificant increase of QE is achieved by exposing Mg
film to controlled fluxes of pure O2. After an initial
increase, strongly dependent on the oxygen dose, thequantum yield deteriorates, pointing to the formation of a
thick oxidized layer that delayed the emission ofphotoelectrons. Similar results were observed in 1935 by
R.J. Cashman and W.S. Huxford [18]. Their findings on
the lowering of the work function during initial oxidationof the Mg surface were confirmed through numericalcomputation by E. Schröder et al. [19].
Our experimental situation was quite different fromthose of the experiments reported in literature. In our caseno fluxes of oxygen have been introduced in the vacuum
chamber. Our working base pressure was 2.5x10-7 Pa andthe O2 partial pressure was two orders of magnitude lower
than that used in other experiments reported in literature[17, 18]. Partial pressures of residual gases were
measured by a quadrupole mass spectrometer. From theresidual gas mass spectra we observed that the mostabundant chemical species were H2, H2O, N2 and O2, withpartial pressures of 1.9x10-7 Pa, 1.5x10-8 Pa, 3x10-8 Pa and8x10-9 Pa, respectively.
According to our readings of partial pressure and to
the duration of the QE acquisitions, which, as reported infigure 5, were performed up to a maximum of about 6hours, we deduced that the Mg surface exposed to O2, atpartial pressure level of 8x10-9 Pa, led to a surface
coverage lower than 1 monolayer. On the contrary, H2
exposure during the same time, due to higher partialpressure of this chemical species with respect toProceedings of FEL 2007, Novosibirsk, Russia
molecular oxygen, may give rise to a surface coverage
higher than 2-3 monolayers. According to R. J. Cashman
and W. S. Huxford [18] who studied the emission
properties of Mg surface exposed to H2 fluxes, weconsider that the increase of the quantum yield of oursample is related to the chemisorption of hydrogen in
subsurface sites of Mg film, and in a lesser extent ofoxygen. This should lead to a decrease of the work
function because an electric dipole is formed under thoseconditions near the surface of the film with orientationthat helps photoexcited electrons to escape in vacuum.
Such idea is partially confirmed by the findings of P. T.
Sprunger and E. W. Plummer [20] who observed adecrease of 0.95 eV of the initial value of the work
function after the complete hydrogenation of theMg(0001) surface due to the formation of a metastable“hydride” phase. They also reported that the activationenergy for the chemisorption of H2 on Mg(0001) surface
was of about 0.5 eV and thus at room temperature theformation of this phase should not be observed. PLD
films grown at room temperature usually do not present awell defined crystalline structure. XRD spectra (here notshowed) reveal that polycrystalline Mg film was formedon laser cleaned areas with slight texture on (002)orientation. Under these conditions, we can expect thatthe activation energy for chemisorption of H2 on Mg
amorphous surfaces may be lower than that reported forMg(0001), as also indicated by Nørskov et al. [21].
Tests performed by irradiating the cleaned area withlaser pulses (λ=266 nm, τ=30 ps) having 5 μJ of energy
show any influence on the QE. This result seems toindicate that the energy required to photo-dissociate the
Mg-H bond should be higher than 4.67 eV.
The emission inside the central part of the laser
cleaned area within a radius of approximately 500 μm andconsidering the limitations of our experimental
arrangements seems to be uniform within 20%. We foundout that the rapid decrease of the efficiency observed forvertical coordinate values close to the extreme of themeasured area is just due to a non-perfect alignment of
the laser beam inside the bore where it has to travel toilluminate the cathode surface. This misalignment does
not influence the measurements in the central zone of thescanned area.

Figure 5: Mg film deposited over the backflange of a
BNL/SLAC/UCLA 1.6 cells S-Band RF gun.

WEPPH017

CONCLUSIONSWe presented the results of laser cleaning effect interms of Quantum Efficiency, emission uniformity,
surface morphology and structure of pulsed laser
deposited pure Mg films on copper substrate. Moreover,the influence of the chemisorption of hydrogen, always
present as residual gas in ultra high vacuum operating
conditions, has been discussed with particular attention
with respect to the efficiency and stability of the emission
performances of Mg surface. Mg films have been grownin the central part of a backflange suitable to be inserted
onto an RF gun and the power tests are in progress (figure5). This work has been partially supported by the EUcommission in the sixth framework program, contract no.
011935 EUROFEL and by MIUR, Progetti Strategici, DD
1834, December 4, 2002.

REFERENCES[1] C. Pellegrini, Proc. of EPAC98, p. 83 (1998)[2] H. H. Braun et al., Proc. of PAC01, p.720 (2001)[3] T. Srinivasan-Rao et al., Rev. Sci. Inst. 62, p. 2292
(1998)[4] L. Cultrera et al., Appl. Surf. Sci. 248, p. 397(2005)[5] A. Perrone et al., Nucl. Instr. Meth. Phys. Res. A
554, p. 220 (2005)[6] L. Cultrera et al., Appl. Surf. Sci. 253, p. 6531
(2007)[7] J. F. Schmerge et al., Proc. of FEL 2006, p. 732(2006)[8] J. Smedley et al., J. Appl. Phys. 98, p. 043111(2005)[9] Chrisey D B and Hubler G K 1994 Pulsed Laser
Deposition of Thin Films (New York, Wiley)[10] Popescu M “Pulsed Laser Deposition of
Optoelectronic
Films”,(Bucharest,
INOE
Publishing) A. Pereira et al., Thin Solid Films 497,
p. 142 (2006)[11] D. T. Palmer et al., Proc. of PAC97, p. 2687 (1998)[12] K. L. Jensen et al., Proc. of FEL 2004, p. 574(2004)[13] X. J. Wang et al., Nucl. Instr. Meth. Phys. Res. A
356, p. 159 (1995)[14] T. Srinivasan Rao et al., J. Appl. Phys. 77, p. 1275
(1995)[15] T. Srinivasan Rao et al., J. Appl. Phys. 69, 3291
(1991)[16] Q. Yuanet al., J. Vac. Sci. Technol. B 21, p. 2830
(2003)[17] R. J. Cashman and W. S. Huxford, Phys. Rev. 48, p.
734 (1935)[18] E. Schröder et al., Phys. Rev. B 69, p. 115431(2004)[19] P. T. Sprunger and E. W. Plummer, Chem. Phys.
Lett. 187, p. 559 (1991)[20] J. K. et al, Phys. Rev. Lett. 46, p. 257 (1981)

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Proceedings of FEL 2007, Novosibirsk, Russia

HIGH BRIGHTNESS C-BAND AND X-BAND PHOTOINJECTORCONCEPTS AND RELATED TECHNOLOGICAL CHALLENGES
M. Ferrario, D. Alesini, V. Fusco, M. Migliorati, L. Palumbo, B. Spataro, INFN-LNF, Frascati,Roma, Italy.
L. Serafini, INFN-Mi, Milano, Italy.
J. B. Rosenzweig, UCLA, Los Angeles, CA, USA.
Abstract
Future light sources based on high gain free electron
lasers, require the production, acceleration and transport
up to the undulator entrance of high brightness (lowemittance, high peak current) electron bunches. Wake
fields effects in accelerating sections and in magnetic
bunch compressors typically contribute to emittancedegradation, hence the photo-injector design and its
operation is the leading edge for high quality beam
production. The state of the art photoinjector beam
brightness can be in principle brought close and above the1015 A/m2 threshold with C-band and X-band guns and aproper emittance compensation scheme. We discuss inthis paper optimized designs of split C-band and X-band
photoinjectors and the further technological developments
required to reach such an appealing goal.

INTRODUCTION
The optimization of a FEL source is quite acomplicated task [1] but the main requirement for theelectron beam in order to achieve short wavelength
radiation in a reasonable long undulator (30-100 m) is
clear: high transverse brightness. Transverse beam
brightness is defined hereafter with the approximated [2]expression:

B" #

2I
$n, x$n, ywhere I is the bunch peak current and εn is the bunchtransverse normalized emittance. The expected transverse
brightness for electron beams driving short wavelength
SASE FEL!facilities is of the order of 1015 – 1016 A/m2.
Wake fields effects in accelerating sections and inmagnetic bunch compressors typically contribute toemittance degradation, hence the photo-injector design
and its operation is the leading edge for high quality beam
production. In a photoinjector the emitted electrons are
rapidly accelerated to relativistic energies, thus partiallymitigating the emittance growth due to space charge
effects that is the dominant source of emittancedegradation in a high brightness photoinjector. One of the
key feature that make RF photoinjectors so actractive isthat the emittance growth is reduced when operated athigh peak field as the one achievable in the RF gun: up to
140 MV/m in a S-band gun. In addition the techniquetermed “emittance compensation” [3] has been
experimentally verified in many laboratories andtheoretically well understood [4].
A lot of efforts has been done in the last years at
SPRING-8 and SLAC in the context of the high
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frequency normal conducting linear collider development,in order to achieve high accelerating gradient in C and Xband accelerating structures. Accelerating gradient in
multi-cell TW accelerating structures as high as 40 MV/m
(C-band) and 100 MV/m (X-band) has been so far
achieved with low breakdown rate. In a different context
an X-band standing wave 5.5 cells photoinjector has beendeveloped at SLAC as a compact electron source forThomson backscattering experiments. As reported in [5] apeak field on the cathode surface of 200 MV/m has beenachieved.
The decision to adopt L-band superconducting
technology for the next International Linear Collider(ILC) has somehow damped the effort towards highfrequency structures development. More recently the
choice to adopt X-band technology in the framework of
the CLIC project [6], which has a less tight temporal timeschedule than ILC, has open up again the interest towards
X-band high gradient cavity R&D. FEL sources driven byhigh brightness linacs will certainly take profit from thisnew effort in the linear collider community, in particular
for the possibility to develop high gradient photoinjectors.
To this end we discuss in this paper possible designs ofhigh frequency RF photoinjectors based on C-band or Xband technology, able to produce beams with brightness
as high as 1015 A/m2 directly from the injector and therelated technological developments required to reach suchan appealing goal

SCALING APPROACH TO HIGHFREQUENCY PHOTOINJECTORSWe decided to investigate a split photoinjector
configuration, consisting in a 1.6 cells standing wave RF
gun followed by a booster, because it is a well know
scheme in the L and S band projects and also because is apromising design to achieve ultra-high gradients
operating at higher frequency: the reduced wall surfaces
implies a lower probability for surface defects that may
cause RF breakdown. Another possible scheme has beenpresented in [17]. In addition following the matchingcondition discussed in [4] a working point very suitable todamp emittance oscillations has been found [7]. As any
well optimised design it can be easily scaled [8,9] to any
other frequency, gradient or charge design.
As a reference design we have taken the S-band (2856
MHz) SPARC [15] photoinjector. In its ideal
configuration the beam consists in a uniform charge
distribution inside a cylinder of length L and radius R,
and we have scaled its parameters (charge Q, beam sizes

Proceedings of FEL 2007, Novosibirsk, Russia

R and L, peak RF field Eˆ and solenoid field B) to its
second (C-band) and fourth (X-band) harmonicfrequencies (5.712 GHz and 11.424 GHz respectively)
according to the following wavelength scaling laws [8]:!
Q " # rf , R,L " # rf , Eˆ " # rf $1 , Bˆ " # rf $1
As discussed in [8] both the space charge and RF
contributions to the total rms emittance scale with " rf , inthermal emittance contribution scale! addition! since the !
!
with the beam radius we can expect a similar scaling also
for " th # $ rf . Hence operation at shorter wavelength!
results a very convenient choice also for the beam
$2
brightness: Bn " # rf [8].
!
Freq.
![GHz]
2.856
5.712
11.424

Tab I: Original and scaled parameters
Q
R
L
Epeak
B
[nC] [mm] [ps][MV/m] [T]
1
1
10
120
0.275
0.5
0.5
5
240
0.55
0.25 0.25
2.5
480
1.1

A direct application of the previous scaling laws leads
to the set of new parameters, reported in table I. In
addition, to fulfil the scaling approach, also the solenoid
length has to be scaled with " rf , from the original 20 cm
long solenoid for the S-band gun design to 10 cm for the
C-band case and to 5 cm for the X-band gun case, see
figure 1.
!

WEPPH018

assumed a thermal emittance of 0.6 µm/mm for a copper
cathode [16].

Figure 2: Envelope and rms norm. emittance evolution
from the cathode up to the booster exit at 180 MeV for
the C-band case.

X-BAND PHOTOINJECTOR CASE
The X-band scaling implies RF and solenoid fields thatare too far from the state of the art to be realistic, see Tab.
I. A first attempt towards a more realistic design can bedone by reducing the solenoid field to 0.575 T and
increasing its length, from 5 cm to 10 cm, basically thesame solenoid adopted for the C-band case. HOMDYN
simulations for the full X-band injector (1.6 cell RF gun,3.75 cm long, followed at z = 0.6 m by 3 X-bandtravelling wave accelerating structures of the SLAC type,
operating at 56 MV/m accelerating field) show for thisoptimistic case an emittance of 0.27 µm, as reported in
Figure 2, with a peak current of 90 A, corresponding to abrightness of Bn of 2.5 1015 A/m2.

Figure 1: Solenoid fields for the original S-band gun
design (black line), the C-band design (green line) and Xband design (red line).

C-BAND PHOTOINJECTOR CASEHOMDYN simulations for the full C-band injector (1.6cell RF gun 7. cm long, followed at z = 1 m by 3 C-bandtravelling wave accelerating structures operating at 40
MV/m accelerating field) show for this case an emittanceof 0.49 µm, as reported in figure 2, with a peak current of
92 A, corresponding to a brightness of Bn of 7.7 1014
A/m2, a factor 4 higher than the corresponding S-band
design [7]. In this and in the following cases we have

Figure 3: Envelope and rms norm. emittance evolution
from the cathode up to the booster exit at 130 MeV for
the X-band case.
Again scaling laws can help us to re-optimize the injector
parameters in order to obtain a less challenging RF peakfield, another important step towards a more realistic
design. A reduced gun peak field results in a lower energy
gain, hence we have to apply the energy scaling laws
derived in [9]:FEL Technology I

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Proceedings of FEL 2007, Novosibirsk, Russia

Bˆ " # , R " # $2 / 3 , L " # $5 / 3
Aiming to reduce the peak filed from 480 MV/m to 350
MV/m (reducing the beam energy at the gun exit from 5.5
MeV down !
to 4.1 MeV)
! the new parameters computed
with!the previous equations are reported in table II:

Freq.
[MHz]
11.424
11.424

Tab II: Original and scaled parameters
Q
R
L
Epeak
B
[nC] [mm] [ps][MV/m] [T]0.25 0.25
2.5
480
0.575
0.25 0.31
4.2
350
0.420

Envelope and emittance evolution as computed by
HOMDYN are reported in figure 4. The final emittance ispractically unchanged compared to previous case,resulting 0.28 µm, while the peak current is affected by
the lower energy bunch elongation in the drift, resulting
58 A. The corresponding brightness is nevertheless quite
high Bn = 1.5 1015 A/m2.

use a 90 deg hybrid junction as sketched in Fig. 5. The
scheme foresees the use of two SW cavities: the gun and asecond compensating cavity that can be installed in theinjector for acceleration. A first analysis of the sensitivityof such a scheme with respect to the cavity parameters or
waveguide electrical length has shown that this solution is
not critical. The scheme is commonly implemented in the
SLED cavities and has been already and successfully
applied to compensate reflections in SW structures forparticle accelerators, as illustrated in [10]. It allows to
perfectly compensating the “steady state” reflections
given by the cavity but it does not allow eliminating thereflected power from discharges or breakdown in one of
the two cavities. A second possible scheme is illustrated
in Fig. 6. In this case the klystron is coupled to the SW
gun through a directional coupler. The power from thesource is split in the two waveguide branches: a fraction
A(<1) of the input power feed the gun while the fraction(1-A) is dissipated into a load or can feed a matched TW
section. In this case, if a discharge occurs in the SW gun
the reflected power to the source is, at maximum, afraction A2 of the klystron initial output power and can be
acceptable if the directional coupler is properly designed.
This scheme allows compensating both “steady state”
reflected power than that given by a discharge in the SW
gun.

Figure 4: Envelope and rms norm. emittance evolution
from the cathode up to the booster exit at 120 MeV for
the X-band case with reduced gun peak field .

TECHNOLOGICAL CHALLENGES
In table III are reported for comparison the RFparameters for the S, C and X band guns. As one can see
the required peak power from RF source are within thestate of the art C and X-band klystron development.

ν [Ghz]Rsh [MΩ/m]Q
Epeak[MV/m]
PRF [MW]Pd at 10 Hz[kW/m]
τ [µs]
Lcav [cm]Tab III: RF gun parameters
2.856
5.712
46
65
15335
10843
120
240
10
14
2.6
3.7
4
15

2
7.5

11.424
92
7668
350
10
2.6
1
3.75

A serious concern is the compensation scheme toprotect the klystron port from RF power reflections since
circulators/isolators are not available in C and X-band. A
possibility to protect the RF source from reflections is to
FEL Technology I

372

Figure 5: Possible scheme with a 90 deg hybrid junction
to protect the klystron from SW gun reflections.

Figure 6: Possible scheme with a directional coupler toprotect the klystron from SW gun reflections.
The request of high peak field in the gun cavity is themain challenge at least for the X-band case. It has beenProceedings of FEL 2007, Novosibirsk, Russia

demonstrated that a way to increase the RF fields inside
the accelerating structure is the use of Molybdenum forcavity irises [11]. An R&D activity on this direction has
been recently started also at INFN-LNF [12] in order todefine the best brazing geometry among Mo irises and Cu
structure [13]. Electroformed structures [14] are also
under study at LNF and a first test of deposition of Mo
over Cu in a 4 cells X-band structure has been alreadysuccessfully done, see figure 6. The lack of X-band powersources at the moment prevents us to perform high power
RF tests.

WEPPH018[13] S. Bini et al., “Status report on SALAF technicalactivity on vacuum brazing on X-band linear accelerating
structures”, SPARC-RF-07/004[14] B. Spataro et al., “Electroforming procedures applied
to the construction of 11.4 GHz linear
accelerating structures”, SPARC-RF-07/003[15] E. Chiadroni et al., these Proceedings[16] W. Graves et al., “Measurement of thermal emittancefor a copper photocathode”, Proc. of PAC 2001.
[17] A. Fukasawa et al., “Charge and wavelength scalingof the UCLA/URLS/INFN hybrid photoinjector”,
Proc. of PAC 2007, New Mexico, USA.

Figure 6: A Mo-Cu electroformed structure produced at
INFN-LNF.

REFERENCES[1]
M. Xie, “Design Optimization for an X-ray FEL
driven by SLAC linac”, Proc. of PAC Conference, 1995.
[2]
C. A. Brau, “What brightness means”, Proc. of
the ICFA workshop on “The physics and applications ofhigh brightness beams”, Sardinia, July 2002, World
Scientific.
[3]
B. E. Carlsten, Nucl. Instrum. Methods A 285,
313 (1989).
[4]
L. Serafini, J. B. Rosenzweig, Phys. Rev. E 55
(1997) 7565.
[5] E. Vlieks et al., “Development of an X-band
photoinjector at SLAC”, Proc. of LINAC 2002, Korea.
[6] H. Braun et al., “Towards a multi-TeV linear
collider”, Proc. of APAC 2007, India[7] M. Ferrario et al., “HOMDYN study for the LCLS RF
photoinjector”, SLAC-PUB-8400, (2000).
[8] J. B. Rosenzweig and E. Colby, “Charge andWavelength Scaling of RF Photoinjector Designs”, in
Proc. of Advanced Accelerator Concepts, AIP Conf. Proc.
335 724 (1995)[9] M. Ferrario et al., “Recent Advances and Novel Ideas
for High Brightness Electron Beam Production Basedon Photo-Injectors”, SPARC-BD-03/003[10] F. Marcellini and D. Alesini, “The RF Deflector for
the CTF3 delay loop”, Proc of EPAC 2006, Scotland.
[11] T. Ramsvik et al., Phys. Rev. Special Topics Accelerators And Beams 10, 042001 (2007)[12] B. Spataro et al., “R&D on X-Band Accelerating
Structures at the INFN-LNF”, SPARC-RF-06/002
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Proceedings of FEL 2007, Novosibirsk, Russia

WAKEFIELD INDUCED ENERGY SPREAD IN THE FERMI UNDULATOR
A.A.G. Lutman∗ , M. Castronovo† , R. Vescovo∗ , Università degli Studi di Trieste, Trieste, Italy
C. Bonţoiu, P. Craievich‡ , L. Rumiz, ELETTRA, Trieste, Italy
Abstract
The FERMI Project aims to achieve very high-brightness
photon beam pulses of minimum bandwidth. These goals
can be marred by the presence of large wakefields along theundulator small-gap vacuum chamber. Estimations of theinduced energy-spread caused by the resistive wall and surface roughness wakefields along the FERMI FEL undulator are presented. The energy spread and losses induced byresistive wall wakefield are determined for three possible
transverse geometries of the vacuum chamber, namely circular, rectangular and elliptic cross-section, while the energy spread and losses induced by the surface roughness
wakefields are obtained for the circular cross-section case.
In this last case in-house surface profile measurements carried on a spare vacuum chamber of ELETTRA are used toprovide realistic estimates.

WAKEFIELDS IN THE UNDULATORVACUUM CHAMBER
In the undulator vacuum chamber the finite conductivityof the metal wall and the roughness of the chamber innersurface wakefields are sources of wakefields. For the FEL
effect, the main concern is the longitudinal wake which
may impress an energy modulation on the electron bunchand consequently degrade the quality of the FEL radiation.
Transverse wakefields are much less disruptive in the undulator and will be neglected.

Resistive Wall Wakefields
The interaction between the electron beam and the metal
wall has been evaluated for circular, rectangular and elliptical cross-section vacuum chambers. Regardless of the
shape of the cross-section, the chamber is modeled as an
infinite pipe with finite conductivity σ, electron relaxation
time τ > 0 and infinite wall thickness. The relative longitudinal displacement from the bunch head will be denoted byz. The almost flat-top short bunches which will be used for
the FERMI FEL contain very high frequencies components
induced by the residual current spikes and thus require, as
pointed out by Bane [1], the use of the AC conductivity
model. In the following formulas the skin-depth related(i + sign(k)) will be used, whereparameter λ = Z0 σ|k|2
Z0 is the intrinsic impedance of the vacuum and k is thewave number.
∗ DEEI† Dipartimento di Fisica‡ paolo.craievich@elettra.trieste.it

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374

Circular cross-section: For the circular cross-section,
the calculations rely on the formula derived by Chao [2].
Denoting with b the radius of the pipe, the longitudinal coupling impedance is given in SI units by:Z(k) =

2Z0 1
λ4π b k − ikb
2(1)

Rectangular cross-section: For the rectangular shapethe evaluation relies on the formulas given by Henke andNapoly [3]. Although the theory is elaborated for two conducting infinite parallel plates, we will use it for a rectangular cross-section neglecting the effects of the lateral walls.
Denoting with b the half gap between the metal plates, thelongitudinal coupling impedance, as given in [4] is in SI
units:
1
Z0 +∞dx
Z(k) =
4π −∞ λk cosh2 bx − ikx cosh bx sinh bx(2)
Elliptic cross-section: For the elliptic cross-section
shape a novel method that holds for AC conductivity andallows one to evaluate the wakes at very short range, hasbeen developed. The fields are obtained by developinga system of solutions to the Maxwell’s equations both in
the vacuum and in the resistive wall and then imposing theboundary conditions on the wall surface similar to what has
been done for the circular case. The longitudinal and transverse wake functions are then calculated using field expansions. Maxwell’s equations have been solved in an elliptic cylindrical system of coordinates (u, v, z) (see Fig. 1),
taking the source as an ultrarelativistic point charge travelling down the pipe, parallel to its axis, located arbitrarilyin (u1 ,v1 ,0). On the cross-section the interface between
the vacuum and the metal wall is the ellipse of equationu = u0 . With the observation that, due to causality, any
field must vanish for z > 0, the Fourier transform of theelectric and magnetic longitudinal fields in the vacuum, canbe written as:
Ẽz =

+∞


An cosh nu cos nv +

n=0
+∞


cB̃z =n=0+∞


Bn sinh nu sin nv

n=1
+∞


Bn cosh nu cos nv −n=1

An sinh nu sin nv(3)
where An and Bn depend on k and are determined by imposing the continuity of the fields Ẽz , B̃z , Ẽv , B̃v . In thevacuum, the transverse fields behavior shows a coupling
between different modes. In detail the components cos nv,

Proceedings of FEL 2007, Novosibirsk, Russia
sin nv depend on the (n − 2)-th, n-th and (n + 2)-th coefficients. Maxwell’s equations in the metal wall, solved byseparation of variables, lead to the angular and radial Mathieu functions [5]. For small skin-depth values, the seriesyMetal
Vacuum q

u=u0

v=cz
z

o x

f2

u
q (v1 ,u1)

o z

f1

a x

Vacuumz<0

The Lorentz force due to the leading charge experienced,
by a trailing charge qt travelling down the pipe at the speedof light with coordinates (u, v, z) is:
FL = qt Ez
FT = qt [û (Eu − Bv ) + v̂ (Ev + Bu )]

y
b
v

z>0

i ∂ ẼzẼv + cB̃u = − hk∂v

Figure 1: Elliptic cylindrical system of coordinates and thesource point charge.
of products of Bessel and Hankel functions for the Mathieu radial functions can be approximated and the boundary
conditions yield a tridiagonal infinite linear system for thecoefficients An and Bn which can be truncated to calculate
explicitly the coefficients. Since in the coefficients matrix
there is no relation between An and Bn , neither between
A2n and A2n+1 nor between B2n and B2n+1 , the wholesystem can be split up in four independent parts. To solvea truncated tridiagonal subsystem for the first M + 1 coefficients, the following formula can be used:⎧c
TM⎪⎪ XM =
⎪
⎨
CM
(4)
⎪
⎪
Tnc − zn Xn+1⎪
⎩ Xn =
n = 0..M − 1Cnwhere:

Next the elliptic cross-section resistive wake function isplotted for several values of the ratio a/b, including thelimiting cases a/b = 1 and ∞, using the materials specified in Table 1.
Table 1: Conductivity and relaxation time for Al and Cu.
Aluminium
Copperσ [Ω−1 m−1 ]4, 22 × 107
6, 45 × 107
τ [s]8, 00 × 10−15 2, 70 × 10−14

As shown in Figs. 2 and 3 the peaks of the longitudinal wake functions continuously decrease from the circular case to the parallel plates. The wake functions obtainedusing copper as material for the vacuum chamber present
more oscillations which are due to the higher electron relaxation time.

n=0
n = 1..Mn = 1..Mn=0
n = 1..M4000

sn , dn , zn and tn are yet to be defined for each kind of coefficient, but in the case of the longitudinal wake-function,
if the leading charge is on axis, only the A even subsystem
is excited and all other coefficients are zero. Denoting witha and b respectively the major√ and the minor half axis of
the cross-section, with l = a2 − b2 the half focal lengthand h = l cosh2 u − cos2 v the metric, the following
formula for the A even subsystem has been obtained:

3000

m

Tnc =

sn−1
Cn−1
t0
c
tn − Tn−1
Dn

The transverse force is obtained numerically inverting the
term:


c∂ B̃z
∂ Ẽz
i
û
− v̂
(8)
hk
∂v
∂v

1000

0

-1000

-2000
2

dn = − coshikl2nu0

sinh (4n+2)u0(4n−2)u0+ sinh8(2n−1)8(2n+1)+

ikl2 (1+δn0 ) sinh (4n+2)u08(2n+1) cosh 2(n+1)u0
sinh (4n+2)u0
ikl2
8(2n+1) cosh 2nu0
q
1 cosh 2nu1
− (1+δn0 )π0 cos 2nv
cosh 2nu0

0..M

0

10

20

30

40

50

60

70

80

Figure 2: Longitudinal resistive wall wake functions foraluminium made walls and b = 3 mm.

cosh 4nu0
λ cosh 2nu0
+l cosh u0 λk cosh2nu0 +
k

zn =
tn =
n =

Aluminiumz [mm]+ ki + 2ik
λ2 2n sinh 2nu0 +sn =b = 3 mm
a/b = 1a/b = 2a/b = 4a/b = ∞

2000

pC

Dn =

(7)

i ∂cB̃zẼu − cB̃v = + hk
∂v

V

Cn =

d0
sn−1 zn−1
dn −
Cn−1

(6)

where L denotes longitudinal and T transverse. The longitudinal wake function is obtained by numerically inverse
Fourier transforming Ẽz in (3), while using the relations:

Metal

Metal

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Surface Roughness Wakefields(5)

The interaction between the beam and the surface roughness of the undulator vacuum chamber is yet another sourceof energy spread which could impact FEL process. To a

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Proceedings of FEL 2007, Novosibirsk, Russia

4000

400
b = 3 mm
a/b = 1a/b = 2a/b = 4a/b = ∞

1000
0measurement

300
200

h [nm]

pC

2000

V

m

3000

0

-1000
-2000
-3000

low-frequency

hrms= 252.41 nm

100

-100

Copper
0

20

40

60

80

100

120

-200

140

z [mm]

Figure 3: Longitudinal resistive wall wake functions forcopper made walls and b = 3 mm.
first approximation the surface roughness makes the vacuum chamber behave like a disk-loaded cavity; there will
be a continuous change of energy between the beam andwhat is called a synchronous field mode [6, 7]. Furthermore, if the roughness can be approximated by a collection of bumps whose tangent to the smooth wall is small,there will be one more contribution to the total roughness
wakefield coming from their individual impedance, averaged over a certain distribution function [8].
Surface analysis: Several AFM surface scans (seeFig.4) have been carried on a spare vacuum chamber of the
ELETTRA storage ring [9] in order to obtain informationon the average peak height and periodicity of the roughness.

high-frequency

hrms= 39.54 nm
0

20

40

60
z [μm]

80

100

120

Figure 5: A Gaussian filter is applied to the real surface
profile (red) in order to detach its low (blue) and high (orange) frequency components
Table 2: Overview of the corrugation parameters.
Componentλhrms
AR = λ/hrms
low-frequency
30 μm 250 nm
120
high-frequency 10 μm 40 nm
250

the Stupakov’s statistical (small-angle) model [8].
Surface wakefield in circular cross-section pipes:
Within the modified resonator model proposed by Stupakov [7], the roughness wake function has a cos-like variation of constant amplitude and is defined as:
46

Z0 c hrms κ
4π
64w|| (z) =cos k0 z(9)where κ = 2π/λ, b is the vacuum chamber radius and k0 =
κ/2 is the rough synchronous mode, while the statisticalmodel predicts a damped wake function with a singularity
at z = 0:
w|| (z) =Z0 c h2rms κ2 1 ∂ cos 12 κz + sin 12 κz
√
√
(10)
4π
b
2 π ∂zκz

Using the parameters in Table 2, both wake functions areplotted comparatively for b = 3 mm in Fig. 6.
Figure 4: Measured 3D surface profile.

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50

pC

m

0
- 50
- 100

V

First, it is necessary to distinguish between the longand short range variation of the surface-vacuum boundary.
Thus, a longitudinal scan over 120 μm has been filtered(Gaussian filter of 15 μm standard deviation) separating out
a low-frequency surface component from a high-frequency
component, (see Fig. 5). Fourier transforms of these twocomponents reveal their frequency content ν = λc which
together with the rms height hrms makes it possible to fit
them to a sinusoidal corrugation model. It turns out that the
low frequency content can be treated within the resonatormodel with some corrections due to the very small size ofthe roughness height [7], while the high frequency component, due to its higher aspect ratio, can be considered within- 150

low-frequency- 200

high-frequency

- 250

0

50

100

150

200

250

z [mm]

Figure 6: Surface roughness wake functions.

300

Proceedings of FEL 2007, Novosibirsk, Russia

WAKEFIELD INDUCED ENERGYSPREAD

WEPPH019

CONCLUSIONSIn this section some results concerning the induced energy spread for the medium bunch configuration of FERMIFEL [10] are presented considering contributions from theresistive wall and surface roughness wakefields.

Table 3 lists the maximum values of the energy spreadin the useful part of the bunch (200 μm for the mediumbunch and 350 μm for the long bunch). If the FERMI
undulator would have vacuum chamber surface comparable with the one analyzed above, that is for AR = 120.
In conclusion, it is recommended for the undulator vac-

Contribution of the electrical resistivity
Considering only Al for the vacuum chamber walls and
AC conductivity, Fig. 7 shows the induced energy spreadobtained through convolution between the circular/elliptic(a/b = 6)/rectangular (parallel plates) cross-section resistive wake functions and the longitudinal bunch profile mentioned above. Therefore, the rectangular cross-section withrounded lateral sides proposed in the FERMI CDR [10] canbe replaced by an elliptic cross-section with a/b > 6 without changing the energy spread.
60
40

medium bunchm0

DE keV20-20

circular, b = 3 mm

-40

elliptic, b = 3 mm,a /b = 6-60parallel plates, b = 3 mmuum chamber to be made of Aluminium, have a rectangularor elliptic cross-section. In what concerns the rectangularcross-section roughness wakefield, calculations are on theway and preliminary results show that the induced energy
spread is 35-40 % lower than for the circular cross-section
case. As for the surface, when AR = 120, the roughness
induced energy spread accounts for about 17 % and 12 %of the resistive induced energy spread, respectively for the
medium and long bunch.

REFERENCES

-80
0

50

100

150

200

250

300

z [mm]

Figure 7: Resistive wall induced energy spread.

Convoluting separately the wake functions given by (9)and (10) with the medium bunch profile [10] the energy
spread is obtained as shown in Fig. 8. As it can be seen, at
4[1] K.L.F. Bane and G. Stupakov, “The Short Range Resistive
Wall Wakefields”, SLAC/AP-87, June 1991.
[2] A.W. Chao, “Physics of Collective Beam Instabilities inHigh Energy Accelerators”, John Wiley & Sons, Inc. 1993.
[3] H.Henke and O.Napoly, “Wake Fields between two Parallel
Plates”, CERN/LEP-RF/89-71 CLIC Note 103, 1989.

Surface roughness contribution[4] K.L.F Bane and G. Stupakov, “Resistive Wall Wakefield in
the LCLS Undulator Beam Pipe”, SLAC-PUB-10707.
[5] P.M.Morse and H.Feshbach, “Methods of Theoretical
Physics”, McGraw-Hill, New York, 1953.
[6] A. Novokhatski and A. Mosnier, “Wakefields of shortbunches in canal covered with thin dielectric layer”, PAC
1997, p.1661.

medium bunchm

2
D E keV

Table 3: Estimated energy spread for the FERMI FEL undulator.
Sourceshort bunch
long bunch
Resistive wall
11.71 keV/m 9. 35 keV/m
Surface roughness 1.73 keV/m
1.17 keV/m
Total
13.44 keV/m 10.52 keV/m

0[7] G.V. Stupakov, “Surface roughness impedance”, SLACPUB-8743, December, 2000.

-2[8] G.V. Stupakov, “Impedance of small obstacles and roughsurface”, Phys. Rev. ST-AB, Vol.1, 064401 (1998).
low-frequency

-4
0

50

100

150

high-frequency

200

250

300

z [mm]

Figure 8: Roughness induced energy spread.

[9] A. Gambitta et al., Experience with aluminium vacuum
chambers at Elettra, Proceedings of EPAC 2000, Vienna,
Austria;[10] FERMI@Elettra Conceptual Design Report, to be published.

the core of the bunch the contribution of the low-frequency
roughness component predominates over the contributionof the high-frequency roughness component both falling inthe same range of magnitude.
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WIDE BAND SEEDING AND WAVELENGTH COMPRESSION
Tsumoru Shintake, RIKEN/SPring-8, 679-5148 Japan
Abstract
The “wavelength compression” has a potentiality togenerate seeding signal at the nano-meter wavelength bysqueezing optical wavelength of the visible laser beam ona high energy electron beam. Applying energy chirp onthe incoming electron beam and overlapping laser beam
to produce micro-period energy modulation at optical
wavelength, the velocity modulation can be converted
into density modulation at shorter wavelength during thebunch compression in a chicane. Using 255 nm 4th
harmonic YAG laser as modulation signal, and if wecompress bunch length 20 times, we can generate
coherent signal below 10 nm. By cascading multiple
bunch compressors, higher compression ratio will beobtained. To go X-ray wavelength, we may use HGHG
scheme after the wavelength compression. Sincecompression factor is variable, it becomes tuneable
coherent source at X-ray wavelength, which is suitable toseeding the X-ray FELs.
Using femto-second laser at the modulator, it will
generate atto-second pulse at short wavelength.

MOTIVATION
SASE-FEL: Self-amplified Spontaneous Emission Free
Electron Laser, as it is named, the spontaneous radiation(noise power) is amplified in the long undulator line. If
the undulator is long enough, power level reaches tosaturation. Since its power level is extremely higher thanconventional X-ray sources, even higher than 3rd
generation light sources, many new scientific applications
are expected with using this source. Also the short pulsefeature in femto-sec range is expected to be an important

Figure 1: Laser optical modulation and wavelength
compression. Applying both the energy chirp at rf
wavelength and micro-period energy modulation at optical
wavelength using laser beam, the modulation pattern canbe compressed into short wavelength during bunch
compression, which provides seeding signal to thedownstream undulator. By combining with HGHG
scheme in the downstream undulator line, an X-ray seeded
FEL will be realized.
___________________________________________#

shintake@spring8.or.jp

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feature for analysing fast chemical and physical reactionof condensed matter.
However, since SASE-FEL process starts from thespontaneous radiation, the resulting saturated radiation
power varies shot-by-shot. And most importantly, there
are many longitudinal modes, similar to old fashion rubylaser, temporal profile has many spikes, thus longitudinalcoherence is quite limited.
If we seed a coherent signal from upstream undulator,
the seeding signal will be amplified and saturated. It
becomes (1) fully coherent, (2) temporally single-mode,(3) stable energy in pulse-to-pulse and (4) power level
controllable. These features are favourable to all kind of
scientific applications. Therefore, various proposals havebeen made on seeding schemes, including HGHG,
TUHG,[3,4,5]. G. Lambert reported first observation of
amplification of seeded FEL using higher harmonic
generation in gas [HHG] at 160 nm in SCSS test
accelerator[7].
They are also promising approach to generate coherent
radiation at nano-meter wavelength. However they are notwavelength tuneable. In actual machine, a small
wavelength shift was observed experimentally at DUV
FEL at BNL[6]. However the observed wavelength shift
was as low as 1%.
For fully tuneable seeding, the wavelength compression
scheme was originally proposed by the author in 1999[1].
As shown in Fig. 2, a modulator, a short undulator was
assumed as energy modulator, where a laser beam wasintroduced from upstream[2]. The velocity modulation iscreated through Et ⋅ vt coupling in the undulator. After theundulator, the electron bunch is accelerated at off-crest
phase to apply energy chirp, then the bunch length iscompressed. After accelerating the beam, the modulated
electron beam is fed into undulator to generate coherent
radiation. This scheme requires many hardware
components, and also spontaneous emission in the
upstream undulator cause additional energy spread on theincoming electron beam.
In the previous paper[2], the author proposed a scheme
to generate energy modulation at optical wavelength
using the focal point laser field. However, the laser beam
has to be focused into a very small spot, and the fractionof overlapping the laser beam to the electron beam isfairly small, as a result overall modulation efficiency
becomes small.
To overcome this difficulty, the author proposes a newscheme which provides higher coupling efficiency.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH021

Figure 2: Original wavelength compression scheme[1], which uses independent undulator at upstream as the opticalenergy modulator, followed by short accelerator to adopt energy chirp. Dispersive section provides two functions ofa bunch compression and energy-to-density conversion of optical modulation.

BASIC CONFIGURATION
Figure 1 shows the basic configuration of the newseeding scheme. We apply energy chirp on the incoming
electron bunch in the upstream accelerator, and add
energy modulation at optical wavelength at the entranceof the chicane, then compress the bunch length throughthe chicane. At the same time the velocity modulation canbe converted into density modulation at short wavelength.
The compression factors for the bunch length and themodulation wavelength are exactly same. After
accelerating the beam to higher energy, and sending into
undulator, the bunch will radiate coherent signal. If the
wavelength of undulator radiation is tuned to thecompressed modulation wavelength, the undulator willradiate coherent radiation at super radiant mode.

MODULATION PATTERN SMEARINGElectron beam has energy spread, which limits thisseeding scheme. The longitudinal diffusion distanceduring acceleration between point-1 and point-2 is given by[2]Δz =Δγ ⎛ 1 1 ⎞⎜ − ⎟γ ′ ⎝ β1 β 2 ⎠γ ′ = eEz / m0 c 2,(1)Δγ = eVspread / m0 c 2For example, to accelerate beam up to 8 GeV (β2 = 1) on
20 MV/m field gradient ( γ ′ = 39.1), assuming the energy
spread 30 eV, which is much higher than the thermionicenergy (74 meV,), to make the diffusion distance being
lower than 1 nm, we found the threshold energy 14 MeV.
If we locate our laser modulator at beam energy higher 14
MeV, we may keep density modulation pattern at 1 nm.
The betatron oscillation of each electron inside thebunch also causes path difference and smearing effect.
Average path difference can be estimated byΔz β =

2ε n

π γ
2

⋅

L

β

(2),

Assuming, ε n = 1× 10−6 π mm ⋅ mrad , L = 300m, β = 30m, the path difference becomes 2 Å. This is negligibly
small for 1 nm modulation.
The space charge effect also contributes to smear out thedensity modulation. This effect can be estimated by theelectron plasma frequency:

ω p = γ −3/ 2
Figure 3: Overlapping laser beam and electron beam withoblique angle at the entrance of the magnetic chicane, theelectron beam energy is modulated at optical wavelength.
Since the incoming beam has energy chirp, the density
modulation pattern is longitudinally compressed into
short wavelength together with bunch length being
compressed. By cascading multiple chicanes, we obtainhigh compression ratio, for example 1/10 x 1/10 = 1/100.

eρ0
meε 0

(3),

where ρ 0 is the electron density. For example, assuming
beam current 100 A at 50 MeV, β-function 10 m, beam
size 0.3 mm, the plasma frequency becomes 25 MHz.
After travelling quarter plasma-wavelength, the density
modulation becomes zero, i.e., after 3 m travel. It is
known that the density modulation will recur again after
quarter-wavelength. Within this length, we may acceleratebeam to higher energy, where the plasma wavelength

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Proceedings of FEL 2007, Novosibirsk, Russia

becomes longer, thus we may keep density modulation.
If we locate modulator at 500 MeV, the quarter plasma
wavelength becomes 100 m. This is long enough tomaintain the density modulation.

CHICANE LASER MODULATIOR
Fig. 4 shows interaction of electron beam with laser field.
Here we assume the laser beam has Gaussian
distribution, its transverse size is w0 . The intensity andfield distributions can be expressed as
2

2

2

/ w02

I = I 0 e −2 x / w0 ,E = E0 e− x,smaller than the synchronous wavelength. From Eq. (8),(4)

We consider one electron passing the laser beam withslope angle of α. The laser beam polarization is in theplane of the drawing. The energy gain of the electron
during the passage is given by the following integration.
∞∞

ΔW = ∫ E ⋅ ds = ∫ Ex ⋅ dx−∞∞

= ∫ E0 ⋅ e,(5)cos(ωt − kz + φ )dx−∞

where φ is the phase of laser field. Assuming the electron
velocity is close to light velocity, the phase term becomesω⎛⎞− k ⎟⋅ z⎝ β c cos α⎠ , (6)kz= 2 (1 + γ 2α 2 ) = k ′z
2γ

ωt − kz = ⎜

k
2γ
, (7)
(1 + γ 2α 2 ), λs = λ022γ
1 + γ 2α 2
2The energy gain becomes,⎧⎪ ⎛ ks l0 ⎞2 ⎫⎪ΔW = π E0 w0 cos φ ⋅ exp ⎨− ⎜⎟ ⎬ , (8)⎩⎪ ⎝ 2 ⎠ ⎭⎪Where l0 is the interaction length of an electron to crossthe laser beam: l0 = w0 / α . In order to obtain
substantial modulation, the crossing length has to be
Table-1: Small and large angle cases.
Crossing
Small Angle
Large Angle
Angle
α = 1/ γα >> 1/ γ
Synchronous
Wavelength
Required
Laser Size
Modulation
EnergyFEL Technology I

380

λs = γ λ02

γλπΔW = π E0 w0w0 <λs = 2λ0 / α
w0 <

(9)

In this condition the modulation energy becomes
ΔW ~ E0 w0 . Using Eqs. (7) and (9), we find thecondition for the laser waist size,

2λ0

γ 2α
π 1 + γ 2α 2

(10)Due to the diffraction effect, the laser size expands along
its path. If the electron trajectory stays within the laser
field longer until the laser spot size becomes larger, theintegral energy gain will cancel and become small.
Therefore, the electron trajectory has to cross the laser
beam with enough angles to make its interaction length
smaller than the diffraction angle.

α>where k’ is the synchronous wave number. It iscorresponding to the wave number of undulator period,and γα is the K-parameter.

ks =

ks l0
λ
< 1, l0 < s ,2πw0 = α l0 <−∞− x 2 / w02

Figure 4: Electron beam passing through laser beam withoblique angle receives energy modulation.

λ0

w0

(11)

Additionally the electron beam size has to be same size or
smaller than the laser size
σ 0 w0(12)
Table-1 summarizes those conditions for two cases. As
seen in the table, for high energy, the required laser size
becomes larger, thus easier to focus the laser beam, while
it request smaller crossing angle. On the other hand, forlower beam energy, the crossing angle becomes large, but
we need to focus laser beam into small size. In practicaldesign of the bunch compressor, to obtain enough R56
parameter, the deflection angle becomes much larger than
1/γ. In this case, α>> 1/γ, the synchronous wavelengthand laser size and also the energy gain becomes nonenergy dependent function. Therefore this system hasvery wide energy bandwidth.

REQUIRED ENERGY CHIRP AND
OPTIMUM MODULATION
For the optical modulation the optimum condition is[2],

2

2λ

πα
ΔW = π E0 w0Vmod−1= m ⋅ ( kmod R56 ) .
E0

(13)

Proceedings of FEL 2007, Novosibirsk, Russia
Table-2: Example laser modulation system for two
difference beam energy.
Target Wavelength10
λ2 (nm)Compression Ratiom
100:1
Laser Source1060
λ1 (nm)Beam Energy
E (MeV)50
100γ
Crossing Angle10
α (mrad)Synchronous Wavelength10
λs (mm)Interaction Length3
Li(mm)
Laser Spot Size
32
w (μm)
0Electron Beam Size(μm)

Laser Power
Field Intensity
Energy ModulationWatt
E0 (MV/m)
ΔW (eV)

100
β=1m
100
6
200

At this condition, the compressed modulation has the
maximum contrast. For example, if we compress bunch
length by 100 times at 50 MeV, m = 0.01, with R56 = 10mm, and λmod = 1064 nm, the required modulation
becomes Vmod = 10 eV . This value can be easily
provided by the laser modulation. However, if the energy
spread is large, the modulation pattern will be totallysmeared out. The energy spread has to be smaller thanmodulation energy.
There are experimental measurements on energy spreadon electron beam from RF guns. Typically, energy spreadright after the gun is about 10 keV or higher. This is muchlarger than the thermal energy spread. This is due to thespace charge effect near by the cathode. In the case of therf photo-cathode gun, the emitted electron beam from thecathode is already bunched, and its has high peak current
value ~100 A. When the electron starts from the cathode,image charge on the cathode pulls the electron back andlowers the effective acceleration gradient. This effectvaries along its radial position within the beam. Therefore,
an electron emitted from the centre of the cathode andfrom the beam edge feels different field gradient, as aresult, it cause energy spread.
On the other hand, in the case of the thermionic DC gun,all electrons gain the same energy, in principle. Only the
self-potential gives energy difference, while it is fairly
small. At 50 MeV, for 1 nC, 10 psec, the self-potential
difference is 12 eV on the electron rest frame. We needfurther careful discussion on how this potential energy
affects on particle motion on the laboratory frame.

DISCUSSIONS
The author has not yet completed quantitative estimation
on various effects concerning to the cross-coupling in thebunch compressor, beam divergence, energy spread,
photo-emission and CSR effect. Therefore the discussions
below are only conceptual.

WEPPH021

The seeded FEL does not require high peak current.
If we can lower the peak current, all problem
associated with the space charge will be solved.
Recently, strong OTR radiation was observed at
visible wavelength in the LCLS injector at SLAC
when the beam was compressed at the first chicane
magnets[8]. If the laser on the photo-cathode has
intensity modulation, which generates density
modulation on the emitted electron beam. When thebunch length is compressed in the chicane, themodulation wavelength was compressed frommicron-meter range to visible wavelength, as just we
discussed in this paper. Further careful analysis isnecessary to proof this hypothesis.

CONCLUSIONS
New optical modulation scheme has been proposed inthis paper. If we apply velocity modulation at optical
wavelength, and compress it together with bunch length,
we may obtain density modulation at shorter wavelength.
Further studies are required on non-linear field in bunch
compressor, cross-coupling (R15, R16), non uniform
velocity distribution in bunch, energy spread due toradiation excitation, etc.
SCSS test accelerator is currently running at 50 nm with
SASE-FEL mode. It will be possible to install a laser
modulator in our test accelerator to demonstrate velocity
modulation, and demonstrate colour change in OTR
radiation, and compress the wavelength by ten times inbunch compression to seed FEL at 50 nm range.

REFERENCES[1] T. Shintake, “wavelength compression”, KEK
Internal Report, AccelLab-99-1.
T. Shintake, "new idesas for future sources", CERN
Accelerator School Brunnen 2-9, July 2003.
[2] T. Shintake, “Focal point laser-field as optical seeder”,
proc. FEL2006, Berlin, Aug. 2006.
[3] L.-H. Yu, Phys. Rev. A44 (1991) 5178
[4] S. G. Biedron et al., "Modula approach to achieving
the next-generation X-ray light source", Nucl.
Instrum. Method A475 (2001) pp.401-406[5] Timur Shaftan and Li Hua Yu, "High-gain harmonic
generation free-electron laser with variablewavelength", Phys. Rev. E 71, 046501 (2005)[6] T. Shaftan et al., "Experimental Demonstration of
Wavelength Tuning in High Gain Harmonic
Generation Free Electron Laser", Proc. FEL 2004, pp.
282-284, Trieste Italy[7] Guillaume Lambert, “First Lasing in Seeding
Configuration at 160 nm Using High order Harmonic
Generated in gas on the FEL of the SCSS Prototype
Accelerator”, this conference.
[8] D. Dowell et al., “Commissioning results of the SLACLCLS gun”, this conference.

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Proceedings of FEL 2007, Novosibirsk, Russia

FEASIBILITY TEST OF LASER-INDUCED SCHOTTKY-EFFECT-GATEDPHOTOCATHODE RF GUN
H. Tomizawa, Accelerator Division, Japan Synchrotron Radiation Research Institute(JASRI/SPring-8), Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan
M. Kobayashi, Research & Development Division, Nanophoton Corporation
A-509, Center for Advanced Science and Innovation, Osaka University, Osaka 565-0871, Japan.
Abstract
We propose a laser-induced Schottky-effect-gatedphotocathode RF gun using Z-polarization of the laser
source. This concept of laser-induced Schottky emission
can be applied to a photocathode DC gun (even for apolarized electron source). Radial polarized laser
propagation modes exist theoretically and were recently
generated practically. Focusing a radial polarized beamon the photocathode, the Z-polarization of the laser isgenerated at the focus point. The generated Zpolarization field can exceed an electrical field of 1
GV/m easily with fundamental wavelength fromcompact femtosecond Ti:Sa laser systems. According toour calculations (NA=0.15 60-% hollow ratio, inside-out
Gaussian beam), the Z-field of 1 GV/m needs 1.3 MW atpeak power for the fundamental (790 nm) and 0.32 MW
for the second harmonic generation (SHG). In the fieldof 1 GV/m, the work function of copper cathode reduces~2 eV. The quantum efficiency is pessimisticallyestimated to be ~10-2 % at SHG by the Schottky effectassociated with the 1 GV/m. This Schottky effect can beused as a gate of the photo-emission process. We report afeasibility study of this new concept of photocathode.

INTRODUCTION
There are three well-known types of electron guns; thethermionic gun, field emission gun, and photocathodegun. They are widely used for many applications. The
future light sources based on linear accelerators such Xray FEL [1,2,3] and ERL [4] required high brightness
electron sources. One of the most promising candidates
for such an electron source is a photocathode RF gun.
The photocathode RF gun needs a UV-laser source(~266 nm) for a long-lived metal cathode like copper andeven for a higher quantum efficiency (QE) cathode suchas Ce2Te. At SPring-8 in collaboration with Hamamatsu
Photonics K.K. a diamond cathode has been developed
as the future transparent cathode candidate [5]. The
diamond cathode is a robust and high QE cathode.
However, it requires a laser wavelength below 197 nm
for acceptable QE. For a robust cathode like copper anddiamond, we need UV-laser light due to their high work
functions. Consequently, the laser system becomes larger
and complex. To make the laser source compact, we needto find a cathode with a lower work function and highQE. However, such a high QE NEA-cathode requires anultra-high vacuum (< 10-8Pa) and does not have a longlife time.
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One solution to make the work function lower is to
apply a high field on the cathode. In the field of 1~2
GV/m, the work function of the copper cathode reduces
2~3 eV. To achieve such a high field (~1 GV/m) on thephotocathode, the tungsten needle photocathode, thephoto-assisted field-emission, was proposed and tested[6]. The dependence of quantum efficiency on a highelectric field was investigated using a tungsten needle(radius: ~1μm) photocathode irradiated by the third
harmonic generation (THG) of a Nd:YAG laser (353 nm)
whose photon energies were lower than the work
function of tungsten. The obtained QE of the needle tip isfound to be proportional to the >10th power of theelectric field over 500 MV/m, and it reached up to 3% at
about 800 MV/m. This observed field-enhancement of
QE is qualitatively explained with a field-emission
process including the Schottky effect and photoexcitation. However, such a needle cathode tip becameround and broken in the cavity during rf conditioning.
Therefore, we started to investigate with a plane-fieldemitter assisted by laser radiation field. We have indirect
evidence of such a laser field effect through comparison
between normal and oblique incidences to the cathode. It
is well known that the oblique incidence obtains higher
QE than normal incidence. In the oblique incidence, themore intensive the laser illuminating the cathode, thehigher a QE we obtain. It cannot be explained only with
Brewster’s angle. However, we have to think about
multi-photon absorption in the case of intensive laser
focusing on the cathode. The oblique incidence makes
the laser spot elliptically larger on the cathode. However,
we can obtain a higher QE. It indicates that the laser field
can assist the Schottky effect on the cathode.
Radial polarized laser propagation modes exist
theoretically and were recently generated practically. The
radial polarization beam is a superposition of π/2 phaseshifted TEM01 and TEM10 mode in the case of apolarisation direction vertical to each other. Focusing aradial polarized beam on the photocathode, the Zpolarization of the laser is generated at the focus point.
The generated Z-polarization can exceed an electricalfield of 1 GV/m easily with fundamental wavelengthfrom compact femtosecond laser systems. On the other
hand, focusing an azimuth polarized beam on thephotocathode results in zero Z-polarization field.
Comparing the radial and azimuth polarization withfocusing, we conduct a feasibility study of the laserinduced Schottky-effect on the photocathode.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH022

PRINCIPLE OF Z-POLARIZATION
Principle of Z-polarization generation
Focusing a radial polarized beam on the photocathodeas shown in Figure 1, the electric field of the laser isgenerated in the laser propagating direction (Z-direction)at the focus point. The Z-field oscillates with a periodic
time of ~2.6 fs at the fundamental Ti:Sa laser (~790 nm).
Roughly estimating in the case of a metal cathode, laser
radiations (wavelength: λ) enter into the cathode surface
with a depth of ~λ/20, and photocathode response is <10
fs. If the Schottky-effect-induced Z-field is large enough,we expected that electrons would make oscillations with
the Z-field frequency on the outermost surface of themetal cathode and are extracted with the external electricfield of the RF cavity. Note that the perfect backreflection on the cathode with normal incidence cancels
out the Z-field generated by laser radiation.

Figure 1: Principle of Z-polarization field on the cathodegenerated from radial polarization

Reflection ratio of cathode candidates
In order to generate the electrical field in theperpendicular direction on a metal cathode, we have toselect a combination of metal cathode material and laser
wavelength. Comparison among laser wavelength
dependencies of reflectivity with different mirrorfinished metal surfaces is shown in Figure 2. Reliablecandidates for the combinations are silver with the THG
of Yb:fibre laser (~350 nm), copper with the SHG ofTi:Sa laser (~395 nm), and aluminium with thefundamental of Ti:Sa laser (~790 nm). The reflection
ratio of the first combination is ~10 %, the second ~30 %,the last ~75%. For the first test run, we chose the second
combination with copper illuminated by the Ti:Sa SHG.

Figure 2: Laser wavelength dependencies of reflection
ratio with different mirror-finished metal surfaces

Figure 3: Several divided waveplates manufactured by
Nanophoton Corporation: (a), (b) 8-divided waveplate
and the direction arrangement of optical axes in eachsegment, (c) 4-divided waveplate with assembling 4 cutsof waveplate, (d) 8–divided waveplate with growing
photonic crystal as a function of waveplate in eachsegment on single base plate.

Radial polarization beam generator
The radial polarization fundamental mode is
generated from a combination of Hermite-Gaussianmode TEM01 and TEM10 [7]. However, directly lasing
with TEM01 mode is not practically simple. Therefore,
we chose a simple divided waveplate as shown in Figure
3 to generate the radial polarization from a conventional
linearly polarized beam. We investigated the divided
number dependency of Z-field at the focus point
generated with the divided waveplate. The intensity
distributions of Z-polarization intensity |E|2 generated
with waveplates with different division numbers of are
shown in Figure 4. In the case of more than eight
divisions, it shows no significant difference from the Zfield intensity generated from ideal radial polarization.

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focusing optics. The Z-polarization field is proportionalto NA raised to fourth power. The laser diameter before
the final focusing lens should be as large as possible. The
focus length should be as short as possible.
To make NA as large as possible, we designed ahollow laser beam generator with an axicon lens pair.
The Z-field dependency of the hollow laser beam ratio isshown in Figure 6 in the case of the Gaussian beamincidence to the axicon lens pair. In our feasibility test
set-up shown in Figure 7, the diameter of the electron
beam is roughly 18 mm. Considering the vacuum duct
inner diameter, realistically R0=30 mm and R1=18 mm.
In the case of Rratio=R1/R0=60%, the hollow beam makes
a 10 times higher Z-field on the photo cathode thanGaussian beam incidence without an axicon lens pair.
Figure 4: Using divided waveplates, the intensity
distribution of Z-polarization intensity |E|2: (a) 2-divided,(b) 4-divided, (c) 8-divided, (d) 16-divided, (e) 32divided, (f) perfect radial polarization (n: infinity). White
scale bar in (f) is 7.5μm @790 nm, NA=0.1 (Flattop).

Z-polarization ratio with divided waveplate

Ratio to perfect radial polarization( n → ∞)The divided number dependence of the radialpolarization ratio to ideal radial polarization is shown in
Figure 5 regarding the simulation results of Zpolarization at the focus point compared with analyticalunder- and over- estimation of the radial polarization
ratio at the focus point.
In the case of the 8-divided waveplate, the radialpolarization ratio to ideal radial polarization is 95% aswith the simulation results of Z-field at the focus point.

Figure 6: Z-polarization field dependency of hollow laser
beam ratio (Gaussian beam incidence to axicon lens pair)

1
0.95
0.9

Z-polarization field ratio(Simulation)

0.85
0.8

2n sin(π/n) / 2π
(Radial polarization ratio）

0.75
0.7

cos(π/n)/cos(0)（Minimum radial field ratio ）

0.65
0.6
4

8

16

32

65536

Divided Number: nFigure 5: The divided number dependence of radialpolarization ratio to ideal radial polarization

Z-polarization electric field dependency of
optical characteristics and parameters
To maximize the Z-polarization field, the opticalparameters should be optimized. The Z-field is reciprocal
proportional to the square of the laser wavelength. This
indicates that the SHG can generate a four-time stronger
field than the fundamental at the focus point. Utilizing
the SHG is totally efficient in Z-field generation, because
the SHG conversion efficiency reaches up to 50%. The
numerical aperture (NA) is characteristic of the final
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Figure 7: Experiment set-up for Z-polarization RF gun
with hollow laser beam incidence optics

TYPE OF LASER INCIDENCE TO
CATHODE
It is possible to make several configurations of normal
incidence to the cathode. Making NA larger, backward
illumination with the transparent cathode can make ashort working distance (see (a) in Figure 8). For normal
incidence to the conventional reflective cathode, it isnecessary to use hollow laser beam incidence as shownProceedings of FEL 2007, Novosibirsk, Russia

in Figure 7. The hollow inside-out Gaussian laser beam
is generated by an axicon lens pair, and then reflected at
the hollow mirror for normal incidence and finallyfocused to the photocathode with a hollow lens in a
vacuum. This Schottky effect can be used separately as agate of the photo-emission process. It is possible toseparate the Schottky-gate laser pulse and photoexcitation source as shown in (b) in Figure 8. In the caseof a polarized electron source with GaAs, thefundamental is used as a photo-excitation source, theSHG as a gate pulse. However, we have to take into
account the time response of the cathode. Several
improvements of response time down to 2 ps for GaAs
were performed [8]. If the diffusion model is in good
agreement in this case, making the cathode even thinner,
it is possible to make the response time less than 1ps.

Figure 8: Z-field gun set-ups for different type cathodes

Figure 9: Concept of feasibility test for Schottky effectdue to Z-polarization at focus point with the comparisonof Z-fields between radial and azimuth polarization

FEASIBILITY TEST PLAN
Up to now, we have only discussed focusing radialpolarization to maximize the Z-field on the photocathode.
On the other hand, focusing an azimuth polarized beam
makes Z-polarization zero. We conducted a feasibility
study of the laser-induced Schottky-effect on thephotocathode with the comparison between radial andazimuth polarization shown in Figure 9. In thisexperiment, the linear polarization of the incidence laser
switches only from vertical to horizontal. In this method,
we can check just the Z-field effect separated from themulti-photon process. Comparing the photo-emission

WEPPH022

process with these polarizations, we make clear thefeasibility of this new concept of photocathode.

SUMMARY AND DISCUSSION
We discussed a new concept of photocathode with Zpolarization and showed the method for its feasibility test.
Focusing a radial polarized beam on the photocathode,the Z-polarization of the laser is generated at the focus
point. The generated Z-polarization can exceed anelectrical field of 1 GV/m easily with the fundamental
from compact femtosecond Ti:Sa laser systems.
According to our calculations (NA=0.15, 60-% hollow
ratio, inside-out Gaussian beam), the Z-field of 1 GV/mneeds 1.3 MW at peak power for the fundamental (790nm) and 0.32 MW for the SHG (395 nm). In the field of
1 GV/m, the work function of the copper cathodereduces ~2 eV.
In our design of the Schottky-effect-gatedphotocathode, the fundamental is used as a gate pulse
and the SHG as a laser source for the photo-excitation
with the copper cathode. (In the case of the polarized
electron source with GaAs, the circular polarized
fundamental wave is used as a photo-excitation source,
the SHG as a gate pulse.) The same single laser pulse canalso gate its emission by itself. To maintain normal
incidence on the cathode, we developed a new type ofhollow beam incidence system for cathode illumination
with an achromatic axicon lens pair.
In the first feasibility test run, we are preparing a Zpolarizer (8-divided waveplate) for the SHG to generateradial and azimuth polarizations. Comparing the photoemission process with these polarizations, we make clear
the feasibility of this new concept of photocathode.
Using femtosecond laser pulses for photocathode RF
guns, a pancake bunch can be created that will evolve
automatically into a uniformly filled 3D ellipsoid [9].
This scenario is needed to reduce laser pulse intensity, toavoid damage of the cathode. The Z-polarization RF gun
can be fit to this scenario. Next, we will test this scenario
to generate a low-emittance beam with our Z-field gun.

REFERENCES[1] “Linac Coherent Light Source (LCLS) Conceptual
Design Report”, SLAC-R-593, April 2002.
[2] “TESLA Technical Design Report, PART V, The XRay Free Electron Laser”, ed. G. Materlik and Th.
Tschentscher, March 2001.
[3] J. Rivers, “SCSS X-FEL Conceptual Design Report”,
RIKEN, May 2005.
[4] I. V. Bazarov, et al. PAC’05, 2005, p. 382.
[5] Japan Patent Application No. 2005-267593.
[6] T. INOUE, et al., JJAP, 41, No. 12, 2002, p. 7402.
[7] S.C. Tidwell, et al., Applied Optics, 29, No. 15, 1990,
p. 2234.
[8] K. Aulenbacher, et al., J. Appl. Phys., 92, No. 12,
2002, p. 7536.
[9] M. J. De Loos et al., PAC’99, 1999, p. 3266.

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Proceedings of FEL 2007, Novosibirsk, Russia

BEAM PROPERTIES FROM S-BAND ENERGY COMPENSATEDTHERMIONIC RF GUN AND LINAC FOR KU-FEL
Toshiteru Kii, Hideaki Ohgaki, Kai Masuda, Satoshi Sasaki, Takumi Shiiyama, Heishun Zen
Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 6110011, Japan
Abstract
Beam properties after the accelerator tube of the KUFEL system were measured to ensure the potential of theenergy compensation technique to compensate for energy
degradation in a thermionic RF-gun. Small growth ofenergy spread and emittance were observed, and its
influence to the FEL gain and evolution of output power
were estimated. It was found that the influence due to theamplitude modulation was so serious, because the small
increase of the energy spread drastically reduces FEL gain.
In addition to the amplitude modulation, phasemodulation will be required.

D1

4.5 cellThermionicRF gun

BPM2

BPM1
Q1

FC2

Q2
D3
3 m accelerator tube
CT5CT3
180 degree arc

BPM3

Undulator

Fig. 1 Arrangement of the KU-FEL.

INTRODUCTION

BEAM PROPERTIESAn MIR-FEL facility, KU-FEL, has been constructed
for application of the energy science[1]. The KU-FEL
consists of a thermionic RF gun and a 3-m accelerator
tube and an undulator to generate 4-13 μm FEL as shownin fig. 1. As an electron injector, we chose a thermionic
RF-gun because of its compactness and an easy-handlingfeature. However, a serious problem of backbombardment limits macro-pulse duration up to several
micro seconds. Then, we have tested an energy
compensation technique[2], which uses an amplitude
modulated rf pulse using remotely controllable pulse
forming network of the Klystron modulator, to reduce theinfluence of the back-bombardment, and successfully
extracted energy compensated electron beam of 4.0 μsec
macro-pulse duration and numerically expected to extractelectron beam with constant energy up to 8.0 μsec[3,4].
On the other hand, the amplitude modulated RF pulse will
give rise to phase difference between RF-gun andaccelerator tube, because timing of RF output fromKlystron will be shifted to earlier timing because thevelocity of the electrons in the Klystron tube is changed
during macro-pulse. Moreover, time-varying beamloading will increase beam emittance due to space charge
effect. Therefore, we have studied influence of the beam
properties, such as temporal current profile, energy spreadand emittance, at the exit of the accelerator tube. We havealso studied on a figure-of-merit of average beam current
and pulse duration, because higher beam current reduces
macro-pulse duration.

We have estimated the influence of the energy
compensation technique from measurements of beam
properties at the entrance and the exit of the accelerator
tube. To estimate the influence of the technique clearly,
two operational modes were selected. In the first mode,
RF pulse of 3 μsec was fed to the RF-gun. Pulse duration
after the first bending magnet was about 1.5 μsec. Thismode was used to evaluate the beam properties without
amplitude modulation. (Mode 1: Non-modulated mode)
In the second mode, RF pulse of 7 μsec was fed. Pulse
duration after the first bending magnet was about 5.2 μsec.
This mode was used to evaluate the effect of theamplitude modulation. (Mode 2: Modulated mode) In
these modes, average beam currents were set to around 30
mA, because if the electron beam with higher beam
currents and shorter macro pulse duration is used as
modulated mode, it is difficult to clear the differences
between two modes.

___________________________________________#

kii@iae.kyoto-u.ac.jp

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Temporal Current Profile
Temporal profiles of the beam current at the entrance
and the exit of the accelerator tube were measured using
current transformers (CT3 and CT5 in fig. 1). As shownin figs. 2 and 3, acceleration was performed well in bothmodes. Although the most of electrons were accelerated
in the modulated mode, macro-pulse duration was
shortened after acceleration, and beam current was
decreased by several percent in the latter part of themacro-pulse as shown in fig 3.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH023

MeV, energy spread of 0.5%, transverse emittance of 3.5π
mm-mrad were assumed. The FEL power evolutions forelectron beam with 0.5% and 1.0% energy spread areshown in fig. 7. As shown in fig. 7, the influence of themodulated RF input is quite serious due to the growth ofthe energy spread. The result indicates that the FEL gain
rapidly decreases in the macro pulse. Phase modulation to
the source RF of the Klystron will be effective to reduce
expansion of the energy spread. It is important to measure
the time evolution of the energy spread, to estimate the
FEL power evolution precisely.

Fig. 2 Temporal profiles of the beam current for nonmodulated mode measured at the entrance of theaccelerator tube (CT3) and at the exit of the accelerator
tube (CT5).
b)a)Fig. 4 Energy spread before the accelerator tube.
a) Non-modulated mode b) Modulated modeb)a)Fig. 5 Energy spread after the accelerator tube.
a) Non-modulated mode b) Modulated mode
Fig. 3 Temporal profiles of the beam current formodulated mode measured at the entrance of theaccelerator tube (CT3) and at the exit of the accelerator
tube (CT5).

Energy Spread
Energy spreads were also measured. Before theaccelerator, the first bending magnet (D1) and Faradaycup (FC2) were used. After the accelerator, the third
bending magnet (D3) and the beam profile monitor(BPM3) was used. As shown in fig. 5, significant growthof the energy spread was observed after acceleration.
Absolute value of the energy spread was expanded withmodulated RF from 170 keV to 400 keV. It was probablethat the phase differences between the stored RF in the
gun and the injected RF to the accelerator tube changed
the accelerating efficiency in the latter part of the macropulse. To estimate the order of the phase difference, phasedependence of the accelerated electron beam energy wasmeasured. Energy difference of 500 keV corresponds tophase difference of about 5 degree around the crest of thephase dependence curve as shown in fig. 6. Therefore,
phase difference of several degrees seems to be
introduced by the amplitude modulation. FEL gains andpower evolutions were also calculated using GENESIS[5]to estimate the influence of the energy spread. In thesecalculations, bunch length of 1.0 ps, beam energy of 25

Fig. 6 Phase dependence of the peak energy of theaccelerated electron beam.

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Power [W]

10

0
8

1

Time [μsec]
2
3

Table 1. Evaluated beam emittances at the entrance andthe exit of the accelerator tube.

4

mode

106
10

Proceedings of FEL 2007, Novosibirsk, Russia

ΔE = 0.5%
ΔE = 1.0%

4

1
2

Emittance @ entrance[π mm mrad]
x : 4.0 , y : 0.9
x : 4.5 , y : 1.0

Emittance @ exit
[π mm mrad]
x : 2.5 , y : 2.5
x : 3.3 , y : 3.5

102
100
0

50
100
Pass Number

150

Fig. 7 FEL power evolutions for different energy spread.

Beam EmittanceBeam emittances were also measured using phase space
tomography method. Although when we apply the
tomography method to the electron beam with energy
spreads, estimated emittance will be overestimated[6], inthese experimental condition, energy spreads were lessthan 2.0%, thus the tomography method was effectively
worked. Phase space distributions before and after theaccelerator were measured using quadrupole magnets(QM1, QM2) and beam profile monitors (BPM1, BPM2).
Reconstructed phase space distributions are shown in figs.
8 and 9. As shown in figs. 8 and 9, main components ofthe electron beams become fuzzy when the modulated RF
were used.

b)a)Fig. 8 Phase space distribution in x dimension before theaccelerator. a) Non-modulated mode b) Modulated mode.

b)a)Fig. 9 Phase space distribution in x dimension after theaccelerator. a) Non-modulated mode b) Modulated mode.

Fig. 10. FEL power evolutions for the electron beam withdifferent emittance.

OPERATION POINT OF THE
THERMIONIC RF-GUN
Although the FEL gain becomes larger when extracted
beam current is increased, the influence of the backbombardment becomes larger, and then the macro pulse
duration becomes shorter. In case for our RF gun,maximum beam current is about 120 mA, but the pulse
duration is limited to less than 500 nsec. On the other
hand, if the extracted beam current is limited to 30 mA,
the pulse duration is reached up to 5 μsec. To find thebetter operational point, power evolution of the FEL forvarious average beam current was estimated. In thesecalculations, bunch length of 1.0 ps, beam energy of 25
MeV, transverse emittance of 3.5π mm-mrad wereassumed. As shown in fig. 11, the FEL gain is sensitive tothe average beam current. Therefore, we have tested toincrease average beam current. As shown in fig. 12, we
successfully extracted electron beam of 50 mA with pulse
duration of 3.5 μsec.

The evaluated rms emittances after the accelerator wereincreased by about 40% with modulated RF pulse as
shown in table 1. To estimate the influence of themodulation, FEL power evolutions were calculated. As
shown in fig. 10, the influence of the emttance growth issmall. In these calculations, bunch length of 1.0 ps, beamenergy of 25 MeV, energy spread of 0.5 %, transverse
emittance of 3.5π and 10.0π mm-mrad were assumed.
Fig. 11. Estimated FEL power evolutions for various
average beam currents using GENESIS.
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Fig. 12 Temporal profiles of the beam current with 50
mA of average current.

CONCLUSION
Beam property measurements were carried out toevaluate the performance of the energy compensation
technique using amplitude modulated RF pulse applied tothe thermionic RF gun in KU-FEL system and theinfluence of the amplitude modulation. It was found thatthe energy compensation technique was effective forextract the electron beam with longer macro pulse, but the
influence to the energy spread was quite serious. To
achieve the first lasing of the KU-FEL, an RF phasemodulation will be required in addition to the amplitude
modulation. The better operational point was also
surveyed for higher FEL output. The new operating modeof 50 mA and 3.5 μsec was successfully found.

REFERENCES[1] T. Yamazaki, et al., Free Electron Laser 2001 (2002),
II13-II14.
[2] T. Kii, et al, Proceedings of the 26th International
Free Electron Laser conference, (2004) 443-446.
[3] T. Kii, et al., AIP Conference Proceedings Volume879,
SYNCHROTRONRADIATION
INSTRUMENTATION:
NinthInternational
Conferenceon
Synchrotron
Radiation
Instrumentation, (2006) 248-251.
[4] N. Okawachi, et al., Proceedings of International
Conference on Free Electron Laser, (2006) 664-667.
[5] S. Reiche, “GENESIS 1.3 User Manual”, (2004).
[6] H. Zen, et al., Proceedings of International
Conference on Free Electron Laser, (2006) 668-671.

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NUMERICAL EVALUATION OF OSCILLATOR FEL WITH MULTIBUNCH PHOTO-CATHODE RF-GUN IN KYOTO UNIVERSITY*
Hideaki. Ohgaki#, Toshiteru Kii, Kai Masuda, Satoshi Sasaki, Takumi Shiiyama, Heishun Zen,
Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto 6110011, Japan
Ryunosuke Kuroda, National Institute of Advanced Industrial Science and Technology, Umezono
1-1, Tsukuba, Ibaraki 3058658, Japan
Masao Kuriki, Nobuhiro Terunuma, Junji Urakawa, High Energy Accelerator Research
Organization, 1-1, Oho, Tsukuba, Ibaraki, 305-0801, Japan
Yoshio Kamiya, Masakazu Washio, Research Institute for Science and Engineering, RISE, Waseda
University, 3-4-1, Okubo, Shinjuku-ku, Tokyo, 169-0072, JapanAn 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 40 MeV andpeak current of -10 A has been successfully accelerated bya linac system which consists of a 4.5-cell thermionic RFgun, a ‘dog-leg’ transport system, a 3m s-band linac, anda 180-degree arc bunch compressor [2]. Figure 1 shows
the schematic view of the linac system which includes thephoto-cathode RF-gun. To reduce the back-bombardment
effect in the 4.5-cell RF gun, several attempts have been
made, and the macro pulse duration of 5 μs has beenachieved [3]. However, there still needs several efforts areneeded both to extend the macro pulse duration and toincrease the peak current to reach the FEL saturation [4].
Replacing the thermionic RF-gun to a photo-cathode RFgun is the most promising way to obtain a high peakcurrent electron beam. Therefore, we made a preliminary___________________________________________*Work supported by Promotion of Collaborative Research Programs in
Universities of High Energy Accelerator Research Organization(KEK).
#
ohgaki@iae.kyoto-u.ac.jp+present address: International Center for Elementary Particle Physics,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033,
Japan

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Accelerator Tube0

INTRODUCTION

design study [5] and start to develop a 1.6-cell photocathode RF-gun [6]. Recently, the improved design of the71

180-degree
ARC

Beam Dump

710

Numerical evaluations have been performed to install aphoto-cathode RF-gun into an oscillator FEL system
which has been developed in Kyoto University. The
original FEL system was consisted of a 4.5-cellthermionic RF gun with S-band accelerator tube of 3-m tooscillate the mid-infrared FEL. The electron beam
properties have been evaluated from an RF-gun to an FEL
by using PARMELA and ELEGANT. On the other hand,
the FEL parameters have been calculated with GENESIS
which takes the optical cavity into account. The evaluatedpeak current of the electron beam was 10-50 times as highas those with the thermionic RF-gun. Since the oscillator
FEL requires a multi-bunch electron beam, evaluation of
the round-trip development of the FEL has been also
performed by a 100 bunch train beam. The results showedthat the FEL gain saturation was achieved within 3 roundtrips.

Undulator

Figure 1: Schematic view of the KU-FEL driver linac.

) 4.5
dra 4.0
m
- 3.5
m
m 3.0
(
e 2.5
c
n
at 2.0
ti
m 1.5
E
e 1.0
sr
e 0.5
v
s
n 0.0
ar
T

εx
εy

π

Abstract

30

40

50

60

70

RF P hase (deg.)

10

)s
p( 8
thg
ne
L6
hc
nu
B4
S
M
R
2

30

40

50

60

70

RF P hase (deg.)
Figure 2: Transverse RMS emittance(a) and energy
spread(b) of the electron beam from the gun as afunction of the laser injection phase.

Proceedings of FEL 2007, Novosibirsk, Russia

1.6-CELL PHOTO-CATHODE RF-GUN
The improved BNL type 1.6-cell photo-cathode RF-gun[10] has succeeded in generation of a high brightness
electron beam, about 1 πmm-mrad with 1.5 nC/bunch. A
multi-bunch operation also succeeded with a 100 bunch
UV drive laser and a Cs2-Te cathode. This type of photocathode RF-gun manufactured in KEK will be installed
into KU-FEL system. As is shown in figure 1, the 1.6-cell
photo-cathode RF gun will be located at the upstream of
the accelerator tube. The RF system will be shared withthe existing thermionic RF-gun. Since the thermionic RFgun operates 2856 MHz bunch train, a large average
power FEL will be generated by the thermionic RF-gun.
On the other hand, the photo-cathode RF-gun can
generate a high peak power FEL but small average power
FEL, because the bunch train is depends on the laser
frequency of the laser (357 MHz).
The electron beam parameter from the 1.6-cell RF-gun
has been evaluated by using PARMELA with the
maximum electric field of 50 MV/m at the cathodesurface which was given by an acceleration test in AIST.
We also assumed that the ratio of the field strength of thehalf cell and regular cell was 1:1 which was measured
with the test gun at KEK. The ratio of the field strength,
which can be tuned from 0.8:1 to 1.3:1, and the maximum
filed strength should be optimized for its’ purpose,
because the electric field for the cavity cell largely affects
the property of the output beam. The driver laserparameters assumed here was a picosecond UV laser [11],whose beam profile was 0.7 mm at the cathode surface
and the pulse duration was 6.0 ps. The Gaussian shapes
were also assumed both for the transverse (1 mm cut-off)and for the longitudinal (12 ps cut-off) distribution tosimplify the calculation. Figure 2 shows the transverse
RMS emittance(a) and energy spread(b) of the electron
beam from the RF gun as a function of the laser injection
timing. We assumed 1 nC/bunch at the cathode surface inthis paper.
It is clear that the transverse RMS emittance of 1 πmmmrad and energy spread of 2% can be generated at the 45
degree of the laser injection phase at the gun exit. The
solenoid field for the emittance compensation [12] which

)
d
ar
m5
m
m
( 4
e
c
n
at 3
ti
m
E
e2
sr
e
vs
n1
ra 0.8Tεxεyπphoto-cathode RF-gun has been installed in the linac in
AIST and succeeded to generate 100-bunch electron beam.
The beam charge of 1.5 nC/bunch has already beenachieved. We are going to install the similar RF-gun
system into KU-FEL system. Thus a start-to-end
calculation with the photo-cathode RF-gun has been
performed. For the electron beam a simulation has been
made by PARMELA [7] and ELEGANT [8] from gun to
undulator. On the other hand, the FEL parameters havebeen calculated by using GENESIS [9] which was
modified to calculate an optical cavity. Then the FEL gain
was compared with the present thermionic RF-gun based
system.

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1 .2

1.6

2.0

2.4

2.8

Solenoid Field (k Gauss)a)Figure 3: Transverse RMS emittance at the exit of theaccelerator tube as a function of the solenoid field.
75

sp
1/ 50
)
Cp
(
eg
ra 25
h
C
b)
0

5.8 ps

10

15

20

25

30

35

T im e (ps)
80

Ve
k 60
01
/)
Cp 40
(
eg
ra
h 20
C
0

dE/ E=0.38%

27.2

27.4

27.6

27.8

28.0

Energy (M eV )Figure 4: Time distribution (a) and energy distribution(b) at the exit of accelerator tube. The RF phase of theaccelerator tube was chosen to ‘on crest mode’.

was the same geometric configuration of ref. 13. The field
distribution was calculated by using POISSON. As shownin fig.3 the transverse emittance of 1.5 πmm-mrad is
obtained from the accelerator tube with the solenoid fieldof 1600 Gauss. Figure 4 also shows the bunch length(a)and the energy spread(b) of the electron beam from theaccelerator tube with the RF-phase of 125 degrees where
the smallest energy spread was obtained.

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Proceedings of FEL 2007, Novosibirsk, Russia

The achromatic 180-degree arc section was tuned bothfor the matching condition of the undulator parameter andfor the bunch compression condition with matrix element,
R56, by using ELEGANT. Figure 5 shows the bunch
length(a) and the energy spread (b) of the electron beamat the entrance of undulator. As is shown in fig.5 (a) the
bunch length successfully reduced below 1 ps, but morethan half of the electrons are spread away from the mainbunch. This is due to a non-linear relation between phaseand energy at the exit of the accelerator tube since the RFphase, 125 degrees, was located at RF crest. We call thisoperation mode as ‘on crest mode’. Thus we also
calculated with the RF phase at 132.5 degrees where therelation between phase and energy was close to a linear
one. We call this operation mode as ‘energy chirp mode’.
Figure 6 shows the bunch length (a) and energy spread (b)of the electron beam at the entrance of undulator with RFphase of 132.5 degrees. As the results the bunch length
was reduced from 0.8 ps to 0.23 ps and the peak current
was increased from 443 A to 2.46 kA.
The expected parameters of the electron beam from 1.6cell photo-cathode RF-gun were listed in table.1.
Consequently, the photo-cathode RF-gun would generate
10-50 times large peak current electron beam to thethermionic RF-gun which generated 40 A peak current of
the electron beam [5].
Table 1 Evaluated Electron Beam Parameters
ThermionicRF gun[5]Emittance(πmm-mrad)
Energy Spread(%)
Bunch Length(ps)Peak Current(A)

11.3(H)10.1(V)

Photo-Cathode RF-gun
EnergyOn Crest
Chirp
mode
mode
5.02(H)
4.42(H)
5.01(V)
3.03(V)

0.40

0.054

0.86

1.8

0.80

0.23

40.0

443

2,460

a)

sp
.20
/)
Cp
(
eg
ra
h
C

443 A

60

0.8 ps

45

30

15

0
- 20

- 15

b)

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0dE/ E=0.054%

0

2 7 .22 7 .32 7 .42 7 .5

2 7 .62 7 .72 7 .82 7 .9Ener gy (M eV )Figure 5: Time distribution (a) and energy distribution(b) at the undulator. The RF phase was ‘on crest
mode’.
a)2.46 kA200

sp
1. 1 5 0
0/
)
Cp
( 100
eg
ra
h 50
C

0.23 ps

27

28

29

30

31

T im e (ps)b)

The FEL gain with the 1.6-cell photo-cathode RF-gun
has been calculated by using above evaluated electron
beam parameters. The undulator and optical cavity
parameters used here are listed in ref. 4. The 1-pass FEL
gains with the ‘on crest mode’ and with the ‘energy chirp
mode’ were calculated as 8.8x104% and 7.6x107% in 12.1
μm wavelength. On the other hand, the 1-pass FEL gain
with the thermionic RF-gun was 38%. The 1-pass gain
was extremely enhanced even with the ‘on crest mode’
because of its’ large peak current, more than 400 A.
Although a large energy spread in the ‘energy chirped
mode’ a huge peak current, 2.4 kA, brought a huge 1-pass
gain.

- 5

200

Ve
k
01 1 5 0
/)
Cp
( 100
eg
ra
h 50
C

0

OSCILATOR FEL DRIVEN BY 1.6-CELL
PHOTO-CATHODE RF-GUN- 10

T im e (ps)

100

Ve
k 80
01
/)
Cp 6 0(eg 4 0rahC 20
0
2 7 .2dE/ E=0.86%

2 7 .42 7 .62 7 .82 8 .02 8 .2

Ener gy (M eV )Figure 6: Time distribution (a) and energy distribution(b) at the undulator. The RF phase was ‘energy chirped
mode’.

Proceedings of FEL 2007, Novosibirsk, Russia
To calculate a round-trip development in an oscillator
FEL, we modified GENSIS which treated the lightpropagation in an optical cavity including an optical loss
in vacuum duct, mirror surface, and hole coupling [4].
The multi-bunch electron beam, a 100-bunch, has alreadybeen achieved by a 100 bunch UV laser system which
was based on 357 MHz mode-locker [6]. However, weshould note that our cavity length of the undulator is 4.51
m and round-trip frequency is about 33.2 MHz. Therefore
about 10 round-trips can be used for the FEL
amplification. So we assumed 10-round-trips, about 0.3
μs in macropulse, in this calculation. The round-trip
development is shown in fig.7. As is shown in fig.7 FEL
saturations are achieved with a few round-trips for both
operation modes. The peak output powers were 10 MWwith ‘on crest mode’ and 400 MW with ‘energy chirped
mode’. The average FEL energies were also calculated as
0.44 mJ/macro-pulse for ‘on crest mode’ and 4.6
mJ/macro-pulse for ‘energy chirped mode’. On the other
hand, the saturated output power of 2.4 MW can beobtained after 70 round-trips with the thermionic RF-gun
system. The average FEL energy can be calculated as 10
mJ/macro-pulse for 3 μs macropulse length whichcorresponds to the 100 round-trips. To increase theaverage energy with a photo-cathode RF-gun, the bunchtrain should be increased. A 300-bunch train, 1 μs macropulse duration, should be the next target for thedevelopment of the photo-cathode RF-gun to replace thethermionic RF-gun completely.

CONCLUSION
An improved BNL type RF-gun, which has alreadybeen succeeded in generation of 100 bunch, about 1
πmm-mrad with 1.5 nC/bunch electron beam in AISTRISE, will be installed in an oscillator FEL system. The
FEL system was originally designed with a 4.5-cellthermionic RF gun with a 180-degree arc worked as abunch compressor to oscillate the mid-infrared FEL in
Kyoto University. To evaluate the FEL performance withthe photo-cathode RF-gun we made a start-to-end
calculation by using PARMELA, ELEGANT and
GENESIS which has been improved to take an opticalcavity into account.
The evaluated peak current of the electron beam at theundulator was 443 A when the RF phase was tuned toobtain the minimum energy spread, dE/E=0.054%, of theelectron beam. When the RF phase was tuned for energy
chirped beam, dE/E=0.86%, the peak current of theelectron beam was 2.46 kA. Since the thermionic RF-gun
generated 40 A electron beam, 10-50 times large peakcurrent was obtained by the photo-cathode RF-gun.
The output power of 12.1 μm FEL, 400 MW, will besaturated within 3 round-trips with the energy chirped
beam. On the other hand, the saturated output power of
2.4 MW can be obtained after 70 round-trips with thethermionic RF-gun system. We should note that only 10
round-trips can be used for the FEL amplification when
we assumed a 100-bunch electron beam. Therefore, the

WEPPH024

1 000 0)W 100 0M(
re 10 0
wo
P 10
ka
e
P 1
tu
pt
u 0.1
O
0 .0 1

Charped12.1 μm

On crest

0

2

4

6

8

10

P ass Num ber

Figure 7: Round-trip development of the FEL
output power.

evaluated average energy of the FEL was 4.6
mJ/macropulse which was smaller than that with athermionic RF-gun, 10 mJ/macropulse.
Consequently a high brightness electron beam from thephoto-cathode RF-gun will generate 100 times high peak
power of FEL. However, the average power of FEL withthe photo-cathode RF-gun will be smaller than that withthermionic RF-gun when we assume a 100 bunch train for
the electron beam. Further developments for generating alonger multi-bunch beam are required to replace athermionic RF-gun into a photo-cathode RF-gun,completely.
The authors would like to thank Mr. T. Takatomi (KEK)for his help for this work.

REFERENCES[1] T. Yamazaki, et al., Free Electron Laser2001 (2002),
II-13.
[2] H. Zen, et al., in these proceedings.
[3] T. Kii, et al., in these proceedings.
[4] S. Sasaki, et al., in these proceedings.
[5] H. Ohgaki, et al., NIM A528 (2004) 366-370.
[6] K. Hirano, et al., NIM A560 (2006) 233-239.
[7] L. M. Young, James H. Billen, LA-UR-96-1835(2002).
[8] M. Borland, “User’s Manual for elegant”, v.15.4.1(2005).
[9] S. Reiche, “GENESIS 1.3 User Manual”, (2004).
[10] Y. Kamiya, et al., Proceedings of the PAC2007(2007), THPMN040.
[11] F. Sakai, et al., Proceedings of the PAC1999 (1999)
2036.; J. Yang, et al., NIM A491 (2002) 15.
[12] R.E. Carlsten, NIM A285 (1989) 313.
[13] F. Sakai, et al., Jpn. J. Appl. Phys., Vol.41 (2002)
1589.

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Proceedings of FEL 2007, Novosibirsk, Russia

PRESENT STATUS OF FEL DEVELOPMENT IN KYOTO UNIVERSITY
Satoshi Sasaki, Heishun Zen, Takumi Shiiyama, Toshiteru Kii, Kai Masuda, Hideaki Ohgaki
Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto, Japan, 611-0011
Abstract

We have constructed an infrared (4-13 μm) FEL facility
for advanced energy researches in Kyoto University. The
numerical studies on the expected FEL gain, which werebased on the experimental measurements both of theundulator and of the electron beam parameters, werecarried out. GENESIS code has been modified to simulate
an oscillator FEL which took into account the chambergeometry and the mirror including hole coupling.
Dependencies on a tilt angle and an offset of the mirror
were evaluated by using this modified code, then for the
first lasing the mirror parameter was optimized. At thepresent stage, we have installed the undulator and themirror cavity. Measurements on spectrum of the
spontaneous emission and electron beam characteristics
were carried out. The measured spontaneous emission wasconsistent with the result of the calculation obtained withmeasured magnetic field of the undulator. Since theevaluated peak current of the electron beam was notenough for the lasing, LaB6 cathode was ready to use.

FEL GAIN CALCULATION
Calculation CodeWe had calculated the FEL gain and round trip
development to optimize the optical cavity parametes, byusing TDA3D[4], but it didn’t take into account the duct
shape, reflection on mirror, absorption, and transmissionof the mirror. In addition, the detuning parameter canhardly be handled.
To cope with these problems in this study, we modified
GENESIS1.3 code taking in the realistic duct shape. We
simulated a realistic FEL gain by using the modified code.
The duct shape taken in the calculation is shown in Fig.1.
The parameters of the electron beam used in the FEL gain
calculation were optimized for the measured undulator
parameters, and are listed in Table 1. The undulator
parameters are listed in Table 2.

Undulator

INTRODUCTION
We have studied and developed an infrared (4-13 μm)
FEL facility (KU-FEL) for advanced energy researches in
Kyoto University. The KU-FEL consists of a 4.5-cellthermonic RF gun, 3 m accelerator, beam transport,
Halbach-type undulator, and optical cavity. The RF gun
and the accelerator operate at 2856 MHz (S-band), andproduce electron beams up to 40 MeV.
To optimize the optical cavity, we calculated the FEL
gain with the measured magnetic field of the undulator[1].
However, the treatment of the loss in the vacuum chamber
and the light output from the cavity was truncated on theassumption of simple Gaussian distributions in transverse
direction. On this assumption, the tolerance of thealignment errors of the optical cavity mirrors could not be
evaluated. In this study, we carried out calculations of thelight propagation taking into account of the duct shapeand reflection/transmission of the light at the mirror for
optimization of the optical mirrors and evaluation of themisalignment tolerance. For this purpose, we havemodified a calculation code, GENESIS1.3[2].
Based on the re-optimized parameters in thesecalculations, we have installed the optical cavity andundulator in the KU-FEL system. We then observed thespectrum of the spontaneous emission, and compared itwith the SRW[3] calculation.
Aiming at a higher peak current, we replaced thetungsten cathode in the RF gun by a LaB6 cathode. In thispaper, the preliminary experimental comparison will bealso reported.
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Figure 1: Duct shape
Table 1: Electron beam parameters
Emittance(x)3.5 πmm-mrad
Emittance(y)3.5 πmm-mrad
0.5 %ΔE / E
Beam size(x)0.6 mmBeam size(y)0.4 mm
3.6
Twiss parameter αx0Twiss parameter αyBeam energy
25 MeV
Table 2: Parameter of Halbach type undulator
total length
1.6 m
Repetition
40
period4 cm
gap
25.5 - 45 mm
Maximam magnetic field
0.26 - 0.0045 T
K value
0.99 - 0.17

Proceedings of FEL 2007, Novosibirsk, Russia

Set Up of the Optical Cavity
Firstly, the mirror curvatures were designed in the
viewpoint of FEL lasing stability as follows. Parametersof the optical cavity were once optimized to obtain thehighest FEL gain by using TDA3D with aforementioned
truncations, and FEL gain was 87% under the electron
beam condition of 25 MeV, while the resultant stability
has not been evaluated. By using the modified
GENESIS1.3, we calculated FEL gain under the same
conditions, and FEL gain was 49%. The reason why FEL
gain decreased was due to the diffraction loss.
The stability was then evaluated by using the modified
GENESIS1.3 and as the result it was found that the
optical cavity was unstable for FEL lasing. The gparameter was found to be 0.93, We thus re-optimized theparameters of the optical cavity by the use of modified
GENESIS1.3, to obtain a g-parameter of ~0.5. As theresult, we have selected the curvature of the upper mirrorof 3.03 m, the down mirror of 1.87 m, the the rayleighlength of 0.7 m, and beam waist of 1.1 m (see Table 3).
Secondly with the specification of the mirrors, themisalignment tolerance was the evaluated. The results ofthe mirror offset and tilt dependency are shown in Fig. 2.
Here, Dm means down mirror, and Um means upper
mirror. X and Y are the direction the mirrors offset andtilt. The FEL gain is seen to decrease ~10% with respect
to the ideal alignment when the offset is 0.4 mm or the tilt
angle is 400 μrad. In comparison, with the original mirror
parameter, the FEL gain is found to decrease by 30%, asshown in Fig.3. The re-optimized parameters are thus
found to lead to a much better misalignment tolerance.
Finally, concerning the diameter of mirror hole, we
simulated the FEL gains for the diameters of 1, 2 and 3mmφ, and the results are summarized in Table 4. As of thenumerical treatment of the out-coupling hole, we foundthat the discontinuity of the optical fields on the edge ofthe hole results in a numerical problem[5]. So, we rather
treated the out-coupling as transpiration. As shown in
Table 4, the FEL gain for 3 mmφ hole is found to be about
a half of that for 1 mmφ. In comparison, the gain decrease
for the 2 mmφ hole is tolerable, and the FEL output ismore than two times higher than that for 1 mmφ. We thus
chose the mirror diameter of 2 mmφ.
The optimized mirrors were then installed in the opticalcavity of the KU-FEL. The picture of the mirror is shownin Fig. 4, and the reflectivity is shown in Table 3.
Table 3: Parameters of the optical cavity
Substance
Au coated Cu mirror
Rayleigh range
0.7 m
Beam waist position
1.1 m
infrared reflection
99.04%
down mirror curvature
1872 mm
upper mirror curvature
3030 mm
Cavity length
4.513 mWEPPH025

Table 4: FEL gain dependence on mirror hole diameter
Pass number
diameter Gain(%) Output(MW)for saturation
44
2.0
70
1mmφ
37
4.9
75
2mmφ
24
4.8
100
3mmφ

Figure 2: Influence of mirror misalignment of 0.5 gparameter

Figure 3: Influence of mirror misalignment of 0.93 gparameter

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Proceedings of FEL 2007, Novosibirsk, Russia

Figure 4: Au coating mirror
Figure 7: Experimental setup
The FEL power evolution calculated by modified
GENESIS1.3 under electron beam condition of 25 MeV isshown in Fig. 5. For comparison, the preliminary result by
the use of TDA3D on same condition is also shown in Fig.
6.
At the present stage, the macro-pulse length of electron
beam is about 3 µs in KU-FEL, so it is necessary forelectron beam peak current to be 40 A in order to realize
FEL lasing.

We observed the spectrum of spontaneous emission,under the condition of the electron beam energy of 29.5
MeV. The electron beam condition is shown in Table 1
except for energy, and the observed spectrum is shown in
Fig. 8. The spectrum shows a peak at 9.2 μm, and its
FWHM is 270 nm. The undulator parameters are listed inTable 1, and the spectrum calculated by SRW by using
these parameters is also shown in Fig. 8 as the dotted line.
The observed spectrum shows exactly the same peakwavelength as the calculation, and the FWHM also agrees
well with the calculation, considering that the FWHM by
the calculation doesn’t include resolution of themonochromator, 100 nm.

Intensity (A.U.)

1

Figure 5: FEL
GENESIS1.3

power

evolution

calculatedbyMeasured
Calculated

0.5

0
8800

40 A

9000
9200
Wave length (nm)9400

Figure 8: Measured and calculated spectrum of the
spontaneous emission

FEL Lasing Experiments
30 A
20 A

Figure 6: FEL power evolution insufficient on mirror anddiffraction losses.

MEASUREMENTS
Measurement of Spontaneous Emission
We measured the spectrum of spontaneous emission
using an InSb detector (Judson, J15D12) and a
monochromator (Digikrom, DK240). We extract the lightfrom the downstream of the mirror chamber, and thenfocus it on the entrance of the monochromator by aparabolic mirror. The experimental setup is shown in
Fig.7.
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We then started FEL lasing experiments of 11 μm
wavelength with an electron beam energy of 26.5 MeV,
macro-pulse length of 3 μs, average current of 40 mA.
The reasons for the choice of 11 μm are as follows. On
one hand, a lower energy electron beam shows in generala higher FEL gain. Furthermore, in the KU-FEL linac,
lower energy operation of the RF gun is found to lead to ahigher peak current[6]. On the other hand, the InSb
detector loses sensitivity rapidly for ~13 μm or longer.
We then carried out experiments aiming at FEL lasing.
We succeeded in accumulating the spontaneous emission,
but neither FEL amplification nor saturation is observedat this moment.
The peak current of the electron beam of ≥ 7 A isestimated by the bunch length measurement[6]. According
to the numerical calculations in the previous chapter, thesum of the diffraction loss and mirror loss exceeds theamplification if an electron beam if 7 A peak current.

Proceedings of FEL 2007, Novosibirsk, Russia
Aiming at a higher peak current, we replaced thetungsten cathode in the RF gun by a LaB6 cathode. An
experimental comparison showed that a LaB6 cathodelead to a higher peak current than a tungsten cathode in an
RF gun[7], probably because a LaB6 cathode is lesssensitive to the back-bombardment effect.
Our preliminary test with a LaB6 cathode when the RF
gun operated at 9 MeV, showed that we obtained a 120
mA average current and 2.5 μsec macro-pulse length,
which is encouraging compared with 70 mA and 3 μsec
by the tungsten cathode.
In the next stage, we will operate the RF gun at 7.5
MeV, which is known as the best operational condition
for the optimal peak current at the undulator [6]. Under
this operational condition, the peak current by thetungsten cathode was ≥ 7 A. According to the current
enhancement by the LaB6 cathode, we can expect anenhanced peak current of ≥ 12 A. The expected FEL gainis ~5.0%, and the FEL amplification would be ~100.

WEPPH025

REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
[7]

M.Nakano, et al.,” Measurement of the undulator in
KU-FEL”, in prceedings of FEL conference 2006
S. Reiche, Nucl. Instrum. Methods , A429(1999)243.
O. Chubar, et al., Proc. of EPAC98, p.1177, 1998.
J.S. Wurtele T.M. Tran. Computer Physics Comm.,
Vol.54, p.263, 1989.
B. Fattz et al., J. Phys. D.: Appl. Phys.
26(1993)1023.
H.Zen, et al., Proc in this conference.
M. Yokoyama et al., Nucl. Instr. and Meth. A 483(2002) 292.

SUMMARY
We modified the calculation code, GENESIS1.3, to
calculate the FEL gain taking into account the duct shapeand mirror, while we applied a truncation in the outcoupling treatment for numerical stability. In order toconsider mirror out-coupling hole realistically, we must
modify the calculation code further.
By using modified GENSIS1.3, we optimized theparameter of the optical cavity, and set up theexperimental equipments. For these parameters, we
calculated the expected FEL gain. As the result, we foundthat if the peak current of electron beam is 40 A, andmacro-pulse length is 3 μs, 12 μm FEL saturation will beachieved on the electron beam condition of 25MeV.
The spectrum of spontaneous emission was measured.
The results agreed well with calculation.
At present, we have not achieved an FEL lasing, mainly
due to the limitation of the peak current and macro-pulse
duration, i.e. the back-bombardment effect in the RF gun.
Against this adverse effect, preliminary tests showed thatthe use of the LaB6 cathode would lead to a higher peakcurrent than a dispenser type one. By the LaB6, 12 A peakcurrent is expected, and the corresponding FEL gain is
5%. Under this condition, we will be able to observe an
FEL amplification.

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Proceedings of FEL 2007, Novosibirsk, Russia

A TRIODE-TYPE THERMIONIC RF GUN FOR DRASTIC REDUCTION OF
BACK-STREAMING ELECTRONS
T. Shiiyama, K. Masuda, H. Zen, S. Sasaki, T. Kii, H. Ohgaki,
Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto, 611-0011, JapanK. Kanno, E. Tanabe, AET, INC., 2-7-6 Kurigi, Asaoku, Kawasaki, 215-0033, Japan
Abstract
We have proposed a triode-type thermionic RF gun
with an additional small cavity replacing the conventional
cathode, which provides the beam extraction phaseindependent of the main accelerating phase to suppress
the back-bombardment effect drastically. In order tocompensate the predicted degradation in transverse
emittance, a design refinement was carried out by the useof numerical simulations in this study. The results showedthat the back-bombardment power can be reduced bymore than 80% and the peak current of the output electron
beam will be enhanced greatly without emittancedegradation. Also the cavity parameters, namely thequality factor and the coupling coefficient of theadditional cavity with the RF feed coaxial cable were
designed to ensure both the induction of the required
cavity voltage and a wide frequency acceptance. The
prototype design of the triode-type thermionic RF gun
was completed and ready for experiments.

INTRODUCTION
We have used a 4.5-cell thermionic RF gun for the
injector of MIR-FEL facility (KU-FEL: Kyoto University
Free Electron Laser) at Institute of Advanced Energy,
Kyoto University. As is well know thermionic RF guns
suffer from the back-bombardment of electrons onto
thermionic cathodes, which eventually leads to an output
beam energy drop and limitation of the macro pulse
duration [1, 2]. This effect is seen significant especially inthe 4.5-cell RF gun in the KU-FEL because of its highcoupling coefficient β and large number of cells. Somecountermeasures were applied so far, such as the use oftransverse magnetic fields [3] and the temporal control of
the RF input for compensating time-varying beam-loading[4] with limited successes. A longer macro-pulse duration
by a new technique against the back-bombardment effectis thus essential for the first FEL lasing.
For this purpose, we have proposed a triode-type
thermionic RF gun [5, 6]. An additional small cavity witha thermionic cathode replaces the conventional cathode in
the RF gun as schematically shown in Fig.1. An RF field
induced at the short gap of the additional small cavity, andboth the amplitude and the phase are controlled
independently of the main accelerating cavities tominimize the back-bombardment of electrons onto thecathode.
Numerical studies so far have shown that the RF triode
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concept could reduce the back-bombardment power
drastically (80% or higher) while it tends to induce
inherent defocusing force at the same time, eventually
resulting in an expense of the transverse emittanceincrease [7].
In this paper, design refinement of a triode-type
thermionic cathode was carried out in order to suppress
the transverse emittance increase. A wehnelt structure
schematically shown in Fig.1 (b) was studied by PIC
simulations to compensate the defocusing effect inducedby the RF triode.
Also discussed in this paper is the selection of cavity
parameters, namely the coupling coefficient β to theadditional RF power feed, and the quality factor Q.
A potential feature of the RF triode concept is that therequirement of the RF power into the additional cavity ismoderate, thus the cost for the RF system modification islow. For the first experiments we have installed a
directional coupler to split the RF power from the existing
klystron to feed < 40kW to the additional cavity.
To ensure a sufficient cavity voltage with the limited
RF power and also expected resonant frequency shifts dueto the beam loading effect and/or the cavity temperaturechange, the tuning curves were calculated by the use of anequivalent circuit model with the beam loading effecttaken into account.

Drift tube
ThermioniccathodeThermioniccathode1st cell

1st cell
Additional cavity(a) Conventional type(b) Triode typeFigure 1: Schematics of RF cavity structures in thevicinity of the thermionic cathode in (a) a conventional,and (b) a triode-type RF gun.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH026

DESIGN REFINEMENT OF THE
ELECTRODE IN A TRIODE-TYPE RF
GUN

Drift tube

Numerical Method

In this study, the cathode mount position was fixed at 6mm with respect to the cathode position in the original
conventional RF gun, according to the numerical results
so far from the viewpoints of reducing the backbombardment power and minimizing the transverse
emittance degradation [7]. To further reducing thetransverse emittance by compensating the defocusing
force induced by the triode system, we adopted a wehnelt
structure. Figure 2 shows the electrode geometry and thedesign parameters in this study, namely the cathode depth
d and the wehnelt angle θ.
For every set of d and θ, the optimum RF phase of theadditional cavity with respect to the main accelerating
cavity of RF gun was searched for the maximum output
beam brightness at the exit of RF gun. The otheroperational parameters were fixed, such as the extraction
current density on cathode surface of 80A/cm2, the cavity
voltage in the additional small cavity of 30kV, and thetotal cavity voltage in the 4.5 main accelerating cavities of
10MV.

θ
d

Figure 2: Close-up of a triode-type thermionic cathodewith wehnelt structure
As the result, the beam brightness shows maximum at d
= 1.6 mm and θ = 40 deg. Figure 3 shows the dependenceof the output beam properties on θ for a fixed d = 1.6mm.
Only the results with over 80 % reduction of the backbombardment power are plotted in the figure.
As seen in Figure 3 we can prevent the transverse
emittance from increasing, and improve the brightness by
15 times at the wehnelt angle θ of 40 degrees.
Finally, with the optimal d and θ, a minor designmodification was then made in practical viewpoints ofminimal edge fields and a deep cutoff between the
additional cavity and the main cavities, and so on. Table 1
shows the expected electron beam properties by the final
design of the refined triode-type thermionic cathode. In
comparison with the conventional RF gun, the refined
triode-type thermionic RF gun is expected to improve thepeak current by 10 times and to reduce the backbombardment power by ~90 % without degradations of
the transverse emittance. The charge in a micro bunch was
77pC.

ε2
ε

εr

15

10

1

B

5

εz

0

normalized Brightness

Design refinement of the cathode by PIC
simulations

Thermioniccathodenormalized r , zDesign refinement of a triode-type thermionic cathodewas carried out by using a cylindrically 2-dimensionalgroup of codes (KUCODE) [8], which calculates electron
dynamics in the RF gun, as follows.
Electric field patterns of cylindrically symmetricstanding waves in the 4.5 cells and in the additional small
cavity for an RF triode are calculated by a 2-dimensional
eigenmode solver (KUEMS). The electric fields are thengiven with cavity voltages and relative phases as the input
parameters, and electron dynamics are calculated by the
PIC simulation code (KUBLAI). In this study forsimplicity, the back-bombardment effect on the temporalbeam-loading variation was neglected, i.e. both the cavity
voltages and the cathode current density were assumed tobe constant. The KUBLAI code takes into account the
space-charge effects by simultaneously solving Maxwell’sequations and Lorentz equation.
We used these codes to calculate the beam quality bychanging the cathode shape and the relative phasebetween the main accelerating fields and the additional
small cavity fields. From results of simulations, we haveevaluated the beam emittance (transverse andlongitudinal) and the peak current of the output beam at
the exit of 4.5-cell RF gun, as well as the backbombardment power onto the thermionic cathode.

0
25

35

45

θ [deg.]Figure 3: Beam properties by the triode-type cathode atthe 4.5-cell RF gun exit as functions of the wehnelt
angle θ showing the transverse and longitudinal rms
emittances εr, εz, and the brightness B normalized bythose by the conventional RF gun.

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WEPPH026

Proceedings of FEL 2007, Novosibirsk, Russia

Table 1: Comparisons of the back-bombardment power
and the output beam properties between the conventional
and the refined triode-type thermionic RF gun at the 4.5
cell gun exit.
Conventional Triode
Pback [kW]36
3.6
Ipeak [A]17114εr [πmm mrad]
2.5
2.0
εz [psec MeV]
0.046
0.012
B [A/(πmm mrad)2 keV]
0.27
1.6

DESIGN OF CAVITY PARAMETERS
In the additional small cavity for the triode system
neither a temperature control nor a frequency tuner is to
be installed for simplicity and low cost. Instead, we rather
set the coupling coefficient β of the additional cavity with
the RF feed coaxial cable at over coupling in order tograde the tuning curve and to ensure a wide frequency
acceptance. For this purpose, we will also consider a low
unloaded quality factor Q0 of the additional small cavity.
At the same time we have to choose β and Q0 so that asufficient RF fields should be induced with the limited RF
feed power supplied of < 40 kWpeak.

Equivalent circuit model
Frequency tuning curves were calculated by using theequivalent circuit model in Figure 4. The RF powersource is represented by a current source Ig, the RF
resonant cavity by a resonant circuit with Gc representing
the cavity loss, and the beam loading by an admittance Yb.
The external load Gex can be expressed by the coupling
coefficient β as Gex =βGc.

ig

The reflected RF power Pref is equal to the power
subtracted the power consumption Pc from the RF input
power Pin as formula (4). We thus can calculate the RF
power reflection ratio by formula (5).

Pref = Pin − Pc
Pref
Pin

=1−

Selection of the coupling coefficient and thequality factor
We used the equivalent circuit model in Fig.4 forcalculation of the required RF feed power fed into theadditional cavity. From formula (1) and (2), we obtained
Fig.5 showing the required RF feed power as a function of
the coupling coefficient β for a cathode surface current
density of 80 A/cm2, and a cavity voltage of 30 kV. The
unloaded quality factor Q0 = 4000 was assumed according
to the eigenmode calculation for an oxygen-free copperwall.
At a coupling coefficient β of 9.6 the required RF feed
power Pin is minimum of ~17 kW, which is below the 40
kW limitation of the experimental RF feed system. Taking
this margin, we then design a lower Q0 and/or a higher β
for a wide frequency acceptance.

In this equivalent circuit shown in Figure 4, the cavity
voltage Vc is expressed as formula (1), and Ig is given by
the RF input as formula (2).
Vc =Ig
(Gc + Gb + Gex ) + j ( Bc + Bb )I g = 8Gex Pin

(1)
(2)

The RF power Pc consumed by Gc and Yb i.e. the cavity
wall loss and the beam the acceleration, is expressed asfollows.
⎡1
⎤
*
*
(3)
Pc = Re ⎢ (Vc I g − GexVc Vc ) ⎥2⎣⎦
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30

Electron beam

Figure 4: Equivalent circuit model of triode system(5)

In the formula (5), the beam admittance Gb and Bb are
determined by the PIC simulations as functions of thecavity voltage Vc and the cathode surface current density.
The cavity admittance Gc and Bc are given by the drive
frequency and the cavity parameters, namely the resonant
frequency (2856MHz), the shunt impedance (R/Q = 63Ω),
and the unloaded quality factor Q0.

P in [kW]4.5 cells RF gun

Pc
Pin

4(Gc + Gb )Gex
= 1−
(Gc + Gb + Gex ) 2 + ( Bc + Bb ) 2

Yb(Vc, Jc)
RF power source

(4)

25

20

15
0

20
40
Coupling coefficient β

Figure 5: RF input requirement as function of the coupling
coefficient β for a cavity voltage of 30kV.

Proceedings of FEL 2007, Novosibirsk, Russia

frequency acceptance f [MHz]for V c > 30kV

50

0.8

30

0.6

20

0.4

10

β= 20,Q0=4000
β=9.6,Q0=1000
β=9.6,Q0=4000

Pref/P in



2850

2860

2870

P ref / P in

40

0
2840

25

1.0

Vc
Cavity voltage V c [kV]Firstly, we drew tuning curves for various coupling
coefficients for Q 0 = 4000 and Pin = 40 kW, and thus
obtained the Figure 6 showing the frequency acceptancefor Vc > 30 kV as a function of β. In Figure 5 and Figure 6,
we can see more than 20MHz of frequency acceptancecan be ensured by β = 20, and the required RF feed powerat resonant frequency is ~20 kW still below the RF feed
limitation of 40 kW.

WEPPH026

0.2
0.0
2880

Drive frequency [MHz]Δ

Figure 7: Tuning curves of the additional small cavity,
taking the electron beam admittance Yb into consideration.

20

SUMMARY
15
5

15

25

Coupling coefficient β

Figure 6: Frequency acceptance Δf for Vc > 30kV, as afunction of the coupling coefficient β (Pin = 40 kW, Q0 =4000)
The red lines in Figure 7 show the calculated tuning
curves of the designed additional small cavity (β = 20 and
Q 0 = 4000 for oxygen-free copper cavity) with Pin = 40
kW. Note that the calculations take the electron beamadmittance Yb into consideration. In Figure 7, the solidlines represent the cavity voltage Vc, the dashed lines the
RF power reflection ratio Pref/Pin. The black lines in
Figure 7 shows those for β = 9.6 and Q 0 = 4000 forcomparison.
Secondly we consider a lower Q 0 of ~1000 for astainless steel (SUS) cavity. The SUS cavity can lower the
coupling coefficient β in the same frequency acceptance,
so the coupler design is easier than over coupling. The
blue lines in Figure 7 show curves for β = 9.6 and Q 0 =1000. It is found that the SUS cavity can realize the moregentle tuning curves by the lower Q0. However thefrequency acceptance for Vc > 30 kV is found not to be
wider, and furthermore the maximum available cavity
voltage Vc at resonance is lower.
Thus the additional small cavity for the triode system is
to be made of an oxygen-free copper with an overcoupling of ~20 with the coaxial RF feed cable.

In this study, we evaluated the reduction of the backbombardment and the output beam properties in a triodetype thermionic RF gun with PIC simulations. With an RF
power of ~20 kW fed to the additional small cavity for thetriode system, the back-bombardment power is expected
to reduce to 3.6 kW from 36 kW in conventional RF gun.
Furthermore, the output beam properties at the 4.5-cell RF
gun exit, such as the beam emittance and the peak current,
are improved as the result of the triode geometryrefinement. Especially a great improvement of the peakcurrent is expected because the bunch length of electron
beams is to be shortened by using the RF triode system.
We also designed the coupling coefficient β, the shunt
impedance R/Q, and the quality factor Q0 to ensure a wide
frequency acceptance. Now we are then designing thecoupler geometry realize the designed coupling
coefficient. We are planning to install a triode-type
thermionic cathode based on the designed geometry andparameters for the first experiment this year.

REFERENCES[1] T. Kii, et al., Nuclear Instruments and Methods inPhysics Research A 475 (2001) 588.
[2] K. Masuda, et al., Nuclear Instruments and Methods inPhysics Research A 483 (2002) 315.
[3] T. Kii, et al., Proc. 9th Intnl. Conf. Synchrotron
Radiation Instrumentation, 2006
[4] T. Kii, et al., Proc of FEl2005 (2006) 584.
[5] E. Tanabe et al., Proc of 27th Linear Accelerator
Meeting in Japan, 2002, pp.57 (in Japanese).
[6] K. Kusukame, et al., Proc of the 30th Linear
Accelerator Meeting in Japan, 2005
[7] K. Masuda, et al., Proc of FEL2006[8] K. Masuda, a dissertation of Ph, D. Kyoto University,
1998

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Proceedings of FEL 2007, Novosibirsk, Russia

NUMERICAL STUDY ON THE OPTIMUM CAVITY VOLTAGE
OF RF GUN AND BUNCH COMPRESSION EXPERIMENT IN KU-FEL
H. Zen#, T. Kii, K. Masuda, H. Ohgaki, S. Sasaki, T. Shiiyama,
Institute of Advanced Energy, Kyoto University, Gokasho, Uji, Kyoto, 611-0011

INTRODUCTION
A mid-infrared free electron laser facility (3-14 μm)
named KU-FEL was constructed for the energy science inInstitute of Advanced Energy, Kyoto University [1]. As
shown in Fig. 1, the facility consists of an S-band 4.5 cellrf gun with a tungsten dispenser-type thermionic cathode,an energy filtering section (Dog-leg), a S-band accelerator
tube (3 m), a bunch compression section (180-deg. arc),
an undulator and an optical cavity. Electron beams weresuccessfully accelerated up to 40 MeV [2]. However, due
to the back-bombardment effect [3,4], the bunch charge
and macro-pulse duration have a trade-off relationshipand the bunch charge was limited to smaller than 30 pC
with the macro-pulse duration of ~3 μs. Thus the bunch
compression is necessary to obtain a peak current of
Dog-leg
4.5 cell Slit
Thermionic
RF Gun180 deg.
ARC
S1

Accelerator Tube

45 deg. Bending Magnet
60 deg. Bending Magnet
Quadrupole Magnet
MirrorBeam Dump
P
Undulator

Figure 1: Schematic view of KU-FEL facility.
___________________________________________#

heishun@iae.kyoto-u.ac.jp

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STUDY ON THE OPTIMUM FIELD
STRENGTH OF RF GUN
Dependences of the longitudinal emittance and theaverage current on the average field strength of the firsthalf cell of the 4.5 cell rf gun were shown in Fig. 2. The
field strengths of other 4 cells are about twice higher thanthat of the first cell. The longitudinal phase space
distributions at the entrance of the accelerator tube wereshown in Fig. 3. As mentioned in the introduction, thehigher average current is available after the energy
filtering section if the higher field strength of the cells is
induced. As shown in Fig. 2 and 3, however, thenonlinearity of the longitudinal phase space distribution
and the corresponding longitudinal emittance rise up if
too high electric fields (>25 MV/m) are induced. Highbunch charge and low longitudinal emittace are required
to obtain high peak current after bunch compression.
200

80
60

Average Current

150

40

100

20

50
Long.
Emittance
0
26
28
30

0
18

20

22

24

Long. Emittance [deg-keV]High peak current (~40 A) electron beams with themacro-pulse duration of 2-5 μs are required for the lasingof Kyoto University Free Electron Laser (KU-FEL).
However, the bunch charge and macro-pulse duration in
the facility have a trade-off relationship, and the bunchcharge is limited to <30 pC when the macro-pulse
duration is ~3 μs. Therefore, the optimization ofoperational condition of our thermionic rf gun and thebunch compression are necessary to achieve such a highpeak current. Optimum field strength of our rf gun was
surveyed by numerical simulation. The result indicatesthat the highest peak current is around 23 A with theaverage field strength of 24 MV/m. Under the same
condition, bunch lengths of electron beams were
measured by using a streak camera. The condition ofbunch compression was also surveyed in experiment. The
measured minimum bunch length was 2.0 ps, which was
as short as the temporal resolution of the measurement
system. Since the bunch charge was 14 pC, the highest
peak current was estimated to be more than 7 A from theexperimental result.

~40 A, which is required to achieve the FEL saturation [5]in KU-FEL. Another feature of the gun is that the higher
average current is available after energy filtering section
if the higher electrical fields are induced to its cavities.
On the other hand, the nonlinearity of longitudinal phasespace distribution, which enlarges a bunch length during abunch compression, increases if too high electrical fields
induced. It means that there is the optimum operational
condition of the field strength of rf gun to obtain thehighest peak current. In this study, first, the optimum fieldstrength of the gun was surveyed by numerical simulation.
Second, the bunch length was measured and the optimum
bunch compression condition was determined under the
gun condition in experiment. PARMELA [6] was used forparticle tracking from the gun to the undulator. And
ELEGANT [7] was used to find the achromatic sets ofquadrupole magnets of dispersive section in simulationand experiment. And the code was also used to calculate
and control the R56 of the arc.

Average Current [mA]

Abstract

Field Strength of First Cell [MV/m]
Figure 2: Longitudinal emittance and average current
as a function of the field strength of first half cell.

1.0

19

24

29 [MV/m]

Energy Spread (rms)dE/E [%]

Relative Energy [%]Proceedings of FEL 2007, Novosibirsk, Russia

0.5
0.0
-0.5
-1.0
-5

0

5

10

0.6

29 MV/m

0.4
24 MV/m

0.2
0.0
120

15

125

Phase [deg.]

Table 1: Typical parameters of the electron beam underthe 24 and 29 MV/m conditions.
Field Strength
Gun
24
29
of First Cell [MV/m]
Peak Energy [MeV]
7.5
9
Gun
Average Current [mA]
320
320
Exit
3.3
3.3
Macro-pulse Duration [μs]AfterAverage Current [mA]40
70
Dog-leg Macro-pulse Duration [μs]2.4
2.4

Figure 4: Energy spread as a function of phase difference
between the rf gun and the accelerator tube.

Bunch Length [ps]There are two candidates of the field strength for thehighest peak current. One is around 24 MV/m which havethe smallest longitudinal emittance with a medium bunchcharge. The other is 29 MV/m which have the highest
bunch charge with the largest longitudinal emittance.
Due to the transient energy drop by the backbombardment effect, in practical experiment, there is atrade-off relationship between the average current and themacro-pulse duration after the energy filter, which meansthat the macro-pulse duration decreases if the average
current increases. Table 1 shows the typical parameters ofelectron beams that have the highest average currents
with the macro-pulse duration of 2.4 μs under the 24 and
29 MV/m conditions. In this numerical study, beam
parameters were adjusted to those shown in Table 1.

130

Phase Difference [deg.]

10
9
8
7
6
5
4
3
2
1
0

29 MV/m
24 MV/m

-0.6

-0.4

-0.2

0.0

R56 of 180 deg. arc
Figure 5: Bunch length as a function of R56 of the 180
deg. arc.
25.4

Energy [MeV]

Figure 3: Longitudinal phase space distribution at theentrance of accelerator tube (simulation).

WEPPH027

25.2
25.0
24.8
-5

0

5

10

15

10

15

Phase [deg.]
The bunch compression properties under the 24 and
29 MV/m condition were examined by numericalsimulation. The energy after the accelerator tube was set
to about 25 MeV by adjusting field strength. Under bothof the two conditions, the energy spread is minimal when
the phase difference between the gun and the tube set to
126 deg. as shown in Fig. 4. An energy chirping isessential for the bunch compression and we gave theenergy chirp by selecting the phase difference of 121 deg.
Dependences of the bunch length on R56 with energy
chirping are shown in Fig. 5. The bunch length wasevaluated by the least square fitting of Gaussian
distribution to the temporal distribution. The longitudinal
phase space distributions under the minimum bunch
length condition are shown in Fig. 6, and the temporal(a) 24 MV/m condition, R56 = -0.3.
25.4

Energy [MeV]

Bunch Compression

25.2
25.0
24.8
-5

0

5

Phase [deg.](b) 29 MV/m condition, R56 = -0.1.
Figure 6: Longitudinal phase space under the minimum
bunch length condition.

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Proceedings of FEL 2007, Novosibirsk, Russia

profiles are shown in Fig. 7. The peak current was also
evaluated by the Gaussian fitting and the results areshown in Table 2. As you can see in Fig. 6 and Fig. 7, all
the electrons are bunched well under the 24 MV/m
condition, and the electrons are not bunched well underthe 29 MV/m condition. Thus the peak current under the
24 MV/m condition was higher than 29 MV/m condition
as shown in Table 2, even though the total bunch charge
was lower.

Charge [pC / 0.1ps]

1.4
1.0
0.6
0.4
0.2
0

2

4

6

8

10

12

14

Phase [deg.]
Figure 7: Temporal distributions with the minimum bunch
length condition.
Table 2: Results of numerical simulations.
Field Strength of First Cell [MV/m]
2429
Total Bunch Charge [pC]
14
25
Bunch Length [ps]0.6 0.5
Peak Current [A]23
16

BUNCH LENGTH MEASUREMENT AND
BUNCH COMPRESSION
The bunch length measurements and the bunch
compression were carried out to determine the optimum
condition of bunch compression in experiment under the
24 MV/m condition. In experiment, the beam parameters
before the accelerator tube were same with ones shown in
Table 1. The central energy after the tube was adjusted to
25 MeV, and the phase difference between the gun andthe tube was adjusted to the condition that the horizontal
beam size at the beam profile monitor S1 in Fig. 1
became minimal.

StreakCameraSlit Width=100 mmParabolic
Mirrorf = 152 mm
r = 25 mm

Parabolic
Mirrorf = 101 mm
r = 25 mm

~3 m

OTR

Electron Beam

Figure 8: Setup of optics and streak camera.
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Klystron
Acc.
Tube

Amp

2856 MHz
CW

Pulse

Amp

Amp

KlystronRF
Gun

89.25 MHz Analog
Frequency
Divider 1/32
Delay

StreakCameraExperimental Setup

0.8

0.0

Pulse

Figure 9: Trigger diagram for the streak camera.

24 MV/m
29 MV/m

1.2

Phase
Shifter

SignalGenerator

A mirror target to generate optical transition radiations(OTRs) from electron beams was inserted at the position
P in Fig. 1, and the OTRs were transported to and focusedon the entrance slit of a streak camera (HAMAMATSU
C6138S) by a pair of parabolic mirrors as shown in Fig. 8.
The focusing mirror enables to minimize the deteriorationof temporal resolution with the least weakening of the
OTR. The slit width of streak camera was limited to over
100 μm due to weak OTRs, and we use 50 ps full scale
range. Then, the temporal resolution was around 2.0 ps.
The trigger diagram for the streak camera is shown in
Fig. 9. The trigger signal was generated by using afrequency divider (1/32) from rf power fed to the rf gun inorder to synchronize the trigger signal with the electron
beam.

Result and Discussion
Figure 10 shows the typical result of the bunch length
measurement and it was integration of 10 shots. When thetemporal profiles were integrated, the mean of eachtemporal profile were aligned in order to mitigate thedeterioration of temporal resolution due to timing jitter(~10 ps) of the trigger signal.

σt = 2.1 ps

300

Count [a.u.]

WEPPH027

200
100
0
0

10

20

30

40

50

Time [ps]Figure 10: Typical result of the bunch length
measurement. This result was integration of 10 shots.
Dependences of measured bunch lengths on R56 of 180deg. arc section were shown in Fig. 11. These results arealso integration of 10 shots. The minimum bunch length
was around 2.0 ps with R56 = -0.3, -0.4. The result was asshort as the temporal resolution of this measurement
limited by slit width of the streak camera. Therefore, theProceedings of FEL 2007, Novosibirsk, Russia
actual bunch length must be shorter than 2.0 ps. The peakcurrent of electron beam was measured to be more than
7 A, since the bunch length was shorter than 2.0 ps andthe bunch charge was 14 pC. Higher temporal resolution
is required to discuss shorter bunch lengths and to shorten
the bunch length under 2.0 ps.

Bunch Length [ps]

4.0
3.5

WEPPH027

system. Thus the peak current was estimated to be morethan 7 A in this experiment. Higher temporal resolution isrequired to discuss shorter bunch length and to obtainhigher peak current. And now, we are preparing a
configuration which enables us measurements with higher
temporal resolution.
The peak current about 23 A is not enough to achieve
FEL saturation [5] in KU-FEL, even if we could shorten
the bunch length to 0.6 ps in experiment. To obtain higher
peak current, we are now preparing a LaB6 cathode [8]and a triode-type rf structure [9,10].

3.0

REFERENCES

2.5
2.0
1.5
-1.0

Resolution
-0.5

0.0

0.5

R56 of 180-deg. arc
Figure 11: Experimental result of dependences of bunch
lengths on R56 of 180-deg. arc section.

CONCLUSION
The optimum cavity voltage of our thermionic rf gun
was studied by numerical simulation. The result indicatedthat the field strength of first cell should be around
24 MV/m to obtain high peak current in present setup.
The highest peak current was about 23 A under thecondition. The bunch length measurement and bunch
compression were performed under the optimum
condition. The measured minimum bunch length was 2.0
ps when R56 was -0.3, -0.4. The minimum bunch length
was as short as the temporal resolution of measurement[1] T. Yamazaki, et al., “KU-FEL: A compact andeconomical S-band linac based FEL for advancedenergy science” in Proc. of 23rd Int’l FEL Conf.,
North-Holland, Amsterdam, ( 2002), II-13.
[2] H. Ohgaki, et al., NIM, A528, 366-370 (2004).
[3] C. B. McKee, et al., NIM, A 304 (1991) 386.
[4] K. Masuda, et al., NIM A 483 (2002) 315.
[5] M. Nakano, et al., Proc. of FEL 2006, 2006, p656660.
[6] L. M. Young, James H. Billen, LA-UR-96-1835(2002)[7] M. Borland, “User’s Manual for elegant”, v.15.4.1(2005).
[8] F. Oda, et al., Proc. of the 26th Linear Accelerator
Meeting in Japan, p67-69 (in Japanese).
[9] K. Masuda, et al., Proc. of FEL 2006, (2006), p656660.
[10] T. Shiiyama, et al., WEPPH026, these proceedings.

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Proceedings of FEL 2007, Novosibirsk, Russia

DEVELOPMENT OF A COMPACT CHERENKOV FREE-ELECTRONLASER OPERATING IN TERAHERTZ WAVE RANGE
Nozomu Miyabe∗ ,Akira Ikeda,Makoto R.Asakawa,Mitsuhiro Kusaba,Yoshiaki Tsunawaki
Kansai University, 3-3-35 Yamate-cho, Suita, Osaka 562-8680, Japan
Osaka Sangyo University, 3-1-1 Naka-gaito, Daito, Osaka 574-8530, Japan

Abstract
We designed a compact Cherenkov Free-Electron Laser(CFEL) oscillator driven by 50keV electron beam. The resonator, called double-slab resonator, consists of a rectangular waveguide partially filled with two lined parallel siliconslabs, whose dielectric constant ε equals to 11.6 in the terahertz frequency range. The operation frequency ranges
from 40GHz to 1THz according to the thickness of theslabs. Numerical calculation predicted 100W-level output
at 46GHz by electron beam with 50keV/400mA.

OPERATING FREQUENCY OF THE
DOUBLE-SLAB RESONATOR
Our purpose is to develop a CFEL oscillator operating in
the terahertz frequency range driven by a low energy electron beam [1]. We examine the operating frequency of the
double-slab resonator fed by 50keV electron beam in thissection.
Fig.1 shows the schematic view of the double-slab resonator. To simplify the problem, it is assumed that its transverse dimensions are 2(D + d) and infinite, where D and d
are the vacuum half width and the thickness of the dielectric slab with dielectric constant of ε, respectively.
X

metallic boundary

d

Z

D

electron beam

dielectric slab

XZ

metallic boundaryY

Figure 1: Schematic form of the waveguide partially filledwith two lined parallel dielectric slabs with the thickness of
d. Electron beam propagates along the Z-axis in the spacing of the slabs with the width of 2D.
In CFEL oscillator, the radiation is gained by the interaction between the longitudinal electric field Ez and thestraightly moving electron [2]. TM modes whose Ez distributes in a symmetrical pattern to the x=0 plane are, therefore, of interest. The electromagnetic field of the symmet∗ sa6m051@edu.kansai-u.ac.jp

FEL Technology I

406

ric TM mode, in concrete terms TM1 , TM3 , TM5 .., is expressed as following. [3]In vacuum region: 0 < |x| < D kz
p sinh px eiθ
E(x, z, t) = Ez0 0i cosh px(1)0H(x, z, t) = Ez0  kp0 sinh px  eiθ
0
In dielectric region: D < |x| < D + d
´
 ³
0
0
kz
εp F cos θ + G sin θ iθE(x, z, t) = Ez0 
e
0
0
0
q
−i εp
(F sin θ − G cos θ )

0
³
´
0
0 

H(x, z, t) = Ez0 kp0 F cos θ + G sin θ  eiθ (2)0where Ez0 is the amplitude of Ez at x=0, kz and ω
are the wavenumber and angular frequency, respectively.
The transverse wavenumbers in the vacuum and dielectric regions are defined as p2 = kz2 − ω 2 /c2 and q 2 =εω 2 /c2 − kz2 , respectively. Here the free-space wavenumber k0 = ω/c, the longitudinal phase of the radiation field0
θ = kz z − ωt, the transverse phase θ = (x − D)q,
the constants determined by the resonator configuration
F = sinh pD, G = ε pq cosh pD.
The dispersion relation is given byp(3)
ε cos qd cosh pD − sin qd sinh pD = 0.
q
Fig.2 shows the dispersion curves for TM1 mode forslabs of silicon (ε=11.6) with thickness d=0.65mm and30µm. In CFEL, the radiation resonates with electron
beam if the phase velocity w/kz is equals to the electron
velocity. Thus the intersections of the curves and the beammode line w = βz kz are the resonant points. The resonant frequencies are 46.0GHz and 983 GHz for d=0.65mm
and 30µm, respectively. The numerical calculations of thedispersion relations found that the resonant frequency wasalmost inversely proportional to the thickness d.
On the other hand, the resonant frequency suggests a little dependence on the width of vacuum region D as shownin Fig.3. It decreases only by 3% as the thickness D increases from 0.325mm to 1.3mm.
However, the vacuum width D has a substantial effecton the radiation filed strength of Ez in the vacuum region,

3000040000

ω／c

WEPPH028

50000

Proceedings of FEL 2007, Novosibirsk, Russia

20000

f=983GHz
f=46.0GHz
(a)

0

10000

D=0.75mm

0

10000

20000

30000

40000

50000

kz

Figure 2: Dispersion curves of the double-slab resonator.
Lower and upper curves show the dispersion for d=0.65mm
and 30µm, respectively. Dashed line shows the velocity of
50keV.

(b)

Figure 4: Field distributions for the vacuum width!"

resonant frequency (GHz)

D=0.5mm#"edγi (t)= − 2 vzi (t)Ez (zi , t)
(5)
dt
mc
where Ez (z, t) = Ez0 cos(ωt − kz zi ), e is the electron
charge, m is the electron rest mass, c is light velocity inthe vacuum, and γ is the relativistic factor. The subscripti refers to the quantities of the i-th particle. The powerincrement for the radiation is related to the decrease in the
average electron energy:

$"

%"

&"

"
"

%""

#""

(""

'""

&"""

&%""

&#""

<

vacuum width (μm)

Figure 3:Thethe vacuum width D.

resonant

frequency

versusi.e. the interaction region. Fig.4(a) and Fig.4(b) show theEz distributions at 46.0GHz for D=0.75mm and 0.5mm,
respectively. As the width 2D decreases from 1.5 mm to
1.0 mm, the Ez0 increases by a factor of 1.6. To obtain
substantial interaction, one should reduce the width of vacuum region D less than 2d. For higher operating frequency,
thus, the beam focusing will be the issue.

In this section, we describe the design of a 46GHz
CFEL oscillator for the preliminary experiment. The required resonator configuration, start-up current, the gain
and the saturation power were investigated by using the
one-dimensional numerical simulation code.
The calculation of CFEL interaction was based on thefollowing equations.
ed2 zi (t)= − 3 Ez (z, t)
dt2
γ m

(4)

(6)

dγ
I
dP
=−<
> mc2
(7)
dt
dt
e
where n is the number of electron, and I is beam current.
The radiation power inside the resonator is calculated byR
P = s S · ez dxdy
(8)2
= A(ω, kz )Ez0
where,A (ω, kz ) =NUMERICAL STUDY ON THE CFEL
OSCILLATOR AT 46GHZ

1 X dγi
dγ
>=
dt
n
dt

kz k0
4εp2

· ³
´
2pD
−2pD
−
2D
ε e −e
2p

+

´
³
´
h ³
2qd
4 F 2 sin4q2qd + d2 + F G 1−cos
2q

+

G2

³

sin 2qd
d
2 −
4q

´ i¸
(9)

From these equations, Ez0 of the gained radiation was
evaluated, and then it is used to calculate the radiation fieldat the next time step.
To gain the radiation at 46.0GHz, the electron energy
should be detuned from the resonant energy of 50keV. The

FEL Technology I

407

Proceedings of FEL 2007, Novosibirsk, Russia

amount of the detuning was represented with a factor αwhich means γ = αγ0 : γ0 = 50/511 + 1. Fig.5 shows thedependence of the small-signal gain on the detuning factor α for the resonator length L=11cm with 400mA electron beam. The meaningful gain is obtained in the range
1.0005 < α < 1.005, and the gain reaches the maximum
at α = 1.0022. Because the optimal α is related to the slippage between the radiation and electron, the optimal valuechanges with the resonator length L.
!"

net gain (%)

small-signal gain(%)#

The radiation grows with a net gain of 3.57% until 600
round-trips, then saturates around the 800 round-trips at thesaturation power of 97W. In the practical situation, the duty
cycle should be limited to 1/1000 to avoid thermal damage.
The average power of the practical device will be 100mW
level.
output power (W)

WEPPH028$%

round-trip
&

"
!'"""

!'""!

!'""&

!'""(

α

!'""%

Figure 5: The dependence of the small-signal gain on the
detuning factor α for the resonator length L=11cm.

CFEL TEST BENCH
To demonstrate 46GHz lasing experiment, we constructed the CFEL device consisting of Spindt-Type Cathode, the silicon double-slab resonator, and superconducting
coil. Spindt-Type Cathode can generate 100mA electron
beam from emission area of 0.52 × π mm2 . Fig.8 shows
picture of the silicon double-slab resonator. The slab has
the thickness of 0.65mm and the width of 5mm. Superconducting coil produces magnetic flux density up to 5T. Thisstrong field will focus the electron beam.

"

#(""!

$

#(""%

#(""'

#"

α

#(""&

#$

small-signal gain(%)

#("#"

α

#("#!

!"

gain (%)

Figure 7: Upper trace shows the output power growth ofthe electromagnetic wave verses the round-trip. Bottom
trace shows the net gain verses the round-trip. The lasing frequency is 46GHz, the resonator length is 11cm. The
electron energy is 50keV, and the beam current is 400mA.

"

!

%

resonator length (cm)
'

&

#"

#!

#%

Figure 6: The dependence of the small-signal gain and optimal α on the resonator length.
Red circles in Fig.6 show the dependence of the smallsignal gain on the resonator length. Blue circles show the
optimal α for each resonator length. The small-signal gain
varies as L3.03 . The optimal α decreases with L: α − 1 isinversely proportional to L. We chose L=11cm for practical design because the gain exceeds enough the loss in theresonator, as well as the slabs of this length can be cut fromthe standard wafer for the semiconductor applications.
Fig.7 shows evolution of the CFEL output power and net
gain. The resonator length is 11cm. We assumed the total
loss of 5% each round-trip including the dielectric loss of
4% and the extraction efficiency of 1%.
FEL Technology I

408

Figure 8: The double-slab resonator

REFERENCES[1] M.R.Asakawa,
K.Nakao,N.Miyabe,
M.Kusaba,
Y.Tsunawaki,
Proceedings
of
FEL
2006,
BESSY,Berlin,Germany, p364.
[2] J.Walsh, B.Johnson, Phys.Rev.Let.Vol.53 (1984) 779.
[3] Wladyslaw Zakowicz, J.Appl.phys.,Vol.55, (1984) 3421.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH029

DEVELOPMENT OF THE LONGITUDINAL PHASE-SPACE MONITORFOR THE L-BAND ELECTRON LINAC AT ISIR, OSAKA UNIVERSITY*
R. Kato#, S. Kashiwagi, T. Igo, Y. Morio, G. Isoyama
ISIR, Osaka University, Ibaraki, Osaka 567-0047, Japan
Abstract
In order to measure the longitudinal phase-space profileof the high-brightness electron beam, we are developing
the measurement system consisted of a profile monitor, abending magnet and a streak camera. Instead of an opticaltransition radiation (OTR) monitor as previously
considered, a Cherenkov radiator with a hydrophobic
silica aerogel is used as a profile monitor. Due to thephysical limitation at the installation location, we
designed a simple radiator supported with a metallic
mirror. The Cherenkov radiator has been designed, and it
is in the process of production.

INTRODUCTION
The performance of the self-amplified spontaneousemission free-electron laser (SASE-FEL) strongly
depends on beam parameters, such as a longitudinal beamprofile, bunch charge, the transverse emittance and an
energy profile. A correlation between longitudinal
positions of electrons in a bunch and their energies has a
crucial effect on the temporal evolution of the opticalpulse of SASE. Several types of methods are extensively
under study to evaluate the longitudinal phase-space
profile of the electron beam [1-4].
A measurement system of the longitudinal phase-space
distribution of electrons using the combination of abending magnet, a profile monitor and a streak camera are
currently under development at the Institute of Scientificand Industrial Research (ISIR), Osaka University. In the
preliminary experiments using an optical transition
radiation (OTR) monitor as the profile monitor, it was
confirmed that the monitor had higher momentum
resolution rather than the ordinary used momentum
analyzer using a slit and a current monitor [5]. However,
we could not get the efficient number of photons to obtain
the phase-space images since, in addition to low photon
yield, the angular distribution of the OTR is too large toconcentrate in the electron energy region of 10 – 20 MeV,
which is suitable energy for THz-SASE and THz-FEL
experiments conducted at this laboratory [6-8]. In order toincrease the number of photons, we try to use a Silica
aerogel as a profile radiator using example from theresults at PITZ [2]. In this report, we introduce the designof the longitudinal phase-space monitor using a Silica
aerogel Cherenkov radiator and the system layout.

___________________________________________*Work supported by Japan Society for the Promotion of Science(JSPS), Grant-in-Aid for Scientific Research (C), 18540273, 20062007.
#
kato@sanken.osaka-u.ac.jp

PROPERTIES OF AEROGEL AND ITS
CHERENKOV RADIATION
Aerogel is a low-density light-weight solid material
produced by replacing the liquid component in the gelwith gas. Silica aerogel, which is a silica-based substance,is the most common type of aerogel and has extremely
light weight, extraordinary thermal insulation abilities, etc
as a feature. We use a hydrophobic silica aerogel
manufactured by Matsushita Electric Works, Ltd. (MEW).
They supply several types of aerogel as shown in Table 1.
In high energy particle physics, these aerogels are also
used as radiators in Cherenkov detectors of the Belle
detector system at KEKB.
Table 1. Characteristics of hydrophobic silica aerogels.
Aerogel type
SP-15
SP-30
SP-50
index of refraction
1.015
1.03
1.05
density (g/cm3)
0.06
0.11
0.19
Cherenkov radiation is emitted when a charged particle
passes through a medium at a velocity greater than the
speed of light in that medium. Cherenkov radiation isemitted in a cone having a subtended angle 2θCR, which isdetermined by the average index of refraction in themedium n and the particle velocity β as follows:cos θ CR =

1 .

βn

(1)

Figure 1 shows the emission angle of Cherenkov
radiation in the aerogel radiator versus the electron energy.
Above the electron energy of 10 MeV, the emission angle
is almost constant. However, the angle is too large togather all rays of light. The number of photons NCR
radiated as Cherenkov radiation with wavelengths
between λ1 and λ2 per a distance d along the path of theelectrons is represented as follows:
⎛1
1 ⎞⎛
1 ⎞
N CR = 2παd ⎜⎜ − ⎟⎟⎜⎜1 − 2 2 ⎟⎟
λ
λ
β
n ⎠,
⎝ 1
2 ⎠⎝

(2)

⎛1
1 ⎞
= 2παd ⎜⎜ − ⎟⎟ sin 2 θ CR
λ
λ
2 ⎠
⎝ 1

where α is the fine structure constant. Figure 2 shows thenumber of photons emitted from the aerogel with different
indices of refraction. In this case, the wavelength region isassumed to be equal to the sensitivity region of the streak
camera (400 ~ 800 nm). The photon yield of Cherenkov

FEL Technology I

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Proceedings of FEL 2007, Novosibirsk, Russia

radiator is attached with a tilt angle of 55.8°. Hereby theeffective thickness of the aerogel becomes 2.7 mm.

20

Emission angle [deg]SP-50(n=1.050)
15

ESTIMATION OF PHOTON YIELD

SP-30(n=1.030)

SP-15(n=1.015)

10

5

0

0

10

20

30

Electron energy [MeV]Intensity [Photons/electron/mm]

Figure 1: The emission angle of Cherenkov radiation in
the aerogels with different indices of refraction.

6
SP-50(n=1.050)

A part of the Cherenkov light cone is taken out from thevacuum chamber to the air through a sapphire vacuum
window and is transported to the streak camera by mirrors.
The light accepted by the first concave mirror is estimatedapproximately to 10 % of the total radiation. In order toeliminate broadening of the pulse width of light in the air,an interference filter will be used. Assuming that the filter
has a wavelength range from 400 nm to 410 nm and thatits transmittance is 40 %, the photon yield on the entrance
slit of the streak camera is expected to 0.027 photons perelectron. The number of electrons in a single bunch
accelerated by the L-band linac is typically about 2 x 1011.
The net number of photons produced by one bunch is
expected to be 5.4 x 109 on the slit.

4SP-30(n=1.030)

20SP-15(n=1.015)

0

10

20

30

Electron energy [MeV]

Figure 2: The number of photons as Cherenkov
radiation per electron per 1 mm distance emitted fromthe aerogels with different indices of refraction.
radiation per incident electron in the visible region islarger than that of OTR by two orders of magnitude.

DESIGN OF CHERENKOV RADIATOR
We intend to install the Cherenkov radiator in the beamtransport line form the linac to the FEL system as shownin Figure 3. Due to the physical limitation at the
installation location, we can not bring a complicatedmechanism into a vacuum. We designed a simple radiator
supported with a metallic mirror as shown in Figure 4. In
this radiator, we use a thin aerogel with a dimension of 45
x 30 mm2 and a thickness of 1.5 mm manufactured by
MEW as a trial. For this thickness, they can produce theaerogels only with the refractive indices of 1.03 (SP-30)
and 1.05 (SP-50). Since the aerogels SP-30 are fragile andalmost half of them were cracked, we decide to use theaerogels SP-50. Figure 5 shows the example of the
manufactured aerogels.
Cherenkov radiation in the aerogel SP-50 is emitted ina cone having a subtended angle of 35.5°. The light isreflected by the metallic mirror into the aerogel again andis refracted by the surface between the aerogel and avacuum. In order that the direction of the Cherenkov
radiation emitted upward in the aerogel may be
perpendicular to the horizontal plane in a vacuum, the
FEL Technology I

410

Figure 3: Configuration of the Cherenkov radiator.

Figure 4: Schematic design of the Cherenkov radiator.

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 5: A thin hydrophobic silica aerogel used as a
Cherenkov radiator with a thickness of 1.5 mm andthe refractive index of 1.05.
In the meanwhile, the view size of a CCD camera usedin the streak camera is 10(H) x 9.5(V) mm2. Since theratio of the entrance lens of the streak camera is 1/3, an
acceptable horizontal width is approximately 30 mm on
the entrance slit. If the effective horizontal size of the
aerogel without a folder (40 mm) is matched to this size,
the aerogel screen size is projected to 30 x 10.5 mm2 on
the entrance slit. If the photons spread on this area
uniformly, the density of photon is 1.7 x 107 photons /mm2. This density exceeds the detection limit of thestreak camera on the entrance slit, 5,000 photons / mm2. A
streak image of Cherenkov radiation will be obtainedusing this system.

EVALUATION OF ENERGYRESOLUTION
The Cherenkov radiator is placed at a position 320 mm
downstream from the first bending magnet as shown in
Figure 3. Since dispersion function η is 0.4 m at theposition of the Cherenkov radiator, the energy acceptanceof the measurement system and the energy resolution on
the radiator are estimated to be 10 % and 0.25 % / mm,
respectively. However, the beam image is considered to
be broadened due to the thickness of the Aerogel. In order

WEPPH029

Figure 7: The drive assembly of the Cherenkov
radiator with a two-staged stroke. The first stage is a
profile monitor with a fluorescence ceramic screen,
and the second stage is the Cherenkov radiator withthe aerogel.
to evaluate this broadening, we plan to measure the beamprofile with a fluorescence ceramic screen with athickness of 0.1 mm at the same location. Figures 6 shows
a drawing of the screen folder mounted with both of theceramic screen and the Cherenkov radiator, and Figure 7
shows the photograph of its drive assembly with a twostaged stroke. There is a wire scanner profile monitor at
the straight beam line of the L-band linac, and we havealready evaluated the broadening of the profile size
obtained by the ceramic screen with the wire scanner.
Calibrating the broadening of that due to the aerogel withthe ceramic screen, the energy resolution will be
evaluated precisely.

SUMMARY
In order to measure the longitudinal phase-space profileof the electron beam, we are developing the measurement
system consisted of a Cherenkov radiator, a bending
magnet and a streak camera. The Cherenkov radiator with
an aerogel has been designed, and it is in the process of
production.

ACKNOWLEDGEMENTS
The authors express their sincere thanks to Mr. T.
Yamamoto for his technical contribution and Mr. S.
Suemine for his support of linac operation.

REFERENCES[1] A. Doria et al., Nucl. Instr. and Meth. in Phys. Res. A
475, (2001) 296.
Figure 6: Screen folder mounted with both of aceramic screen and a Cherenkov radiator. (1) The firstscreen is a profile monitor with a fluorescenceceramic screen with a thickness of 0.1 mm and it istilted vertically by an angle of 45° with respect to thebending orbital plane. (2) The second screen is the
aerogel radiator and it is tilted of 55.8°.

[2] J. Rönsch et al, “Investigations of the longitudinalbeam properties at the photoinjector test facility in
Zeuthen”, FEL’06, BESSY, Berlin, Germany, August
2006, p.597, http://www.jacow.org.
[3] H. Loos et al, “Experimental Studies of Temporal
Electron Beam Shaping at the DUV-FELFEL Technology I

411

WEPPH029

Proceedings of FEL 2007, Novosibirsk, Russia

Accelerator”, FEL’05, Stanford, August 2005, p.632,
http://www.jacow.org.

[6] R. Kato et al, Nucl. Instr. and Meth. in Phys. Res. A
445 (2000) 164.

[4] S. Zhang et al, “Temporal Characterization ofElectron Beam Bunches with a Fast Streak Camera at
the JLab FEL Facility”, FEL’05, Stanford, August
2005, p.640, http://www.jacow.org.

[7] R. Kato et al, Nucl. Instr. and Meth. in Phys. Res. A
475 (2001) 334.

[5] R. Kato et al, “Longitudinal phase-spacemeasurements of a high-brightness single-bunchbeam”, FEL’06, BESSY, Berlin, Germany, August
2006, p.676, http://www.jacow.org

FEL Technology I

412[8] R. Kato et al, Nucl. Instr. and Meth. in Phys. Res. A
483 (2002) 46.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH030

DEVELOPMENT OF A PRECISE TIMING SYSTEMFOR THE ISIR L-BAND LINAC AT OSAKA UNIVERSITY
Shigeru Kashiwagi*, Goro Isoyama, Ryukou Kato, Shoji Suemine
ISIR, Osaka University, 8-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan
make an arbitrary delayed timing signal, a standard digitaldelay generator is used to make a gate signal for a GaAs
rf switch, which slices out one of the 27 MHz clock
pulses to generate the delayed timing signal. Any timing
signal can be made at an interval of 37 ns and the timing
jitter of the delayed signal is less than 2 ps (rms). We willreport the new timing system and its performance in detail.

Abstract
We are developing a free electron laser (FEL) in theinfrared region and also conducting Self-Amplified
Spontaneous Emission (SASE) experiment in the same
wavelength region using the L-band linear accelerator at
the Institute of Scientific and Industrial Research (ISIR),
Osaka University. In order to conduct such studies, astable operation of the linac is critical, so that we havedeveloped a highly precise and flexible timing system fora stable generation of the high intensity electron beamwith the energy region of 10-30 MeV. In the timing
system, a rubidium atomic clock producing 10 MHz rf
signal is used as a time base for a synthesizer which isused as the master oscillator for generating theacceleration frequency of 1.3 GHz. The 1.3 GHz rf signal
from the master oscillator is directly counted down to
produce the clock signal of the timing system at 27 MHz
and the four rf signals for the linac and laser used in the
beam experiments. The start signal for the linac isprecisely synchronized with the 27 MHz clock signal. To
EXT.

SR 625
RUBIDIUM TIMEBASELine sync.
Timing module(17K34A)

AC 100V
freq. = 60Hz

SMIQ04B
Maser Oscillator

10MHz

INTRODUCTION
The L-band electron linear accelerator is used forstudies on nanotechnology and beam science as well as
for basic studies in the related fields at the Radiation
Laboratory of the Institute of Scientific and Industrial
Research (ISIR), Osaka University. The L-band linac can
produce electron beams of different time structures, like asingle-bunch, multi-bunch with 9.1 ns spacing and so on,corresponding to various beam experiments. The highintensity single-bunch beam is the most characteristic
beam of this L-band linac and it is very useful forradiation chemistry studies by means of pulse radiolysis

1.3GHz

1300MHzRF GATEGATE&DELAY(PS794)Frequency Divider

Master RF part

RF Switch

L-band timing system 2007 August 20
Shigeru KASHIWAGI

60Hz (pulse)
Fanout(PS757)

1/6

Rf

1/12

1/16

Rf

Rf

1/48
AND
(PS756)

27MHz clock

Ext Trig.

Reset

F/F
(PS794)200W Amp.

Digital Delay(DG-535_4)
AB B C D

10dBm
10dBm

DELAY line (15ns)

81MHz(Laser Ref.)

10dBm

216MHz(SHPB)

108MHz(SHPB)

108MHz(SHPB)TTL

DELAY line (24ns)

AND(PS756)

To Klystron
27MHz
clock

1300MHzRF GATE

AND(PS756)Frequency Divider &DIGITAL DELAY
Clock(17K32A)

EXT. Enablefrom SEKI
nano-pulse

960Hz
TTL-->NIM

Fanout(PS757)

60Hz

Reset

27MHz
clock

1/N-out

960Hz Signal
for Laser Regen Amp. system

EXT. Enable(Femto)SelectBeam Repetition Preset Scaler(KN-140)(Max. 60Hz)

Fanout(PS757)
B

Synchronized BEAM
Repetition Signal
Ext Trig.

Cont. Enable signal

AND(PS756)A

B

AND(PS755)
RF Switch
19494(4)
(1)

27MHz
clock

B

RF Switch
(2)

AVAL.
Driver

AVAL.
Driver

GUN
START

GUN
STOP

140V, 50ns

140V, 50ns

C

Trig. To Linac
From FEMTO(EXT. Exp.Enable)

A

OR(PS756)

B

B

Fanout(PS757)
GATE&DELAY(PS794)

GATE&DELAY(PS794)

A

B

A

A

27MHz
clock
(FD output)

GATE&DELAY(PS794)

GATE&DELAY(PS794)B

Fanout(PS757)

EXT. Enable(Femto)GATE&DELAY(PS794)Cont. Enable signal

OR(PS756)C

TTL-->NIM

Digital Delay(DG-535_1)
A B C DA

DEXT. Enablefrom #2room
Majima Lab.

Ext Trig.

GATE&DELAY(PS794)

Digital Delay(DG-535_2)
C
A
B

EXT. Enablefrom SEKI
nano-pulse

D

A

27MHz
clock
(FD output)

RF Switch(3)

GATE&DELAY(PS794)

TTL-->NIM

Fanout(PS757)

GATE&DELAY(PS794)B

Driver
(11Vpp)Driver(4Vpp)

AVAL.
DriverExperiments
40V, 50ns

Laser Start Signal(Laser-1)
To Femto

DELAY(PS794)

NIM-->TTL

BufferFanout(PS757)

INSTR.
SYNC.

RF Switch
(4)

AVAL.
DriverGATE(PS794)

AND(PS756)

SHB3(216MHz)
TriggerA

AND(PS756)

B A

A
B

B

AND
(PS756)

Driver
(11Vpp)

Kly.
Modulator
Trigger

A

27MHz
clock
(FD output)

GATE&DELAY(PS794)

AND(PS756)
EXT. Enablefrom SEKI
nano-pulse(Laser)D

AND(PS756)A

TTL-->NIM

GATE(PS794)

AND(PS756)C

OR(PS756)

AND(PS756)

GATE(PS794)

AND(PS756)

Synchronous
timing part

Fanout(PS757)

Digital Delay(DG-535_3)
A B C D

INT. Enable signal

GATE&DELAY(PS794)

27MHz
clock

Fanout(PS757)

Driver(+10V)

GATE&DELAY(PS794)

Ext Trig.

SelectModulator Repetition

Preset Scaler(KN-140)

LINAC TRIG.
To #2 room
SEKI
Nano-pulse

Driver
(11Vpp)SHB1&2(108MHz)
Trigger
Laser Start Signal(Laser-2)
To #2 room Majima Lab.

Laser Start Signal(Laser-2)
To #2 room nano-pulse

Fig. 1: Block diagram of the new timing system for the L-band linac at ISIR, Osaka University.
___________________________________________*shigeruk@sanken.osaka-u.ac.jp

FEL Technology I

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WEPPH030

Proceedings of FEL 2007, Novosibirsk, Russia

in the time range down to sub-picoseconds [1,2] and basic
study of SASE in the far-infrared region [3,4].
The timing system of the linac plays a very importantrole in generating a high quality and stable electron beam.
The timing jitter between a trigger signal for the electron
gun and a reference rf signal of accelerator system
directly affects the stability of the electron beam in termsof intensity and energy. Experiments using the L-band
linac require synchronized trigger pulse for their dataacquisition, and rf signals for laser oscillator. In order toenhance the stability of the linac, we have developed a
new highly precise and flexible timing system for the Lband linac at ISIR, Osaka University.

CONFIGURATION OF L-BAND LINAC
AND LASER SYSTEM
The fundamental accelerating frequency of the L-band
linac at ISIR is 1.3 GHz. The linac has been optimized forgenerating the high-intensity single-bunch beam. The Lband linac is consisted of a high-current triode electron
gun, three stage sub-harmonic bunchers (two operate at
108 MHz, which is a 12th subharmonic of the fundamental
frequency and one at 216 MHz, a 6th of 1.3GHz), two
fundamental traversing wave bunchers and 3m-long main
accelerating structure. The SHB system is used mainly forsingle-bunch operation. The timing system is required togenerate three rf signals for these rf components.
Two grid pulser circuits of the electron gun are used forgenerating single-bunch and multi-bunch beam. The
trigger pulse for the gun grid has to be synchronized with
1.3 GHz rf signals precisely. In single-bunch operation,
one trigger pulse for the gun grid with 120V height and50ns duration is distributed from the timing system at thecontrol room. In multi-bunch operation, two triggers for astart and a stop of pulse are necessary to decide the pulse
length of multi-bunch beam in the grid pulser circuit. The
trigger pulse for single-bunch and the start trigger ofmulti-bunch generation are common, and the input trigger
pulse for the trigger circuit of the gun is switched byoperation mode of the linac.
The laser system for a sub-picosecond pulse radiolysis

experiment consists of a CW green laser, a femtosecond
Ti:sapphire laser operated at 81 MHz, Nd: YLF laser witha regenerative amplifier operated at 960 Hz, an opticalparametric amplifier (OPA) and a pulse generator. Thus,
the laser system requires the 81 MHz rf signal andthre960 Hz and 60Hz trigger pulses to the timing systemof the linac [1].

NEW SYNCHRONOUS TIMING SYSTEM
To achieve the stable and precise synchronization
between RF signals and trigger pulses for the accelerator
system, the timing system has been replaced with a newone completely. The new timing system of the linac
comprises of a master rf part and a synchronous timing
part. It provides four synchronous rf signals and a 27
MHz clock signal as well as various timing signals for
operation of the linac and for the experiments. Figure 1
shows a block diagram of new timing system for the Lband linac.

Master RF partIn new timing system, some necessarily harmonicfrequencies for the linac operation are produced by
dividing a master frequency of 1.3 GHz, because thephase fluctuation of the dividing frequency is muchsmaller than the multiplied one [5]. The master RF of 1.3
GHz is generated by a frequency synthesizer (Rohde &Table 1: RF signals and triggers for the L-band linac
RF signal
1300 MHz
Main accelerating frequency
216 MHz 6th subharmonic buncher
108 MHz 12th subharmonic buncher
81MHz
Laser system (seed resonator)
Clock signal
27 MHzMain clock of accelerator
960 MHz
Laser system (Regen Amp)
Trigger pulse
Electron gun trigger (STARt/ STOP)
Experimental trigger
Laser trigger
Others (kly. modulator, SHB amplifiers )FEL Technology I

414

Fig. 2: Frequency spectrum of 81MHz rf signal withoutband-pass filter (upper) and with crystal narrowband pass filter (lower).

Proceedings of FEL 2007, Novosibirsk, Russia

Fig. 3: Timing chart and block diagram ofsynchronizing system using (A) a logic circuit(Phillips-756) and flip-flop circuit (Phillips-794) and(B) a fast GaAs rf switch.
Schwarz: SMIQ04B) and a rubidium atomic clock
producing 10 MHz rf signal is used as an external timebase for the frequency synthesizer to realize long term
stability. The 1.3 GHz rf signal is directly counted andfrequency-divided using a ripple counter circuit toproduce rf signals of a 6th and 12th sub-harmonics at 108
MHz and 216 MHz, and a 16th sub-harmonic at 81 MHz
together with the NIM-level clock signal of a 48th subharmonic signal at 27 MHz. This synchronized 27MHz
clock pulses are used as timing step of trigger pulses. The
sub-harmonic rf frequencies are amplified to +10dBm
level and sent to the SHB main amplifiers and the laser
system. The pulse width of 1.3 GHz driving rf pulse forthe klystron can be control using a fast rf switch with asynchronized trigger pulse. The width is typically 15 μs in
linac operation.
Band-pass filters are introduced at the frequency
divider output to suppress the unnecessary higher andlower harmonic frequencies. Figure 2 shows thefrequency spectrum of 81 MHz rf signal, which is used asa reference signal for the Ti:Sapphire laser system,without a band-pass filter (upper figure) and with anarrow-band crystal filter (lower figure) at the output of
the frequency divider. The generated rf signals are
distributed to the laser system or an rf components.

Synchronous timing partThe synchronous timing part was fabricated using
commercially available components and devices, such as
standard NIM logic modules and digital delay generators,
so that it is flexible for future expansion and development.

WEPPH030

The linac must be operated synchronously with the ACline frequency, which is 60 Hz in the western half ofJapan, and the maximum repetition rate of the linac
operation is also 60 Hz. In the synchronous timing part,the start signal is produced from the AC line voltage
synchronized with the 27 MHz clock signal. Fig. 3(A)shows the timing chart and block diagram ofsynchronizing system using standard NIM modules anddelay lines. The repetition rates of rf pulses and the beam
are determined with two preset counter modules,
respectively as shown in Fig. 1. The 960 Hz clock for thelaser system is generated using synchronous universal
counter, which counts the 27 MHz clock pulse anddivides the clock frequency by 28212 [6].
To make an arbitrary delayed timing signal, the startsignal is sent to standard digital delay generator (Stanford
Research Systems: DG535) as the external trigger and it
produces preset delayed signals. One of their delayed
signals is used for producing a gate signal to slice out oneof the 27 MHz clock pulses. Since the gun (start and stop),
the experimental and the laser triggers, have to besynchronized with the reference rf signal precisely, we
therefore use a fast GaAs RF switch (Mini-Circuits:
ZASWA-2-50-DR) to slice out the timing pulses from the27MHz clock as shown in Fig. 3 (B). The fast RF switch
is a passive device, thus the time jitter of the sliced out
timing pulse is determined by stability of the 27MHz
clock. This is expected the timing jitter to be smaller thana few ps. Any timing signal can be generated at an integer
multiple of 37 ns, which is a period of 27 MHz clock. The
timing jitter of the delayed pulse does not depend on the
delay time by using this delay method. To make othertrigger pulses, such as the klystron modulator trigger, thedelayed signals are made to be coincident with the 27
MHz clock using a logic module (Phillips-756). The time
jitter of the logic module is expected to be about 5 ps.

Avalanche pulser
The avalanche pulser circuit is used to make highvoltage pulse with less than a nanosecond rise time at theoutput part of the timing system. The timing jitter of thearbitrary delayed timing signal for triggering eachcomponent is mainly determined by a time jitter of theavalanche pulser. The required avalanche pulser outputs
are 140 V for the Gun-start and stop triggers and the 50 V
for the Experimental and Laser triggers, respectively. The
synchronized timing pulse, which is sliced out by the fast
GaAs rf switch, is applied to the avalanche pulser circuit
as a trigger. The time jitter of avalanche pulser is strongly
dependent on the leading-edge and the voltage of thedrive pulse for the avalanche transistor. To get goodleading-edge of the drive pulse, a transistor is used as a
pre-amplifier with gain 5 (the output voltage: ~3V) and an
emitter follower circuit is used for the last pre-amplifying
stage of the circuit to provide low output impedance. In
this circuit, two transistors are used to provide the drive
pulse with good leading-edge for avalanche transistor.
The timing jitter of this circuit was smaller than that of

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the circuit, which uses only one transistor in emitterground circuit.

TIMING JITTER MEASUREMENT AND
RESULT
The timing jitter measurement have been performed forthe produced subharmonic RF signals and thesynchronous trigger pulses relative to the master reference
RF of 1.3 GHz using the Tektronix Communication
Analyzer (Tektronix CSA8000B with 80E03 sampling
module). In the measurement, the subharmonic RF signals
or the timing pulses are used as a trigger of theoscilloscope. Absolute timing jitters of subharmonicfrequencies relative to the 1.3 GHz master reference RF
are approximately 1.3-2.0 ps (rms) with bandpass filter
and the jitter of 27 MHz clock was 0.96 ps (rms). The
timing jitter of the arbitrary delay timing signals slicedout by the fast RF switch from the 27 MHz clock pulses
were also measured, and they are approximately 1.1-1.6
ps (rms).
A rise-time (10-90%) of amplified trigger pulse wasmeasured using the sampling module with 20 GHz
frequency bandwidth. The measured leading-edge of the
50V trigger pulse with -46 dB attenuator is shown in Fig.

4 (upper) and the rise-time of the 140 and 50 V trigger
pulses were 1.86 ns and 0.44 ns, respectively. Absolutetiming jitter (rms) of the 140 and 50 V trigger pulses
relative to the master RF were 2.7 ps (pk-pk = 16.4 ps)
and 1.5 ps (pk-pk = 10.0 ps) in 1 hour measurement,
respectively.

SUMMARY
The new highly precise and flexible timing system has
been developed for the L-band linac and now it is used inreal beam operation. Performance of new timing system
exceedingly improved than a former one. In the timing
jitter measurement, the jitter of the 50 V trigger pulse
relative to the master reference RF was 1.5 ps using new
synchronizing technique with the fast GaAs rf switch,
before installation of new timing system it was about 7 ps.
About other signals such as the subharmonic rf signals,
their performances were also improved than before. In thepresent new timing system, the absolute timing jitter of
the arbitrary delayed trigger pulse is mainly determined
the stability of the 27 MHz clock pulse. To improve theprecision of the 27MHz clock, we are planning to use thelimiting amplifier for the 27 MHz clock generation.

ACKNOWLEDGEMENTS
The authors would like to thank Drs. Takao Asaka,
Yoshitaka Kawashima and Hirofumi Hanaki of SPring-8
for their help on the fabrication and measurement of the
new timing system of the ISIR L-band linac.

REFERENCES[1] A. Saeki, T. Kozawa, S. Kashiwagi, K. Okamoto, G.
Isoyama, Y. Yoshida and S. Tagawa, Nucl. Instr. andMeth. A 546 (2005) 627.
[2] T. Kozawa, Y. Mizutani, K. Yokoyama, S. Okuda, S.
Tagawa, Nucl. Instr. and Meth. A 429 (1999) 471.
[3] R. Kato, M. Fujimoto, T. Igo, S. Isaka, T. Onishi, S.
Furukawa, S. Okuda, S. Suemine, G. Isoyama, Nucl.
Instr. and Meth. A 507 (2003) 409.
[4] R. Kato, R. A. V. Kumar, T. Okita, S. Kondo, T. Igo,
T. Konishi, S. Okuda, S. Suemine, G. Isoyama, Nucl.
Instr. and Meth. A 445 (2000) 164.
[5] M. Sawamura, E. J. Minehara, R. Nagai, M. Sugimoto,
M. Takao, R. Kato, N. Kikuzawa, M. Ohkubo, Nucl.
Instr. and Meth. A 358 (1995) ABS 73-74.
[6] H. Suzuki, H. Ego, M. Hara, T. Hori, Y. Kawashima,
Y. Ohashi, T. Ohshima, N. Tani, H. Yonehara, Nucl.
Instr. and Meth. A 431 (1999) 249.

Fig. 4: Measured leading-edge and timing jitter of 50
V trigger pulse. The rise time of one was 0.44 ns andthe timing jitter was 1.51 ps (rms) and 10.0 ps (pk-pk)
in 1 hour measurement.
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WEPPH031

DEVLOPMENT OF A LOW EMITTANCE DC GUN FOR SMITH-PURCELLBWO FEL
K. Kasamsook#, K. Akiyama ,K. Nanbu, M. Kawai , F. Hinode, T. Muto , T. Tanaka, M. Yasuda,
Y. Mori, H. Hama, Laboratory of Nuclear Science, Tohoku University,
1-2-1 Mikamine, Taihaku-ku, Sendai 982-0826, Japan
Abstract
An electron DC gun capable for producing very low
emittance beam is now under evaluation of beam qualities
at Laboratory of Nuclear Science, Tohoku University.
The DC gun employs a high voltage of 50 kV to extractelectrons, which is suitable to drive Smith-Purcell
backward wave oscillator free electron laser (BWO FEL)
[1]. From a result of numerical simulation using a 3-D
finite deference time domain (FDTD) method [2], theBWO FEL oscillation at the terahertz wavelength region
maybe achieved by using the electron beam with anemittance lower than 1 π mm mrad. Average power is
expected to be more than 100 W/mm2.
In addition to which a very small cathode of LaB6
single crystal is employed for the gun [3], the geometricalstructure is optimized to produce the lower emittancebeam. A numerical calculation of the electro-static modelfor the DC gun to solve equilibrated beam envelope
predicts a normalized beam emittance of 0.3 π mm mrad
will be possible for the beam current of a couple ofhundreds mA. Particularly by applying additional bias
voltage between the cathode and the wehnelt, thetransverse distribution of electrons is possibly becoming
to be an ideal Kapchinskij-Vladimirskij (K-V) beam [4],so that the space charge effect will be minimized.

INTRODUCTION
Smith-Purcell BWO FELIn order to understand the characteristics of the BWO
FEL and the interaction between the DC beam and theevanescent waves supported by a grating, an FDTD
simulation has been performed. Nonlinear behavior of theSmith-Purcell radiation was already observed [5]. That
was coherent and has been presumed to result from thebeam microbunching effect due to interaction with theevanescent modes.
We have chosen a model grating for the simulation as
indicated in Fig. 1. The period length λg = 400 μm, thegroove width W = 200 μm, the groove depth d = 300 μm
and the grating full width L = 2 mm, the number of periodof 50 are employed, respectively. The sheet DC beam,
which has the emittance of 1 π mm mrad for the both
directions, is generated by very low horizontal andvertical beta functions of 6.25 cm and 0.4 mm,
respectively. Since the evanescent wave is exponentiallydecreasing as the distance from the grating surface
increases, the sheet beam has to travel just above thesurface in order to have sufficient overlapping with theevanescent wave (here we have chosen 100 μm).

Figure 1: A model grating for FDTD simulations.
The Smith-Purcell BWO FEL is not driven byponderamotive potential as conventional FELs withwigglers. The microbunching is occurred by thelongitudinal electric field (Ez) in the evanescent wave, andthe conventional Smith-Purcell radiation becomes
coherent. The evanescent mode is much more excited by
the bunched beam, so that the gain is yielded.
The FDTD simulation was performed with a DC beam
current of 150 mA. To avoid beam brow-up the strong
external longitudinal field (Bz ~ 1 T) applied. From thedispersion relation of the evanescent wave [6], the groupvelocity at the beam frequency negative, so that this is the
backward-wave. Time dependent evolutions of radiatedpower observed at the grating upstream end are shown for
two different emittance cases in Fig. 2.
We notice that for the normalized emittance of 1 π mm
mrad case, the power increased up to several hundreds
W/mm2 and a damping oscillation was excuted after
saturation. Meanwhile a larger normalized emittance case,such as 5 π mm mrad shown in Fig. 2(b), the FEL
oscillation was not occurred. The results show the beamemittance is very crucial for the Smith-Purcell BWO FEL.
The frequency spectrum obtained Fourier transform of
the power evolution of Fig. 2(a) is shown in Fig. 3. In thisgrating case, an intense sub-Terahertz radiation may beobtained.

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potential surface can be manipulated by applying thenegative bias between the cathode and the wehnelt
electrode. In the simulation, an extremely low emittanceless than 1 π mm mrad is achieved [7].
The schematic diagram of DC gun power supply isshown in Fig. 4. The fabrication of the DC gun had been
finished and we succeeded to extract the electron beamover 300 mA exceeding our target value [8]. The main
design parameters are shown in Table 1. This low
emittance DC gun has been studied both experimentallyand theoretically. The paper will present the status of thedevelopment of the low emittance DC gun.

Figure 2: Simulation results of the FDTD Smith-Purcell
BWO FEL. (a)The normalized beam emittances are 1 π
mm mrad, and (b) 5 π mm mrad, respectively.

Figure 3: Frequency spectrum of simulated Smith-Purcell
BWO FEL (corresponds to Fig. 2(a)).

Low emittance DC gun
The DC gun has been designed with a wehnelt
electrode to manipulate electric field arround the cathode.
The feasibility study of the gun for the Smith-Purcell
BWO FEL has been investigated by the simulation. Fromthe simulation results, we have presumed that theemittance is very sensitive to the equi-potential surface
around the cathode. Consequently we found that the equiFEL Technology I

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Figure 4: The schematic diagram of DC gun power supply.
Table 1: Design parameters of electron gun.
Beam energy

50 keV (Max.)

Peak current>300 mA

Pulse width (FWHM)

1-5 μsec

Repetition rate

50 ppsNormalized emittance< 1 π mm mrad.

Normalized thermal
emittance

0.25 π mm mrad**theoretical

Cathode diameter

1.75 mm.

DC GUN DEVELOPMENT
Beam quality measurements
An experimental set-up for beam size measurements is
depicted in Fig. 5. The beam size was measured atdownstream of the DC gun by applying the focusing
power of the solenoid lens. The main components in thissection are solenoid lens, current transformer (CT), theslit and a Faraday plate. The overall beam current wasmeasured by the CT located at the downstream of thesolenoid lens. Meanwhile the beam current passing
through the slit was measured by the Faraday plate.

Proceedings of FEL 2007, Novosibirsk, Russia

DC gunSolenoid lensCT

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Slit

Faraday plate(inside)Figure 5: The DC gun configuration for beam size
measurement

Figure 6: Measured minimum beam size profile at various
beam currents.

A slit plate used for the beam size measurement ismade of SUS 316L and its thickness is a 50 μm. Twoperpendicular slits for X and Y direction with width of 50+ 2 μm were manufactured by wire cut method, and its
width was measured by a high precision microscope. The
moving direction of the slit stage is 45-degree between X
and Y axes, because only one move can make two axes
scans.
The slit plate was mounted on an insertable androtatable actuator powered by 5-phase stepping motor(Oriental Motor PK545AW-P7.2). This allowed us toalign the slits to the beam and insure the proper angle
with respect to the beam. Combining the ball bearing
spindle (1 mm pitch for one revolution) and the precise
stepping motor, the maximum resolution of step is 1/3600
mm. The scanning speed is around 15 second for one
beam profile.
The measurement are made as follow; (1)set the slit
movable stage to the initial position at first, then using a
Faraday plate get the signal of the beam passing throughthe slit, (2)go to the next stage position, then repeat again
until the end position coming. Signals from the CT and
the Faraday plate are connected to digital oscilloscope
and analyzed by software.
All measurements were performed at various beam
currents of 50, 180 and 430 mA that are corresponding toheater current of 7, 7.5 and 8.0 A, respectively. Taking
look at the V-I characteristic curve of our DC gun [8], wehave chosen 8 A of heater current for an ordinal operating
condition. The minimum rms beam size less than 2 mm inboth X and Y directions was obtained at the operating
condition. The measured beam profiles are shown in Fig.
6. One can notice the shift of a beam position in eachcase. Possible reasons are alignment errors of the cathodeand the solenoid lens. The beam size becomes bigger
when the beam current increases and a stronger focusing
strength of the solenoid lens is required to confine thebeam. It seems the space charge effects play a significant
role for the beam size at the higher beam current.

Transverse beam emittanceIn the following analysis, we assume an axissymmetric electron beam confined by a longitudinalmagnetic field of solenoid lens. This method is used todeduce a tentative beam emittance of our DC gun. So themeasurement can be understood by examining theevolution of the rms beam size in a drift length following
a thin lens of focal length f. The beam is transported
through a solenoid. In this case, the beam matrix
transforms at the slit position given by

σ 1 = Rσ 0RT ,(1)

where R is the transfer matrix in drift space (L) andsolenoid lens (the magnetic strength, Q) represented by⎛1

R = ⎜⎜

L ⎞⎛ 1
⎟⎜

⎛1−QL
⎟=⎜
⎜
⎝ −Q

0⎞

⎟⎜
⎟
⎝ 0 1 ⎠⎝ −Q 1 ⎠

L⎞
⎟.
1 ⎟⎠

(2)

In this linear analysis, we have explicitly ignored spacecharge effect. By applying initial conditions to eq. (1), we
can solve the equation for the square of the rms beam sizein the term of focal length of the solenoid lens as

σ 1 =< x2 >= L2σ 0 .Q2 − 2[ Lσ 0 + L2σ 0 ].Q +

11
1
11
11
12
(3)
2
0
0
0
L σ + 2 Lσ + σ .
22
12 11
In this form, we can see that the square of the rms beam
size at the end of the drift should depend on the square of
the magnetic strength of the solenoid lens. The scan isdone by varying the strength of the solenoid lens andmeasure the beam size at the fixed distance from the lens.
In the eq. (3) we can simplify the form as

σ 1 =< x2 >= aQ2 + bQ + c = a⎜ Q+
11

1

⎛
⎝

b ⎞2 4ac−b2
⎟ +
2a ⎠
4a

(4)

= a' (Q + b' )2 + c'.

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The normalized rms emittance is calculated by anequation
ε

n,rms

βγ
= βγ < x02 >.< x'02 >−(< x0.x'0 >)2 =4a'c' ,
2L2

(5)

where β is the beam velocity divided by light velocity, γ isthe relativistic mass factor, and a’, b’, c’ are coefficientsof quadratic function deduced from curve fitting. For
solving this problem numerically, an internal MATLAB
solver is used [9]. The MATLAB consists of a constrained
non-linear least-square fit algorithm based on theLevenberg-Marquardt method. The robustness of thealgorithm needs to be assured.
Particularly, thisalgorithm should work for noisy data, such as
experimental data.
For the data at the beam current of 430 mA, theemittance is then calculated by fitting the data using thequadratic beam transport equation. The results of fitting
are shown in Fig. 7 and Fig. 8. The normalized rms
emittances, 2.46 and 2.66 π mm mrad are obtained for thehorizontal and the vertical axes, respectively
We calculated the propagation of error by eq. (6). The
deduced errors are + 0.89 and + 1.05 π mm mrad for thehorizontal and vertical normalized rms emittances,respectively.
Δε

n,rms

=

βγ
2L2

⎛ c' ⎞
2 ⎛ a' ⎞ 2⎟Δa' +⎜ ⎟Δc' .
⎝ a' ⎠⎝ c' ⎠. ⎜(6)

The same analysis was performed on data taken at 50
and 180 mA of beam currents, respectively. The fits to thedata give the normalized rms emittance of 1.14 + 1.17π
mm mrad (horizontal emittance) and 0.82 + 0.72 π mm
mrad (vertical emittance) for 50 mA. For the beam
current of 180 mA, the results are 1.84 + 1.87 and 1.72 +1.36 π mm mrad for the horizontal and the verticalnormalized rms emittance, respectively. Though theseerrors seem to be high compared with expected values ofnormalized rms emittance, anyhow, it seems the current
dependence of the emittance exists.

Figure 7: Square of beam radius in the horizontal axis
plotted as a function of magnetic strength of solenoid lens.
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Figure 8: Square of beam radius in the vertical axis
plotted as a function of magnetic strength of solenoid lens.
In this linear analysis, we ignore the space charge
effects and approximate the effect of solenoid lens by thinlens as well. A rigorous error analysis was not performedin the analysis of the data. We have estimated only theerrors result from the uncertainty of the quadratic fit. For
this reason, it is highly desired to use the high precision
technique instead of the solenoid scanning method toconfirm the emittance value.

SUMMARY
We have developed a very low emittance DC gun
employing a single crystal of LaB6 cathode. Preliminary
value of the measured normalized emittance was around 2
π mm mrad. Further investigation including manipulationof the equi-potential surface around the cathode by
applying the additional bias voltage will be performed.

REFERENCES[1] V. Kumar and K-J. Kim, Phys. Rev E 73 (2006)
026501.
[2] H. Hama, et al., to be published.
[3] H. Kobayashi et al., Proc. 1992 Linear Accelerator
Conf., Ottawa, Canada, August 1992.
[4] I.M. Kapchinsij and V.V. Vladimirskil, Proc. Int. Conf.
on High Energy Accelerators p. 274 (CERN,GENEVA, 1959).
[5] J. Urata, M. Goldstein, M.F. Kimmitt, A. Naumov, C.
Platt and J. Walsh, Phys. Rev. Lett. 80 (1998) 516[6] H. L. Andrews et al., Phys. Rev ST Accel. Beam 8,(2005) 050703.
[7] K. Kasamsook et al., Proc. FEL2006, Berlin, Germany(2006) 680.
[8] K. Kasamsook et al., will be appeared in Proc of
APAC2007 , Indore, India (2007).
[9] MATLAB, User’s Manual,
http://www.mathworks.com/access/helpdesk/help/too
lbox/curvefit/curvefit.shtml

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH032

ZZZ
ZZELECTRON- LINAC BASED FEMTOSECONDTHzZZZ∗ZRADIATION SOURCE AT PAL*
H. S. Kang† , C. M. Lim, W. W. Lee, B. R. Park, H. G. Kim, S. C. Kim, Y. G. Jung,
M. S. Lee, Y. J. Park, J. Choi, and I. S. Ko
Pohang Accelerator Laboratory, POSTECH, Pohang 790-784, KOREA
A 60-MeV electron linac for intense femto-second THz
radiation source is under construction at PAL, which is thebeamline construction project to be completed by 2008. To
get intense femto-second THz radiation up to 3 THz, theelectron beam should be compressed down to below 100
fs. The linac will use an S-band photocathode RF-gun as
an electron beam source, two S-band accelerating structures to accelerate the beam to 60 MeV, a chicane-typebunch compressor to get femto-second electron bunch, andan optical transition radiation (OTR) target as a radiator.
The PARMELA code simulation result shows that the 0.2
nC beam can be compressed down to a few tens of femtoseconds, and the higher charge of 0.5nC to about one hundred femto-seconds. Also, the linac will be able to provide femto-second electron beam for electron pulse radiolysis and compton-scattering experiment for femto-second
X-ray.

INTRODUCTION
THz radiation source which can provide rich scienceand unexplored technology is becoming popular. And, subpico-second radiation at that wavelength can provide an unprecedented probe for ultra fast dynamics like electronic
excitations and magnetic excitations [1]. Pohang Accelerator Laboratory (PAL) is constructing a 60-MeV electron linac for intense femto-second THz radiation source,which is the beamline construction project to be completed
by 2008. The radiation wavenumber to provide is 10-100
cm−1 (0.3 - 3 THz) and the radiation pulse duration should
be shorter than 200 fs.

DESIGNTo achieve this goal, we will make use of relativistic
electron beam with the bunch length of shorter than a few
hundred femto-seconds. Relativistic particles emit incoherent radiation at all wavelengths, and additional enhanced
coherent radiation at wavelengths of the order of the bunch
length and longer. The total radiated spectral power from amono-energetic bunch of Ne electrons at wavelength λ is
P (λ) = p(λ)Ne [1 + (Ne − 1)f (λ)],(1)

where p(λ) is the spectral radiation power from a single
electron and f (λ) is a form factor for an azimuthal symmetric bunch, which is the Fourier transform of the actual∗ Work supported by Korean Ministry of Science and Technology† hskang@postech.ac.kr

particle distribution. The first term in the square brackets is
the incoherent part of the radiation while the second term
corresponds to the coherent radiation which is Ne times theincoherent part assuming f (λ) ≈ 1. The form factor is defined asZ(2)
f (λ) = | S(x)exp{i(2πx/λ)}dx|2 .
where S(x) is the normalized longitudinal density distribution of electrons in a bunch.
Bending Magnet Radiation

16

10

1 fs
14

10

Photons / rad * 1%BW

Abstract

100 fs

10 fs

12

10

Energy: 50 MeV
Charge: 0.2 nC
Bending radius: 1 m

10

10

8

10

incoherent

25 fs
6

10

4

10

0

10

1

10

2

10
Wavelength [um]

3

10

4

10

Figure 1: Coherent enhancement of synchrotron radiationfrom a bending magnet at different bunch lengths in rms.
Figure 1 shows the coherent enhancement of synchrotron
radiation from a bending magnet at different bunch lengths
in rms. The parameters used for the calculation are an electron beam energy of 50 MeV, a bending radius for synchrotron radiation of 1 m, and the electron bunch chargeof 0.2 nC. The photon flux of coherent radiation is muchhigher than that of the incoherent part, simply Ne times.
From Figure 1, one can find how small the bunch length
should be to get coherent THz radiation. Coherent enhancement of radiation is determined by the bunch form
factor in Eq. (2). The required bunch length is as short as
one tenth of the period of radiation to get the bunch form
factor close to 1. For example, to get 10 THz radiation (period = 100 fs), the bunch length should be smaller than 10
fs, which is obviously impossible to get with 0.2 nC charge
beam. So, the target bunch length to achieve in this projectis about 50 fs with 0.2 nC beam, which can generate coherent THz radiation below 3 THz.
Figure 2 depicts the layout of the electron linac. The
linac will use an S-band photocathode RF-gun as an elec-

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Proceedings of FEL 2007, Novosibirsk, Russia
ICT/
Screen

ICT/
BPM

PGV

BPM/
Screen

PGV

QD2

QD1

ScreenScreenQT1Compton
Scattering

AC2
RF-gun

BAS1

FS

AC1

BAS2

Chicane1

BAS3

Chicane2

CSR FIR
moni OTR
tor

Figure 2: Layout of FIR Linac. (QD: quadrupole doublet, ICT: integrated current transformer, FS: focusing solenoid, AC:accelerating column, QT: quadrupole triplet, OTR: optical transition radiation, BAS: beam energy analyzer, and YAG:YAG screen).
Table 1: Parameters of the Linac

Table 3: OTR energy vs. bunch charge

Parameters
Beam energy
Beam Charge
Beam EmittanceBeam Pulse Repetition rate

Bunch charge [nC]
0.2
0.5
1

Value
60 MeV
0.2 - 0.5 nC
5 mm-mrad
60 Hz max.

Table 2: Relation of bunch charge and bunch length
Beam charge
0.2 nC
0.5 nC

Bunch length
after RF-Gun
0.5 ps2 psBunch length
after chicane
50 fs
150 fstron beam source, two S-band accelerating structures (AC1and AC2) to accelerate the beam to 60 MeV, a chicane-typebunch compressor to get femto-second electron bunch, andan optical transition radiation (OTR) target as a radiator.
Parameters of the Linac are listed in Table 1. The beamenergy is 60 MeV and the beam charge is 0.2 to 0.5 nC.
The relation of bunch charge and bunch length is shown in
Table 2. The bunch length is designed to be 50 fs with 0.2
nC beam and 150 fs with 0.5 nC. To get short bunch length
after bunch compression, the bunch length at the gun is 0.5
ps with 0.2 nC beam, which is the reason why the emittanceis relatively high, 5 mm-mrad.
As a wide-band radiation source, optical transition radiation was chosen rather than bending magnet radiation
which is difficult to get a good pointing stability of radiation. On the other hand the undulator radiation which isnarrow-band is not going to be used at the beginning, but
the space is reserved, because the temporal length of the radiation exceeds 1 ps due to the wiggling motion of electron
beam in undulator.
Optical transition radiation is generated when an electron crosses the boundary between two different media.
Coherent transition radiation energy obtained from Ne
electrons is [2]
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Radiation energy [µJ]
3.5
22
88

dWN
dW1
= Ne 2|f (ω)|2
dω
dω

(3)

1
where dWdω is the radiation energy generated by single electron, and f (ω) is the form factor defined in Eq. (2). Table
3 shows the optical transition energy as a function of bunchcharge assuming the bunch form factor of 1. A dramaticincrease of radiation energy is expected with 1 nC while
the radiation bandwidth must be limited because a few tensof femto-second bunch is impossible to get with 1 nC, evenwith 0.5 nC. So, there should be a compromise between theachievable radiation bandwidth and the radiation energy.

SIMULATION RESULTThe beam dynamics design was carried out by using the
PARMELA code. It was designed to be that the beam with
0.2 nC charge can be compressed down to about 30 fs in
rms at the position of OTR target by Chicane-2. Figure 3
shows the bunch profile before and after Chicane-2. The
rms bunch length is 920 fs before the chicane and 29 fs
after the chicane. The parameters of Chicane-2 used in thesimulation are: the beam energy is 55 MeV, the bending
angle is 10 degrees, and R56 is -2.07 cm.
Beam dynamics design was also done for higher chargeof 0.5nC. As a result, the bunch length is expected to beabout one hundred femto-seconds.
Figure 4 shows the longitudinal bunch profile of electron beam after the 0.2 nC beam is compressed in Chicane2, which is calculated by using the PARMELA code data.
Making use of the longitudinal bunch profile, we can calculate the bunch form factor of the given distribution. Figure
5 depicts the bunch form factor at different bunch charges,

Proceedings of FEL 2007, Novosibirsk, Russia

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1
0.2 nC
0.5 nC

0.9

Bunch Form Factor

0.8
0.7
0.6
0.5
0.4
0.3
0.2

(a)

0.1
0 1
10

2

10
Wavelength [um]3

10

Figure 5: Bunch form factor at different bunch charges, 0.2
nC and 0.5 nC.

(b)
Figure 3: PARMELA simulation result: bunch shape before (a) and after (b) Chicane-2. es represents the synchronous particle energy, phis the synchronous particle
phase. The vertical axis is e - es in MeV and the horizontal axis is phi - phis in degrees. One degree corresponds toabout 1 ps.

Figure 6: Photo of the linac tunnel.

2500

CONSTRUCTION STATUS AND
SUMMARY

Charge = 0.5 nC
N = 10,000

2000

1500

1000

500

0
−0.3

−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5

Phase [deg]Figure 4: Longitudinal bunch profile of electron beam after
the 0.5 nC beam is compressed in Chicane 2
0.2 nC and 0.5 nC, as a function of radiation wavelength.
The bunch form factor at 100 µm reaches 0.7 with 0.2 nC
beam while it is at most 0.2 with 0.5 nC beam.
In the PARMELA code simulation, the effect of CSR(Coherent Synchrotron Radiation) in the chicane was notincluded. CSR in the chicane deteriorates the electron
beam energy distribution, which causes an increase of emittance and bunch length. The effect of CSR will be checkedwith other simulation code like ELEGANT.

The construction of the linac is on the way as shown in
Fig. 6. The installation will be completed at the end of2007 and the beam acceleration test will start at the beginning of 2008.
The 60-MeV electron linac was designed to generateintense femto-second THz radiation with the radiation
wavenumber of 10-100 cm−1 (0.3 - 3 THz) and the radiation pulse duration of shorter than 200 fs. The linac will
be able to be used for other applications such as electron
pulse radiolysis, X-ray generation by Compton scattering,and SASE-FEL experiments, etc. A space after the chicane
2 is reserved for Compton-Back-Scattering experiment andFEL experiments as shown in Fig. 2.

REFERENCES[1] DOE-NSF-NIH Workshop on Opportunities in THz Science, February 12-14, (2004).
[2] L. Wartski, et al., Journal of Applied Physics, 46, 8, 3644
(1975).

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STABILIZATION OF A KLYSTRON VOLTAGE AT 100 PPM LEVELFOR PAL XFEL
J. S. Oh#, J. H. Suh, Y. G. Son, S. D. Jang, S. J. Kwon, PAL/POSTECH, Pohang 790-784, Korea
E. H. Song, Changwon National University, Changwon 641-773, Korea
Rcharging

Abstract
The PAL XFEL needs a stable electron beam. The
stable charging of PFN (pulse forming network) of a
klystron-modulator is essential to provide the stableacceleration field for an electron beam. For PAL XFEL,
stabilization of klystron voltage pulses at 100-PPM levelis required. Short-term stability is determined by aminimum resolution of a charging system. Long-term
stability is determined by a thermal stability due to thetemperature drift. This paper shows details of hardware
R&D and test results to achieve the target stability.

INTRODUCTIONPAL XFEL is proposed as a 4th generation light sourcethat is a coherent X-ray free electron laser by utilizing an
existing 2.5-GeV linac [1]. Reasonably stable SASE
output requests the RF stability of 0.02% rms for both RFphase and amplitude [2]. This is one of technologicallychallenging issues for PAL XFEL.
The smart modulator driving a klystron RF source for
PAL XFEL will use an inverter charging system.
Therefore, the stability of RF sources is directly
determined by the one of inverter power supplies. In orderto stabilize the charging level, we need an ultra fineinverter power supply and a correct feedback signal of thecharging voltage. The proper conditioning of feedback
signal with a thermally stable probe is necessary to realize
an ultra stable charging performance. This paper shows
the hardware development and analysis of the charging
stability.

INVERTER CHARGING SYSTEM
A traditional klystron-modulator adopts the resonant
charging scheme that uses a constant voltage source. A
charging scheme that uses a constant current source suchas a inverter power supply provides high reliability: athyratron switch is safely turned off because next
charging schedule is digitally controllable, it is fail-safe
system under short-circuit condition due to the current
limit feature. In addition, it is naturally compact by using
a high frequency inverter [3]. These features are wellmatched to the next generation modulator for PAL XFEL
facility. Figure 1 shows the circuit diagram of a modulator
adopting an inverter power supply as a PFN charging
power supply. Table 1 summarizes the parameters of amodulator that will provide ultra stable pulses to a
klystron (model: Toshiba E3712).
___________________________________________#

jsoh@postech.ac.kr

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HVInverterPower
SupplyRINV

ZPFN, N Stage

REOLC
DINV

DTAIL
RSNUB

Thyratron

Pulse
Transformer
1:n

CSNUB
RTAIL

Figure 1: Circuit diagram of a modulator adopting an
inverter power as a PFN charging power supply.
Table 1: Modulator specifications
Peak power
Peak output voltage
Pulse repetition rate
Pulse width
Pulse energy
Flat-top width
Pulse transformer turn ratio
PFN impedance
PFN capacitance
Main charging inverter
Fine charging inverter
Maximum charging voltage

160 MW
370 kV60 Hz
4.7 μs750 J
1.7 μs
1:17
2.9 Ω
0.8 μF
60 kJ/s
2.3 kJ/s
50 kVThis modulator is to be used for a new facility (fs-THz
beamline) of PAL [4], which requires equivalent stability
as the one of PAL XFEL. Therefore, this modulator isgood test bench for the hardware R&D of the inverter
charging system with 100 PPM stability for PAL XFEL.
Figure 2 shows the schematic diagram of the klystronmodulator control including coarse inverters, a fineinverter, a RF driver, a klystron, a thyratron switch of themodulator, a digital inverter controller, a high voltage
probe, and a master timing controller (DG535). All the
charging inverters are connected to the PFN in parallel.
The fine charging inverter has special features that cancontrol the amount of charges per switching cycle tocontrol the regulating ripple of a charging voltage.
Figure 3 shows the timing diagram of a modulator
control. The master timing controller provides a charge
signal (DG535_A) for inverter power supplies, athyratron trigger (DG535_B), and a driver trigger for a
klystron RF input. The digital inverter controller provides
RUN/STOP signals for coarse charging and fine charging.

Proceedings of FEL 2007, Novosibirsk, Russia
C

RF

RF
DriverB

THYRATRON
Driver

DG535 Thyratron

Klystron

Vf
A
DigitalInverter
CHARGE Controller
PLC

Vr

WEPPH033

35.6 V(6*RMS)

Fine
InverterCoarseInverter #1
CoarseInverter #2
CoarseInverter #3

30V/10kV(6mV/2V)

Figure 2: Schematic diagram of the modulator control.
CHARGE
DG535_ATHYRATRON

DG535_B
DG535_C
CoarseInverter
Run/Stop
Fine
Inverter
Run/Stop

Figure 4: Regulating waveform of PFN voltage at thelevel of 10 kV with a PFN capacitance of 1.4 μF. The
accumulation time for statistical distribution of PFN
voltage is 1 hour.

RF

LP fc = 2 kHz, ξ = 0.7

CoarseCapacitor voltage

Fine

V_PFN

Figure 3: Timing diagram of the modulator control.
The coarse charging level is determined at about 99%of the target charging level. The fine charging unit will
charge and regulate the final charging voltage. The
increment of the PFN charging voltage per inverter
switching cycle, ΔVPFN is given by
ΔVPFN = I dc /(C PFN f SW ) = VPFN /(TC f SW )(1)

where Idc is an average charging current, CPFN is a PFN
capacitance, TC is a charging time and fSW is a switchingfrequency. We have to reduce charging current or increaseswitching frequency in order to make the charging step
small. The charging current has to be large enough tocharge the PFN to the target level within the charging
time limited by a pulse repetition rate. The switchingfrequency is also limited to less than 100 kHz due to theswitching loss of the solid state devices used in the
inverter. Therefore, the PFN charging voltage stability is
usually around 0.1% for 100 Hz operating condition.
Figure 4 shows typical example of the regulation
waveform of a standard inverter, which results 35.6 V
fluctuation that is equivalent to 790 PPM at 45 kV with
the PFN capacitance of 1.4 μF and a average charging
current of 1.8 A.
The charging voltage is not rising smoothly andmonotonically but includes high-frequency spikes. The
spike is made by the circuit components connected inparallel to the pulse transformer [5]. The noisy spikes
have to be removed for the feedback circuit to correctlycompare the charging level with a reference level.

Filtered signal

Feedback signal

Figure 5: Detail structure of charging regulation.
The conditioning of a feedback signal removes the
spiky component by the low-pass filter given by

H (s) =ϖ o22s 2 + 2ζϖ o s + ϖ o(2)where ωo is a cut-off frequency and ξ is a damping factor.
However it results phase delay of feedback signal. This
causes the limitation of fine regulation of the charge levelas shown in Figure 5 that shows the detail structure of
charging regulation. The signal is filtered with a cut-off
frequency of 2 kHz and damping factor of 0.7.

DIGITAL INVERTER CONTROLIn order to overcome the phase correction difficulties ofan analog feedback, we adopted a digital controller. The
digital controller naturally requires a digital reference
command for a charging level of the PFN. This condition
is good fit to the upper level control system for thecommunication. It is also useful to keep a stable reference
free from any thermal drift and harmful noise. A DSPbased digital controller is developed for the realization ofhighly stable inverter charging system. This controller hasa high-resolution 18-bit ADC (AD7634) and a high-speed

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Proceedings of FEL 2007, Novosibirsk, Russia

DSP (TMS320F2811). Optical fibbers are used for theinterfaces to the inverters to be free from the noise.
The measured value of the PFN Voltage by the digital
controller is checked by the DAC output as shown in
Figure 6. The built-in software filter with cut-off
frequency of 1 kHz makes the signal delay of 0.45 ms thatis close to the rise time of 0.35 ms due to the bandwidthof the feedback system. Therefore, the filter has to be
included to reduce the noise but a reasonable bandwidth
has to be provided to provide less phase delay of feedback
signal.

<RC Filter (DSP IIR Filter)>

C= 0.5 uF
Inhibit

DSP Clock (15 pulses)

PFN Voltage(Tektronix 6015)
162 V

(a)
Probe signal<Digital control of DSP clock>(Yellow)

C= 0.5 uF

Inhibit
DAC output
With 1 kHz software filter(Sky blue)

18 V

PFN Voltage (Ross Probe 5000:1)

PFN Voltage (Tektronix P6015)

Figure 6: Effect of a digital filter at the charging level of
7.2 kV. The left is fast charging portion of PFN. The rightis falling portion at the thyratron switching time.

Inhibit
Settling Time = 0.2 sec
Max. PRR = 5 Hz
PFN Voltage (Ross Probe 5000:1)

PFN Voltage (Tektronix P6015)

C= 0.5 uF(a)Inhibit
DSP ClockPFN Voltage (Ross Probe 5000:1)

PFN Voltage (Tektronix P6015)

C= 0.5 uF(b)
Figure 7: Digital control of charging overshoot. (a) The
charging is done with a digital filter. (b) The charging isdone with digital control of a charging pulse rate.

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426

DSP Clock (1 pulse)(b)
Figure 8: Digital control of charging regulation. (a) The
charging pattern shows multiple current pulses with adigital filter. (b) Digital control of DSP clock permits only
one current pulse per each step.
There is also a certain amount of overshoot due to thephase delay of the digital filter as shown in Figure 7-(a).
Even a small overshoot, it takes long time to return to thetarget level within the 100 PPM error, which is enough tolimit the pulse repetition rate, for example, 5 Hz in thistest. By digitally controlling the pattern of charging pulse
rate near the target level, we can charge the PFN smoothly
without losing a charging time as shown in Figure 7-(b).
Due to the same reason, the overshoot also makes theregulation poor at the target charging level as shown in
Figure 8-(a). There are 15 DSP clocks corresponding to
the charging command for an inverter switching in case adigital filter is used. We already know that one charging
pulse is enough to recover charging level. Therefore, one
charging command is only permitted then next pulses areblocked for a while. After suitable settling time, we cancorrectly see the charging level that is to be comparedwith a target level as shown in Figure 8-(b).
Further improvement of the charging regulation is doneby reducing the size of a bucket. PWM (pulse widthmodulation) is a typical method for the bucket size
control. After PFN voltage reaches the target level,
charging revel is regulated by smaller bucket with PWM
mode.

Proceedings of FEL 2007, Novosibirsk, Russia<PWM mode ON (5 mv/div)>

WEPPH033

C= 0.5 uF

PFN Voltage (Tektronix P6015)

PFN Voltage (Ross Probe 5000:1)

7 V =100 PPM@ 0.8 uF/43.5kV

Figure 9: PWM mode and charging regulation.
Figure 9 shows the effect of PWM mode on theregulation of charging level. Turning on the PWM mode
improves the regulation down to 7 V as shown in Figure 9,
which is corresponds to 100 PPM regulation at 45 kV.

PROBING SYSTEM
We need a high voltage probe to measure and feed backthe PFN voltage to a controller. A compensated resistive
divider is typically used as a high voltage probe. For the
stable measurement, the constant division ratio of theprobe insensitive to the temperature variation is essential.
However the high voltage resistor is temperature sensitive
due to the thermal variation of resistance value. Figure 10
shows the mean drift of the charging voltage around 10
kV during 14 hours. It is equivalent to 500 PPM at the 50
kV level. Therefore, we have to use a precision resistor
having less temperature coefficient or keep thetemperature of the probe body constant by using sometemperature control devices such as a Peltier element.

SUMMARY AND DISCUSSION
The charging resolution is determined by the minimum
size of charging bucket and the frequency response of a
feedback circuit including a probe. The inverter charging

Figure 10: Long-term drift of the PFN charging voltage
around 10 kV during 14 hours.
system with 100 PPM stability is possible with following
considerations. (1) Inverter charging system can meet the
short-term stability by choosing both a suitable minimum
resolution of a charging system and correct signal
conditioning. (2) Long-term stability can be provided by ahigh precision resistor or a temperature control device ofthe probe. (3) The residual slow drift can be corrected byadjusting the reference command of the PFN charging
voltage in order to provide constant RF amplitude.

REFERENCES[1] I. S. Ko, “PAL XFEL project,” Proc. FEL2005,
Stanford University, USA, 2005
[2] Y. Kim, et al., “Start-To-End Simulation of the PAL
XFEL Project,” Proc. FEL2004, Trieste, Italy, 2004[3] J. S. Oh, et al., “Development and Application of an
Inverter Charging Supply to a Pulse Modulator,” theXXI International LINAC Conference, Korea, 2002
[4] H. S. Kang, et al., “Design of Coherent FemtoSecond THz Radiation Source using 60 MeV
Electron Linac,” Proc. SRI2006, Daegu, Korea, 2006
[5] J. S. Oh, et al., “Analysis of Inverter Charging
Waveform for Ultra Stable SCSS Modulator,” Proc.
FEL2006, Berlin, Germany, 2006

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Proceedings of FEL 2007, Novosibirsk, Russia

FOURIER AND NON-FOURIER MODELS FOR PHOTOEMISSION
F. Scarlat, M. Oane, Anca Scarisoreanu, Ecaterina Mitru
National Institute for Laser, Plasma and Radiation Physics - NILPRP, Bucharest, Romania
E-mail of corresponding author: scarlat.f@gmail.com
Abstract
This paper is a theoretical study on the photoemission
properties of metallic photocathodes in the high intensity
ultrashort laser pulse regime, using Fourier and non
Fourier models. First of all the Fourier-model was used.
Next an analysis of the electron gas heating phenomenon
and how this phenomenon leads to coupled heat equations(two temperature models) was conducted. The authors
also tried to show that it is possible to use, in the second
approximation, a non-Fourier model instead of two
temperature models, using a single temperature
hypothesis (the electron gas temperature equals the lattice
temperature). The distributions for the thermal fields andphotocurrents function of space, time, laser-intensity,
incident angle and relaxation time are also represented.

INTRODUCTION
Free electron lasers (FELs) operate over a large portionof the electromagnetic spectrum, i.e.from a μ-wave to the
VUV. At the high frequency end of the spectrum, FEL
operation is severely limited by a number of factors,
among which the transverse beam emittance, which isinvers proportional with the square root density current. A
high electron density implies not only a high peak current
but also a low rms normalized emittance, εn. For example,
in the case of X-FEL projects, εn[mm.mrad] has thevalues: 1.4 - XFEL [1], 1.2 - LCLS [2] and 0.85 - SCSS
[3]. Recent development in the tehnology of photemissive
electron sources offer promising advances over theconventional electron injectors [4], [5].
All photo-injector concepts share a drive laser which
produces short bunches of photons and a photocathodewhich converts the photon bunch into short bunches ofelectrons [6], [7]. Photoemission from photo-cathodes ispossible when the work function (or potential barrier, eФ)of the material is less than the photon energy (ћω) used,by at least: 1 eV if the material is a metal (in this caseelectrons are extracted from the conduction band) and 2eV if the material is a semiconductor (electrons are here
extracted from the valence band).
A photocathode is characterized by four parameters:
quantum efficiency (QE), maximum laser wavelength(λm), life time (τ) and its ability to sustain a high electricfield (E). For FEL nano-Coulomb pulses in picosecond
time are required. The advantages of photoemission are
the followings: high peak current density (> 100 A); fasttime response (picosecond to femtosecond) andpossibility to generate polarized electrons. As drawbaks:
the need for very good vacuum, limited lifetime (fewmonth) and very expensive (vacuum systems & laser).
Metal cathodes have poor QE but are robust (τ ~ years).
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428

Alcaline cathodes have good QE but are delicate andthey need very good vacuum conditions < 10 -10 torr.
Starting from the above considerations as well as the
NUCLEU program [8] for to conduct studies by means of
the Nd:YAG laser system with 50 mJ at 1064 nm, 24 mJ
at 532 nm, 8 mJ at 355 nm and 4 mJ at 266 nm, this paper
represents a start in the metal photocathode studies using
Fourier and non Fourier models for photoemission [9].

FOURIER MODELS
Fourier model starting from the basic Fourier heat
equation, represented the input of our models [10]∂ 2T ∂ 2T ∂ 2T 1 ∂T
Q ( x, y , z , t ),+ 2 + 2 −
=−
2
γ ∂t
K
∂x
∂y
∂z

(1)

where K - the thermal conductivity of the sample; γ - thethermal diffusivity of the sample (γ = k/c·ρ ); c -the heat
capacity of the sample; ρ - the mass density of the sample.
Q(x, y, z, t) represents the heat rate (per volume and timeunit) produced by the laser in the solid sample.
Based on Spatial Transform and Laplace Transform,
the eigenfunctions from the standard theory and theeigenvalues from the boundary conditions were
determined.
So for the proposed device a parallelepiped solid
sample with dimensions a, b, and c was considered.
Considering a linear heat transfer (h – heat transfer
coefficient) at the sample surface (the “radiation”
boundary condition), we have:hh⎡ ∂K x⎡ ∂K⎤⎤− Kx ⎥= 0; ⎢ x + K x ⎥ = 0 ,⎢ ∂x
K ⎦ x=− aK ⎦ x= a
⎣
⎣ ∂x
2

(2)

2

⎡ ∂K y⎤⎡ ∂K y⎤hh+ Ky⎥= 0; ⎢+ Ky⎥= 0 , (3)
⎢
∂
y
K
∂
y
K
b
b
⎣
⎦ y =−
⎣
⎦ y=
2

2

h
h
⎡ ∂K z⎤⎡ ∂K⎤+ Kz ⎥= 0.
= 0; ⎢ z + K z ⎥
⎢
c
K
K
⎣ ∂z
⎦ z =−⎣ ∂z⎦ z= c2(4)

2

The semi-analytical solution to Fourier equation is:∞∞∞

ΔT (x, y , z , t ) = ∑∑∑ a(α i , β j , χ o ) ⋅i =1 j =1 o =1

⋅ b(α i , β j , χ o , t )K x (α i , x )K y (β j , y )K z (χ o , z ),(5)

Proceedings of FEL 2007, Novosibirsk, Russia
where we have:

αI oxa (α i , β j , χ o ) =e (KC i C j C o ∫

)

b
c
+
2
2
2
2
2 − 2 y + z / wox
b
c
−
−
2
2

⋅∫

+

∫

b(α i , β j , χ 0 , t ) =(− 1− e2−γ ijo(t − t o )

a
+
2 −αx
a
−
2

e

K x (α i , x )dx ⋅(6)

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The thermal fields versus the incident angle of the laser
beam are given in Fig.3.
If there is no vacuum than at the margins of thephotocathode temperature decreases.

K y (β j , y )K z (χ 0 , z )dydz,[1 − eα +β +χ1

2
i)h(t − t ),2j2
− γ ijo
t

2
o

−

(7)

0

and

γ ijo2 = γ (α i2 + β j2 + χ o2 ) .

(8)The photocathode employed for the study is 4 mm x 10mm for a Kerst injector. Using a laser of the intensity (I0x)
plotted in Fig.1, by means of equations (5), (6), (7) and(8), some thermal distributions in different situations wereplotted.

Figure 3: The thermal field produced by a flat laser beam.
The spatial distribution of the thermal field for a given
incident angle and a flat laser beam (Fig. 4) when vacuum
around the photocathode exists, is presented.
T [a.u.]

1
0.8
0.6
0.4
0.2

Figure 1: TEM00 classical laser field.
Fig. 2 presents the temperature generated by thecathode surface when the incident laser beam acts in
TEM00 mode

0.25

0.5

0.75

1

1.25

1.5
θ [rad]Figure 4: Photocathode temperature vs. the laser
incidence angle.

THE NON-FOURIER MODELSThe Fourier model [10] contains several inconsistent
implications. The most important is that the model
implies an infinite speed of heat propagation.
The non Fourier Models start from the non-Fourier heat
conduction equation:

τ 0 ∂ 2T 1 ∂T ∂ 2T 1 ⎡∂Q ⎤ ,+= 2 + ⎢Q ( x, t ) + τ
2α ∂t
α ∂t ∂x
λ⎣∂t ⎥⎦Figure 2: Photocathode temperature.

(9)

where a, λ, τ0 are thermal diffusivity, thermal
conductivity, and relaxation time of the medium.
One of the models is the Anisimov model or the twotemperature model [11]. The coupled differential
equations relating the electron temperature Te to thelattice temperature Ti are given by the equations (10)where g represents the connection between electrons and

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lattice; C and K are the heat capacities and thermal
conductivity respectively:
∂
∂ ⎡
∂ ⎤
C e Te = ⎢k (Te , Ti ) Te ⎥ − g (Te − Ti ) + I ( z , t ) ,
∂t
∂z ⎣
∂z ⎦
∂
(10)
Ci Ti = g (Te − Ti ) .
∂t
Instead of the above model, the hyperbolic heat
equation was used; assume that: Te = Ti, which is valid
when the puls length is comparable to the relaxation time
and the electron temperature is higher than the lattice
temperature.
Assume a sample with the thickness L with initial
temperature distribution T(x,0) = T0. Starting with thetime t = 0 the front surface of the sample is irradiated bya laser-pulse with the laser pulse of energy intensity:⎧ Q0 ⎛ t ⎞⎪ ⎜ ⎟ exp − t / t p
Q( x, t ) = ⎨ Δx ⎜⎝ t p ⎟⎠
⎪
,
⎩0

(

) , 0 ≤ x ≤ ΔX,(11)

Te(z) = T0 + [Te(0)-T0]exp(-z/L),(12)

where: L = n(ħkF/m)τ with: kF - the Fermi momentum andthe factor n given the electron scattering will mimic a
random walk – should be on the order of the square rootof the ratio of the laser pulse time scale with thescattering time scale, or n = (1 ns/0.1 ps)1/2 ≈ 100. τ is therelaxation time. The plot is presented in Fig. 5.

Figure 5: The temperature distribution versus depth in a
Non Fourier model: the first curve, which is close tounity, is for the relaxation time 10-3 s (a), the others arefor 10-6 s (b), 10-9 s (c) and 10-12 s (d).

430

EXAMPLES
Fig. 6 is a plot of the current densities vs temperaturefor different photocathodes.
Log j
18

ΔX ≤ x ≤ L,

where tp denotes the time duration of the pulse, Q0 is thetotal energy intensity of a single pulse. According tocommon theory, Δx is corresponding to the skin depth ofelectromagnetic waves penetrating into the surface of thesample, L is the thickness of the medium.
The boundary conditions are:∂T (0, t ) / ∂x = 0 , ∂T ( L, t ) / ∂x = 0 and the initialconditions are: T(x,0)=T0 and ∂T ( x,0) / ∂t = 0 .
Suppose that: Te=Ti, than the solution is the following:

FEL Technology I

LIMITS OF THE TWO MODELSThe shorter the relaxation time, the two different
models (Fourier and non Fourier) would give the same
results. It is obvious that the classical treatment is more
powerful than the Quantum Mechanics models for thiscase of laser-solid interaction. The temperature fielddepends on the incident angle. The experiments showsthat Fourier model is valid up to 10-6 s and the non
Fourier model is valid up to 10-9 s.
Our simulations strongly suggest that all thephenomena are taking place at the sample surface rather
than in the volume. Also our simulations prove that thehigher the vacuum, the higher the temperature field is.
(A(x,y,z,t)=rS·δ(z); δ(z) - Dirac Function ).

a

16

b
14

c
d

12

200

400

600

800

1000
T, [K]

Figure 6: Variation of the current density vstemperature for: bright tungsten (a); lanthanum
hexaboride (b), thoriated tungsten (c) and impregnatedtungsten (d).
Fig. 7 presents the 3D (Cartesian coordinates) thermal
fields for a laser beam heating the FEL photocathode atan angle of π/4. The laser beam is supposed to act in a
Gaussian mode. The exposure time is 10-9 s. (Fouriermodel was used).

Figure 7: Thermal field for the exposure time of 10 – 9 s.

Proceedings of FEL 2007, Novosibirsk, Russia
One can observe the edge effects due to the boundary
conditions.
For nano and picoseconds exposure time, Figs. 8 and 9(radial coordinates versus time) are suggestive. For
femtoseconds exposure times the Fourier model breaks down. In order to overcome the edge effect, it is possible
to use the “state of the art” technologies regarding
implantations of nano-particle (Au, Al, Ag, Cu, Ni)
networks of 100 nm size, at 400 nm distance between
them, on the photocathode edges.

WEPPH034

CONCLUSIONSFirst of all Fourier models can offer useful information
about the photochatode thermal field, especially when
dealing with long a term pulses (μs) and powerful heating
sources. In the range of picoseconds one has to take into
account non-Fourier models, which imply a finite
propagation speed of the thermal waves (in contrast with
the Fourier models which involve infinite speed
propagation). For non-Fourier models the problem to deal
with is the relaxation time. If the heating pulse time is of
the order of magnitude (or smaller) than the relaxation
time, the differences between the two models are greater.
In the range of femto- and atto- seconds one has to deal
with a quantum heat transfer model. In fact the nonFourier models are semi-classical models which take into
account the quantum effects via the relaxation time (in an
empirical style).
Another conclusion and a suggestion is that nanoparticle networks, with a very high absorption coefficient,can improve the photochatode properties.

REFERENCES
Figure 8: The thermal field for nano-seconds exposure
time (radial coordinates versus time).
Table 1
PhotocathodeAbsorption
Material
coefficient (cm-1)
CsI
40
Au
0.77 x 106
Ag0.83 x 106
Al
106
Cu
16.6.106Ni
13.106The big difference between the absorption coefficients(Table 1) of CsI, on one hand, and Al, Au, Ag, Cu, Ni on
the other hand, makes our proposal realistic. For example,
Fig. 9 presents the thermal field at the surface for a 100
nm diameter Au nano-particle which is at 400 nm depth.
One can observe that the peak temperature is increased.

[1]. M. Altarelli et al. (Eds.), The European X-Ray Free
Electron Laser (XFEL), Technical Design Report, Preprint
DESY
2006-097,
DESY,
Hamburg,2006,(http://xfel.desy.de)[2]. J. Arthur et al., Linac Coherent Light Source (LCLS).
Conceptual Design Report, SLAC-R593 Stanford 2002
(http://www-ssrl.slac.stanford.edu/lcls/cdr).
[3]. Spring 8 Compact SASE Source (SCSS) X-FEL:
Conceptual Design Report, RIEKEN, Japan, May 2005
(http://www-xfel.spring8.or.jp).
[4]. K. L. Jensen, D. W. Feldman, M. Virgo, P. G. O’Shea,“Measurement and analysis of thermal photoemission froma dispenser cathode”, Phys. Rev. S.P.- Accelerators andBeams, 6, 083501,2003.
[5]. C. Travier, B. Leblond, M. Bernard, J.N. Kaila, P. Thomas,
and P. Georges, Proceedings of the 1995 Particle
Accelerator Conference, Vol.2, pp. 945-947, 1995.
[6]. G.R. Neil and L. Merminga, “Technical approaches forhigh-average-power free-electron lasers”, Rev. Mod. Phys,74, 685 - 699, 2002.
[7]. M. E. Couprie and J. M. Ortega, “Free-electron lasers
sources for scientific applications”, Analysis 28, pp.725736, 2000.
[8]. F. Scarlat, M. Oane, A. Scarisoreanu, E. Mitru, ”TestingStand for Experimental Studies on PhotocathodeMaterials”, PN06 360503 NILPRP Program, 2006.
[9]. D.W. Tang, N. Arald, “Analytical solution of non-Fourier
temperature response in a finite medium under laser-pulse
heating”, Heat and Mass Transfer 31 (1996) 359, Springer Verlag, 1996.
[10]. M. Oane, Shyh - Lin Tsao, F. Scarlat, “Temperature field
distribution in multi-layered solid media interaction”,
Optics & Laser Technology, Vol.39, Nr.1, Pg. 179 - 181,
February 2007.
[11]. S. I. Anisimov, V.A. Khoklov, “Instabilities in LaserMatter Interaction”, Boca Raton”, FL: CRC, 1995.

Figure 9: Thermal field at the surface for a 100 nm
diameter Au nano-particle.
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Proceedings of FEL 2007, Novosibirsk, Russia

COHERENCE OF SPACE CHARGE VIBRATION AND PARAMETERS OF
ELECTRON GUNS
S. V. Miginsky#, Budker INP, Novosibirsk, Russia
Abstract
Space charge effect always determines the motion ofparticles in electron guns. Coherence of space charge vibration leads to oscillation of the emittance along a gun ora charge affected beamline. This phenomenon is closely
related to a technique known as emittance compensation.
It has been considered in the paper. The optimal parameters of guns and the expected emittance of the beam fromthe optimal ones have been estimated and scaled.

INTRODUCTION
Emittance compensation technique has been mentioned
first probably in [1]. It was explained and developed further in [2] and other papers. The two basic effects, causedby the longitudinal nonuniformity of charge density andthe transverse one, and their combination in uniform andnonuniform beamlines were considered in [3] - [6], alsowith accelerating and bunching. The main results of thelatter works is that both effects separately or together canbe compensated, the charge phase advance through thebeamline should be 2nπ (n is integer) and the focusing
should be optimal. Then the normalized emittance dilution is well estimated asI,
ε n ≅ ε c xe
(1)
I 0 βγwhere xe is the rms size of the beam at the entrance; I is
the peak current; I 0 = 4π ⋅ mc 2 Z 0 e , ≈ 17.045 kA forelectrons; β = v / c ; γ = 1 / 1 − β 2 ; v is the longitudinalvelocity; and εc is the dimensionless coefficient depended
on the type of the beamline.
In this paper we consider electron guns in the sameview. We take into account only macroscopic spacecharge effect and neglect thermal and grid emittance. The
main difference between a gun and a beamline is thepresence of metallic electrodes near the emitter. Theircharge depends on the one of the beam and generates
comparable fields, so exclusion of near-cathode electrodes from simulation of beam motion in a gun causes
lost of accuracy.

EMITTANCE DILUTION IN GUNS
Phenomena and Basic Scaling
If the emitter is round and the beam is homogeneousand stationary, the gun geometry can be optimized so thatthe space charge effect doesn't affect the emittance, as in
the well known Pierce gun. If the beam is not longitudinally uniform, the transverse phase portraits of its slices
differ and their emittances are not zero. Let's consider____________________________________________#

S.V.Miginsky@inp.nsk.su

FEL Technology I

432

these phenomena and estimate the total emittance.
Particle motion in the same gun is similar if its voltage
and current meet Child-Langmuir law I ∝ U 3 / 2 . In thiscase the emittance (not normalized!) doesn't depend on
the current [5] 4.1. At the same time, the brightness isI ε 2n ∝ U . If all the dimensions of a gun are changed
proportionally, its quality factor εc preserves while its

brightness is ∝ U r 2 . Thus, one should find εc and the
optimal compensation beamline for any gun.

Charge Amplitude and Phase
General equation of small charge vibrations has been
derived in [3] (3). It generates a transformation matrix
between two arbitrary points of a beamline [5] (2.16). The
charge vibration phase is defined in [5] (2.19). Now we
can define the differential characteristics of a bunch [5]4.1, [6]. The local charge phase is⎛ dx ′ x ′ dx ⎞⎜⎟−⎛ − C ′x ⎞
⎜ dI
⎟
x
dI
⎜
⎟
(2)
ϕ = arctan= arctan⎜⎟,⎜C j ⎟
1
1
dx
⎞
⎛
⎝
⎠
⎜⎜ ⎜
⎟
j
−
⎟ ⎟
⎝ ⎝ 2 I x dI ⎠ ⎠where x is the rms-size of a slice, j = I/I0, C and C' are thetransformation matrix elements associated with cos-liketrajectories. The quadrant is chosen so that the signs of
sinφ and cosφ coincide the ones of the numerator and thedenominator respectively. x and x' are considered as functions of the slice current I.
It is also useful to define the relative amplitude ofcharge vibrations to estimate emittance dilution in a compensation beamline [5] 4.1, [6] (5):a=(C ′x / j ) + C .
2

(3)

2

Then the relative amplitude of a slice is [5] (4.10), [6]
(13):
2

2

1 ⎛ ⎛ dx ′ x ′ dx ⎞ ⎞⎛ 2 I dx ⎞−− 1⎟ + ⎜⎜ 2 I ⎜
A= ⎜
⎟⎟ .
x dI ⎠ ⎟⎠j ⎝ ⎝ dI⎠
⎝ x dI(4)

Basic Gun
A simple diode gun has been simulated first. Its geometry is shown in fig. 1. The emitter radius was 5 mm, thedistance between the electrodes was 123 mm, while thebeam was observed at 200 mm from the cathode. The
perveance was very close to the "natural" one, so the optimal current was 2 A at 300 kV. SAM simulation code [7]was used to calculate beam motion in the gun. As usuallyfor emittance compensation, a bunch has been divided byslices, and each slice was considered independently as asteady-state beam. The current density at the cathode wasalways homogeneous.

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 1: The geometry of the basic gun, red solid lines
are electrodes.
The calculated beam parameters depending on the
beam current are depicted in fig. 2. They were calculatedby the following formulae:
x = < x2 >,(5)x ′ =< xx ′ > / < x 2 > ,this system, (ii) which slice should be matched to thecompensation beamline, and (iii) what is the optimalphase advance of the latter.
Each slice was considered as a number of particles, representing the motion of the appropriate ring. The longitudinal charge distribution was presumed as Gaussian. An
ideal beamline with phase advance φ matched with a slicewith the current j0 and the state x0 and x0' has the following produces the following linear transformation:
x ′ → x ′ − x ⋅ (x 0′ / x 0 ),⎧⎪ x → x 0 + ( x − x 0 ) cos ϕ + x ′x 0 / j sin ϕ,(6)⎨⎪⎩ x ′ → x ′ cos ϕ − ( x / x 0 − 1) j sin ϕ.
Then φ and j0 were optimized for each peak current value.
For example, the minimum for 2.2 A is 1.03 mm·mrad
and is situated at I = 1.043 A and ϕ = 3.91 ≅ 1.246π . The
phase is quite near the predicted value.

ε = < x 2 >< x ′ 2 > − < xx ′ > 2 .

10
4

16
3

, ε ,mm·mrad

8

4

1 x, mm" x', mrad

12

4

0.1

2
2

1

1
0
0

0
0

1

I, A

2

3

Figure 2: Beam parameters vs. beam current: rms-size, its
derivative and emittance.
8

4
4
2
2

0

, relative amplitude

6

6

1φ

0.01
0

-4

ε / xe j1/2, m

6

ε, mm·mrad

20

WEPPH037

0
0

1

I, A

2

3

Figure 3: Charge phase and relative amplitude vs. beam
current.
The dependencies of the phase and the amplitude on thecurrent for the mentioned gun are shown in fig. 3.It isseen that the phase is almost constant within current limits
from 1 to 3 A and its value is ≈ 2.5 ≈ 0.8π. Thus, if an
ideal uniform beamline (where the phase advance doesn't
depend on the amplitude) with the phase advance ≈ 1.2π
is placed after the gun, one should expect the minimal
emittance. The following questions are still left: (i) what
peak current of a bunch gives the minimum emittance in

1

Ip, A

2

3

Figure 4: Emittance (solid) and εc (dashed) vs. peak current. Blue – no compensation, red – ideal beamline, green– non-uniform beamline.
Plots of the emittance and the quality factor vs. thepeak current of a Gaussian bunch with and without theideal compensation beamline are depicted in fig. 4. One
can see that (i) the beamline reduces the emittance six
times and (ii) εc weakly depends on the peak current. A
non-ideal compensation beamline increases the quality
factor by ([3]: (5), (15), Table 1)x
ϕ(7)0.037 0 A 3≈ 0.13 ,xe
2πwhere all the parameters belong to the matched slice.
Thus, imperfection of the compensation beamline canweaken the compensation significantly.
Consider then a simplest non-uniform beamline thatconsists of two gaps of different lengths and a thin lensbetween them. Then the motion of charged rings throughit is described by the following equation [3] (12):~2j(8)
x ′′ =,
x~where j is the current within the ring. The motion is presumed as laminar. Both lengths and the lens strength were
optimized. The optimal emittance and εc are also placed in
fig. 4. It is clear that both beamlines give almost equal
results if the peak current is bigger than 2 A.

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Proceedings of FEL 2007, Novosibirsk, Russia

Other Guns
Seven other guns have been simulated in the same way
to investigate the influence of the gun geometry. In five
first ones the emitter radius was the same while the length
was varied. The electrodes were shaped to make perfectelectric field. Additional electrodes were added to theguns "Short 2", "Long 2" and "Long 3" to equalize theirperveance to the primary one. The cathode electrode in"Long 3" is planar. The optimal current in all the cases
above was ≈ 2 A. The two last guns are similar to firsthalf-cells of 1.3 GHz photo-electron RF guns. The emitterradii in these cases are 2 mm. The results are placed intable 1. The values in parentheses in the second column
mean the observation points. The last three columns contain quality factors of non-compensated guns, with ideallines and with non-uniform lines respectively.
Gun
Basic
Short
Short 2Long
Long 2
Long 3
RF 1
RF 2

Table 1: Simulated guns parametersεcεcLength,U,εcn/c,ideal, n/u,
mm
kV
m
m
m
123 (200) 300
0.3
0.05
0.065
61.5 (100) 150
0.3
0.04
0.05
61.5 (100) 300
0.35
0.055 0.15
246 (400) 850
0.43
0.085 0.14
246 (400) 300
0.26
0.04
0.065
246 (400) 300
0.4
0.07
0.023
50 (70)1000 0.28
0.05
0.02
50 (70)2000 0.28
0.05
0.02

PARAMETERS OF EXISTING GUNS
It is interesting to compare the theoretical parameters
above with ones achieved in real guns. One can find themin table 2. Only guns demonstrated record brightness wereselected there. The lengths and voltages at the first halfcell of guns were used to calculate εc.
GunTable 2: Existing guns parameters
Ip,
x e,
εn,
Ref. Ekin,
MeV A
mm
mm·mrad
[8]
2.0
50
1
0.83
[9]
1.05
100 1
2.7
"
"
43
0.57 1.7[10] 1.33
67
0.3
1.4

εc, m

LCLS*
0.034
DESY
0.06
"*
0.10
BNL
0.14
IV
"*
"
"
133 "
1.35
0.095
MIT
[11] 0.27
50
0.5
3.5
0.14
* Guns with bunch shaping.
The best εc of existing guns are close to ones estimatedabove, although exceed them. On the one hand, bunch
shaping permits to reduce the emittance, as the Gaussianlongitudinal distribution was considered in estimations.
On the other hand, the rectangular transverse distribution
in estimations yields better emittance then the Gaussian
one typical for photo-electron guns. Also the temperatureof photo-electrons was not taken into account. For example, the emittance of LCLS gun is lower than the temperature limit [9]:FEL Technology I434

ε n = xe

2E k
3m e c 2≅ 1 mm ⋅ mrad .

(9)

There could be two explanations: (i) the light spot size
was reduced and/or (ii) the temperature of electrons leaving copper cathode is less then of ones from CsTe cathode(0.8 eV by [9]).

CONCLUSIONS• Appropriate emittance compensation applied to anelectron gun always improves emittance by factor
3…15.
• Both effects of the longitudinal nonuniformity ofcharge density and the transverse one can be compensated well.
• The expected normalized emittance of a welldesigned gun with an optimal compensation beamline isII
ε n ≈ 0.02...0.07 x e= 0.01...0.035re, (10)
I 0 βγI 0 βγwhere xe is the rms beam size at the emitter and re is
the emitter radius.
• Quality factors εc of best existing guns approach
theoretical limitation. Further improvement is possible with beam shaping.

REFERENCES[1] B.E.Carlsten. NIM A 285 (1989) 313.
[2] L.Serafini, J.B.Rosenzweig. Phys. Rev. E 55 (1997)
7565.
[3] S.V.Miginsky. NIM A 575 (2007), 234-237.
[4] S.V.Miginsky. Optimal Beamlines for Beams withSpace Charge Effect. RuPAC 2006.
[5] S.V.Miginsky. Space charge effect, coherence of
charge vibration and emittance. Prepr. BINP #200711,
Novosibirsk,
2007.
http://www.inp.nsk.su/activity/preprints/files/2007_0
11.pdf[6] S.V.Miginsky. Electron Guns and Beamlines in the
View of Emittance Compensation. APAC'07, Indore,
India, Jan 29 - Feb 2 2007.
[7] M.A. Tiunov, B.M. Fomel and V.P. Yakovlev. SAM– an Interactive Code for Evaluation of Electron
Guns, Budker INP prepr. 96-11, Novosibirsk, 1996.
[8] http://www-ssrl.slac.stanford.edu/lcls/ http://wwwssrl.slac.stanford.edu/lcls/parameters.html[9] V. Miltchev, K. Abrahamyan, G. Asova, et al. Transverse Emittance Measurements at the Photo Injector
Test Facility at DESY Zeuthen. FEL'04, Trieste, Italy, Aug 29 – Sep 3 2004.
[10] J. Yang, F. Sakai, T. Yanagida, et. al. Experimental
Studies of Photocathode RF Gun with Laser Pulse
Shaping. EPAC'02, Paris 3-7 June 2002.
[11] W. J. Brown. Low emittance electron beam production and characterization with a 17 GHz photocathode RF gun. Ph. D. thesis. MIT 2001.
http://dspace.mit.edu/handle/1721.1/8287

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH038

LOW POWER CONSUMING HYBRID BENDING MAGNET AT THE XFELBEAM DUMP
F. Hellberg, H. Danared, A. Hedqvist, Manne-Siegbahn Laboratory, 10405 Stockholm, Sweden ∗W. Decking, B. Krause, A. Petrov, J. Pflüger, M. Schmitz, DESY, 22603 Hamburg, Germany
MAGNETIC FIELD CALCULATIONS

Abstract
At the end of the European XFEL the electron beam isseparated from the photon beam and directed towards thebeam dump with a bending magnet. This dipole magnet isdesigned to bend 10-25 GeV electrons by 1 ◦ /m and is 10
meter long in total. By integrating permanent magnet material into a conventional electromagnet, this so-called hybrid
magnet with a 1 T bias magnetic field consumes no powerat the nominal energy of the XFEL, 17.5 GeV. The magnetic field can be increased or decreased by magnet coils
to obtain 1◦ /m deflection for all energies between 10 and
25 GeV. Here a proposal for such a hybrid configuration ispresented together with its characteristics.

In a conventional dipole electromagnet the magnetic
field is confined in a steel yoke (μ rel ≈ 1000) and a small
air gap (μrel ≈ 1). If the air gap is increased more current isneeded to maintain the field strength (the slope of the magnetization curve dB/dI becomes smaller). Because thepermeability of PMM is similar to the permeability of air,the insertion of PMM in the yoke results in lower dB/dI.
Despite this it can be favourable to use a hybrid magnet
under certain conditions.
Consider a C-shaped dipole electromagnet and assume
that the magnitude of the field in the gap is the same as in
the yoke. The Maxwell equation important in this case canbe presented in integral form by applying Stokes’ theorem:

INTRODUCTION
In a free electron laser the electrons are bent away fromthe laser light with electromagnets and stopped in a beam
dump situated away from the experimental hall. At the European XFEL the electrons are bent vertically 10 ◦ in a 10 mlong double bending achromat magnet [1]. Each beam line
ends with such a magnet. It is the largest electromagnet of
the XFEL and it consumes a significant amount of power. It
is therefore desirable to find a way to lower the power consumption of these magnets. This report presents a feasibility study of the use of a permanent magnet/electromagnet
hybrid for this purpose [2, 3]. At the nominal energy of the
XFEL, 17.5 GeV, the electrons require a magnetic dipole
field of 1 T in order to bend 1 ◦ /m. Integrating permanent
magnet material (PMM) into an electromagnet to produce
a 1 T bias field in the pole gap results in a bending magnet that consumes no power at the nominal energy. Magnet
coils can then be used to increase or decrease the magnetic
field in the pole gap. The aim has been to design a hybrid
magnet that uses less power than a conventional electromagnet between 10 and 25 GeV (0.58 and 1.46 T).
A passive safety system must exist in order to prevent theelectron beam from reaching the experimental hall in caseof component failure. With conventional electromagnets
in the bending unit it is necessary to place an additional
permanent magnet further down the photon beam line forsafety. The advantage of a hybrid magnet is that the bias
magnetic field of the permanent magnet also works as anintegrated safety system.
∗ This project was performed within the framework of the Stockholm-

Uppsala Centre for Free Electron Laser Research. For more information,please visit: http://www.frielektronlaser.seB = N I,· dl =
J · dS
μμ0
S(1)

where I is the current and N the number of turns. For anelectromagnet equation 1 can be written as,
NI =

B
B
lg +
ls ,
μ0
μs μ0

(2)

where lg the size of the gap, l s the average length of thesteel yoke, μs permeability of steel, and μ 0 is permeabilityof air. By replacing part of the steel yoke with PMM a bias
magnetic field passes through the yoke and the gap. The relationship between B and H in the direction parallel to theeasy axis (the main axis of magnetization) of a PMM is linear in a wide range with slope μ p ≈ 1. The magnetization
curve can therefore be written as,
Bp = μ0 μp Hp + Br ,(3)

where Bp is the magnetic field, Hp is the magnetic field
intensity, and Br is the remanent field of the PMM. The
magnetic equation for the hybrid magnet can written, similar to equation (1), as
NI =B
B − Br
B
lg +
lp +
ls ,
μ0
μ0 μp
μ0 μs

(4)

where lp is the length of the permanent magnet material
along the easy axis. Equations (2) and (4) show that themore PMM is added to increase the bias field the more current needs to go through the coils for a specific correctionof the magnetic field. This is illustrated in figure 1 where
the ratio of the power consumption of the two types of magnets is plotted as function of beam energy. It is clear that
this simple type of hybrid magnet is not a good option for
10-25 GeV electrons.

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Proceedings of FEL 2007, Novosibirsk, Russia

l =l

7

p

g

l =2*lp6

l =4*l
p



g
g

/P

3

hyb

4

P

em

5



2
1
0






8

10

12

14



16

18

20

22



24

E (GeV)

Figure 1: The ratio of the power of a conventional electromagnet and a hybrid magnet with the same geometry as
function of beam energy. The hybrid magnet is favoured
for ratios lower than 1.

Figure 3: Parameters adjusted in the calculations to optimize the hybrid magnet.
2
1.8
1.6
1.4
1.2

B [T]

A better alternative is to concentrate the magnetic fieldwith several blocks of PMM. Here an alternative design
made of rectangular blocks of PMM is presented, similar
to one presented by K. Halbach [4]. The configuration of
the blocks is shown figure 2. Calculations were performed

1
0.8
0.6
PMM: rectangular blocks
Selection limit
Optimized 17.5 GeV

0.4
0.2


0

200

400

600



800

1000

1200

1400

Permanent magnet material [kg/m]



Figure 4: Field strength and mass of PMM per unit lengthplotted for different hybrid configurations.











amount of PMM the points left of black curve in figure 4
were plotted as black rings in figure 5. From investigating

2
PMM: rectangular blocks
Selected blocks
Optimized 17.5 GeV

1.8

Figure 2: A 2D view of a hybrid dipole made from rectangular blocks of permanent magnets.

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1.4
1.2

B [T]

using the Pandira program [5] to optimize the magnet withrespect to the amount of PMM and dB/dI. Vacomax 225(Sm2 Co17 ) with remanent field B r =1.03 T and H c =720kA/m was used as input in Pandira and B as function of
H was assumed to be linear in the second quadrant of themagnetization curve. In order to determine the size of theblocks to minimize the amount of PMM a number of geometries were used as input in Pandira. Figure 3 shows
the parameters a, c and d that were changed in the simulation. The pole width b was fixed. Results of the calculations are shown in figure 4 and it shows a distinct limit
for the minimum amount of PMM for a certain bias field.
The second important parameter is the efficiency of thecoils of the hybrid magnet. The magnetic field derivative(dB/dI) is approximately constant in the working range ofthe magnet and was calculated for all configurations. Figure 5 shows the magnetic field strength B at zero current
versus dB/dI. To highlight the configurations using a low

1.6

1
0.8
0.6
0.4



0.2
0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

dB/dI [normalized units]

Figure 5: Field strength B and dB/dI for different hybrid
configurations.
configurations with bias field close to 1.02 T (17.5 GeV)
it is concluded that a possible design is made from blocks
with the same thickness as the pole gap (3 cm). Having
a,d<3 cm enhances dB/dI, but more of the field from thePMM leaks through the block of PMM instead of passing
through the pole gap. This can be compensated for example by increasing c, but results in an increase of the to-Proceedings of FEL 2007, Novosibirsk, Russia
tal amount of PMM. On the other hand a configuration ofblocks slightly thicker than 3 cm uses less PMM, but has alower dB/dI.
Figure 6 shows the characteristics for the optimized hybrid magnet in the interval important for the XFEL bending
magnet together with an ideal electromagnet (infinite permeability of iron). The difference in power consumption
1.8
Hybrid magnet
Ideal electromagnet

1.6
1.4

B [T]

1.2
1
0.8
0.6
0.4



0.2
-3

-2

-1

0

1



2

3

4

NI [A]

4

x 10

Figure 6: Characteristics for an optimized hybrid magnet
and an ideal electromagnet.
between a hybrid magnet and a conventional magnet canbe illustrated by plotting the ratio of the power of the hybrid magnet over the power of an electromagnet as functionof electron beam energy. Figure 7 shows that this particular hybrid configuration using Vacomax 225 is better thana conventional electromagnet for beam energies larger than
11 GeV.

1em

REFERENCES[1] European XFEL Technical design report, edited by M.
Altarelli et. al., DESY 2006.
[2] F. Hellberg, ”Investigating the possibility of a hybrid magnet
design for BV/BW dipole magnets at the XFEL, MSL-06-1,
2006.
[3] F. Hellberg, ”Comparison of two hybrid magnet designs”,
MSL-07-01, 2007.
[5] POISSON/SUPERFISH group of codes, Los Alamos National Laboratory.

1.2[6] J. Alderman, P. K. Job, R. C. Martin, C. M. Simmons, G. D.
Owen, Nucl. Instr. Meth. in Phys. Res. A 481, 2002, p. 9-28.

0.8

hyb

/P

power than a conventional electromagnet for electron energies >11 GeV. The hybrid magnet can be optimized evenfurther by using permanent magnet material with higher B r
and reducing the bias field in order to make the magnet
power efficient between 10 and 25 GeV. The issue whether
the hybrid magnet represents a better choice than the conventional electromagnet still needs to be addressed. The
hybrid magnet include PMM, is more complicated to manufacture and therefore more expensive than an electromagnet. The higher cost to manufacture the hybrid magnet
must be returned by a lower power consumption. Additionally, the hybrid magnet is situated close to the electron
beam dump region and is therefore exposed to neutron radiation backscattered from the dump. The permanent magnet material must be able to withstand this [6]. Any lossof bias field due to demagnetization by radiation must becompensated for by the coils and the hybrid will loose its
advantage.
If the hybrid magnet can be made cost efficient and radiation resistent it represents an interesting solution for thebending magnet unit as well as the passive safety system of
the European XFEL.

[4] K. Halbach, J. Appl. Phys. 57, 1985, p. 3605.

1.4

P

WEPPH038

0.6

0.4

0.2

0


10

12

14

16



18

20

22

24

E [GeV]

Figure 7: The optimized hybrid magnet compared witha conventional electromagnet. The hybrid magnet isfavoured for ratios lower than 1.

SUMMARY
Here a proposal for a permanent magnet/electromagnet
hybrid for the XFEL beam dump magnet has been presented. The hybrid magnet has a 1 T bias field and consumes no power at the nominal energy of the XFEL. Magnet coils are used to change the magnetic field when changing the beam energy. The hybrid magnet consumes less
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INSTALLATION OF THE OPTICAL REPLICA SYNTHESIZER IN FLASH
G. Angelova, V. Ziemann, Uppsala University, A. Meseck, BESSY
M. Hamberg, P. Salén, P. van der Meulen, M. Larsson, Stockholm University
S. Khan, J. Bödewadt, A. Winter, Universität Hamburg
E. Saldin, H. Schlarb, B. Schmidt, E. Scheidmiller, M. Yurkov, DESY
Abstract

UNDULATORS AND CHICANE

During the shutdown in spring 2007 the optical replica synthesizer, a novel device to diagnose ultra-short electron
bunches, is assembled in the FLASH accelerator. We report on the status of the construction work with emphasison the two electro-magnetic undulators needed for microbunching and replica-pulse generation.

INTRODUCTION
Monitoring and tuning the bunch size are essential forthe reliable operation of linac-based SASE free-electron
lasers such as the FLASH [1], XFEL [2], or LCLS [3].
This need has triggered the development of new diagnostic methods based on a transversely deflecting cavity [4]or electro-optical sampling [5]. The optical replica synthesizer (ORS), a complementary scheme that was introduced
in Ref. [6], is similar to an optical klystron FEL seededby an infrared laser as is shown in Fig. 1. In the modulator the interaction of the laser with the transversely oscillating electrons causes an energy modulation. A small
chicane turns this energy modulation into a corresponding
density modulation at the wavelength of the light. In a following radiator undulator the micro-bunched beam radiates
coherently and the emitted light pulse has the same longitudinal profile as the electron beam. Hence the name optical replica synthesizer. The replica pulse is then extracted
from the vacuum pipe by an off-axis mirror and directed toan optical table with optical diagnostics where it will be analyzed by a commercially available second-harmonic generation FROG (frequency resolved optical gating) device,called GRENOUILLE [7].
During the spring shutdown 2007 most components suchas the undulators, external laser building, seed laser transport system, and the optical stations were installed and wereport on these activities.

Figure 1: The principle of the optical replica.
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The undulators were designed, assembled and tested at
Scanditronix Magnet AB, Sweden and were delivered to
DESY in March. They have a length of 1450 mm, a widthof 454 mm, a height of 817 mm, and weight 480 kg. The
gap is 40 mm in order to accommodate the standard 38 mm
vacuum pipe without having to break vacuum. The period
length is 200 mm with 14 poles and 28 coils connected in
4 separate coil circuits. This allows adjusting the field inRL
RLRz
tegrals I1 = 0 B(z)dz and I2 = 0 0 B(z 0 )dz 0 dz bycontrolling the end coils in the 1/2, -3/4, +1 pattern. The
first and last coil (with 1/4-excitation) have independent
supplies and the second and 13th coils are powered in series by another supply. Finally, the ten central coils areconnected in series to a fourth power supply. The maximum magnetic field is 0.5 T and nominal field 0.3 T. The
undulators can be mounted horizontally or vertically to induce vertical or horizontal beam oscillations, respectively.
Upon arrival at DESY field measurements were performed with a Hall probe and power supply settings were
found that zero the field integrals in order to avoid perturbing the electron beam outside the undulator. The individual Hall probe measurements have an accuracy ε ofa few Gauss, but the calculation of the first and√ second)=ε
Ldz andfield integrals
hasanaccuracy
of
σ(I
1
√
√
σ(I2 ) = εL Ldz/ 3 where dz is the distance between
consecutive Hall-probe measurements [8]. This allows us
to measure the field integrals with an accuracy on the order of 10−5 Tm or 10−5 Tm2 , respectively, provided weuse a small step size of dz = 2 mm. We then determinedsettings of the power supplies for peak fields of 0.1, 0.2,

Figure 2: The modulator which causes vertical oscillations.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH039

Figure 3: The radiator which causes horizontal oscillations.
0.3, 0.35, 0.4 T for which the field integrals are less than
0.5 × 10−4 Tm and 2 × 10−4 Tm2 . In order to achieve
reproducible settings we always cycle the power supplies
from zero to the 0.48 T-value, back to zero and then up to
the set-value.
After the completed field measurements the undulators
were installed in the FLASH beam line after the dog-leg
chicane used for momentum collimation. Figure 2 shows
the modulator which causes vertical beam oscillations at its
final location in the FLASH beam line and Fig. 3 shows theradiator which causes horizontal beam oscillations. This
will allow to separate the weak replica pulse from thestrong seed laser pulse by polarizers.
The chicane consists of four standard steering dipole
magnets which allow a maximum excursion of the beamof 15 mm, thereby producing an R56 of 300 µm.

SEED LASER, LASER TRANSPORT AND
OPTICAL STATIONSThe seed laser consists of an erbium-fiber oscillator [9],developed at DESY, that can be synchronized to theaccelerator-RF. The pulse from the oscillator is frequencydoubled and then fed into a regenerative Ti:Sa amplifier(Clark CPA-2001), based on chirped-pulse amplificationand pumped by a Nd:YAG laser. This system, initiallyprepared at Stockholm University, delivers a pulse output
of 0.8 mJ with pulse length of about 170 fs, center frequency 772 nm and 1 kHz repetition rate. The laser will beshipped to DESY in August and then installed in a newly
erected 150 m2 laser building next to the FLASH tunnel.
For replica operation the laser stretcher and compressor
will be re-tuned to provide about 2 ps pulses and will be
synchronized to the beam. The anticipated repetition rate is
5 to 10 Hz. A sketch of the layout along the tunnel is shownin the top of Fig. 4 and a view from above in the lower partof Fig. 4, which shows the 12 m long laser transport systemfrom the laser to the entrance port to the beam vacuum system in the dog-leg chicane. Just before the entrance win-

Figure 4: View along the tunnel and top view of the layoutof the optical replica synthesizer experiment.
dow a remotely adjustable three-lens telescope will permit
adjusting the diameter and the waist position of the laser
inside the modulator undulator. The laser transport system
was installed and aligned during the recent shutdown.
Also indicated in Fig. 4 are two optical stations with optical tables and OTR chambers with a set of different foils
that can be viewed by a CCD camera in order to analyze
the seed laser or replica pulse and the beam profile. In station I located in the center of the chicane we can image theseed laser, modulator radiation, and the electron beam ontoa CCD camera to optimize the spatial overlap of laser andelectrons and onto fast photo diodes to optimize the temporal overlap. In station II we will analyze the replica pulse

Figure 5: Optical station 2.

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OUTLOOK
There are 15 shifts alloted for the optical replica synthesizer during September and October when we will startby commissioning the undulators and software to control
the beam steering and the beta functions to compensate theweak focusing of the undulators. We then need to verify
parasitic operation of the undulators and the chicane during
SASE operation. In a second block we will commission theseed laser and optical station I and achieve spatial overlapof laser and electron beam. In a third block of shifts weplan to achieve temporal overlap of seed laser and beam,commission optical station II and eventually record the first
FROG traces on the GRENOUILLE.
Figure 6: A realistic longitudinal bunch profile (red solidline) and the temporal profile of the emitted replica pulse(black asterisks). The inset figure shows a zoom of the peakregion.

generated in the radiator. A picture of optical station IIthat was installed during the recent shutdown is shown in
Fig. 5. At the top of the figure, the beam pipe is visible withthe beam moving from right to left. In the top left cornera window from the vacuum tank containing remotely controlled mirrors to extract the replica pulse is visible. The
pulse is then vertically deflected by remotely controlled
mirrors onto an optical table which contains power meters,
fast photo-diodes and the GRENOUILLE [7] that will be
used to determine the temporal profile of the replica pulse
and thereby the bunch profile. The GRENOUILLE is theblack box visible at the right side of Fig. 5.

ACKNOWLEDGMENTS
With pleasure we acknowledge the extensive help of the
DESY groups involved in the FLASH installation, as wellas the support of the technical groups of the Institut für Experimentalphysik at Hamburg Universität and the help of
R. Ruber and M. Johnson, Uppsala University. M. Dohlus,
DESY kindly provided beam distributions from start-toend simulations. This work is supported by the UU-SUKTH FEL-center.

REFERENCES[1] V. Ayavazyan, et.al., Eur. Phys. J. D37 (2006) 297.
[2] P. Audebert, et.al., “TESLA XFEL: The first stage of the
X-ray laser laboratory - Technical Design Report,” DESY
2002-167.
[3] The LCLS Design Study Group, “LCLS Design Study Report,” SLAC-R-593, 2002.

SIMULATIONS
We perform numerical simulations of the replica process using the Free Electron laser code GENESIS 1.3[10]where the energy modulation in the modulator undulator
and the output power from the radiator undulator are calculated. The magnetic chicane is modelled by a transfer matrix. Fig. 6 shows a realistic current profile at the entranceof the modulator determined in start-to-end simulation [11]as the line and the replica pulse as asterisks, both normalized to the same peak value. We observe that the replica
pulse faithfully reproduces the initial electron distribution.
Simulations, however showed that it is necessary to makethe electron beam in the radiator as small and as round as
possible in order to achieve the faithful representation, because otherwise diffraction effects of the finite beam size
will deteriorate the quality of the reproduction. A slight effect of smearing due to the finite slippage of the electrons
with respect to the emitted light is also present, but can easily be de-convoluted, which was, however, not done here.
FEL Technology I

440[4] M. Hüning, et al., “Observation of femtosecond bunch
length using a transverse deflecting structure,”Proceedingsof the 2005 FEL conference, 538.
[5] G. Berden, et al., “Electro-Optic Technique with Improved
Time Resolution for Real-Time, Nondestructive, SingleShot Measurements of Femtosecond Electron Bunch Profiles,” Phys. Rev. Lett. 93 (2004) 114802.
[6] E. Saldin, E. Schneidmiller, M. Yurkov, “A simple method
for the determination of the structure of ultrashort relativistic
electron bunches,” Nucl. Inst. and Methods A 539 (2005)
499.
[7] R. Trebino, “Frequency Resolved Optical Gating”, Kluwer
Academic, Boston, 2000.
[8] V. Ziemann, “How accurately can we measure the field integrals of an undulator?” unpublished note, dated 26.3.2007.
[9] A. Winter, et.al., “ High-precision laser master oscillators for
optical timing distribution systems in future light sources”,
EPAC 2006, p. 2747.
[10] S. Reiche, Nucl. Inst. and Methods A 429 (1999) 243.
[11] M. Dohlus, FLASH Start-to-end simulations, private communication.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH041

7TH HARMONIC BUNCHER EXPERIMENT AT THE
UCLA NEPTUNE LABORATORY
P. Musumeci*, S. Ya. Tochitsky#, R. Tikhoplav*, J. B. Rosenzweig*, C. Joshi#
Abstract
Since typically FEL undulator magnets have period
length in the cm range, and the normalized magnetic fieldstrength K is usually close to unity to guarantee a good
coupling, a very high energy electron beam is needed toaccess the UV and x-ray region of the electromagnetic
spectrum. One way to reduce the beam energy necessary
for short wavelength light sources consists of exploiting
the FEL harmonic interaction. An experiment aimed atdemonstrating the efficiency of harmonically coupled
schemes is proposed for the Neptune Laboratory at
UCLA. We plan to inject the 12.4 MeV beam from thesplit photoinjector in an already available undulator withperiod = 3.3 cm and K = 1.8. The FEL resonant
wavelength with these parameters is 74.2 μm. A
copropagating high power 10.6 μm CO2 laser bunches thebeam via 7th harmonic FEL/IFEL interaction. Preliminary
calculations show that even though the interaction is
weakened by the high harmonic number, only 5 -10 MWof laser power are required in order to induce fullbunching on the beam in the 10 period long undulator.

INTRODUCTION
Free-electron laser (FEL) amplifiers operating at shortwavelengths (<100 nm) are undoubtedly one of the top
research fields nowadays because of the new possibilities
opened by generation of powerful, short pulses in a rangeof the electromagnetic spectrum important for materialscience, biology and chemistry. The lasing wavelength ofan FEL depends primarily on the undulator magnet
characteristics --period and field amplitude-- and on theelectron energy. Since the undulator magnet has typicallyperiod lengths in the cm range, and the normalized
magnetic field strength K is usually close to unity toguarantee an efficient coupling, a very high energy
electron beam is needed to access the UV and x-ray
region of the electromagnetic spectrum.
One way to reduce the necessary beam energy is to utilize
the FEL harmonic interaction[1-5]. The FEL resonancecondition, i.e. the condition for efficient energy exchange
between the transverse EM wave and the electrons, takes
place at electron energies such that the wiggling inducedby the laser field has the same frequency as the wiggling
induced by the undulator in the electron rest frame.
However, a planar undulator resonance can also occur
when the laser frequency is a multiple of the undulator
wiggling frequency and electrons of a given energy
interact with the fundamental radiation frequency andwith its higher harmonics[6]. In some cases, when the*#laser frequency is constrained by the source availability
and the energy of the beam is so low that in order todesign an FEL at the resonant condition the undulator
parameters are unfeasible or the normalized vector
potential K has to be very small to reduce the magnetic
amplitude induced frequency red-shifting, harmonic
coupling becomes the only viable solution to ensure astrong interaction.
Even for FEL cascade schemes, one of the factors limiting
the frequency multiplication of all cascade schemes isrelated to the necessity of operating all the stages of thecascade with the same electron beam energy. The change
in the resonant wavelength for the different sections must
be compensated by variations of the undulator period and
K parameter. Using the conventional techniques forundulator magnet construction, the span of thesevariations is limited and harmonic coupling has been
considered as a possible solution [7].
Here we propose and discuss an experiment to be carriedout at the UCLA Neptune Laboratory to test the efficiency
and feasibility of a high order harmonic FEL/IFEL
interaction. For this purpose an existing short undulator
with a period of 3.3 cm and K = 1.8, for which theresonant wavelength with a 12.4 MeV electron beam is74.2 μm, will be seeded with a CO2 laser radiation. This
will allow to study the microbunching obtained by 7th
harmonic FEL/IFEL interaction, since 10.6 x7=74.2μm.

EXPERIMENTAL LAYOUT
Table 1: Parameters for Neptune 7th harmonic interaction
experimentBeam energy
Beam energy spread
Emittance
Current
Laser wavelength
Laser seed Power
Laser size (at focus)
Undulator period
Undulator K
Undulator length12.4 MeV< 0.2 %
5 mm-mrad
100 A
10.6 μm
10 MW
650 μm
3.3 cm
1.8
33 cm

UCLA Department of Physics and Astronomy,
Los Angeles, CA 90095-1547
UCLA Department of Electrical Engineering.

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Quadrupole Spectrometer

Quadrupoles

Insertable screen

OAP

To streakcameraE-beam
The
Nept
une
labor
atory

Undulator
Mirror box

Laser

2nd
Grating

Detectors
3rd

CTR microbunching diagnostics
Figure 1: A simplified experimental layout for the 7th harmonic buncher experiment.

hosts a split rf photoinjector capable of producing 10-14
MeV beam with a peak current in excess of 100 A and an
emittance as low as 5 mm-mrad.

actually very strong and comparable to the fundamental
coupling if the normalized magnetic field amplitude K islarger than 1. The coupling coefficients can be written as:

The CO2 laser system, which has been reported in detailelsewhere[8], has the capability of producing 1 TW midinfrared laser pulses. However, the repetition rate at thishigh power is limited to one shot per few minutes by themain discharge capacitor cooling time. Recently a new
high-pressure CO2 laser amplifier was installed which iscapable to produce ~1mJ at 1 Hz. By shortening the seedpulses to <100 ps in principle up to 10 MW of drive CO2
laser power is available to drive the interaction. Such a
power level, as will be shown below, is sufficient tobunch the electron beam. At the same time the high pulse
repetition rate allows parametric studies of the system
which would be otherwise very difficult in a single-shot
experiment.

JJ n = J n −1/ 2 (n ⋅ ξ ( K )) − J n +1/ 2 (n ⋅ ξ ( K ))FEASIBILITY OF THE 7TH HARMONICBUNCHING
It can be shown that in planar geometries the coupling
between the beam electrons and an electromagnetic wave
at a harmonic of the resonant undulator frequency is
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2

2

In Fig. 2, assuming an undulator period of 3.3 cm, we plot
the coupling coefficients for different K values and thecoupling strengths for the first odd harmonics. The
normalized vector potential K to obtain resonance at thefundamental is only 0.1. If the coupling is on the 7th
harmonic, K = 1.8 and the effective coupling strength is 2
times higher. This example illustrates the main
advantages of choosing an harmonic coupling when
designing an undulator/beam interaction.
K JJn(K)JJn(K)

0.6

Coupling strength

A conceptual design of the experiment is shown in Fig. 1.
A laser beam is focused by an off-axis parabolic mirror(F/50 scheme). After the FEL interaction in the undulator
the electron beam is sent to a high resolution spectrometer(horizontally focusing quadrupole + bending dipole) todetect the energy modulation imparted by the laser.
Electron microbunching at 10.6 μm is observed bymeasuring the coherent transition radiation spectrum froma foil screen inserted at 25 cm from the exit of theundulator. Because of the background noise due to thehigh drive laser power, detection of the harmonics issuggested as a way to measure the beam microbunching.
A diffraction grating separates the different wavelength
content in the beam generated radiation and MCT
detectors are placed at the angles corresponding to the 2nd
and 3rd harmonic of the CO2 laser line. The main CO2
laser beam is sent to a streak camera to enable temporally
resolved diagnostic.

for n = 1,3,5,7…where ξ ( K ) = K / 4 + 2 K .
Moreover, for a given laser frequency and electron beamenergy one has to maintain the resonant condition so theundulator K changes as the square root of the harmonic
number. The effective interaction coupling strength is
KJJ n ( K ) .

0.5
0.4
0.3
0.2
0.1
0.0
1

3

5

7

9

11

13

Harmonic number

Figure 2: Coupling coefficients and coupling strength.
Fundamental parameters of the interaction like the energy
width of the ponderomotive bucket and the synchrotron
oscillation frequency depend on the coupling strength. A
simple estimate of the power required to bunch the beam

Proceedings of FEL 2007, Novosibirsk, Russia

7TH HARMONIC BUNCHERSIMULATIONS

can be obtained requesting that ¼ synchrotron oscillation
is obtained during the undulator length. The synchrotron
period is given by:

λw 1 + K 2 / 2n

2 KK r JJ n

where K r = eE0 λ0 / 2π m0 c

2

is the normalized electricfield associated with the radiation. With the request thatalong the undulator particles would perform ¼ ofsynchrotron oscillation i.e.

zs / 4 = Lu
we can solve for the minimum electric field to achieve
microbunching. With the parameters of the short
undulator available at Neptune, reported in Table 1, we
obtain Kr = 1.2e-4, and E0= 40 MV/m which corresponds
to a laser intensity of I = 0.2 GW/cm2. The estimate
reported here shows that even though the interaction is
weakened by the high harmonic number, it is required touse only modest levels of power to induce full bunchingon the beam using the 10-periods long undulator.
The amplitude of the ponderomotive bucket in the energy
plane is given by:

2 KJJ n K r
δγ
=
2
γ
1+ K
2

which for our parameters is very small ( ~ 0.5 %) and
imposes an important experimental constraint on thequality of the input beam. Thus the energy spread of theelectron beam must be well below 0.5 % rms.
Another important constraint in the design is imposed by
the amplitude of the beam wiggling oscillations. As
shown in Fig.3, the focused CO2 laser beam must cover
the entire trajectory of the wiggling electron beam inorder to achieve the same acceleration gradient forparticles at different distances from the axis. To maintainthe required laser intensity level with a spot size of 650
μm at the focus and a relative Rayleigh range of 10 cm, aminimum drive laser power of ~3 MW is required.
1.5

12.25

12.20

12.15
0.39996

0.399980.40000

0.400020.40004z (m)Figure 4: Longitudinal phase space at the undulator exit
for 10 MW input CO2 power and initial e-beam energy
spread of 0.2 %.
The code GENESIS 1.3 has been used to simulate thethree dimensional interaction between the electrons andthe laser pulse in the undulator. The code has been
recently upgraded to be able to simulate the interaction of
the particles with the harmonic of the fundamental field[9]. In Fig. 4 one can see that electrons at the exit of theundulator are fully bunched when a 10 MW CO2 laser isused as a seed.
Along with the goal of first experimental demonstrationof the 7th harmonic interaction of a relativistic electron
beam and a laser in an undulator, the proposed experimentaddresses a couple of other important issues.
For a 0.5 mJ, 100 ps long laser pulse interacting with a 10
ps long electron beam, the energy of the laser available
for the electrons to absorb corresponds to 50 μJ of IR
power. This energy is the amount required to accelerate a
500 pC beam by 0.1 MeV.
CO2 Laser pulse power (MW)Beam current (amp)

120

10
100

0.5
0.0
-0.5
-1.0
-1.5

8

80

6

60

4

40

2

20

0

0.1

0.2

0.3

0.4

z (m)

Figure 3: Particle trajectory and laser beam size inside theundulator.

-20

0

20

40

Current (A)Laser power (MW)1.0

X (mm)

12.30

particle trajectory
laser beam size

2.0

-2.0
0.0

Longitudinal phase space
Current density

12.35

Energy (MeV)zs =WEPPH041060Time (ps)Figure 5: Beam loading in the 7th harmonic IFEL
accelerator for a 100 Amp beam current and 12.3 MeV
input energy. The beam current longitudinal profile is also
shown.

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Detuning slightly the input electron beam energy andinjecting the beam 100 KeV below resonance, theparticles will extract energy from the laser via 7th
harmonic interaction. With a temporally resolved
diagnostics of the infrared power, one could observe thepump depletion (beam loading) of the laser wave. Up to
30 % of power can be absorbed from the laser as it isshown in the time domain simulation reported in Fig. 5.
Finally, the 10.6 μm buncher running at 1 Hz will allow adetailed study of various microbunching diagnostics [10].
The coherent transition radiation foil has to be located as
close as possible to the undulator exit, since the beam
debunches quickly due to its low energy and strong
longitudinal space charge forces. At 20 cm from theoutput the bunching factor is still greater than 0.3 and any
radiation emitted by the beam (via transition or
Cherenkov mechanisms) will be enhanced by the coherent
form factor at the bunching wavelength 10.6 μm and therelative harmonics. In Fig. 6 we show the evolution of thebunching coefficients at the 10.6 μm, and its second andthird harmonic along the undulator. Because of the strong
space charge force and of the low beam energy,
debunching quickly takes place after the particles leave
the interaction region.
The effect of the finite transverse beam size on theradiation emission is particularly interesting when theemission mechanism has a preferred angular direction as
it is the case of a Cherenkov radiator.

1st harmonic 10.6 μm
2nd harmonic 5.3 μm
3rd harmonic 3.5 μm

0.6Bunching factor

0.5

Microbunching
diagnostics

0.4
0.3
0.2
0.1

End of undulator
0.0
0.0

0.1

0.2

0.3

0.4

0.5

Distance along the undulator (m)Figure 6: Bunching coefficients at the drive laser
frequency and relative harmonics.

CONCLUSIONS
We have proposed and discussed here an experiment to be
carried out at the UCLA Neptune Laboratory with thegoal to measure the efficiency of a high order harmonic
FEL/IFEL coupling. The experiment also addresses
important issues like the development of diagnostics forlongitudinal microbunching and the beam loading in a
vacuum laser accelerator. The implementation costs arevery low since most of the hardware is in house
FEL Technology I

444(undulator already installed on the beamline after aprevious experiment [11]). Some experimental efforts areneeded to set up the microbunching diagnostics, however
for the relevant wavelengths — harmonics of CO2 laser
frequency — a number of components, optical elements
and detectors are already available in the Neptune
laboratory.

ACKNOWLEDGEMENTS
This work has been partially supported by DOE grant No.
DE-FG03-92ER40727 and DOE grant No. DE-FG0392ER40693.

REFERENCES[1] W. B. Colson, G. Dattoli and F. Ciocci, Phys. Rev. A
31, 828 (1985)[2] H. P. Freund, S. G. Biedron and S. V. Milton, IEEE J.
Quantum Electronics. 36, 275 (2000).
[3] Z. Huang and K. J. Kim Phys. Rev. E, 62, 7295
(2000)[4] P. G. O’Shea et al, Phys. Rev. Lett., 71, 3661 (1993)[5] B. W. J. McNeil, G. R. M. Robb, M. W. Poole M W
Phys. Rev. Lett., 96, 084801 (2006)[6] P. Musumeci, C. Pellegrini, J. B. Rosenzweig, Phys.
Rev. E, 72, 016501 (2005)[7] L. Giannessi, P. Musumeci, New Journal of Physics,
8, 294, (2006)[8] S. Y. Tochitsky et al., Opt. Lett. 24, 1717 (1999).
[9] S. Reiche, P. Musumeci and K. Goldhammer,
Proceedings of 2007 Particle Accelerator Conference,
Albuquerque, NM (2007)[10] R. Tikhoplav et al., These proceedings.
[11] C. Sung et al. Proceedings of Particle Accelerator
Conference 2007, Albuquerque, NM (2007)

Proceedings of FEL 2007, Novosibirsk, Russia

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The UCSB MM-FEL Injection Locking System ∗G. Ramian, S. Takahashi, and M. Sherwin
Dept. of Physics (IQCD and CTST)
University of California, Santa Barbara, CA 93106, USA
Abstract
An Injection locking system has been implemented on
the Millimeter Wave Free-Electron Laser (MM-FEL) at
the University of California, Santa Barbara (UCSB). It it
is based on a commercially available varactor multipliersource and quasi-optical isolator operating at 240 GHz.
Lasing on multiple longitudinal modes is shown to collapse
to a single repeatable mode by introducing a low power
CW signal into the FEL resonator through a silicon-plate
coupler. High power and extremely narrow linewidth operation will enable new experimental opportunities such as
FEL based pulsed electron paramagnetic resonance spectroscopy.

(a)0

100 200 300 400 500 600 700 800 900 1000
ν − MHz(b)INTRODUCTION
Injection locking of the UCSB MM-Free-Electron Laser
has been demonstrated as shown in Fig. 1. Lasing that normally occurs on a number of longitudinal modes is seen tocollapse to a single mode at a single repeatable frequency
with less than 1 MHz linewidth. This result is importantin demonstrating the suitability of an FEL for applications
where extremely narrow linewidth is required.

0

100 200 300 400 500 600 700 800 900 1000(c)

Linewidth
The UCSB MM-FEL is based on an electrostatic accelerator. As such it does not exhibit the picosecond microstructure, characteristic of RF accelerator driven FELs,
that Fourier transform limits their linewidth to hundreds ofGHz. Instead, a several microsecond quasi-DC macropulse
allows sub-MHz width.
The MM-FEL [1, 2] uses a 6.25 meter long resonator
which can be described by its Fabry-Perot characteristics.
It has a free-spectral range (fsr) of c/(2L r ) = 24 MHz. It
has finesse F√= π/(2 asin(1/F√ )), where coefficient of finesse F = 4 1 − l /(2(1 − 1 − l ) − l). l is the power
loss per pass. Because of its length, the resonator has extremely high Q = FN where N is the order or simply
number of half wavelengths between mirrors. For nominal 25 % loss at 240 GHz, F = 193, F = 21.8, Q = 218000.
Linewidth is then 240 GHz / Q = 1.1 MHz.
It is important to emphasize that this linewidth is an upper limit, since line-narrowing may take place as in conventional lasers. Line-narrowing can reasonably be expected
when lasing is a consequence of stimulated emission andother inhomogeneous broadening effects are correspondingly small.
∗ Work supported by NSF grants DMR-0321365 and DMR-0520481

490.2

495.2

ν − MHz 500.2

505.2

Figure 1: (a) FEL spectrum without injection locking. The
spectrum show many longitudinal modes spaced by 25
MHz. (b) FEL spectrum with injection source on. Only
single mode lasing with no pulse-to-pulse frequency fluctuation is observed. (c) 1 MHz width is transform limit ofsampling window, indicating actual linewidth is much less.

Longitudinal Modes
Another important consequence of the long resonatoris the number of longitudinal modes available for lasing.
Fig. 2 shows the longitudinal mode structure in relation to
the MM-FEL’s gain curve. Hundreds of modes would beabove threshold and might be expected to lase. However,this doesn’t actually happen. Many fewer are seen to lasewith only a few growing to dominance. This effect canbe understood in terms of the stochastic nature of startup.
Startup is from spontaneous emission, essentially noise, so

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INJECTION LOCKINGFEL GAIN CURVE
236

239.75237

238

239.85239

239.95240

ν − GHzν − GHz241

240.05242

240.15243244240.25Figure 2: Resonator longitudinal mode structure in relation
to gain curve. Hundreds of modes have sufficient gain tolase.

One method of improving this situation is injectionlocking or seeding. This has long been used in conventional lasers [4] and is now planned for several VUV/Xray
FELs in the form of harmonic injection seeding[5].
Injection locking was partially demonstrated on the original UCSB FEL [7] using a CW molecular laser as the injection source. At that time it was only possible to inject
power through a tiny hole coupler which scattered mostof the power into high order transverse modes. Since thesource was not tunable, the FEL resonator was mechanically tuned with great difficulty. Finally, no spectrometer
was available, so locking could only be inferred from a reduction in mode beating and shorter startup time. The current injection locking system overcomes all these problems
so is much better suited for users’ experiments.

Power Requirement
exhibits a fluctuating spectral density distribution. Its basis
is “shot-noise” which represents a variance in the statistical distribution of electrons. As these electrons traverse theundulator, they become uncoupled oscillators. The small
distributional non-uniformity causes random phase fluctuations that can interfere giving
rise to larger amplitude fluc√tuations than the mere n/n shot noise variance would
suggest. At startup, some modes then appear to enjoy asignificant initial advantage over others. The process ofstimulated emission then keeps multiplying the advantage.
Another form of mode competition can be expected. As
the advantaged modes approach saturation, they cause gain
for all modes to diminishes. Since loss remains in full effect for all modes, eventually only the few advantaged ones
remain above threshold while the rest die. Manifestationof this effect, however, may take longer than the available
pulse duration.

Single Mode Lasing
Single mode lasing can occur naturally as has been
demonstrated by for example the EA-FEL at the Universityof Tel Aviv [3]. Lower frequency, a shorter resonator withwider mode spacing, and other parameter differences may
explain why this can happen. This clearly doesn’t happen
with the UCSB MM-FEL so other means of achieving single mode operation were sought. Conventional lasers use
intra-cavity etalons. Use of a Fox-Smith coupler was investigated but achieving sufficiently high Q to significantly
suppress adjacent 25 MHz spaced modes proved impractical. Further, proposed research with single mode capability requires that each pulse occur on the same frequency
and that that frequency be precisely setable. The normal
stochastic startup results in about a 0.05 % distribution of
the pulse to pulse startup frequency that is unacceptable formany users’ experiments.
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A fundamental requirement of injection locking is thatthe power that is finally coupled into the mode that is tolase must exceed the startup power from spontaneous emission by a some margin. The peak spectral density at zeroforward angle is [3]dP
4πq 2 cγ 2 K 2 N n= 2dνλu (1 + K 2 /2)
where q= electron charge, c = light velocity, γ = Lorentz
factor, K = undulator parameter, N = number of periods,n = λu Ib /(qβz c) = number of electrons radiating per period, and λu = undulator period. For the MM-FEL running at 240 GHz, γ = 6.773, K = 0.7071, N = 42, λ u =7.14 cm, and β z = 0.9835. The resulting spectral density isthen 1.39 x 10 −13 Watts/Hz. For a mode-width of 1 MHz,power is 0.139 μWatts, making the estimated 28 μW thatis available well exceed the requirement.

Injection System
Fig. 3 is an illustration of the injection locking system.
The CW injection source was built by Virginia Diodes
Inc. (VDI) [9], consisting of a 15 GHz phase-locked oscillator, doubler, RF amplifier, and three varactor doubler
stages, which provides as much as 30 mW power at 240
GHz. The source frequency is tunable within small frequency range by employing a tunable 100 MHz digital synthesizer as a reference for the source’s oscillator. This tunability is essential to match the injection source frequency
to the FEL’s resonator and to precisely set operating frequency for users. A key component is a quasi-optical,
Faraday-rotation, isolator developed by Thomas-Keating
Ltd. [8] that provides more than 50 dB isolation. Insertion
loss is about 6 dB. This is essential to protect the last multiplier stage from the FEL power following startup. Table 1
shows approximate power budget for the injection signal.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH043

Figure 3: Schematic of the injection locking system for the UCSB MM-FEL. The injection source, the isolator and atunable 100 MHz synthesizer are located in free-electron laser lab. Output radiation is sent to the users lab throughvacuum optical transport system.
Table 1 Power Budget
30 mW VDI Source output
7.5 mW Isolator output (6 dB insertion loss)
6.9 mW TPX window (∼92 % transmission)
690 μW Beam splitter
552 μW quartz window (∼80 % transmission)
28 μW silicon plate (5 % coupling)

OpticsWhen used with injection locking, the FEL’s resonatoris used in a two arm configuration as shown in Fig. 2.
The resonator is a parallel-plate waveguide terminated withcylindrical mirrors. A plano-ellipsoidal mirror couples themain arm to the secondary arm. The lowest order mode hascos2 intensity distribution in the vertical plane and Gaussian horizontally. Horizontal waists are formed in eacharm. Parameters are given in table 2.
Table 2 Resonator Parameters
Length Lr = 6.253 m
Mirror 1 R = 2.970 m
Mirror 2 f1 = 0.501 m
f2 = 3.375 m
Mirror 3 R = 0.0796 m
Waist 1 w = 1.962 cm
Waist 2 w = 3.051 mm
A silicon plate, offset slightly from Brewster’ angle, is located at the waist in the short arm and couples injection
power in and FEL power out. This allows full coupling
to the FEL resonator’s fundamental mode. This will also
serve as cavity dump coupler when we acquire a suitabledoubled-YAG drive laser. The Si plate is rotated to lessthen Brewster’s angle and provides variable coupling to optimize FEL performance. The highly elliptical beam profile, reflected from the silicon plate, is also reflected froma second flat mirror that rotates with the silicon plate tomaintain beam alignment. The narrow horizontal dimension diffracts much more rapidly than the large vertical dimension, so a combination of conical and plano-paraboloid
mirrors are used to transform the beam to a larger, approximately round, collimated one. A second beam-splitter directs about 90 % of the FEL power to the users lab. Beamtransport is through an evacuated, periodic focussing system. Note that 240 GHz does not correspond to any strong
atmospheric absorbtion lines so can be transported shortdistances through air. In fact, both the source and isolator
are outside the vacuum system.

Spectrum Analyzer
A spectrum analyzer located in the users’ lab measures
the FEL’s radiation spectrum. It is based on a double heterodyne detection system shown in Fig. 4. The FEL radiation is attenuated and directed to a sub-harmonically
pumped mixer driven at 115 GHz by a second digitally controlled VDI multiplier chain as Local Oscillator (LO). The
10 GHz intermediate frequency (IF) signal is then amplified, filtered, and sent to a second mixer for final downconversion to a 1 GHz band centered at 500 MHz. A steepwalled bandpass filter in the 10 GHz IF chain prevents negative frequency artifacts in the final down-conversion. A
2 channel, 8 bit, 5 GS/s digitizer (Tektronix TVS 625A)
records both the 500 MHz, and rectified 10 GHz, IF signals.

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Proceedings of FEL 2007, Novosibirsk, Russia
and Theoretical Limitations,” Phys. Rev. Lett., V82, N26,
1999, p. 5257
[4] P. Flamant, R. Menzies, “Mode Selection and Frequency
Tuning by Injection in Pulsed TEA-CO2 Lasers,” IEEE Journal of Quantum Electronics, QE19, N5, 1983, p. 821[5] L. Yu., et al.,“High-Gain Harmonic-Generation FreeElectron Laser,” Science, V289, 11-Aug-2000, p. 932[6] J. Jackson, “Classical Electrodynamics,” 3rd ed., Wiley(1999), p690
[7] A. Amir, J. Knox-Seith, M. Warden,“Narrow-Bandwidth Operation of a Free-Electron Laser Enforced by Seeding” Phys.
Rev. Let., V66, N1, (1991)[8] Thomas Keating Ltd. Station Mills, West Sussex, RH14 9SH,
UK http://www.terahertz.co.uk[9] Virginia Diodes Inc., 979 Second St. S.E., Suite 309, Charlottesville, VA 22902, USA http://www.virginiadiodes.com

Figure 4: Schematic illustration of the 240 GHz spectrum
analyzer.
A Labview program does fast Fourier transform processing
for immediate display. A more accurate analysis can beapplied to saved data using the Wiener-Khinchin theorem,
DFT, and more sophisticated windowing later as needed.

RESULTS
Fig. 1(a) shows the recorded spectrum without injection
locking. Many longitudinal modes with 25 MHz spacing
are seen. Fig. 1(b) is the spectrum with injection on.
The effect is immediate and unequivocal. Lasing is seen
to always occur at one frequency on the same longitudinalmode selected by the injection source frequency. The injection locking is observed only when the source frequency
matches one of the resonator’s longitudinal modes. The
linewidth shown in Fig. 1(c) corresponds to the analysis
window, indicating an actual linewidth less then 1 MHz as
expected.

CONCLUSION
In summary, we have demonstrated injection-locked
FEL operation with sub-MHz bandwidth using a tunablesolid state source as an injection source. The high-power,
tunability, and extremely narrow linewidth of the FEL
opens up the possibility for new applications such as ahigh-power, high-frequency, pulsed EPR spectroscopy. We
wish to thank David Enyeart for his support of the injection
locking system installation and FEL operation.

REFERENCES[1] http://sbfel3.ucsb.edu/[2] G. Ramian,“The New UCSB Free-Electron Lasers,” NIM
A318, 1992, p. 225[3] A. Abramovich, et al.,“High Spectral Coherence in LongPulse and Continuous Free-Electron Laser: Measurements
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Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH046

A SUPERCONDUCTING RF PHOTO-INJECTOR FOR OPERATION AT
THE ELBE LINEAR ACCELERATOR*
J. Teichert#, A. Arnold, H. Buettig, D. Janssen, M. Justus, U. Lehnert, P. Michel, K. Moeller,
P. Murcek, Ch. Schneider, R. Schurig, F. Staufenbiel, R. Xiang, FZD, Dresden, Germany,
J. Stephan, IKS, Dresden, Germany, W.-D. Lehmann, SGE, Pirna, Germany,
T. Kamps, BESSY, Berlin Germany, G. Klemz, I. Will, MBI, Berlin, Germany,
D. Lipka, A. Matheisen, B. v. d. Horst, DESY, Hamburg, Germany
P. vom Stein, ACCEL Instruments, Bergisch Gladbach, Germany
V. Volkov, BINP, Novosibirsk, Russia
Abstract
For the ELBE superconducting linear accelerator at
FZD a radiofrequency photoelectron injector with asuperconducting cavity (SRF gun) is under development.
The SRF gun combines the excellent beam quality which
can be delivered by RF photoinjectors with the possibilityof continuous wave operation.
The superconducting niobium cavity of the injector
consists of 3½ cells and contains a Cs2Te photocathodewhich is normal-conducting and cooled by liquid
nitrogen. The RF frequency of the cavity is 1.3 GHz. The
final electron energy will be about 9.5 MeV and theaverage electron current will be 1 mA. In the past years
the SRF photo injector has been designed and fabricated.
Several critical subsystems have been tested. For thecavity, the results of the RF measurements will be shown.
An UV driver laser system has been developed which
fulfils the different requirements (77 pC @ 13 MHz, 1 nC
@ 500 kHz) for the future operation at ELBE. A photo
cathode preparation system was developed and installed.
The equipment is now in operation and the first series of
Cs2Te photo cathodes have been produced.

INTRODUCTION
In 2004 a R&D program for the development of asuperconducting radiofrequency photoelectron injector(SRF gun) was initiated at Forschungszentrum DresdenRossendorf (FZD). This project continues the earlier
efforts in SRF gun development [1, 2] with the aim todevelop a fully operable SRF photo injector for the ELBE
superconducting linear accelerator [3].
Compared to the thermionic injector in use, the new
SRF gun will reduce the pulse length and the transverse
emittance for the standard FEL operation mode with
77 pC bunch charge and 13 MHz pulse repetition rate.
Furthermore a second operation mode is now planned at
ELBE with a bunch charge of 1 nC and a repetition rate___________________________________________* We acknowledge the support of the European Community-Research
Infrastructure Activity under the FP6 “Structuring the European
Research Area” programme (CARE, contract number RII3-CT-2003506395) and the support of the German Federal Ministry of Education
and Research grant 05 ES4BR1/8.
#
j.teichert@fz-rossendorf.deof 500 kHz. Beside the essential beam quality
improvement for ELBE, the project should demonstrate
the operation of a SRF gun at an accelerator facility forthe first time, and the gun will serve as a test bench for
R&D studies in this field (beam parameter measurements
and optimize operation, long term studies, investigation ofphoto cathodes, study of emittance compensation
methods). For that reason a sophisticated diagnostics
beamline has been designed and constructed [4]. In
particular, the operation with 2.5 nC bunch charge will be
studied which is essentially important for futureapplication of the SRF gun at the BESSY FEL [5]. The
Table 1 gives an overview of the SRF gun parameters andplanned operation modes.
Table 1: Gun design parameters and expected beamvalues for the planned operation modes
ELBE high charge BESSYmodemode
FEL
RF frequency
1.3 GHzbeam energy
9.5 MeVOperation
CW
drive laser wave length
262 nmPhotocathodeCs2Te
quantum efficiency>1 %average current
1 mA
0.5 mApulse length
5 ps
15 ps
Repetition rate
13 MHz500 kHzbunch charge
77 pC
1 nC
transverse emittance
1 µm
2.5 µm1)>2.5 %
2.5 µA40 ps
1 kHz
2.5 nC
3 µm1)

flat top laser

An overview of the ELBE accelerator facility is shownin Fig. 1. The heart of the radiation source is asuperconducting linac with a thermionic injector and two
cryomodules each containing two TESLA-type RF
cavities. The accelerator operates in CW, the maximum
electron energy is 40 MeV, and the average current is
1 mA. The electron beam is used in two FELs for thegeneration of infrared radiation, to conduct nuclear
physics and radiation physics experiments, and to produce
neutrons and positrons.

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Fig. 1: Layout of the Radiation Source.
The SRF gun project is a collaboration of BESSY,
DESY, MBI and FZD. A detailed description of the SRF
gun design is given in Ref [6]. We will spend the rest of
the paper reporting the progress of the SRF gun
construction during the last year and showing the

PHOTOCATHODE PREPARATION
In normal-conducting RF photoinjectors thesemiconductor cesium telluride is the preferred photo
cathode material. Cs2Te has a high quantum efficiency for
UV light, a long lifetime and requires a moderate vacuumof about 10-10 mbar. Due to the good experience innormal-conducting RF photoinjectors, Cs2Te seems to be
the preferred material for SRF photoinjectors too. For a
CW electron current of 1 mA and a typical quantum
efficiency of 1 %, the UV laser power must be about 1 W.
Suitable driver laser systems with such power have beendeveloped [7].
A photocathode preparation system for the depositionof the Cs2Te layers has been designed and constructed.
The equipment is installed in a clean room in order toensure low particle contamination of the cathodes. Maincomponents are the vacuum chamber for the Cs2Te
deposition, a UV laser system (4 mW @ 262 nm) for
online measurements of the quantum efficiency, theexchange and storage system for the photocathodes, andthe electronics units for process control. The deposition
equipment allows standard deposition technology (Te andCs in succession) as well as the simultaneous evaporation
proposed at CERN [8]. Two quartz monitors measure thedeposition rates of Te and Cs separately, and the processcomputer controls the heating power of the evaporators inorder to adjust the stoichiometric ratio of 1:2 between Te
and Cs. Although the improvement and optimization isstill ongoing, a number of cathodes with quantum
efficiencies >4 % have been prepared.
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NIOBIUM CAVITY
The 3 ½ cell niobium cavity has been the most criticalcomponent. A 3D drawing of this cavity is shown in
Fig. 2. After fabrication, the two cavities, one of Nb grade
RRR 300 and one of grade RRR 40 (model fortechnological and RF tests) were warm tuned at FZD andthen prepared at DESY (100 µm BCP etching inside, 20µm etching outside, and 800 °C backing in the UHVoven). After these treatments a second warm tuning was
performed.

Fig. 2: 3D model of the SRF gun cavity.
Following the tuning, the RRR 300 cavity was moved
to DESY for low temperature RF tests. For thesemeasurements the cavity was cleaned by bufferedchemical polishing (40μm BCP) and high pressure rinsing(HPR). During the cool down from 4.4 K to 1.6 K theunloaded quality factor was measured at low rf power andthe residual surface resistance was determined to Rres=3.4nΩ.
The results of the Q versus E measurements at 1.8 K ofthe first vertical test measurements are shown in Fig. 7.
For comparison, the values are plotted as function of thepeak field in the TESLA cells. All together, four verticaltests were carried out. As shown in the figure, fieldemission started early and the quality factor decreases.
Further increasing of rf power results in strong fieldemission and Q-switches, which are probably caused byProceedings of FEL 2007, Novosibirsk, Russia
thermal breakdown at activated field emitters. The
behaviour of the Q-switches is most likely due to surface
pollution. This might be induced by the hardly cleanablechoke filter. Because of the narrow cathode feed throughbetween choke filter and gun cell, direct cleaning of thefilter cell was not feasible.
Based on this experience, an improved cleaning was
realized by the company ACCEL Instruments. A special
high pressure rinsing lance was built to enable anadditional cleaning of the choke filter beside theestablished preparation of the cavity cells. Due totechnical problems during the cleaning the achieved
results of the followed 2nd and 3rd tests are unsatisfactory.
Caused by the shortage of time the 4th preparation andthe vertical test had to be the base for further assembly.
As in the tests before, the limit in the gradient resultsfrom field emission. Beside particle pollution the reason
could be a small scratch that we found inside the cavity atthe back plane of the half cell. The damage results from acollision between the cavity and the high pressure rinsing
lance during the cleaning. So its removal will result in abetter performance. Unfortunately there is no time for a
5th vertical test so we have to wait for further tests until
the cryostat is completely assembled.

WEPPH046

Fig. 4: Field distributions of the four pass band modes.
peak axis-field in gun cell @ 1.8K for different modes

Q0
1E10

1E9

1/4 Pi-Mode
2/4 Pi-Mode
3/4 Pi-Mode
Pi-Mode (3.Messung)

0.0

5.0M

10.0M

15.0M

20.0M

Epeak in V/mFig. 5: Measured curves for the four pass band modes.
In the graph Q0 is plotted versus the peak fieldin the half-cell.

achieved peak axis fields of all 4 vertical test benches

Q0

1E10

1E9

all 4 tests limited by field emission
0,0

10,0M

20,0M

30,0M

V-Test 1
V-Test 2
V-Test 3
V-Test 4
40,0M

50,0M

Epeak in V/mFig. 3: A comparison of the four vertical test
measurements of the SRF gun cavity.
A further indication that the field emission problem
limiting the gradient of the cavity is located in the halfcell delivers a comparison of the measurements for thefour pass band modes performed in the 4th vertical test.
The field distributions of the four modes are shown in
Fig. 4. As can be seen, especially the π/4 mode is mainly
located in the half-cell. In the results for the four modes
shown in Fig. 5, where Q0 is now plotted versus the peakfield in the half-cell, the drop-down of the curves happensat the same field value in the half-cell.
At ACCEL Instruments the helium vessel was weldedaround the cavity following vacuum leak checks and RF
field profile measurements in spring 2007. Then the
etching of the cavity was carried out (20 µm BCP, cleanwater rinsing, drying in class 10 clean room), pick-up
and HOM feed-throughs were attached in the clean room,and the cavity was finally cleaned (high pressure rinsing,
drying in class 10 clean room, valve assembly, vacuum
leak check, filled with clean N2 gas).

In the class 10 clean room of the FZD the further
assembly work was carried out: mounting of cavity tuner
parts, assembly of the main power coupler antenna and of
the pick-up antenna in the choke filter, temporary
insertion of an RF antenna for HOM coupler tuning andadjustment of the choke filter frequency. Finally the beamline parts were mounted at the down-stream side and thecomplete cathode cooling and support system at the upstream side of the cavity. Therewith the clean room work
was finished and the cavity can now be inserted into thecryostat.

CRYOMODULE
The design of the SRF gun cryostat is presented inFig. 6. The stainless steel vacuum vessel has a cylindricalshape with 1.3 m length and 0.75 m diameter. The He
port and the N2 port are on top on the right hand side.
From the port the He flows through a heater pot and thetwo-phase supply tube into the chimney of the He tank.
For the cooling of the thermal shield, liquid nitrogen isused. The 70 K shield consists of a cylindrical Al sheet
welded to two circular tubes filled with N2. The liquid N2tank is in the upper part of the module. The cavity is
passively protected against ambient magnetic fields bymeans of a µ-metal shield, placed between the 80 K shield
and the vacuum vessel.
For a check of all components the cryostat wasassembled with exception of the He tank and the cavity inthe workshop end of 2006. In May 2007, the final
assembly started after delivery of the cavity welted in the

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He tank and the following work in the clean roomdescribed above. Fig. 7 shows the still open cryostat
vessel with the He tank covered with super-isolation.

Fig. 6: Design of the SRF gun cryostat.

In the future the SRF gun will improve the beam quality
for ELBE users (higher bunch charge, lower transverse
emittance).

Fig. 8: Photograph of the SRF gun installed in theaccelerator hall.

REFERENCES

Fig. 7: Photograph of the vacuum vessel and the He
vessel during moving in.

INSTALLATION
During the summer shut-down of ELBE in July 2007,
the SRF gun cryostat was installed in the accelerator halland connected to the He refrigerator. The cool-down was
successfully carried out on August 3-4. First
measurements with low power RF were performed inorder to check the RF installation, the tuning systems andto characterize the cavity. Beside the cryostat, the firstpart of the diagnostics beamline with the solenoid, thelaser input port and a beam dump was installed (seeFig. 8).

SUMMARY AND OUTLOOKA SRF photo-injector has been installed at the ELBE insummer 2007. The next steps on the way are thecommissioning of the high power RF system, andinstallation of the 500 kHz driver laser. Then the firstbeam can be produced with the SRF gun. In the following
shut-downs of ELBE in autumn and winter, thediagnostics beamline and the cathode transfer system will
be installed, which will then allow beam parametermeasurements with Cs2Te photocathodes.
FEL Technology II

452[1] D. Janssen, et al., “The Development of aSuperconducting RF Gun: Status of the Drossel
Collaboration”, Proc. of PAC´97, Vancouver,
Canada, 1997, p. 2838.
[2] D. Janssen, et al., “First operation of aSuperconducting RF-Gun”, Nucl. Instr. and Meth. A
507, 314 (2003).
[3] P. Michel, et al., “The Rossendorf IR-FEL ELBE”,
Proc. FEL 2006, Berlin, Germany, p. 488.
[4] T. Kamps, et al.,”Diagnostics Beamline for the SRF
Gun Project”, Proc. of FEL´05, Stanford, USA,2005, p. 530.
[5] “The BESSY Soft X-ray Free Electron Laser”, TDR
BESSY March 2004, eds.: D.Krämer, E. Jaeschke,
W. Eberhardt, ISBN 3-9809534-0-8, Berlin (2004).
[6] A. Arnold, et al., “Development of aSuperconducting Radio Frequency Photo Electron
Injektor”, Nucl. Instr. and Meth. A 577, 440 (2007).
[7] I. Will, et al., „Photocathode Laser for theSuperconducting Photo Injector at the
Forschungszentrum Rossendorf”, Proc. FEL´06,
Berlin, Germany, 2006, p. 564.
[8] G. Suberlucq, “Technological Challenges for High
Brightness Photo-injectors”, Proc. of EPAC´04,
Lucerne, Switzerland, 2004, p. 64.

Proceedings of FEL 2007, Novosibirsk, Russia

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ELECTRO-OPTIC SPECTRAL DECODING FOR SINGLE-SHOT
CHARACTERISATION OF THE COHERENT TRANSITION RADIATIONPULSES AT FLASHV. Arsov, E.-A Knabbe, B. Schmidt, P. Schmüser, B. Steffen, DESY, Hamburg, Germany
Abstract
We report preliminary single-shot electro-optic spectral
decoding (EOSD) measurements of coherent transition
radiation (CTR) pulses, generated by the electron bunchesof the free-electron laser (FLASH) at DESY, Hamburg.
The THz radiation is transported through a 20 m long
beam-line from the accelerator tunnel to an experimental
station outside. The measurements are performed in
vacuum with a 0.5 mm ZnTe crystal in crossed-polarizer
and near crossed-polarizer detection schemes. Pulses withcomplex structure and sharp peaks have been detected.
The different components have full width at half
maximum in the range 400-900 fs.

the so called balanced detection scheme. Here we present
similar EOSD measurements with ZnTe, but carried out
in vacuum, using crossed-polarizer and near crossedpolarizer detection schemes [6].

EXPERIMENTAL SETUPThe CTR electric field temporal profiles are resolved
with a spectral decoding electro-optic technique [6], [9][11].

INTRODUCTION
Intense relativistic electron bunches with a duration
less than 100 fs are needed in contemporary light source
accelerators, such as the ultraviolet and soft x-ray freeelectron laser at Hamburg (FLASH) [1], as well as the
future x-ray FELs like the Linac Coherent Light Source at
SLAC [2] and the European XFEL [3]. With this there isa growing demand for ultra-fast characterisation of theelectron bunches. Some of the leading longitudinal
diagnostic techniques with fs abilities are the spectral, theelectro-optic (EO), the transverse deflecting cavities and,since recently, the optical replicas [4]. The spectral
techniques refer to spectrum measurements of thecoherent transition radiation (CTR), diffraction andsynchrotron radiation, etc. A Fourier transformation of
the measured spectrum has resolved structures with lessthan 10 fs duration in a single-shot acquisition [5]. In thecase of FLASH the single shot CTR spectrometer issituated outside the accelerator tunnel, which isconvenient from experimental point of view, but requires
knowledge of the transfer function of the beam line.
Therefore an independent CTR pulse length
measurement, such as an EO technique applied inside thespectrometer can facilitate the interpretation of the CTR
spectra.
The EO techniques allow direct characterization of
THz fields both in the spectral and in the time-domain.
Depending on the analyzer orientation, the measured
signal is either linear or quadratic with the THz field[5],[6]. Recently EO signals as short as 55 fs (rms) havebeen observed, which is a new record in the EO detectionof single electron bunches and close to the limit imposedby the properties of the EO material [7].
The temporal profiles of the CTR pulses at FLASH
have been measured for the first time by Berden et. al.
[8]. Their measurements were carried out in air with
ZnTe, using electro-optic spectral decoding (EOSD) in

Figure 1: Set-up for electro-optic spectral decoding
measurements of coherent transition radiation (CTR).
Notations: (l/2), (l/4) – half and quarter wave plates;(P1,2) – polarizers; (L1,2) – lenses; (BC) – indium tinoxide beam combiner; (EO) – 0.5 mm thick ZnTeelectro-optic crystal; (PM) – parabolic mirror
A diagram of the experimental setup is shown on Fig.
1. The CTR is generated from single bunches, kicked to
an off-axis screen. A diamond window is used to couple
the radiation from the ultra high vacuum environment into
a 20 m long transfer line, where the pressure is lower than
0.1 mbar. The beam line is equipped with high reflectivity
focusing mirrors, designed specially to minimize thediffraction. Special care has been taken to avoid wave
guide effects in the pipe by using corrugated bellows. The
lowest frequency (ca. 300 GHz) is determined by thediameter of the pipe, which is ca. 200 mm [12]. Outside
the accelerator runnel the THz beam line is connected toan evacuated vessel containing several diagnostic
experiments, including a single-shot THz grating
spectrometer and an EO setup. Alternatively, the radiation

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can be coupled out of the vacuum pipe of the transfer line
through a single-crystal quartz window for experiments inair. However this is at the expense of suppression of CTR
frequencies above 4 THz due to the absorption in quartz
and especially by the broad band absorption in air. The
CTR radiation is focused on the 0.5 mm thick ZnTe
crystal with an off-axis parabolic mirror. The spatial
overlap with the probe laser beam is achieved with anindium tin oxide (ITO) beam combiner.
The probe optical pulse is produced by a titaniumsapphire laser (center wavelength 790 nm, bandwidth 36
nm, pulse length 40 fs and repetition rate 1 kHz),synchronized to the 1.3 GHz accelerator frequency. The
probe beam is stretched to 7.7 ps in a 40 cm long SF11
glass block (stretcher on Fig. 1). The length of the probe
pulse is chosen to be larger than the length of the CTR
pulse in order to encompass the whole CTR electric field
temporal profile. The chirp of the optical pulse is linear
and so is the time-frequency mapping of thecorresponding intensity profiles. The probe optical pulse
and the THz radiation propagate collinearly in the EO
crystal. For ZnTe there is a close match in the groupvelocities of the THz and the optical pulses. In the ideal
case the instantaneous frequency of the probe laser pulseinteracts with the same portion of the THz field, thus
experiencing a phase retardation in the EO crystal
proportional to the local electric field. The specific phaseretardation is made apparent by an analysing polarizer P2.
Thus the CTR temporal profile is imprinted on the
spectrum of the optical pulse and can be resolved with aspectrometer.
The half wave plate preceding the input polarizer P1(Fig. 1) serves to attenuate the energy of the probe laser
pulse below the damaging threshold of the EO crystal (~5 mJ)
In the absence of a CTR pulse the transmittancethrough the polarizer P1 and P2 is minimized. This is theso called acquisition at crossed polarizer. In thisarrangement the measured intensity is proportional to thesquare of the THz electric field. The advantage of thisarrangement is the low background in comparison to thebalanced detection scheme. The residual birefringence
due to mechanical stress in the EO crystal is removed by
the quarter wave plate. In the present experiment alsomeasurements at few degrees off-crossed polarizer havebeen made. The advantage is the higher sensitivity andlower signal to noise ratio at the expense of a slightly
higher background [6]. An additional advantage is that theEO signal is linear with the CTR field. The corresponding
polarizer arrangement is chosen with the half wave platein front of P2.
The spectra are resolved with a 0.15 m spectrometer,
equipped with a 600 grooves/mm grating. The images arerecorded with a 1280x1024 pixel intensified CCD camera(ICCD). The time axis is along the longer side of thesensor. In the other direction the spectra occupy ~ 90
pixels, which is used for binning.

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RESULTS AND DISCUSSION
The upper panels of Fig. 2 show the raw CTR signals,
measured with 0.5 mm thick ZnTe at different
polarization schemes. The leading edge is on the left. The
green traces represent the spectral intensities of the probe
laser pulse with CTR being blocked (spectrum A). These
traces are averaged along 20 laser shots. Since the laser
pulse is linearly chirped and its duration is known, thesetraces are also used for time-calibration of the horizontal
axis. The blue traces are taken with the presence of theprobe laser and CTR radiation (spectrum B) and represent
a single-shot measurement. At the beginning and the endof each measurement series separate background spectra
have been taken without the presence of laser and CTR(spectrum C). These traces are not represented on Fig 2,
but are used for the signal normalization. The lower
panels of Fig. 2 show the normalized electro-optic
signals. For the case near crossed polarizer the following
relation is used for normalization: B − A , where A, B andA−C
C are the above mentioned spectra. For the case ofcrossed polarizer the normalizing relation is: B − A ,D −Cwhere is D the laser spectrum taken at few degrees offcross polarization without the presence of CTR.
The left panel of Fig. 2 represents measurements with
0.5 mm ZnTe in vacuum at crossed polarizer. The
measured EO signal has a complex structure. The mostpronounced one has a broad base with width 3.3 ps andamplitude 0.4, followed by a sharp peak with normalized
amplitude 1.15 and 440 fs width. The rest of the signal ishardly distinguishable from the noise.
The right panel of Fig. 2 shows similar measurementswith 0.5 mm ZnTe in vacuum, but with -2° deviation fromcrossed polarizer. This increases the sensitivity at theexpense of slightly increased background. The normalized
signal amplitude is also higher. Again a complex CTR
structure is observed with two pronounced peaks. The
highest peak is 700 fs wide. Its normalized amplitude is1.6. The preceding lower peak has a normalized
amplitude 0.5 and width 900 fs.
The data of Fig. 2 shows the clear difference between
the measurements in crossed- and near crossed
polarization. In the first case the EO signal is proportional
to the square of the CTR electric field. This is the reason
for the observed broader step preceding the sharp peak on
the left image of Fig. 2. In the case of measurements nearcrossed polarizer, the EO signal depends linearly on the
CTR electric field. As seen from the right image of Fig. 2,
there is a negative swing with smaller amplitude at theposition, where a broad step in crossed polarizer isobserved.
As pointed out by [4] and [8], pulse lengths shorter
than 2.4 T0TC should be distorted with EOSD
measurements. T0 is the initial length of the laser pulse,which in our case is 40 fs; TC = 7.7 ps is the length of the
chirped laser pulse. For the lower limit of the CTR pulse
one obtains 1.3 ps. The measured pulse widths are nearProceedings of FEL 2007, Novosibirsk, Russia
this limit. The choice of the chirped pulse length is acompromise between the possibility to have wide enoughtime-window and the ability to resolve narrow temporal

WEPPH047

components. In our case a clear structure in the CTR
signal is distinguishable. A distortion free measurement
would require temporal decoding set-up [4],[6], [7],[13].

Figure 2: Electro-optic spectral decoding signals of coherent transition radiation (CTR), measured with 0.5 mm
ZnTe in vacuum. Upper panels: raw data; the green traces are the laser spectral intensities without CTR
radiation; the blue traces are the corresponding intensities with CTR radiation. Lower panels: normalized
spectral intensities. The leading edge of the CTR is on the left. Left panel: measurements at crossed polarizer.
Right panel: measurements at -2° off- crossed polarizer.
An important result are the sharp and high CTR peaks,
despite the lower cut-off frequency (4THz) of ZnTe. Suchpeaks are familiar from EO measurements of the electron
bunch lengths directly in the FLASH tunnel [6],[7],[10].
This demonstrates, that the optics of the THz beam line
maintains the amplitude and the phase information in thiswavelength range and properly images the electrical fieldfrom the CTR screen to the experimental station outside
the tunnel. These results are rather preliminary and a more
systematic study is necessary with the use of GaP, which
has a higher cut-off frequency (11 THz) and better opticalproperties.

CONCLUSION AND OUTLOOK
A comparison between electro-optic spectral decoding
measurements of CTR radiation with crossed polarizer
and near crossed polarizer arrangements in ZnTe has beenmade. In both cases the ability to resolve structure in the

CTR signal and sharp peaks is quite promising. Since theTHz diagnostics are situated outside the DESY-FLASH
tunnel, it is necessary to verify experimentally the transfer
function of the THz beam line, which at this point is
known through simulation. For this purpose more
systematic EO studies with GaP in vacuum with variationof the THz focus are necessary. In addition temporal
decoding measurements are foreseen in order to resolve
shorter time structures and to avoid a possible signal
distortion.

REFERENCES[1] V. Ayvazyan et al., Eur. Phys J. D 37, 297 (2006)[2] http://www-ssrl.slac.stanford.edu/lcls/[3] http://www.xfel.net[4] S.P. Jamison et al., Proc. EPAC 2006, Edinburgh,
Scotland, p. 915.

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Proceedings of FEL 2007, Novosibirsk, Russia[5] H. Delsim-Hashemi et al., Proc. 37th Advanced ICFA
Beam Dynamics Workshop on Future Light Sources,
FLS 2006, Hamburg, Germany[6] B. Steffen, PhD Thesis, DESY-Hamburg, Germany,(2007).
[7] G.Berden et al., Phys. Rev.Lett. (2007). (accepted for
publication)[8] G.Berden et al., Proc. EPAC 2006, Edinburgh,
Scotland, p. 1058.
[9] I. Wilke et al., Phys. Rev. Lett. 88, 124801 (2002).
[10] B. Steffen et al., Proc. 27th International Free
Electron Laser Conference (FEL 2005), Stanford,
USA 2005, p. 549.
[11] G.Berden et al. Proc. 7th European Workshop on
Beam Diagnostics and Instrumentation for Particle
Accelerators (DIPAC 2005), Lyon, France, 2005. p
69.
[12] S. Casalbuoni et al, TESLA-FEL report 2006-4.
[13] G.Berden et al., Phys.Rev. Lett. 93, 114802 (2004).

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WEPPH048

XPS STUDIES OF Cs2Te PHOTOCATHODES∗
S. Lederer† , J.H. Han, and S. Schreiber (DESY, Hamburg, Germany)
A. Vollmer, R. Ovsyannikov, M. Sperling, and H. Duerr (BESSY GmbH, Berlin, Germany)
F. Stephan (DESY, Zeuthen, Germany)
P. Michelato, L. Monaco, C. Pagani, D. Sertore (INFN Milano - LASA, Segrate (MI), Italy)

Abstract
Cesium telluride (Cs2 Te) photocathodes are used assources for electron beams because of their high quantum
efficiency (QE) and their ability to release high peak current electron bunches in a high gradient RF-gun. Starting from a high QE level of about 10 % the quantum efficiency of these cathodes decreases during operation ina photo-injector to below 0.5 %. To understand this behaviour, XPS investigations on the chemical composition
were performed at BESSY. In this contribution we compare
two fresh cathodes from INFN with one used under normal
operation at FLASH and one used at PITZ at a higher thanusual RF-gradient of 60 MV/m.

vey scans is given, followed by a more detailed presentation of precise XPS-studies of the Te 3d levels. In the lastpart, results of work function determinations are given.

RESULTS AND DISCUSSION
In figure 1, survey scans with photon energies of 900 eV
are presented for the two fresh and the two used cathodes.
For all spectra, the main peaks correspond to Cs 3d andTe 3d. While for fresh cathodes peaks corresponding to

INTRODUCTION
The photocathodes used at FLASH and PITZ are prepared at INFN-LASA (Milano, Italy). The electron emitting film is deposited on polished molybdenum plugs in
two steps [1]. First, the plug is coated with 10 nm tellurium. During the following cesium deposition, the quantum efficiency (QE) is monitored, and when maximum QE
is reached the Cs evaporation is stopped. During the preparation process the temperature of the plug is kept at 120 ◦ C.
The diameter of the Cs 2 Te coating is 5 mm. Right after the
production of the Cs 2 Te cathodes, the QE is about 10 %[2].
During operation in electron guns of accelerators, theQE reduces to below 0.5 %. For a better understanding of
the QE degradation, the chemical composition of two new(#90.1 and #42.3) and two used cathodes (#34.6 and #92.1)
are investigated by x-ray photoelectron spectroscopy (XPS)at BESSY (Berlin, Germany). In addition, the work function of the cathodes was measured. Cathode #92.1 wasused at FLASH under the nominal operation condition for
SASE FEL generation for 39 days with a final QE of 0.1%. Cathode #34.6 was operated at PITZ with accelerating
gradients at the cathode of up to 60 MV/m for several days.
The QE of this cathode decreased to 2 %.
In this paper first results of the XPS measurements arepresented. In the first part an overview in the sense of sur∗ This work has partly been supported by the European Community,

contracts RII3-CT-2004-506008 and 011935, and by the ’Impuls- undVernetzungsfonds’ of the Helmholtz Association, contract VH-FZ-005.
† sven.lederer@desy.de

Figure 1: Survey spectra measured at photon energy of
900 eV for fresh cathodes (red: #42.3, magenta: #90.1)
and used cathodes (black: #34.6, blue: #92.1)
O 1s are visible, these lines reduce with operation time.
We interpret this as a cleaning process during operation
caused by the laser pulses (wavelength 262 nm) and thehigh electrical field at the cathode. Both effects results in

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a local heating up of the photocathode. This is consistent
with the effect, known now for several years, that Cs 2 Te
photocathodes poisoned with oxygen can be rejuvenatedby a heating process [3, 4, 5]. A further difference in the
spectra is that on used cathodes F 1s and C 1s lines appear. The amounts of both elements are non negligible, be-Figure 2: Te 3d lines measured with photon energies of
900 eV (top) and 1250 eV (bottom) at the center of cathode#90.1. In both graphs the measurements as well as the fits
to the measurements are presented.
cause of the approximately one order of magnitude smaller
photoionization cross sections in comparison to Cs 3d andTe 3d [6]. The origin of this contaminations can be related
to some teflon parts inside the beamlines of both facilities
right after the gun section.
In figure 2 precise measurements of the Te 3d lines offresh cathode #90.1 are presented. In this and the following figures, the measured kinetic electron energies (E kin )are converted to the binding energies E b by the classicalformula:Ekin = Eph − Eb − Φ(1)with Eph being the photon energy and Φ the work function of the analyser. The spectrum on the top of the figure
was obtained with an photon energy of 900 eV, the one at
the bottom with 1250 eV. For the higher energy the analyzing depth is around 2.5 nm, for the lower 1.5 nm. The
dominant peaks in both spectra are assigned to Te −2 3d5/2
with Eb = 571.6 eV and Te−2 3d3/2 with Eb = 581.9 eV.
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In coincidence with the oxygen found in the survey scan(figure 1), additional lines caused by chemical shifts arepresent (Te+4 and Te+6 ) for both spin orbit couplings ofthe 3d electrons. Also a small amount of metallic tellurium
is visible.

Figure 3: Te 3d lines measured with photon energies of
900 eV (top) and 1250 eV (bottom) at the center of cathode#92.1. In both graphs the measurements as well as the fits
to the measurements are presented.
The picture of the Te 3d lines changes dramatically forused cathodes as shown in figure 3. Like for the fresh
cathode, measurements were performed in the center of thecathode. Here the dominant peaks for both photon energies
are related to the Te 0 3d5/2 and Te 0 3d3/2. For 1250 eV
photon energy the amount of Te −2 with Eb = 571.1 eV forj = 5/2 and Eb = 581.5 eV for j = 3/2 is higher thanfor the lower energy. Since the analyzing depth is lower forthe latter one, the metallic Te states are located close to thesurface, while in the bulk region Cs 2 Te is still present. The
oxidation states Te+4 and Te+6 disappeared in comparison
to the fresh cathodes. This result of being mainly Te 0 on theused cathode we interpret as reason for the reduced QE ofthis cathode, since a large amount of the cathode changed
from Cs2 Te to metallic tellurium. Due to the work functionof tellurium of 4.95 eV [7] electron emission caused by thedrive laser of the accelerators should be strongly reduced.
As seen in figure 4 (left) [2] cathode #92.1 shows a darkarea in the center, which has approximately the same diameter as the laser spot size during operation. This area is sur-

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Figure 4: Photograph (left) and QE-map of cathode #92.1.

Figure 6: Secondary electron cut offs measured at the center of the two fresh and one used cathode; black curve:#90.1, blue curve: #42.3, red curve: #92.1. For comparison all spectra are normalized to their maximum.
100 eV photon energy for the two new and one used cathode (#92.1). The plot clearly shows that there is a shift of
the work function between the fresh cathodes and the used
one of about 0.5 eV. Since the lasers at PITZ and FLASH
have fixed energies of 4.72 eV, which leads to kinetic energies of 0.55 eV of the emitted electrons, the increase in thework function of 0.5 eV decreases the emission probabilityof the excited electrons. This results in a strong reductionof the QE (down to 0.1 % for cathode #92.1).

CONCLUSIONS

Figure 5: Te 3d lines measured with photon energies of
900 eV (top) and 1250 eV (bottom) at the outer part (fordetails see text) of cathode #92.1. In both graphs the measurements as well as the fits to the measurements are presented.
rounded by a brighter ring, which also has still some pointsof higher QE (figure 4 right). Figure 5 shows the measurements of the Te3d lines for 900 eV (top) and 1250 eV(bottom) photon energy together with the fits obtained in
the described outer ring. Despite the fact that the laser was
most of the time not hitting this area no tellurium oxides
can be identified. While the QE of this ring is in some regions higher than in the center of the cathode, the Te 3d
spectra measured at both points are comparable. Confirming the observations for the center spot, the main peaks infigure 5 correspond to Te 0 and only small amounts of Te −2
with binding energies of E b = 571.4 eV for j = 5/2 andEb = 581.5 eV for j = 3/2 are found.
In figure 6 secondary electron cut offs are measured with

The chemical composition of Cs 2 Te photocathodes has
been analyzed by XPS. Both fresh cathodes were contaminated with oxygen, while on the used ones these lines disappear with longer usage in the gun. Survey spectra of
the used cathodes clearly showed F and C. The source of
these contaminations was identified as teflon parts inside
the beamlines at FLASH and PITZ, which will be removed
in future.
Precise measurements of the Te 3d levels show, that themain contribution for fresh cathodes originates from Te −2 ,which corresponds to the expected chemical compositionof Cs2 Te. In the case of the used cathode #92.1, the main
peaks are related to Te 0 (metallic tellurium). These results
are confirmed by comparing the work functions of used andunused cathodes. An increase of about 0.5 eV for usedcathodes was obtained, resulting in a reduced QE.
Based on the measurements performed in this work werelate the decreasing of the QE of Cs 2 Te photocathodes toa change in the chemical composition. Starting from Cs 2 Te
after cathode production, metallic tellurium is formed during operation, which leads to the QE degradation.

REFERENCES[1] D. Sertore et al., ”Review of the production process of the
TTF and PITZ photocathodes”, PAC05, Knoxville, Ten-FEL Technology II

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nessee, USA, 2005.
[2] http://wwwlasa.mi.infn.it/ttfcathodes/[3] S.H. Kong, J. Kinross-Wright, D.C. Nguyen, and R.L.
Sheffield, J. Appl. Phys. 77, 6031 (1995).
[4] S.H. Kong, D.C. Nguyen, R.L. Sheffield, and B.A. Sherwood,
Nucl. Instrum. Methodes A 358, 276 (1995).
[5] A. di Bona, F. Sabary, S. Valeri, P. Michelato, D. Sertore, G.
Suberlucq, J. Appl. Phys. 80, 3024 (1996).
[6] J.J. Yeh, and I. Lindau, At. Data Nucl. Data Tables 32, 1(1985).
[7] H.B. Michaelson, J. Appl. Phys. 48, 4729 (1977).

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TEST OF A WIRE SCANNER IN THE
DIAGNOSTIC SECTION OF PITZ*
Hans-Juergen Grabosch# , Galina Asova##, Juergen Baehr, , Jang Hui Han§, Sergiy Khodyachykh,
Sergey Korepanov, Mikhail Krasilnikov, Velizar Miltchev§§, Anne Oppelt§§§ , Bagrat Petrosyan,
Martin Sachwitz#, Lazar Staykov, Frank Stephan, DESY, 15738 Zeuthen , Germany.
Abstract
The Photo Injector Test facility at Zeuthen (PITZ) has
been established to produce and optimize electron beams
of high brilliance. One wire scanner station, developed
and used in the undulator section of the FLASH at DESY
[1] [2] , has been installed in the diagnostic section of
PITZ. Measurements of beam-profile and beam-position
were performed to test the usability of such type of wire
scanner at PITZ. The test has shown that wire scanners of
this type can be well used as complementarymeasurement device at PITZ. In the final state of theextension of PITZ, two wire scanners are foreseen as
standard diagnostic tools for beam-profile and beamposition measurements.

INTRODUCTION
Wire-scanners are important diagnostic tools forparticle accelerators in order to tune the beam-line and tomeasure the beam-profile. Various types of wire-scanners
have been developed for different particle accelerators[3][4][5]. In PITZ the beam-electrons will undergoscattering processes when hitting the wire. Once scattered
the electron will hit the beam pipe and create a shower ofelectrons and photons. The shower signal of electrons andgammas can be observed by means of scintillator counters
placed nearby the beam pipe. The measured correlation
between the wire position and scintillator signal gives

information about the beam-position and the beamprofile.

SETUP AND MEASUREMENT
The configuration of PITZ in the year 2005 (PITZ1.5)
with the wire scanner station is shown in Figure 1. A wire
scanner station consists of two independent scanners forthe vertical- and horizontal-direction, respectively. Eachscanner is equipped with two tungsten wires of 30 μm
diameter in a distance of 10 mm.The whole set up is
combined with a scintillation counter. The counter detects
secondary particles which are created when the wireinteracts with the electron beam. The light of thescintillation counter is read out by wavelength shifter bars
and guided via clear fibers to the photomultiplier H67804. The gain of the photomultiplier is steered by areference voltage vref. and ranges from 102 – 106. For thismeasurement a gain of ~ 500 is mostly used. The
photomultiplier signal is read out and digitized by aTektronics TDS 5104 oscilloscope. Together with thephotomultiplier signal the position of the wire is stored
and analyzed afterwards. Vertical and horizontal scansprovide vertical resp. horizontal measurements of beamThe
profile and beam-position with μm resolution.
system allows scanning speeds from 5 μm/sec up to 1
m/sec. Absolute position determination in the range of 50
μm is achieved by calibrating the wires. The wire scanneris integrated in the coordinate system of PITZ.

Figure 1: Configuration of PITZ .
___________________________________________* This work has partly been funded by the European Community, contract
no.RII3-CT-2004-506008 and 011935 and by the ’Impuls- undVernetzungsfonds’of the Helmholtz Association, contract no. VH-FZ-005.
#
hans-juergen.grabosch@desy.de , martin.sachwitz@desy.de##

On leave from INRNE, 1784 Sofia, Bulgaria
now at DESY , 22603 Hamburg , Germany§§
now at Hamburg University, 22761 Hamburg, Germany§§§
now at PSI, 5232 Villingen, Swizerland§

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Thee parameter settings for this measurement were:Beam charge
Beam momentum
Bunches/Train
Rep.Rate
Focus Point(Screen )Wire scanner Position

0.5 nC
12 MeV/c
10
2 Hz
5.74 m from cathode6.28 m from cathodeRESULTSTo exploit the possibilities of the wire scanner
different measurements have been performed. Scanswith different step sizes, variation of the gain ( vref. andvariation of the beam-size. In Figures 4 and 5 scans of
the beam with different step sizes are shown.
The obtained RMS values are XRMS = 1.27 mm and
YRMS = 1.79 mm.

Beam x-profile
Pulse Height, V

0.08

0.06

0.04

0.02

Figure 2: Wire scanner station
Figure 2 shows the wire scanner station mounted at
PITZ. The different scanner modules for horizontaland vertical scans respectively, can be seen.

0

0

5

10

X-Scan, Wire Position, mm

Figure 4: Scan in horizontal direction (the second wireis shifted by 10 mm with respect to the position of thefirst)

Pulse Height, V

Beam y-profile
0.6

0.5

0.4

0.3

Figure 3: Screen shot of the wire scanner signal
In Figure 3 a typical photomultiplier signal on theoscilloscope (green) is shown together with the signals
from the 3 Integrating Current Transformers (ICTs,
yellow, blue and magenta), which represent the beam
charge before and after the wire scanner. The signal
exceeds 0.7 mV when the wire is in the centre of thebeam. If the wire is outside the beam a backgroundsignal of 0.2 mV is observed. This gives a S/N rationof about 3.5.
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0.2

0.1

0

-5

0

5

10

Y-Scan, Wire Position, mm

Figure 5: Scan in vertical direction (the second wire isshifted by 10 mm with respect to the position of thefirst)

Proceedings of FEL 2007, Novosibirsk, Russia
The overall measurement error is estimated of about
10 % , the small differencies between the red and black
curves in Figure 4 and 5 ( wire1 and wire2 ) may becaused by fluctuations in the electron beam.
To check the capability to measure very small
charges with the wire scanner a 50 μm slit 1 wasinserted into the beam 199 cm upstream of the wire
scanner position. Figure 6 shows this beamlet on a
YAG-Screen 54 cm before the wire scanner position.

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CONCLUSION
Beam-profiles and beam-position could be measured
at PITZ with a new type of wire scanner developed for
FLASH at DESY. The capability to measure beams ofsmall sizes and charge was also demonstrated. In the
final state of the extension of PITZ, two wire scanners
are foreseen as standard diagnostic tools for beamprofile and beam-position measurements.

REFERENCES

Figure 6: Beamlet from a 50 μm slit
The beamlet was scanned with a step-size of 50
μm/sec in vertical direction. The result of this scan isshown in Figure 7. The beamlet is well resolved. The
average RMS value of the measurement is 250 μm, thedistance between the wires is measured by 10.10 mm
which is 100 μm lager than expected.

[1] N.von Bargen, et al., ’Prototyp eines Wirescanners
fuer TTF II’TESLA Collaboration, TESLA 2002-08[2] P.Castro, et al., ‘ Wire Scanners in the undulator
section of the VUV-FEL at DESY’
Proceedings DIPAC 2005, p. 205.
[3] M.C. Ross, et al., ’Experience with wire scanners
at SLC’, SLAC-PUB-6014[4] P. Emma, et al., ’Beam Dispersion Measurementswith Wire-Scanners in the SLC Final Focus
System’, SLAC-PUB-6208[5] P. Elmfors et al., ’Wire-scanners in low energy
accelerators’, NIM A 396 (1997 ) 13-22.

Beamlet y-profile
Pulse Height, V

0.25

0.2

0.15

0.1

0.05

0

0

5

10

Y-Scan, Wire Position, mm

Figure 7: Scan of the beamlet from a 50 μm slit
From simple geometrical considerations one canestimate that the charge of the beamlet must be theorder of a few tens of pC.
1

Tungsten slits are used in PITZ to measure the local divergence

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Proceedings of FEL 2007, Novosibirsk, Russia

DEVELOPMENT OF A BEAM CURRENT TRANSFORMER FOR THE XFEL PROJECT IN SPRING-8
Atsushi Higashiya #, Hirokazu Maesaka and Yuji Otake
SPring-8 Joint-project for XFEL/RIKEN, 1-1-1,Kouto, Sayo-cho, ayo-gun, Hyogo JAPAN
679-5148.
Abstract
The SCSS prototype accelerator has been constructed
at SPring-8. The output signal of a current transformer(CT) for measuring the electron-beam current in the
SCSS prototype accelerator had a few megahertz (MHz)noise emitted from the thyratron of a klystron modulator,
a ringing signal caused by the weak field of the electron
beam. The long-period undulation of an electrical groundlevel at the CT monitor output also occurred due to alarge electric current generated by the klystron modulator,
which flows into ground. As a result, it is difficult tocorrectly measure the beam current. Therefore, we
devised a new CT monitor and the differential circuitfrom CT monitor in order to improve the problem
mentioned above.
The improved points are: (I) We think that the thyratronnoise and undulation of the ground level comprisecommon mode noise. Therefore, these noises werereduced by using a differential detection circuit, andcontacting between the ground of the CT case and theouter surface of a CT signal cable. (II) The ringing signal
was suppressed by intercalating a dumping resistancematerial into the space between the case and the ferrite
core of the CT monitor. By these developments, theenvironmental influence to the CT monitor could be
suppressed in its output circuit. In an experiment toevaluate the CT monitor, the output waveform of the CT
monitor was very clean without any noises as mentioned
above.

INTRODUCTION
The X-FEL prototype accelerator (SCSS project) wasconstructed at SPring-8. SASE (self amplification of
spontaneous emission) at a wavelength of about 50 nm
and was successfully observed during the last year. The
X-FEL project, based on SASE, is currently inprogress.[1,2]In generally, it is important to correctly investigate thebeam properties such as the current of an electronic beam.
For this reason, in the SCSS prototype accelerator, we use
CT monitors.
In commissioning of the prototype accelerator, wefound that the CT output signal was influenced by theenvironment such as noise produced by high-voltage
switching in the thyratron of a klystron modulator andoccurred due to large electric current flow into theground, which is also generated by the klystron
modulator. Figure1 (a) shows the ringing noise in the CT_________________#

codbelo@spring8.or.jp

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(a)

~4ns

(b)

(1.1V)
500 mV/div

4 ns/div

10 mV/div
1 μs/div(d)(c)
Klystron voltage~220
10 mV/div

40 μs/div

Figure 1: (a) Ringing of the CT output. (b) A few
megahertz noise at CT output. (c) Long-period
undulation of the electrical ground level at the CT
output. (d) Picture of CT at the SCSS prototype
accelerator.
output. The ringing has a period of about 4 ns (500 MHz).
Figure 1 (b) also shows a few megahertz noise emitted
from the thyratron. First, in order to eliminate thethyratron noise, we made a contact between the ground of
the CT case and the outer surface of the CT signal cables
as shown in Fig.1 (d) (indicated by a red circle). As aresult of the contact, the noise seemed to be suppressed.
However, instead of this noise, a long-period undulationof the electrical ground level (about 220ms) appears asshown in Fig.1 (c). Therefore, it was difficult to correctly
determine the beam current (electrons charge amount) due
to these problems.
In order to improve the problems of the few megahertz
noise, the ringing signal and the long-period undulation of
the electrical ground level, we devised a differential
output-type CT monitor with two output ports and adifferential detection circuit to modulate the undulation.
In this paper, we introduce the points of our
improvements in the CT used at the prototype accelerator,
the detailed configuration of the differential detection
circuit, and also demonstrate the clean output waveform
without any noises obtained by the differential outputtype CT.

Proceedings of FEL 2007, Novosibirsk, Russia

SYSTEM OF DIFFERENTIAL OUTPUT–
TYPE CT MONITOR WITH TWOOUTPUT PORTS
Figure 2 shows a schematic cross-sectional view of thedifferential output-type CT monitor with two output ports.
In this figure, the CT monitor has an amorphous ferrite
core with two-one turn coils and two output ports locatedabove and below the core. The upper and lower ports aredesigned to make opposite signs of the output signals.
The amorphous core makes the time response of the CT
monitor faster.
As the cause of the ringing signal, we suggested that a

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frequency obtained from Fig. 1 (a), a cavity surface
resistivity of more than 3.0 x 10-12 m2Ω is required tosatisfy the condition. Consequently, we achieved thiscondition by coating a Ni film of 10 μm on the innersurface of the CT case after coating a chrome film of 30
μm. Figure 3 shows the frequency response of the CT
monitor having a dumping resistance, which was obtained~50Ω
Dumping resistance

2.226GHz

Ceramic

Ferrite core
SMA connector~50Ω

Figure 2: Cross-sectional view of the differential
output-type CT monitor.
weak field generated by the electron beam produced
ringing. The outer case of the CT monitor could behave asa resonant cavity. To suppress the effect of the wake field,
we considered that the damping parameter to the field in
the cavity was effective. Therefore, we intercalated the
dumping resistance material into the space between thealuminium case and the ferrite core of the CT, shown as
the hatched part of Fig. 2. To calculate the resistance atthe design stage, a cavity resonant frequency of about 500
MHz was estimated from the case diameter as the cavity,
effect of the permeability of the core, and the measured
time between the broken red lines, as shown in Fig. 1 (a).
The equation of the resonant cavity for an evaluation
circuit is represented byL(d2q/dt2)+R(dq/dt)+(1/C)q=0,(1)
where L, R, q and C are the inductance and the wall
resistance of the cavity, the cavity wall current charge
induced by the electron beam and the capacitance of theaccelerating gap of the cavity, respectively. According to
the equation, an adjustment of R was needed to obtain theproper damping effect to suppress the ringing. Namely, it
was necessary to fit R to the value of the critical dumping
condition of the equation. From a straightforward
calculation using this equation and the resonance

Figure 3: Frequency characteristics of the CT bymeans of a network analyser.
by a measurement using a network analyzer. A resonantpeak at a frequency of 500 MHz existed before coatingthese films. After the coating, the 500 MHz peak
disappears as shown in Fig. 3. However, we can findanother resonant peak located at a higher frequency of
about 2.2 GHz instead of the 500 MHz peak.
When we thought about the problem of a long-period
undulation of the ground level, the undulation was
thought to be common mode noise. We then considered
how the CT monitor outputs the signal, and devised thefollowing ideas. The devised CT monitor has two output
ports at opposite poisons of the case circumference, andthe detection circuit is the differential circuit shown in
Fig. 4. The two output signals from the CT monitor,
indicated as (I) and (II) in Fig. 4, are transmitted to thedifferential detection circuit by using a 100-ohm
differential cable. Then, these signals are terminated by a100 Ω resistance and imported into the differential circuit.
Since the noise of the output waveform is the common
mode, the noise components of the wave forms have thesame signs, as indicated by the two solid lines of (I) and(II) in Fig. 4. On the other hand, the two necessary signals
generated by the electron beam are of the opposite signs,
as shown by the dashed lines of (I) and (II) in Fig. 4.
Therefore, the common noise of the signals at the circuit
input is suppressed when these signals pass through adifferential amplifier just in front of an AD converter(ADC), as indicated by the solid line (III) in Fig. 4. In
addition, the necessary signal at the converter input makes
its voltage double by adding signals (I) and (II), as shown

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Proceedings of FEL 2007, Novosibirsk, Russia

CT monitor(I)
Differential
Amplifier

ADC

(II)

(III)

Figure 4: Schematic circuit diagram for the differential reception.
by the dashed line (III). The output signal from thedifferential amplifier is transferred to the ADC.

DETAILED CONFIGURATION OF
DIFFERENTIAL DETECTION CIRCUITFOR CT MONITOR

Figure 5 shows the detailed configuration of thedifferential detection circuit for the CT monitor. The
differential circuit is composed of a preamplifier, a 100
ohm differential cable, a main amplifier, and a VME
ADC module. The output signal from the CT monitor istransferred to the preamplifier. Then and there, the gain
adjustment to the amplitude of the CT signal by theCT preamplifier

50

Differential cable+-

CT monitor

50

Gain adjustment

GND
Main amplifier

ADC module

Attenuator (ATT)+
AmplifierDifferential amplifier

ATT computer

Remote Control
by computer

Device-Network
Figure 5: Differential circuit design of CT monitor

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ADC
(IC)

VME Computer BUS

Proceedings of FEL 2007, Novosibirsk, Russia

preamplifier is done. After then, the signal is transferredto the main amplifier through the differential cable, inwhich its cable length is about from 10 m to 20 m. The
main amplifier includes differential amplifiers and aswitching attenuator array. The attenuator array also
adjusts the amplitude of an input signal from the CT
monitor. The switching of the attenuator is remotely
controlled from a computer through the Device-Network.
The output signal from the main amplifier is transfer tothe VME ADC module that works like an oscilloscope
having a differential input, a 12 bits dynamic range, a 238
MHz clock drive circuit. At the present, this differential
detection system is under development. However, we
believe that a genuine large beam current signal withnoise suppressed by the system could be successfully
obtained.

TEST OF DIFFERENTIAL OUTPUT-TYPE
CT MONITOR
We installed a differential output-type CT monitor to
the SCSS prototype accelerator (as shown in Fig. 6 (a))
for a test, and directly measured the output wave forms
from the CT monitor, induced by the beam, by using anoscilloscope having a measurement bandwidth from DC
to 12 GHz. Figures 6 (b) and (c) show the obtained output
wave forms. In these figures, the green, yellow, and redlines are the signal from port 1 and port 2, and theirdifference (port1-port2), respectively. As shown by the
red line, the long-period undulation disappears and theground level is nearly flat due to the common moderejection effect.

SUMMARY
In order to eliminate the ringing signal caused by the
weak field of the electron beam, the few MHz noise andthe long-period undulation of the ground level at the CT
output, we devised a differential output-type CT monitor.
The waveforms obtained by the CT monitor showed
(a)

(b)

Port 1WEPPH051

clear output signals, which indicated that our
improvement could successfully suppress the noise fromthe environment around the CT monitor. The ringing
effect caused by the weak field induced by the electron
beam is successfully suppressed by inserting the dumping
resistance. Furthermore, the CT monitor time response
was fast due to the time response of the amorphous ferrite
core with the one-turn coils, and due to the frequency
response of the effective permeability of the core up to
about 1 GHz. The waveform rise time is less than 200 ps.
The obtained signal waveforms had a few structures. At
the present time, the reason why the waveform had thestructure is not clear. There is some possibility that thetrue waveforms could have a different shape, and could
be hidden due to the limited bandwidth of theoscilloscope. Therefore, we need more accurate
measurements using an oscilloscope with higher
bandwidth than 12 GHz, or streak camera in order toverify the true waveforms. The differential detection
circuit for this CT monitor is still under development, andhowever, it will be tested within several months.
Consequently, we think that it is possible to measure thebeam current (the electrons charge amount) more
precisely.

ACKNOWLEDGMENT
We thank the members of the SCSS prototype
accelerator group for their help with the experiment. For
CT monitor production, we are grateful for the effort ofMr. Koji Kase (Toyama corporation, 4-13-16 Hibarigaoka
4-chome, Zama-shi, Kanagawa Prefecture, JAPAN 2280003).

REFERENCES[1] SCSS X-FEL R&D Group (http://www-xfel.spring8.or.jp/)[2] H. Tanaka, et al., Beam Performance of the SCSS Prototype
Accelerator, The 3rd Annual Meeting of Particle
Accelerator Society of Japan (2006).

(c)

Port 2

Figure 6: (a) Picture of the CT monitor installed in the SCSS prototype accelerator. (b) Output waveforms
induced by the electron beam displayed in the wider time span (500ps/1div). (c) Output waveforms displayed in
the narrower time span (200ps/1div.).

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Proceedings of FEL 2007, Novosibirsk, Russia

IN-SITU UNDULATOR FIELD MEASUREMENT WITH THE SAFALISYSTEM
Takashi Tanaka, R. Tsusu, T. Nakajima, T. Seike and H. Kitamura
RIKEN SPring-8 Center, Koto 1-1-1, Sayo, Hyogo 679-5148, Japan
Abstract

A new scheme of undulator field measurement has been
proposed, which makes it possible to do field mapping inside the vacuum chamber to verify the final magnetic performance of in-vacuum undulators (IVUs) after assembly.
Optical laser beams are used in order to measure the positions of the Hall probe during actuation along the longitudinal direction, and dynamic feedback of the positionis carried out to ensure a high stability and accuracy ofthe measurement. A field measurement system based on
this concept has been developed at the SPring-8 in order tomeasure two different types of IVU. Principle of the newmeasurement scheme and details of the developed system
are described together with the results of the field measurement.

INTRODUCTION
Shortening the undulator period is crucial to reducing theelectron energy required to get angstrom x-rays in the SR
and XFEL facilities and thus the total cost of construction.
The in-vacuum undulators (IVUs) have many advantages
over out-vacuum devices toward shorter magnetic period
and thus have been adopted in a great number of SR facilities all over the world. It should be noted, however, thatmagnetic measurement after final assembly including thevacuum chamber, i.e., final verification of magnetic performance, is not an easy task. In addition, remeasurement
after installation in the accelerator beamline is not trivial.
The situation is more severe for cryogenic permanent magnet undulators (CPMUs)[1], an extension of IVUs.
We have recently developed a magnetic measurement
system to measure the field inside the vacuum chamber.
With optical laser beams introduced into the vacuum chamber, the alignment of the Hall probe positions is dynamically carried out, which ensures a high stability and accuracy of the measurement. This system is called SAFALI
for Self-Aligned Field Analyzer with Laser Instrumentation. The SAFALI system has been applied to field measurement of two different undulators. One is an IVU installed in Swiss Light Source in 2001 and had been operated for about 3 years. The other is a CPMU prototype
to demonstrate the principle of CPMU. The purpose of theformer measurement is to investigate the radiation damage
during operation, while that of the latter is to check thevariation of the magnetic properties according to the temperature change of magnets. In this paper, details of the
SAFALI system are given together with the results of the
field measurements.
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PRINCIPLE

In the conventional magnetic measurement system, amagnetic sensor such as a Hall probe is placed on a cantilever supported by a 2-axis (x,y) stage mounted on a longactuation table with a high mechanical accuracy, which isusually made of granite. Due to pitching, rolling and yawing of the actuation table, the Hall probe position during
actuation can fluctuate. To perform a magnetic measurement with a high accuracy, the positional fluctuation should
be kept as low as possible. The positional error of a typicalmeasurement bench is around 30 µm, which corresponds toa field error of 0.02% for an undulator with a magnetic period of 10 mm, and thus enough for magnetic measurementof most undulators. In addition, the measurement result isquite well reproducible: typical deviation of the magnetic
measurement in terms of the r.m.s. phase error is usually
lower than 0.3 degree. It should be noted, however, thatsuch a Hall-probe scanning method cannot be applied to
the field measurement of IVUs as is. We have to modify
the actuation method to be adapted to the field measurement of IVUs after assembly.
The most straightforward way is to install a huge vacuum chamber that can accommodate a rigid and robust linear guide with a mechanical accuracy comparable to thatof the granite bench, which is not only impractical but also
inefficient. Another way is to monitor the position of theHall probe during actuation along the longitudinal axis andperform a dynamic feedback to ensure that the Hall probe
is always in position. In this case, the linear guide does nothave to be necessarily rigid or robust: any method of actuation is acceptable unless the positional variation during
actuation is too large to be compensated by feedback.
We can consider several methods to measure the Hall
probe position. Among them, we decided to use optical laser beams combined with position sensitive detector(PSD) and irises attached to the Hall probe, because they
are cost effective compared to other methods. In order
to measure the longitudinal position, we can use a commercially available laser scale with a resolution better than
0.1mum. Hereinafter, let us call the field measurement
method based on this concept “SAFALI”, for Self-Aligned
Field Analyzer with Laser Instrumentation. We have so far
developed two SAFALI systems for measurement of two
different IVUs, the details of which will be discussed in
the following sections.

SAFALI FOR IVU24
In 2001, an IVU with a magnetic period of 24 mm andmagnetic length of 1.5 m (IVU24) has been constructedat the SPring-8 and installed in the storage ring of Swiss

Proceedings of FEL 2007, Novosibirsk, Russia

Light Source (SLS) as a collaboration to aim at utilizationof angstrom x rays in the medium-sized SR facility. After
3-year operation, IVU24 has been replaced with another
IVU and returned to SPring-8. It is important to measure
the magnetic field of IVU24 and compare with the initialstate, and to check the variation of magnetic performancesfrom the point of view of demagnetization due to electron
irradiation during operation.
Top View
iris

PSD

undulator magnet

Hall probe

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the rail. Figure 2 shows the variation of the Hall probe position measured with and without the feedback procedure.
We can clearly find the effects due to the feedback. The
magnetic error due to the positional deviation of 5 µ is just
5×10−6 for an undulator with a magnetic period of 10 mm,
and smaller for a longer period.
As a field measurement system for undulators, the reproducibility is the most important. We measured the magnetic field distribution of IVU24 four times under the same
condition to examine the reproducibility. The results areshown in Fig. 3 in terms of the phase error as a functionof the pole number, where we find quite a good agreement
between the measurement results.
6

Side View

stepper
motor

rail carriage

Figure 1: Schematic illustration of the SAFALI system for
the CPMU prototype.
Figure 1 shows a schematic illustration of the SAFALI
system for IVU24. We have installed a rail and carriage toactuate the Hall probe by means of a tensioned loop wire
driven by a stepper motor. The Hall probe cantilever was
attached to the carriage together with the cubic mirror toreflect the laser beam of the laser scale to measure the longitudinal position of the Hall probe. In addition, two irises
are attached at the both ends of the Hall probe cantileverwith a diameter of 2 mm. In order to measure the transverse
Hall probe position during actuation, two laser beams wereintroduced to irradiate the irises and create laser spots atthe opposite side. The positions of the laser spot were measured with position sensitive detectors (PSDs), the averageof which defines the position of the Hall probe.
Horizontal
VerticalTransvers Position (mm)

0.3

0.2

with feedback
σx=4.9µm,σy=3.9µm

without feedback
σx=51µm,σy=79µm

0.1

0.0

-0.1
-1000 -800

-600

-400

-200

0

200

400

600

800

1000

z (mm)

Figure 2: Variation of the Hall probe position with andwithout feedback.
The feedback of the Hall probe position is done by moving the rail with the three sets of 2-axis stages supporting

Phase Error (degree)

laser diode2-axis stage

1st
2nd
3rd
4th

4

corner cube

laser scale

2
0
-2
-4
-6
-8
-10
0

10

20

30

40

50

60

70

80

90

100 110

Pole Numbere

Figure 3: Reproducibility of the field measurement in termsof the phase error distribution.
As described above, the developed SAFALI system has
been found to have a performance good and reliable enoughto measure the magnetic field of IVU24.

SAFALI FOR CPMU PROTOTYPEThe CPMU is a novel undulator proposed at SPring-8
in 2004 [1]. The permanent magnets in the IVU is cooled
down to improve the magnetic property in terms of the remanence and coercivity. The operation temperature will bearound 100∼150K where the remanence becomes maximum, and much higher than liquid helium, so the operation
will be much more feasible than superconducting undulators composed of NbTi wires. We have constructed a prototype of CPMU with a magnetic length of 600 mm and amagnetic period of 15 mm and made experiments to investigate the feasibility of CPMUs such as the cooling capability, variation of the magnetic gap and tapering during thecooling process [2]. Although promising results have beenobtained in these experiments, we have to establish a fieldmeasurement technique to be adapted to the CPMUs. So,
we have developed a system based on the SAFALI method
to measure accurately the magnetic performance at a cryogenic temperature [3].
Figure 4 shows a schematic illustration of the SAFALI
system for the CPMU prototype. A pair of O-ring recipro-

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Proceedings of FEL 2007, Novosibirsk, Russia

Top View

64axis-stage(remote 2axis)

to TMPSide View
O-ring reciprocating seal

SUS pipe

2nd Field Intgegral (103G.cm2)

xy linear
guide

x,y stage

4

0

-4

-3
6

-8

0

θz rotary
stage

to TMP

March 2007 (SAFALI)
8
July 2000 (Conventional)

20mm

3

8

14mm

3

4

0

-4

-3
6

-8

0

Phase Error (degree)

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10mm

3
0
-3
6

8mm

8
4
0
-4
-8
8

3

4

0

-4

-3
6

-8

0

θx,y stage

Figure 4: Schematic illustration of the SAFALI system for
the CPMU prototype.

8

6mm

3

4

0

-4

-3

-8

0

-800

-400

0

400

800

0

10 20 30 40 50 60 70 80 90 100 110

z (mm)IVU24
We measured the magnetic distribution at the gap valuesof 6, 8, 10, 14, and 20 mm and compared the magnetic performances with those measured by a conventional method
in July 2000, just after the field correction and before installation in the SLS ring. The results are shown in Fig. 5in terms of the electron trajectory (2nd field integral) andphase error distribution.
We find negligible difference between the two measurements in terms of the electron trajectory, while a small discrepancy in the phase error distribution suggests that themagnetic field distribution has changed slightly. It shouldbe emphasized, however, that the variation is very small
and less than 0.5 degree in r.m.s. So we can conclude
that no significant demagnetization took place in the IVU24
during operation.

CPMU Prototype
We measured the field distribution of CPMU prototype
at different temperatures and found that the peak field became maximum at a temperature of 130 K. During the measurement, the gap was fixed at 5 mm by measuring directly
the distance between the top and bottom magnet arrays bymeans of a laser scan micrometer. From the point of viewof field correction, what is important is the phase error variation due to temperature change. Figure 6 shows the magnetic performances measured at room temperature and 130
K in terms of the electron trajectory and phase error. We
find negligible difference between the performances at two
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different temperatures, suggesting that cooling the permanent magnets did not induce a large change in the error
magnetic components that could affect the undulator performance. This is a very encouraging result toward realization of CPMUs.
1.5
1.0

6

300K
130K

4
Phase Error (degree)

RESULTS OF MEASUREMENT

Pole Number

Figure 5: Comparison of magnetic performances of IVU24
between July 2000 and March 2007. Note that measurement in July 2000 was done by a conventional method.

2nd Field Integral (103G.cm2)

cating seals have been installed to insert the SUS tube to fix
the cantilever of the Hall probe, which is actuated by meansof pushing or pulling the end of the tube. The Hall probe
position feedback is performed by the multi-axis stage supporting the vacuum duct including the O-ring seal. The
variation of the Hall probe position during actuation wasslightly worse than the system for IVU24 described in thepreceding section, however, the reproducibility was similar. For details, refer to [3].

0.5
0.0
-0.5
-1.0

2
0
-2
-4
-6

300K (3.3o)
130K (3.2o)

-8

-1.5

-10
-300 -200 -100

0 100 200 300
z(mm)

0

10

20

30

40

50

60

70

Pole Number

Figure 6: Variation of magnetic performances of CPMU
prototype at room temperature and 130 K.

SUMMARY
We have described the SAFALI system as a new schemeof undulator field characterization and its practical application. It should be also stressed that the SAFALI system is portable: the magnetic performance of IVUs can bechecked at any time without moving to the laboratory or facility for the field measurement. Such a portability is very
important especially in X-ray FEL facilities where a number of undulators will be installed. The SAFALI system canbe used not only for the final check after assembly but also
to monitor the magnetic performance as the FEL driver. We
also note that most undulators nowadays have a C-shaped
frame, but not a O-shaped frame, in order to ensure openings for field mapping with Hall probe scanning, whether
they are in-vacuum or out-vacuum. This imposes a severe
restriction on the undulator design, because C-shape frameProceedings of FEL 2007, Novosibirsk, Russia

is much less rigid than the O-shape frame. By means of the
SAFALI method, the mechanical frame does not have to be
C shape from the point of view of field measurement and
new undulator designs would be be possible.

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REFERENCES[1] T. Hara, T. Tanaka, H. Kitamura, T. Bizen, T. Seike, T. Kohda,
and Y. Matsuura, Phys. Rev. ST-AB 7, 050702 (2004).
[2] T. Tanaka, T. Hara, T. Bizen, T. Seike, R. Tsuru, X. Marechal,
H. Hirano, M. Morita, H. Teshima, S. Nariki, N. Sakai, I.
Hirabayashi, M. Murakami and H. Kitamura, New J. Phys. 8287 (2006).
[3] T. Tanaka, R. Tsuru, T. Nakajima and H. Kitamura, J. Synchrotron Rad., 14 416 (2007).

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Proceedings of FEL 2007, Novosibirsk, Russia

NON-DESTRUCTIVE SINGLE-SHOT 3-D ELECTRON BUNCH MONITOR
WITH FEMTOSECOND-TIMING ALL-OPTICAL SYSTEM FOR PUMP &PROBE EXPERIMENTS
H. Tomizawa, H. Hanaki, Accelerator Division, Japan Synchrotron Radiation Research Institute(JASRI/SPring-8), Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5198, Japan
T. Ishikawa, The Institute of Physical and Chemical Research (RIKEN Harima/SPring-8),
Kouto, Sayo-cho, Sayo-gun, Hyogo 679-5148, Japan
Abstract
We are developing a non-destructive single-shot 3-D
electron bunch monitor based on EO sampling, using theyearlong stable femtosecond laser source developed for
the SPring-8 RF gun. The probe laser for spectral
decoding EO sampling has been prepared as radialpolarized and completely linearly chirped bandwidth(~500nm) supercontinuum generation. The EO-probeelement is made of 8 EO-crystals with the assembling ofeach EO-crystal’s optical axes along radial beam axes.
The linearly chirped probe laser is longitudinally shifted
in 8 transverse sectors for spectral decoding. We areplanning to use organic polymer film as a femtosecond
resolution EO-probe instead of crystals. This 3-D bunchmonitor with spectrograph detects and analyzes the
Coulomb field of electron bunches as longitudinally
spectral decoding and transversely multi-pole expansion.
Our single-shot bunch monitor can characterize the 3-D(both longitudinal (1D) and transverse (2D)) distribution
and position of an electron bunch with femtosecond
resolution. This non-destructive monitor can be used as
an electron energy chirping monitor at a dispersive
region for XFEL commissioning. Additionally, the EOsampled probe laser pulse will be used as a femtosecondtiming signal pulse. This signal pulse is amplified with a
NOPA, developing an all-optical timing system.

INTRODUCTION
At the SPring-8 site, construction of the XFEL project[1] has begun under a RIKEN and JASRI joint project. It
will enter operation in 2010. For this project, it isnecessary to monitor femtosecond electron bunch lengthfor its commissioning. At the moment, the mostpromising femtosecond electron bunch monitor with an
RF deflector, the LOLA cavity [2], is planned to beinstalled in the 1-GeV energy region of the 8-GeV
SPring-8 XFEL linac. However, this monitor requires a
few-meters-long cavity structure, and has to measure thebunch length on a fluorescent screen installed a few
meters further downstream. The compactness isimportant in the XFEL project at SPring-8. Therefore,
the shorter bunch monitor system is required for bunch
length measurement, especially in the 8-GeV region.
In terahertz technology, femtosecond laser pulse
duration has been measured utilizing the Pockels effectof ZnTe and so on. This method was the so-called
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472electro-optical sampling (EOS). The variation of the
Coulomb field of the electron beam bunch with aduration of less than 1 ps corresponds to terahertz (>1012
Hz) in frequency domain. Against this background, thisEOS-based bunch monitor has been developed in theaccelerator field [3-6]. The advantage of the EOS
monitor is that it is non-destructive and has a highresolution of sub-picosecond. To use the laser as a probe
allows a timing jitter of femtosecond, and a readout of
the monitor head without signal cables. However, thetemporal response of inorganic crystals like ZnTe islimited by 110 fs.
There are several types of EOS measurements. One isso-called spectral decoding, that decodes the longitudinal
electron bunch structure on the spectrum of the chirped
probe laser pulse. One of the others is so-called temporal
decoding that is used as conventional pulse measurementwith a correlation technique for a femtosecond laser.
The spectral decoding EOS makes possible single-shotmeasurement with a high repetition rate. Its encoding is
simple to perform with a conventional spectrometer.
Despite spectral decoding being a convenient method, it
is well known that the sensitivity of the signal pulse isreduced because of certain interferences occurring
between neighbouring wavelengths. Generally, thetemporal resolution Rres is given by
R res ≅ t 0 t c ,where the Fourier transform limit of the probe laser is t0,
and the probe chirped laser pulse duration is tc [5-6].
Therefore, it is the tendency for measurement with highprecision to use the temporal decoding method, which issuperior in resolution. With a broadband (> 400 nm)
laser square pulse chirped linearly, for instance, if t0=2.5
fs, tc=160 fs, Rres is improved around 20 fs.
In our point of view, spectral decoding is simple toencode and useful for measuring more information about
the electron bunch. If the three-dimensional charge
distribution of the electron bunch is measurable, it isquite useful for many applications. We investigated thebunch-by-bunch measurement possibility of thetransverse charge distribution of the electron bunch with
spectral decoding. In our strategy, temporal decoding,
AO-modulator-based SPIDER [7] (Spectral Phase
Interferometry for Direct Electric field Reconstruction)measurement will be used as a precise calibration for our
spectral decoding EOS 3-D bunch monitor.

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Figure 1: 3-D bunch structure monitor and its probe laser optics:
The probe laser for spectral decoding EOS is prepared as radial polarized and completely linearly chirped bandwidth(~500nm) supercontinuum generation. The EO-probe element is made of 8 EO-crystals (organic films) with theassembling of each EO-crystal’s optical axes along radial beam axes. The linearly chirped probe laser is longitudinallysifted in 8 transverse sectors for each spectral decoding to analyze transversely multi-pole expansion.
at the same time) squared by a broadband AO-modulator(DAZZLER: UWB650-1100; FASTLITE). The squared
linear-chirped broadband pulse is radial polarized andconverted to a hollow laser pulse with optics we invented[9]. This hollow laser pulse is used as the probe laser for
EOS as shown in Figure 1. Using this probe hollow laser
pulse, the single-shot 3-D bunch monitor shown in
Figure 2 is possible. We propose a single-shot EOSbased 3-D bunch monitor and report the optics forgenerating a hollow broad-bandwidth laser probe pulse.
Figure 2: The principle of single-shot EOS-based 3-Dbunch monitor: This 3-D bunch monitor with
spectrograph detects and analyzes the Coulomb field ofelectron bunches as longitudinally spectral decoding andtransversely multi-pole expansion. In the figure, theCoulomb fields of monopole, dipole, and quadrupole inthe bunch slice are shown.
The probe laser will be generated with a photonic
crystal, using the yearlong stable femtosecond laser
source [8] developed for the SPring-8 RF gun. Recently,
the photonic crystal has generated supercontinuum with abroad bandwidth of more than 500 nm. This broadband
laser source is linearly chirped and temporally (spectrally

CONFIGRATION AND COMPONENTS
OF EOS-BASED 3-D BUNCH MONITOR
Radial polarizer for hollow broad-bandwidthlaser beam as EOS probe
A radial polarized beam can be generated with 8divided waveplates [10] as shown in Figure 1. However,the divided type has difficulty being utilized for broad
bandwidth (500 nm) supercontinuum. For a broadband
source, it is possible to use a radial polarizer based on
liquid crystal. In Figure 3, the radial polarization test
samples with 90-degree rotation of an additional

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polarizer for a white light source are shown, using theradial polarization converter based on liquid crystal.
It is necessary to generate the hollow laser beam forthe probe laser, avoiding interaction with the electron
beam bunch. The hollow laser beam is generated by anaxicon lens pair, and then reflected in and out at thehollow mirrors in a vacuum. The ring width of thehollow probe beam is half of the incident beam radius at
the axicon lens pair. The width should be as narrow as
possible for accuracy to decode the field of the electron
bunch slice.

We tested spectrum shaping with the AO-modulator
DAZZLER, which can compensate optical dispersion up
to 4th order in the phase spectrum and gain-narrowing in
the intensity spectrum. We installed DAZZLER after the
stretcher of the CPA configuration of the Ti: Sapphireterawatt laser. Because of too large a stretching factor of~19000, it is beyond DAZZLER’s capability tocompensate GDD (Group Delay Dispersion) in this test.
Therefore, we compensated just the gain-narrowing ofspectrum for squared pulse generation. Streak
spectrographs (streak image in spectrum) are shown in
Figures 1 (initial) and 2 (square-shaped). It clearly showsthat a square shape is generated successfully.

Figure 3: Radial polarization converter (ARCoptix,
Switzerland) based on liquid crystal: Comparing the rightand left (rotated 90 degrees from each other), it is clearthat the converter generates a radial polarization.

Supercontinuum generation and transport
In order to generate supercontinuum (650-1100 nm)
with a femtosecond laser oscillator, we selected a
photonic crystal. The generated broadband laser has to betransported with optics without distortion in intensity andphase over the spectral range. It is difficult to maintainthe whole spectral range, especially for a polarizer. The
present status of the optical configuration is shown in
Figure 4. At the moment, we have chosen the Glan-Laser
Carsite Polarizer limited by the upper limit wavelengthof 1000 nm. To maintain the entire supercontinuum
spectrum, we are designing a Fresnel-Rohm andapochromatic waveplate.

Figure 4: Supercontinuum generator (650-1100 nm) andbroadband transport optics

Squared linear-chirped supercontinuum withcompensation of transport distortion
The generated broadband laser is distorted in intensityand phase spectra. However, by introducing an AOmoderator, such distortion on intensity and phase spectra
can be compensated. We want to prepare the probe laser
pulse as a squared linear chirped pulse because it avoids
computation to encode the electron-bunch-informationdecoded spectra through detection with a spectrometer.
Without complex computation to encode, it helps todetect the 3-D bunch structure at a high repetition rate.
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Figure 5: Initial intensity spectrum and chirp of thefundamental of Ti: Sapphire laser (after the stretcher):
The linear chirp is measured by monochrometer
combined with streak camera (Hamamatsu Photonics
K.K.)

Figure 6: Squared intensity spectrum with a hole madeon its spectrum by DAZZLEREOS BUNCH MONITOR CHAMBER
It is possible to make several configurations of EOSmonitors with different functions and with different
boundary conditions (3-D monitor shown in Figure 7,
BPM-function shown in Figure 8). Besides, the temporal
resolution τ that depends on the distance r between themonitoring probe laser position at the EO element andthe charge centre of the electron bunch slice is given byτ = r γc ,Proceedings of FEL 2007, Novosibirsk, Russia

where the Lorenz factor is γ, and the light speed is c. At
the energy region of 8 GeV, with monitoring position rof 1 cm, temporal resolution τ will be 2 fs. The broad
bandwidth of 400 nm determines the resolution of 20 fs(already mentioned). At the beginning of the test, theradial EO-probe element will be made of 8 EO-crystals
with the assembling of each EO-crystal’s optical axes
along radial beam axes as shown in Figure 7. We areplanning to use organic polymer film [11] for a
femtosecond resolution EO-probe instead of inorganic
crystals. The existing π-bonding in organic polymer
causes a higher response of electrons for Pockels effectthan inorganic crystals with only σ-bonding.

Figure 7: EOS bunch monitor for 3-D electron
distribution monitor function: The linearly chirped
hollow probe laser is shifted by the spiral timing shifterin 8 transverse sectors for spectral decoding. It has alsofunction of total timing delay of the hollow probe laser,
avoiding interaction with the electron beam bunch.

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as longitudinally spectral decoding and transversely
multi-pole expansion. The analysis of transversely multipole expansion can be done with the similar manner of amulti-strip-line-electrodes-type BPM [12].

SUMMARY AND DISCUSSION
We discussed a new concept of a 3-D electron bunchmonitor based on EOS (spectral decoding), and showed
the method for its optical configuration. Our single-shotbunch monitor can characterize the 3-D distribution andposition of an electron bunch with femtosecond
resolution. This EOS 3-D bunch monitor with
spectrograph detects and analyzes the Coulomb field ofelectron bunches as longitudinally spectral decoding andtransversely multi-pole expansion. This non-destructive
monitor can be used as an electron energy chirping
monitor at a dispersive region for XFEL commissioning.
The probe laser for EOS has been prepared as radialpolarized and completely linearly chirped broadband(limited by 350 nm) supercontinuum generation. We areplanning to use organic polymer film for a femtosecond
resolution EO-probe instead of inorganic one.
At the encoding with the spectrometer theinterferences will make resolution worse. Defusing
techniques should be applied with the spectrometer.
In addition, we are developing an all-optical system
for femtosecond-timing pump & probe experiments. The
EO-sampled probe laser pulse will be used as afemtosecond-timing signal pulse. This signal pulse isamplified with a NOPA (noncollinear optical parametricamplifier), using an SHG of Yb fibre laser as a pumplaser.
The total design of the EOS-monitoring and all-opticaltiming system can be improved and simplified with therecent progress of laser technologies.

REFERENCES

Figure 8: EOS monitor for BPM function: The 3-D
monitor EOS chamber shown in Figure 7 is installed
between two BPM EOS chambers.
With variation of distance r and boundary condition ofa cylindrical metal wall, the combined EOS bunchmonitor should be optimized in their geometry. The 3-D
monitor function EOS chamber is installed between two
BPM function EOS chambers. Analysis of threedimensional charge distribution requires the charge
centre position of the electron bunch slice at the EO
element (see Figure 2). A spectrograph encoder detects
and analyzes the Coulomb field of the electron bunches[1] J. Rivers, “SCSS X-FEL Conceptual Design Report”,
RIKEN, May 2005.
[2] R. Akre, et al., Proc. of EPAC 2002, Paris, France,
2002, 1882-1884.
[3] P. Bolton et al., AIP Conf. Proc 648, 2002, 491.
[4] G. Berden, et al. DIPAC ’05, 2005, 69.
[5] Jamison et al. Opt. Lett. 18, 2003,1710.
[6] I. Wilke et al PRL 88, 2002, 124801.
[7] C. Iaconis, et al., IEEE J. of Quantum Electron, 35,
1999, 50.
[8] Tomizawa, et al., Russian Journal of Quantum
Electronics, 2007, 697.
[9] Japan Patent Application No. 2007−133046.
[10] H. Tomizawa, et al., ”Feasibility test of Laser
induced Schottky-effect-gated photocathode RFgun”, FEL ’07, 2007, to be published.
[11] Hattori T. and Kobayashi T., Chem. Phys. Lett., 113,
1987, 230.
[12] T. Suwada, Jpn. J. Appl. Phys. Vol. 40, 2001, 890.

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COHERENT THZ LIGHT SOURCE USING VERY SHORT ELECTRONBUNCHES FROM A THERMIONIC RF GUN
Toshiya Muto#, Takumi Tanaka, Fujio Hinode, Masayuki Kawai, Ken-ichi Nanbu, Kittipong
Kasamsook, Kazushi Akiyama, Mafuyu Yasuda, Yoshinosuke Mori, Hiroyuki Hama
Laboratory of Nuclear Science, Tohoku University.
Abstract
We have planned to establish intense terahertz lightsource using coherent radiation from undulator. In order
to emit coherent radiation, it is important to generate very
short electron beam with a bunch length around 100fs.
Now we have developed an injector to generate such shortbunch beam. The injector consists of an Independent
Tunable Cells thermionic rf gun (ITC rf gun) and amagnetic bunch compressor. Longitudinal and transverse
phase space distribution can be controlled by changing
input power of each cells and phase difference between
cells in this gun. The compressor can change compression
rate R56 and 2nd order dispersion effect by 2 sets ofquadrupoles and a set of sextupoles, respectively. Testmodel of ITC rf gun was manufactured and basic
parameters were measured. From tracking simulation, it
has been turned out the bunch compressor can reduce tobunch length less than 100fs. In this paper, we show
overview of the coherent terahertz light source and thedetail of the ITC rf gun and the bunch compressor.

INTRODUCTION
Intense coherent radiation at the terahertz region (λ ~300μm) will be powerful probe for bio-medical science,solid state physics and other many scientific fields. There
was not such intense terahertz light source so far. There
are two type of terahertz source, or laser based andaccelerator based. We have developed accelerator basedterahertz light source using intense coherent radiation [1].
Now a coherent terahertz source using undulator radiation
has been planed.
In order to get coherent terahertz light, electron beamwith very short bunch length σt < 100fs must be produced.
Therefore an injector, which consists of Independent
Tunable Cells rf gun (ITC rf gun) and magnetic bunch
compressor, has been developed.
In this paper, the project of undulator coherent terahertz
light source and the detail of the ultra short bunch injector
are presented.

UNDULATOR COHERENT TERAHERTZ
LIGHT SOURCE
A light source consists of an injector, an accelerating
structure and an undulator. The schematic design is shownin Fig.1. The injector which consists of the ITC rf gun andmagnetic bunch compressor generates electron beam withenergy E ~2MeV, normalized emittance εn < 1πmmmrad____________________________________________#

muto@lns.tohoku.ac.jp

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and bunch length ~100fs. By the accelerating structure,
beam energy goes up to 12 MeV. The ultra short bunch
beam is passing through the undulator, then coherent
terahertz light is emitted.

Figure 1: The schematic design of undulator coherent
terahertz light source
The parameter of coherent terahertz light source is listed
in Table 1.
Table 1: Parameters of coherent terahertz source
Energy E

12MeV

Normalized emittance εn< 1 πmm mrad

Bunch length σt~100fsBunch charge Ie~20pC

Undulator
period length λp

8 cm# of periods

15

Peak magnetic field Bymax

0.3 T

Calculated terahertz spectrum from the undulator was
shown in Fig.2 and Fig.3, where bunch length σt=100fs,
number of electrons Ne = 1.25 x108 electrons /bunch(bunch charge is 20pC).
The fundamental wavelength λ1 and its harmonics λi is

λi =

λp ⎛

⎞
K2
⎜
+
+ γ 2θ 2 ⎟⎟ ,12 ⎜2
2γ i ⎝⎠(1)

where i is harmonic number, K=93.4 Bymax[T] λp[m] is thestrength parameter, γ is Lorentz factor, θ is theobservation angle with respect to the axis[2]. In thiscase, the fundamental wavelength λ1 is 257μm. Sincebunch length σt=100fs ~ 30μm, only the radiation with
fundamental wavelength is coherent, so proportional to N2~ 1016. Therefore, compared with the fundamental
radiation, higherharmonics is suppressed (See Fig.2 and3).

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By using a self-developed 3-dimensional Finite
Difference Time Domain (FDTD) simulation code[3],operating parameters of ITC rf gun was optimized [1].
Table 2 shows optimized operating parameter andgenerated beam parameter under that condition.
Simulation result of longitudinal phase space distribution
is shown in Fig.4. The momentum spread Δp/p of thebeam from the gun is ranging from maximum momentum
Pmax =1.77MeV/c to almost 0MeV/c. By using
momentum slit put on the downstream of the gun, Δp/p
will be selected to be less than 2%. From Fig.4, one cansee the beam extracted from the gun has bunch length ~5ps (full width) within momentum spread Δp/p=2%.

5

4

3

2

1

0
50

100

150

200

250

300

350

Table 2: Parameters of the rf gun and the extracted beam
for simulation

400

wavelength λ [μm]2. 5 1017

1

2 1017

0. 8

1. 5 1017

0. 6

1 10170. 4

5 10160form factor

dN/dωdΩFigure 2: Spectrum of undulator radiation from single
electron (θ=0)

0. 2

0

50

100

150

200

250

300

350

0
400

wavelength λ[μm]Figure 3: Spectrum of coherent undulator radiation at
Ne=1.25x108 electrons/bunch, σt=100fs, θ=0 (red) andbunch form factor σt=100fs(blue)

AN INJECTOR FOR VERY SHORT
BUNCH

rf gunMax electric field of 1st cell E1st
Max electric field of 2nd cell E2nd
phase difference between cells
current density at cathode(φ1.75)
electron beam at the rf gun exit
maximum momentum Pmax
energy spread Δp/p(full width)normalized emittance εnTwiss parameter (β,α,γ)momentum[MeV/c]

0

25 MV/m
50 MV/m
18 deg
50 A/cm2
1.77 MeV/c
2%0.77πmmmrad(1.11,1.21,2.22)

1.77
1.765
1.76
1.755
1.75
1.745
1.74
1.735
1.73

471

472

473 474 475 476 477
Arrival time at RF gun exit(ps)Figure 4: Longitudinal phase space distribution (FDTD
simulation)

ITC RF Gun

Magnetic Bunch Compressor

The ITC rf gun has two cells with a very low coupling,or independent cells as its name indicates. There are two
rf input ports at each cells to feed the rf power from a
klystron. By changing each input power of two cells andphase difference between cells, longitudinal andtransverse phase space distributions at the gun exit can becontrolled.
In order to generate low emittance beam with sufficientbeam current, the cathode should have small radius andcan produce high beam current. Consequently a single
crystal LaB6 cathode with the diameter φ1.75mm has beenchosen.

As shown in Fig.4, the relationship between momentum
and time (=longitudinal position) is almost linear. Usuallyan α-magnet is used to bunch compression for athermionic rf gun injector [4]. For our gun, a bunch
compressor with the Triple-Bend-Achromat (TBA) likelattice has been designed. In addition, a set of sextupole
magnets is installed in this bunch compressor.
Consequently, this bunch compressor has properties 1) By
two sets of quadruple magnets between bends, transfer
matrix R56 can be changed to fit various (Δp/p)/Δt, 2) By a
set of sextupoles, 2nd order dispersion function can be

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controlled. Especially it is difficult to obtain latter featurefor α-magnet.
By the accelerator design code SAD[5], the optics ofthe bunch compressor is designed and shown in Fig.5.

Δp/p

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0.01

0.005

0

β function[m]

3

B

B

SD

0.35

QF1

QF2

0.3

B

SD

2

QD1

1.5

β

-0.01

QD2

QD2

QD1

η

0.2

0.5

β
0

-0.015-5-5-5-5-0.0001 -8 10 -6 10 -4 10 -2 10

0.15

x

y

1

0.4

0.8

-5

z[m]

0.05
x

1.2

1.6

2

2.4

0

Using the result of FDTD simulation, tracking simulationin the bunch compressor was done by SAD. In thistracking, the space charge effect is not considered. The
tracking result of longitudinal phase space distribution
with/without sextupoles is shown in Fig.6, 7 respectively.
From tracking results, bunch lengths σt were obtained
43fs, 38fs respectively. One can also see the 2nd orderdependence can be compensated by sextupoles. It was
confirmed that this injector can generate very short bunchless than 100fs.
Δp/p

2 10

Figure 7: Longitudinal phase space distribution after
bunch compressor with sextupole magnet

Figure 5: the optics design of bunch compressor

0.01

0.005

0

-0.005-0.01-0.015-5-5-5-5-0.0001 -8 10 -6 10 -4 10 -2 10

0

-5

2 10

z[m]

Figure 6: Longitudinal phase space distribution after
bunch compressor without sextupole magnets

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0.1

s[m]

478

-0.005

0.25

2.5

0

x

QF2

QF1

η [m]

3.5

PERFORMANCE MEASUREMENT OF
ITC RF GUN PROTOTYPE
The prototype of ITC RF-gun had been manufactured andbasic parameters of rf cavities were measured. Results areshown in Table 3.
Table 3: Cavity parameters of ITC RF-gun prototype

resonant freq.( f 1 , f 2 )coupling( β1 , β2 )Unloaded Q ( Q1 , Q2)( R/Q1, R/Q2)(2810.81, 2825.36)GHz( 2.3, 3.4 )( 9984, 9600 )( 117, 129 )Ω

As shown in Table 3, resonant frequencies of each cells
is different from design frequency 2856MHz. From the 3dimentional electromagnetic field calculation code
Microwave-Studio[6], it was found that this frequency
shift is caused by the effect of the coupling port between
waveguide and cavity. The amount of shift is consistent
with the Microwave-Studio’s prediction.
Using a bead perturbation method, electric field
distribution along the beam axis was measured. In Fig.8, ameasured result is shown. The electric field distribution
calculated by SUPERFISH is also shown.
A result of the electric field distribution is consistent
with SUPERFISH calculation. R/Qs in Table 3 are
calculated using measured data shown in Fig.8. From
SUPERFISH, R/Qs are predicted to be 98.2Ω, 114.6Ω
respectively and consistent with measurements.
In these measurements for the prototype, we confirmedthat basic parameters of the rf gun are consistent withSUPERFISH’s prediction except for resonant frequencies.
The resonant frequencies can be predicted by 3-Delectromagnetic field calculation including rf coupling
ports. Now we have designed a modified ITC RF-gun.

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Proceedings of FEL 2007, Novosibirsk, Russia

results of beam parameters. The design of bunch
compressor strongly depends on input beam parameters.
We will compare with our simulation code and othercommercial codes such as General Particle Tracer (GPT)[7]. At the present, the tracking simulation in the bunch
compressor is not included space charge effects. We will
investigate whether that space charge effects don’t affectto the beam in the bunch compressor.
Additional optimization of the bunch compressor isneeded to have wide capability to fit various input beam
parameters.
The prototype ITC rf gun has been manufactured andparameters of the cavity also has been measured. Frommeasurements for rf properties, cavity performance canbe predicted by using calculation code. We have been
designing the modified ITC rf gun.

12
1st cel l measur ed
2nd cel l measur ed
1st cel l SUPERFI SH
2nd cel l SUPERFI SH

10
8
6
4
2
0
-2

0

2

4

6

8

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10

z[cm]

Figure 8: The electric field distribution (circle: results ofbead perturbation methods. line: SUPERFISH
calculation)

SUMMARY
An intense coherent terahertz light source using
undulator radiation has been designed. In order to obtaincoherent terahertz radiation, it is important to generate
electron beam with very short bunch σt < 100fs. To
realize such a short electron beam, the injector which
consists of the ITC rf gun and the magnetic bunch
compressor has been developed. From numericalcalculation, it has been turned out that the injector can
generate electron beam with very short bunch length σtaround 50fs. Since it is difficult the beam simulation
including space charge effects in low energy region suchas the inside of gun, an initial small fluctuation affects

REFERENCES[1] H. Hama et al., New Jour. of Phys. 8(2006) 292[2] Alexander Wu Chao and Maury Tigner, ”Handbookof Accelerator Physics and Engineering”,World
Scientific 1999
[3] H. Hama et al., Nucl. Instr. and Meth. A 528 (2004)
371[4] H. A. Enge, Rev. Sci. Instrum. 34 (1963) 385; M.
Borland,”A High-brightness Termionic Microwave
Electron Gun”, Ph.D. Thesis, Stanford University,
1991[5] http://acc-physics.kek.jp/SAD/sad.html[6] http://www.cst.com/Content/Products/
MWS/Overview.aspx[7] http://www.pulsar.nl/gpt

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CHARACTERISTICS OF SMITH-PURCELL RADIATION FROMDIFFERENT PROFILE GRATINGS*
G. Naumenko#, B. Kalinin, G. Saruev, NPI, Tomsk, Russia
D. Karlovets, Yu. Popov, A. Potylitsyn, L. Sukhikh, V. Cha, TPU, Tomsk, Russia
Abstract

INTRODUCTION
Smith-Purcell radiation (SPR) is widely considered as
the spontaneous mechanism for FEL (for example[7]). In
recent experiments [1,2], the possibility of creating a
monochromatic radiation source of the THz range on thebasis of the Smith-Purcell radiation (SPR) has been
demonstrated. The SPR from low relativistic electrons is
also used in orotrons. For the nonrelativistic electronenergies ( Ee ≤ 100kev ), the approach developed byvan den Berg [3,4] ensures a reasonable agreement withexperiment [5,6]. In [8] the different models for SPR
characteristics calculation were compared for highrelativistic electrons. There was shown that thepredictions of most models differ by approximately 2orders of magnitude for the electrons with energy ∼20
MeV [9] and by several orders for the electron energies
Ee=855 MeV [10]. The available experimental results do
not provide an ultimate conclusion on the validity of oneof these models.
We distinguish two types of periodic targets, which canbe used to generate the SPR: “Volume” gratings (alamellar grating (Fig. 1) and a grating which consist of aperiodic set of conducting strips separated by vacuumgaps) and “Flat” gratings (consisting of separate
conducting strips having the thickness essentially smaller
than a wavelength).
The coherent Smith-Purcell radiation (CSPR) emitted
from the first-type targets with different profile wasstudied experimentally by several experimental groups([11, 12]). However, all these works differ in the applied
methods. On the other hand, it was shown in works [13,1] that flat targets are more effective in order to obtain an
intensive monochromatic radiation. Therefore, the directcomparison of the measured characteristics of radiationfrom these targets is difficult. That is why the research of
the CSPR characteristics from the targets of different
types but under similar conditions is desirable.

* The work was supported by the Ministry of Education and Science ofRussian Federation [project no. 2.1.1.889 “Development of ScientificPotential of Higher School (2006-2008)”].
#
Naumenko@npi.tpu.ru

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MODELS
There are few theoretical models to calculate the SPR
characteristics for the different grating profiles. We
consider here three models: van den Berg's (vdB) model[3] (applicable for volume gratings), surface current(SC) model [14,15] (the SPR is considered as aradiation generated by the current induced by the field ofa particle moving in vacuum close to a perfectconducting periodic surface), and resonant diffraction
radiation (RDR) model [16] (for gratings consisting of
infinitely thin perfect conducting strips separated by
vacuum gaps).

Comparison of models for thin strips grating
We use for calculations the formulas from [8] for thecase Φ = 0 (see Fig. 1)

Fig. 1. Scheme of the Smith-Purcell radiation generation
The calculations (Fig. 2) were made for the Lorenzfactor γ = 12 and the grating period d = 8 mm.
10-6
10-7

dW1 ⎛ eV ⎞⎜⎟d Ω ⎝ sr ⎠γ=12, Φ=0, h=10 mm
d=8 mm, a=4 mm

10-8
10-9

Experiment

To choose the most effective grating the absolutecoherent SPR characteristics were measured on the 6.2
MeV electron beam. Gratings with lamellar, triangularand so-called “flat” gratings were studied. It was shown
the grating consisted of the conductive strips is more
preferable target for SPR generation.

10-10
10-11
10-12
10-13
10-14
10-15
10-16
20

40

60

80

100

θ(deg)

120

140

160

Fig. 2. Angular distribution of the SPR intensity for a flat
grating according to the RDR model (red solid line),surface current model (blue a dashed curve) and for van
den Berg's model (green dash-dotted line, b/d = 0.001).
We can see from the Fig. 2 a large discrepancy between
radiation yields obtained using these three models.

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH055

d 2WSP ( λ , h,θ )⎛ λ ⎞Y ( h,θ , σ z ) = N 2 ⋅ ∫ f z ⎜ ⎟ ⋅ ∫d Ω ⋅εd λd Ω
⎝σz ⎠ ΩΔλ2

SPR from different type structures
Let us compare the angular distribution of thecalculated SPR intensity from different gratings
according to the van den Berg's model (Fig. 3): for a
volume grating with vacuum gaps and strips 4 mm
thick and a for flat grating with b/d=0 . 001. One may
see from the Fig.3 that the intensity of the SPR froma "thick" grating is by 2 orders of magnitude greater.

( λ )d λwhere Wsp(λ,h,θ) is the intensity of incoherent SPR, ε(λ)
is the spectral efficiency of a detecting system.

EXPERIMENTAL SETUP AND
TECHNIQUE
Electron beam

4e-8

dW1 ⎛ eV ⎞⎜⎟d Ω ⎝ sr ⎠The experiment was carried out on the extracted
electron beam of the microtron of the Tomsk Institute for
the Nuclear physics.
The scheme of the the experimental zone setup waschanged depending on a problem statement (see Figs 5,6).
The beam parameters are given in Table 1.
Table 1: Electron beam parameters

γ=12
d=8 mma=4 mmh=1 mm

3e-8

2e-8

1e-8

0
0

20

40

60

80

100

120

140

Θ(deg)

Fig. 3. Angular distribution of the SPR intensity for a flat
grating (blue solid line; is multiplied by 10) and for a
volume grating (red dashed line).

Coherence
Let’s consider the approximation for the case when thesize of an electron beam is much smaller than the impact
parameter h. In this approximation in terms of the SmithPurcell geometry longitudinal and transverse distributionsof electrons in a bunch are factorized, which enables one
to extract the longitudinal and transverse geometric formfactors of a bunch in the form of separate factors. In thiscase only the longitudinal form-factor plays the essential
role (see [17]).
The typical dependence of the longitudinal form-factor
via the wavelength for the normal (Gauss) distribution ofelectrons in a bunch is shown in Fig. 4.

Electron energy
Macro-pulse duration
Pulse repetition rate
Micro-pulse length
Number of electrons per
micro-pulse
Number of micro-pulses per
macro-pulse
Beam size at the microtron
outputEmittance: horizontal
vertical

6.1 MeV≈4 ms
1 – 8 Hz
≈6mm
108
104
4 ×2 mm23⋅10-2 mm×rad
1.5⋅10-2 mm×rad

Detector
To register the radiation within a millimeter
wavelength range the authors applied the roomtemperature detector operating on the basis of abroadband antenna supplied by a high-frequency diode.
The latter was produced at the Institute for Semiconducting Devices (Tomsk, Russia). The main
parameters of the detector for room temperature are:wavelength range: Δ λ = 3 ~ 20 mm,
sensitivity = 0.3 V/mWatt

Techniques for angular measurements
Cut-off filters cutting passage of the radiation with thewavelengths, exceeding the critical length λ C , were used.

Fig.4 The Dependence of the squared form-factor moduleon the radiation wavelength for the normal longitudinal
distribution of electrons in a bunch with bunch length σz.
The registered emission of radiation in the wavelength
range Δλ may be written as:

To compare our data with the theoretical calculations
obtained using the classical models we should be sure thatthe obtained experimental results correspond to the farzone approximation. In paper [18] it was shown that theeffect of pre-wave zone may be suppressed while
applying the parabolic optics, when a detector is placed in
the focus of a parabolic reflector. For this purpose theparabolic reflector with diameter equal to 140 mm and the
focal distance equal to 430 mm was used during theexperiment.
The scheme for the azimuth angular dependence
measurements is presented in Fig. 5

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Proceedings of FEL 2007, Novosibirsk, Russia

EXPERIMENTAL RESULTS

The scheme of the of radiation intensity dependenceson the polar angle measurements is shown in Fig. 6.
Detector together with the parabolic reflector was fixed
on a radial rod, which rotated around the target at theangle θ.

160
140

P (Watt/steradian)Fig. 5. Experiment scheme for azimuth dependences
measurement

The measurements of the azimuth angular intensity
distributions of the CSPR were made with thearrangement presented in Fig. 5 when the value of thepolar observation angle was equal to θ = 130º, whichcorresponds to the wavelength of SP radiation λ = 13.2
mm. Fig. 7 presents the azimuth angular distribution of
the CSPR from a flat target 1 with the use of the two cutoff filters having the critical wavelength λc=14 mm and
λc=17.5 mm. The value of Φ = 0 corresponds to thedirection in the plane which is perpendicular to the target
plane. The measurements with the use of cut-off filterswith λc < 14 mm give the values which practicallycoincide with the background.

Targetθ

Faradaycup

λc=17.5 mm

120
100
80
60

λc=14 mm40
20

Detector

f=151mm

0
-30

-20

-10

0

10

20

30

Φ (degree)licabo
Par irrorm

Fig.6. Experimental scheme for the angular dependences
measurement

Fig.7. Azimuth CSPR distribution from the target 1 withdifferent cut-off filters.
The absolute azimuth intensity distribution of the CSPR
from targets 1, 2, 4 with different profiles for λc=17.5 mm
is presented in Fig. 8.

Targets

160

Table 2. Target parameters (size unit is mm)
P (Watt/steradian)

1. Flat thin target

Target 1
h=7.5 m m

140
120
100
80

Target 4
h=7 m mTarget 2
h=6 m m60

2. Flat volume target
40
20

3. Lamellar grating

4. Grating with triangularprofileIn the experiment the characteristics of the radiationfrom both volume and flat targets were studied. The
parameters of the targets used are given in the Table 2.

FEL Technology II

482

0
-30

-20

-10

0

ϕ (degree)

10

20

30

Fig.8. Azimutal CSPR distribution from flat and volume
targets for λс=17.5mm.
The azimuth intensity distribution of the CSPR withdifferent values of the impact-parameter (Fig. 9) shows
the principle influence of the impact-parameter value.
The measurements of the dependences of the CSPR
intensity on the value of the polar observation angle werecarried out according to the scheme shown in Fig. 6 withthe value of the azimuth angle equal to Φ=0.

Proceedings of FEL 2007, Novosibirsk, Russia

assert as for the maximum efficiency of flat conducting
thin-stripped targets (Table 3).
Comparing the absolute experimental data from Table
3 with the theoretical predictions (Fig. 2) ascertain that
the RDR and SC models .

70

P (Watt/steradian)60

h=7m m50

40

h=27m m30

REFERENCES

20

10

0
-40

-30

-20

-10

0

10

20

30

ϕ (degree)

Fig.9. Azimutal CSPR distribution from target 4 fordifferent values of impact-parameter and λс=17.5mm
The radiation cutting off across the wavelength wasprovided by a cut-off wave-drive with λc=17.5 mm todecrease the background contribution from a RF systemof an accelerator. The typical CSPR intensity dependence
via the polar observation angle for h=7 mm is shown in
Fig. 10.
140
120

P (Watt/steradian)

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100
80
60
40
20
0
80

90

100

110

120

θ (degree)

Fig.10. Polar dependence of CSPR from flat target 1

Discussion
Suppression of the pre-wave zone effect by means ofwave optics on this experiment enables one to compare
the obtained experimental results with the conclusions of
the SPR theory in the far zone (Table 3).
Table 3: Target efficiency (experiment)
CSPR density dW dΩTargetWatt sreV sr per electron

1. Flat thin target
2. Flat thick target
3. Volume target withsquare profile
4. Volume target withtriangular profile

0.153
0.039

and per period
4.8⋅10-9
1.2⋅10-9

0.012

0.37⋅10-9

0.029

0.9⋅10-9[1] Yukio Shibata, Shigeru Hasebe, et. al., Phys. Rev. E
57, 1061 (1998).
[2] S.E. Korbly, A. S. Kesar, J.R. Sirigiri, and R. J.
Temkin, Phys. Rev. Lett. 94, 054803 (2005).
[3] P.M. van den Berg, J. Opt. Soc. Am. 63, 1588 (1973).
[4] P.M. van den Berg, J. Opt. Soc. Am. 63, 689 (1973).
[5] A. Gover, P. Dvorkis, and U. Elisha, J. Opt. Soc. Am.
B 1, 723 (1984).
[6] Y.N. Adischev, A.V. Vukolov, D.V. Karlovets,
A. P. Potylitsyn, and G. Kube, Pis'ma Zh. Eksp. Teor.
Fiz. 82, 192 (2005) [JETP Lett. 82, 174 (2005)].
[7] H. Backe, W. Lauth, H. Mannweiler, et. al., in NATOWorkshop ‘‘Advanced Radiation Sources and Applications’’ (Springer, New York, 2006), pp. 267-282.
[8] D. V. Karlovets* and A. P. Potylitsyn, Phys. Rev. ST
AB 9, 080701 (2006)[9] A.S. Kesar, Phys. Rev. ST Accel. Beams 8, 072801(2005).
[10] G. Kube, H. Backe, H. Euteneuer, et.al.,
Phys. Rev. E 65, 056501 (2002).
[11] D. С Nguyen, Nucl. Instrum. Methods Phys. Res.,
Sect. A 393, 514 (1997).
[12] S.E. Korbly, W.J. Brown, M.A. Shapiro, and R. J.
Temkin, in Proceedings of the Particle Accelerator
Conference, 2001, Chicago, USA (IEEE, New York,
2001), pp. 2347-2349.
[13] A. Doria, G. P. Gallerano, E. Giovenale, G. Messina,
G. Doucas, M. F. Kimmitt, H.L. Andrews, and J. H.
Brownell, Nucl. Instrum. Methods Phys. Res., Sect.
A 483, 263 (2002).
[14] J. H. Brownell, J. Walsh, and G. Doucas, Phys. Rev.
E 57, 1075 (1998).
[15] J. H. Brownell and G. Doucas, Phys. Rev. ST
Accel. Beams 8, 091301 (2005).
[16] A. P. Potylitsyn, Nucl. Instrum. Methods Phys.
Res., Sect. B 145, 60 (1998).
[17] A. N. Aleinik, A. S. Aryshev, B. N. Kalinin, G. A.
Naumenko et.al, JETP Letters, 76, 6,(2002), p. 337.
[18] B. N. Kalinin, G.A. Naumenko, A.P. Potylitsyn,
G.A. Saruev,L. G.Sukhikh, and V.A. Cha, JETP
Letters, 84, 3, (2006), p. 110.
[19] J.H. Brownell, J. Walsh, G. Doucas, Phys. Rev. E
57 (1998)1075.
[20] A.P. Potylitsyn, Phys. Lett. A 238 (1998) p.112.

On the coherency conditions the CSPR is observed in
the range of polar angles exceeding 100º (see Fig.10). The
measured azimuth distribution of the targets having a
different profile under similar conditions enables us to
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Proceedings of FEL 2007, Novosibirsk, Russia

GAIN AND COHERENCE ENHANCEMENT OF SASE FEL USING LASERPREBUNCHED ELECTRONS
Yen-Chieh Huang and Chia-Hsian Chen, Institute of Photonics Technologies, National Tsinghua
University, Hsinch 30013, Taiwan
Wai-Keung Lau and Gwo-Huei Luo, National Synchrotron Radiation Research Centre, Hsinchu
30076, Taiwan
Abstract~ ω pb / N pb , which, for a large number of periodic electron

We conduct a simulation study on the acceleration of
periodically loaded electrons in a 6-MeV photocathodeelectron gun driven by a laser beat wave with a beatfrequency of 4.35 THz. The density modulation of theelectrons is well preserved during particle acceleration.
The periodically bunched electrons are then injected intoa single-pass free-electron laser to quickly generate a few
tens of kW electron superradiance at 63.5 μm.

bunches, could be much narrower than the intrinsic
spectral linewidth of a radiation device governed by(dW dω )1 . Therefore, a self-amplified spontaneousemission (SASE) free-electron laser (FEL) is expected tohave enhanced gain and coherence when driven by aperiodically bunched electron beam. Since electrons are
discrete particles, the term Mb(ω)Mpb( ω), describing thedegree of electron bunching at the frequency ω, issometimes called the electron bunching factor.
Previously we have proposed the use of a laser beatwave to excite periodic emissions of electrons from thephotocathode of an electron accelerator [2]. In this paper,
we study a THz single-pass FEL driven by such a laserbeat-wave (Labew) photocathode accelerator. The system
configuration of this study is depicted in Fig. 1, consistingof two major components, a RF photocathode gun and asolenoid-derived wiggler. The periodically bunchedelectrons are excited by a laser beat wave at the cathode,accelerated by a 1.6-cell S-band accelerator, and directly
injected into a solenoid-derived wiggler to generate theelectron superradiance.

INTRODUCTION
It is well known that, if the electron bunch length issignificantly shorter than the radiation wavelength, thespectral power of the electron radiation is proportional to
the square of the electron current or to the square of thetotal number of electrons participating in the radiation
process. This coherent radiation is dubbed as electron
superradiance.
To facilitate the discussion, we briefly describe in thefollowing the theory of electron superradiance based on
Gover’s formulation [1]. In general, the spectral energy of
the radiation from an electron bunch with a bunch length
τb and an electron number Nb is expressed by the equation(dW d ω )SR = N b2 (dW d ω )1 M b2 (ω ) ,(1)

where (dW/d ω)1 denotes the spectral energy emitted froma single electron with W being the radiation energy and ω
being the angular frequency of the radiation, Mb(ω) is theFourier transform of the electron pulse-shape function
with a unitary peak amplitude. If the radiating electron
beam contains Npb such electron bunches repeating at a
rate ωpb / 2π , the total radiated spectral energy becomes( dW dω )SR, pb =,2
Nb2 N pb
( dW dω )1 M b2 (ω )M pb2 (ω)
where
2
M pb
(ω ) =

Figure 1: The system configuration for studying a THz
superradiance FEL driven by a Labew photocathode gun.
(2)

sin 2 ( N pbπω / ω pb )2
N pb
sin 2 (πω / ω pb ),(3)
is the coherent sum of the radiation fields from all the
micro-bunches and has a unitary peak amplitude at thefrequencies ω = m ωpb (m = 1, 2, 3…). For a short electron
bunch, M b2 (ω ) is usually a broad-band function. The
spectral linewidth of M pb2 (ω ) at ω = mω pb is given by
FEL Technology II

484

Labew PHOTOCATHODE GUN
In this section, we study the acceleration of periodicallybunched electrons in the BNL/UCLA/SLAC 1.6-cell Sband photocathode electron gun [3] by using the spacecharge tracking code ASTRA [4]. We operate the gun at apeak acceleration gradient of 140 MV/m. The electrons
are emitted from the photocathode with a radial
distribution within a 0.75-mm rms radius. For the firstcase in our simulation, we emitted a total of 1-nC
electrons uniformly distributed over 10-ps duration. For
the second case in our simulation, we equally divided theProceedings of FEL 2007, Novosibirsk, Russia

Table 1. Output beam characteristics for single-bunch
acceleration and periodic-bunch acceleration. The two
sets of parameters are nearly identical.

number of macro-particles

-4

10

rms
beam
radius10

6.3 MeV

3.6%

2.8 π-mmmrad

1.3
mm

10

3.9%

2.6 π-mmmrad

1.3
mm

-5

(a)

10

10

10

10

20
0
-0.5

0

0.5

1

1.5
z (mm)

2

2.5

3

100

(b)

60
40
20
0

0.5

1

1.5
z (mm)

2

2.5

0

2

4

6

8

10

12

14

12

14

bunching frequency (THz)

40

0
-0.5

-3

10

rms
emittance

60

80

-2

10

rms
energyspread

6.3 MeV

(a)

-1

10

rms
beam
energy

100
80

0

10

bunching factor

number of macro-particles

Singlebunch
acceleration
Periodicbunchacceleration

The degree of electron bunching can be better
described from the magnitude of the bunching factor⎜Mb( ω)Mpb( ω)⎜. We plot is Figure 3 the values of⎜Mb( ω)Mpb( ω)⎜ versus frequency before and after theacceleration of the periodically loaded beam. It is seen in
Fig. 3(a) that the periodic bunches are nicely loaded at
4.35 THz at the cathode. In Fig. 3(b), the redistribution of
the particles at the gun output causes some frequency
broadening and magnitude reduction to the bunching
factor. The fundamental frequency of the peak bunchingis also shifted from 4.35 THz to 4.72 THz. Neverthelessthe bunching factor is slightly reduced from 0.6 to 0.2 at
the fundamental bunching frequency. In the next section,
we show the importance of this bunching factor whendriving a THz superradiance FEL.

bunching factor

1-nC charges into 44 micro-bunches over the same 10 psduration. The micro-bunch separation is set to be six
sigma of the Gaussian bunch length. For both cases,
14080 macro-particles were used in the simulations. The
output beam parameters for the two cases are listed inTable 1. Although the essential beam parameters of themacro pulses at the gun exit are nearly identical for bothcases, the longitudinal micro-structures of the electrons
for the two cases are very different. Figures 2(a) and (b)show a comparison between the longitudinal distributionsof the accelerated single electron bunch and theaccelerated periodic electron bunches, respectively. The
longitudinal distribution of the single-bunch beamremains more or less uniform after acceleration, whereasthat of the periodically bunched beam shows
redistribution of electrons after acceleration. Although theleading part of the periodically loaded beam retains
periodic bunching, the trailing part has no apparent
bunching features. The particle redistribution is due toboth the space charge field and the acceleration field
during the acceleration process.

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3

Figure 2: The electron distributions at the exit of thephotocathode gun (a) for single-bunch acceleration and(b) for periodic-bunching acceleration.

0

-1

(b)

-2

-3

-4

0

2

4

6
8
10
bunching frequency (THz)

Figure 3: The bunching factor of the periodically loaded
electron beam (a) before and (b) after acceleration in thephotocathode gun. The space charge field and theacceleration field redistribute the electrons during
acceleration and result in frequency broadening andmagnitude reduction to the bunching factor.
SUPERRADIANCE FEL
The FEL wiggler in our choice for our simulation is a
staggered-array solenoid-derived planar wiggler [5].
Among several advantages of using such a wiggler, thesolenoid field is important for confining the low-energy
electron beam. The system parameters chosen for our
simulation study are: wiggler period = 1.5 cm, peak
wiggler field = 7.2 kG., and solenoid field = 7.5 kG. For
the 6.3 MeV driving beam, the synchronism wavelengthof the FEL radiation is 63.5 μm.
We simulated the FEL power growth as a function of
the wiggler length in the computer code GENESIS [6].
We use the Labew-gun beam parameters from ASTRA as

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the input beam parameters for the FEL simulation in
GENESIS. To see the influence of the initial bunching,
we varied the bunching factor when simulating the FEL
performance. Figure 4 shows the FEL powers as afunction of the wiggler length for initial bunching factorsof 0, 10-8, and 2×10-2. To our surprise, the typical
exponential growth of the (SASE FEL power is not seenin the range of our simulation study. With the zerobunching factor, the FEL gain is too low to build up the
FEL power. However, for a strong initial bunching, theFEL power flats out at a high value almost immediately.
This phenomenon suggests a strong superradiance
process.

Figure 4: FEL power versus wiggler length with initialbunching factors = 0, 10-8, and 0.2. With the 0.2 bunching
factor, the FEL power quickly builds up to tens of kW.

the balance between the debunching force from the spacecharge field and the bunching force from the radiation
field. The space-charge induced debunching becomessignificant for a low energy beam and is not commonly
seen for a short-wavelength SASE FEL. Without initialbunching, it is unlikely for the single-pass THz FEL
power to grow to an appreciable value.
CONCLUSIONS
An single-pass FEL driven by laser-prebunchedelectrons can be a promising radiation source. We
simulated the performance of a Labew photocathode gun.
With 44 periodic Gaussian bunches loaded at the cathodeover 10 ps, the bunching factor of the 6.3-MeV output
beam is slightly reduced from an initial value of 0.6 to 0.2
at the fundamental bunching frequency. The debunchingis a consequence of the redistribution of electrons under
the space charge force and the acceleration force.
By using the beam parameters generated from the gun
simulation, we simulated the performance of a single-pass
FEL radiating at the fundamental bunching frequency of
4.72 THz. The laser pre-bunched beam promptly
generates tens of kW radiation power in the single-pass
FEL. This quick generation of the FEL power suggests
the potential of implementing an ultra-compact FEL byusing the Labew accelerator technology. Our study also
shows that it is unlikely to build a single-pass FEL byusing such a low-energy driving beam without initialbunching, because the strong space charge force prevents
the electrons from forming micro-bunches.
This work is supported in part by National Science
Council under Contract NSC 95-2112-M-007 -027 -MY2
and by National Tsinghua University under Code
96N2534E1.
REFERECES[1] Avi Gover, “Superradiance and stimulatedsuperradiant emission in prebunched electron-beamradiators. I. Formulation”, Phys. Rev. ST AB, 8,030701 (2005).
[2] Y. C. Huang, “Laser-beat-wave bunched beam for

Figure 5: The variation of the bunching factors in the
wiggler for the three initial bunching values, 0, 10-8, and2×10-2. The space charge force in the low-energy beam
tends to debunch the electrons.
Figure 5 shows the variation of the electron bunching
factors in the wiggler for the three initial bunching values,
0, 10-8, and 2×10-2. It is interesting to see that thebunching factor does not increase over the wiggler length
as usually seen in a SASE FEL, but tends to settle to asteady-state value despite of strong initial bunching. For
example, the initial bunching factor 0.2 is reduced toabout 10-3, although the FEL power quickly reaches a few
tens of kW. The steady-state bunching value is a result of
FEL Technology II

486compact superradiance sources,” International Journalof Modern Physics B, Vol. 21 Issue 3/4, p277-286(2007).
[3] D. T. Palmer, X. J. Wang, I. Ben-Zvi, R. H. Miller,“Beam dynamics enhancement due to accelerating
field symmetrization in the BNL/SLAC/UCLA 1.6
cell S-band photocathode RF gun,” Proceedings of theIEEE Particle Accelerator Conference, Vol. 3, V. 3, p.
2846-2848 (1997).
[4] K. Floettmann, ASTRA User Manual,
http://www.desy.de/~mpyflo/Astra_dokumentation/.
[5] Y.C. Huang, H.C. Wang, R.H. Pantell, J. Feinstein,
and J. Harris "Performance Characterization of a Far
Infrared, Staggered-array Wiggler", Nucl. Instrum.
and Methds, A341, 431-435 (1994).
[6] S. Reiche, GENESIS User Manual,
http://pbpl.physics.ucla.edu/~reiche/

Proceedings of FEL 2007, Novosibirsk, Russia

WEPPH058

APPROACHES IN MODELLING A WAVEGUIDE RF-LINAC THz-FEL
Yu. Lurie , Y. Pinhasi, Ariel University Center of Samaria, Ariel, Israel
M. Tecimer, NHMFL / Florida State University, Tallahassee, FL 32310, USA
Abstract
A widely used approach in describing radiation fields
generated by short pulse rf linac FEL oscillators is basedon modal expansion of the intracavity fields and solving
the wave equation for the amplitudes of the excited transverse cavity eigenmodes, in time and axial dimension. In
this time domain approach, mode amplitudes are calculated
by adopting the slowly varying envelope approximation
(SVEA). The longitudinal propagation numberof thecarrier wave is usually assumed to represent a group velocity and a wave impedance of the frequencies encompassed
within the spectral bandwidth of the optical pulse envelope
as it evolves within the interaction region. However, incases where dispersive effects arising from a waveguided
cavity become influential, the space-frequency approach isa straightforward method to tackle the problem without introducing further approximations. One such case is being
studied based on a highly slippage dominated short pulse
rf-linac FEL operating at long wavelengths.

INTRODUCTION
The aim of this paper is to present numerical design
tools for investigating the temporal and spectral characteristics of THz pulses generated by short pulse rf-linac based
waveguided FEL oscillators. We demonstrate applicationof these numerical tools on the design study and parameter
optimization of a THz FEL system that is expected to operate over a frequency range between 100-1100 microns [1].
Combination of effects resulting from the use of picoseconds short electron pulses and long radiation wavelengths
spread over such a wide spectral range on the one hand andpropagation of short radiation pulses in lengthy waveguideresonators (as required in most of the rf-linac driven FELs)
on the other hand, necessitate a careful analysis of the interplay between enhanced coherent spontaneous emission(CSE), waveguide dispersion (group velocity dispersion),slippage and cavity desynchronisation effects. In devising
the numerical design tool, we adopt space-frequency approach [2, 3] which enables a correct description of theseeffects but it is time consuming when simulating an oscillator FEL configuration. On the other hand, employing an
additional formalism to model the relevant aspects of the
problem in an approximated way while creating practicalmeans in terms of cpu usage. The former rigorous formalism is used to validate the application range of the latterin tackling the design problem with a reasonable accuracy
and replace it in cases of shortcomings in modelling properly the physics of the above mentioned THz FEL system.

ylurie@yosh.ac.il

The two methods presented in the paper are contemplated
for the design study of the planed wide spectral range, longwavelength, short pulse waveguide THz-FEL oscillator.
Sample results are given applying the developed formalisms on a highly slippage dominated FEL regime wheresubmillimeter to millimeter wavelength radiation is generated by a few picoseconds long high peak current electron
bunches.

DESCRIPTION OF THE MODELS
Time domain model
The time domain approach presented here and the implemented numerical algorithm is described in details in[4, 5]. Several assumptions are adopted in the model that
reduce greatly the computational effort in order to enable
an optimization of the system parameters. The longitudinal motion of each macroparticle is tracked whereas thetransverse motion is accounted for by the beam envelope
equations [4]. The latter includes the influence of 3D beameffects in an averaged manner. The profile of the opticalfield is defined by the transverse modes that are excitedin a parallel plate (PP) waveguide resonator [5, 6]. The
evolution of the mode amplitudes is governed by Eq. (1)where, by adopting SVEA and introducing
the transformations     and     , the inhomogeneous
wave equation simplifies into:    

!#"%$'&)( - .
/*  ,+ 0 .


12 !   45 3       

6 798 ;: =<>?A@BDC=EGF H 8 ;: =<(1)

In (1)    is the complex envelope of a modulatedwave  train with carrier? frequency and axial wavenumberof the excited I ’th mode, which satisfy the waveguidedispersion relation. J !    is the ponderomotive phase.
The longitudinal distribution of the(;particles
is representedMN O.
5  
5  by the term     , where  KL  
3denotes the number of particles within a fraction of the radiation period allowing for a more accurate description of
CSE effects when the current profile of the electron bunch
varies significantly at the scale of the radiation period [5].
The source term is averaged over
the associated subwaveO "length long beam segment . is the filling factor. 2 !   results from averaging the source term over the transverse
gaussian density profile of the electron beam. For the caseof a parallel plates (PP) waveguide it can be expressed by

FEL Theory

487

WEPPH058

Proceedings of FEL 2007, Novosibirsk, Russia

the analytical term:

2 !    @QP

R ST%UV 

W @EX#Y#Z=[]\@E_^#XY#Z=[a` Space-frequency model for FEL oscillators
(2)

T
UV
and
with
the parameters b , , c and J defined in [5].
Ud
are the rms transverse dimensions of the beam, determined by solving the beam envelope equations in terms of
the longitudinal position  [4].
Due to the waveguide dispersion, slippage effects inshort pulse waveguide FELs exhibit differences in comparison to open resonator FELs. The slippage length egf / forthe resonant radiation wavelength hi is defined as:Yo  9qr j .9st .
54j

Kp

egf / hilknm%
(3)
o 
54j
where
and
are the number of the wiggler periods
and the cutoff wavenumber of the I ’th transverse mode,
respectively.
The boundary conditions for the transverse modes are
imposed by the resonator and can be formulated as follows:<<
8 u!v <
 Gw w t  4yxD#  {z 8 t z 8 .
8 <8 < @9C H w w 8  < 8 u <1 >   e j #Gi  (4)Gt w w~Gw G. w~:Gw }||
8u < jwhere    e #G  denotes the complex amplitude of the? at the pass
I ’th
? mode at the exit of the interaction region
L and Gi eg K _i is the cavity round-trip
number
time.
<
8 <
8
Gw wGw describeszsignifies reflectivity of the mirrors.
|
modes conversion, cavity losses and outcoupling.
The group velocity dispersion effects might influence
the dynamics of the FEL amplification process in multiple round-trips. The inclusion of group velocity dispersion
into the time domain model requires the solution of thesecond order wave equation [7]. In the presented model,
the quadratic term associated with the group velocity dispersion is omitted in the waveguide dispersion relation
as a consequence of SVEA. Instead, the dispersion is allowed for in an approximate manner in the model. Usinga Fourier series expansion (FSE), the complex field amplitude    is expressed, at each pass, at the end of
the FEL interaction in terms of longitudinal eigenmodes* M
K Gi andof the cold cavity with the respective -  + !~- . Each  ’th longitudinal mode propagates with theown !~-  over the dispersive feedback section. Prior
entering the interaction region,the fieldB amplitudes of thelongitudinal modes are summed (FSE t ) to yield the updated ! xD#  which encompasses the effect of groupvelocity dispersion over the “drift” section in the preceding
round-trip. Subsequently, starting the new round-trip, theprocedure is repeated within the interaction region, after
carrying out many integration steps in solving the first orderwave equation as described in Eq. (1). Although the outlined algorithm makes use of the longitudinal cavity modes
in representing the complex field amplitude !   , itcircumvents to reformulate the wave equation (1) for theamplitudes of the longitudinal modes and spares solving alarge number of coupled axial mode equations.
FEL Theory

488

Assuming a uniform cross-section resonator (usually awaveguide), the total electromagnetic field at every plane can be expressed in the frequency domain as a sum of aset
  ! of transverse (orthogonal) eigenfunctions with profiles
#  [2, 3]. At the beginning of a round-trip number L ,eachof the modes is assumed to have an initial amplitude< 8 u  xD  and the total field at x is given by:<<>  8 u     !
  8 u 
#QxD  
xD 
(5)
# 


j
At the end of the interaction region 4ye , the field is:<<>@ v C= 7 H 8 <D  8 u  j    
  8 u j 
#Qe   
e  
# 

(6)
The amplitude of the I th mode
excitedbytheelectron<
8 u 
beam with current density
#Q  is given by:<< 8 u  j  8 u  
m
1

e 

xD 
*9 
D

  8 u <@BDC= 7 H 8 <¡ #Q      # 

(
+



(7)

where the normalization of the mode amplitude is made

via the complex Poynting vector power  [3]. The spectral density of the energy flow after the interaction with theelectron beam at the L th round-trip is:¢ 8 u <<e j >
 8 u  j  . me   *¥¤§¦ ¨
(8)
£
£
£
£
£
£
After a round-trip in the resonator of length eg , the fieldat the entrance of the interaction region is [8]:<<> G8 wu!v      w   8 u!v tt
#Q4yxD
xD 
#  
Gw



>

>
Gwª©« Gw w

z  w  ww<
@ v C= 7 H w 8 <®
  8 wu w  j e  n¬­  w  # (9)where z GwGw w is a complex coefficient, expressing the intermode field reflectivity of transverse mode I  to mode I ,due to scattering of the resonator mirrors or any other passive elements in the entire feedback  loop. Scalar multipli
cation of both sides of Eq. (9) by   #  , results in theinitial mode amplitude:
<
<
<®
>
  8 u!v   G8 wu w  j  @ v C= 7 H 8
#


w
w
t xD  
z
e  
(10)
Gw w
which is required in equation (7) to solve the field excitedin the consecutive round-trip. In the frequency domain, theProceedings of FEL 2007, Novosibirsk, Russia

Table 1: Operational parameters of THz-FEL.

0.035

WEPPH058

Nrt=1 (spontaneous emission)f = 282.7 GHz
s

N =2
rt

THz FELh¯mm)xx%° m±Ua´  Nm)x]²m)³ MeV µ·¶  ¯yxD¸ ³ %U¹   Nºµ·m)¶ ³» pC
 ºm¸ x'²³D¸ » ps
23.6 MHzSjh N µ·¶ x mm (hybrid.)S yxD¸ ²³D¸ ½
¼ 
54j
¾x
S
Rectangular1 ( ³ 1 m)x mm. )or PP2 waveguide ( m)x mm)

Resonator roundtrip length:

Nrt=5
N =35
rt

Bunching Factor

PARAMETER
Wavelength:
Beam energy:
Energy spread:
Bunch charge:
Pulse length:
Repetition rate:
Wiggler period:
Wiggler:Number of periods:
Waveguide:

0.03

0.025

0.02

0.015

0.01

0.005

0

0

50

100

150

200

250

300

z [cm]

Figure 2: Evolution of the bunching factor along the wiggler for different oscillator round-trips.

¿]ÀyÁD¸ ³» m

SIMULATIONS
total out-coupled radiation obtained at the oscillator out5
put after round-trips is composed of a summation of thecirculated fields (6) inside the resonator: Â &)Ä 
Ã



 

>


ÆÅ

>

6

u!Ç

<
@ v C= 7 H 8 <D  8 u  j    !


(11)
e

#


(

where  is I th mode field transmission of the out-coupler.
ÅThe energy spectrum of the electromagnetic radiation ob5
tained at the output after round-trips is given by:¢Â &)Ä  5



>

ºÈ

6

.
<
 8 u  j m¤ ¦ ¨ (12)e   £ * §
(
£ u!Ç
£
£
£
£
£
£
£

 £

>

where  ÊÉ  É . is the power transmission coefficient ofÅÈmode I .

−5

5

x 10

4.5

d W/d f [pJ/GHz]

4
3.5
3
2.5
2
1.5
1
0.5
0
260

265

270

275

280

285

290

295

300

Frequency [GHz]

Figure 1: Spontaneous emission spectrum.

(
To simplify the analysis, single transverse mode Ë'± t is
assumed in the simulations. Operational parameters of thesystem is given in the table 1. Drive electron bunch con*sists from short Ë ÍÌÎ¸ ps bunches with Gaussian longitudinal distribution and with an energy-phase correlation
similar to the ones considered in [9, 10]. Figure 1 demonstrates spectrum of spontaneous emission obtained in thefrequency domain by the WB3D code [3, 8]. The simu5
lations were carried out with / Ïm)xxx macroparticles;
the resulted spectrum
was thennormalized to the number
5 @5 ´of electrons
¹ K  /  in the simulation (see [11]for8 details).
The power of spontaneous< emission is Ðf / <Ñ Ä 8Â f Ä/
Ñ Ä Â f Ä/KÒ f / ¯»r¸ »l° W, where¯ÊxD¸ » fJ is the totalenergy flux of spontaneous emission
foundby integration(jjof the spectrum, and Ò f / ªe K
e K _i ¯ªxD¸ mm ns
is the slippage time.
The following results relate to FEL oscillator configuration, based on a train of bunches with repetition rate ofabout 23.6 MHz.
Ô Ä F 8 =2< shows evolution of the bunching@ C jQFig.

factor Ó  along the wiggler as function ofoscillator round-trip number. At the first round-trip, spontaneous emission takes place. At this stage, the intensityof the radiation is rather low and variations in the bunching
factor are mainly due to the initial energy-time correlationin the electron bunch. At further round-trips, the emitted
field causes additional bunching in the electron beam.
Evolution of the stored intracavity energy during thefirst round-trips is presented in Fig. 3. Fabry-Perot resonator lineshape is also drawn for the comparison. The*Ät Ú
free-spectral range is ÕlÖØ×Ù¯¯³D¸ Á MHz, where*Gi·eg K _i§¯¾ ¸ ¾ ns is the round-trip time. The fullwidth half-maximum of the transmission peaks is givenè é byÑºÛÜÕÞÝ¥á ßà ¯âxD¸ Á» MHz, where ãäæågB ç è é t S³ÁD¸ x is the Finesse of the resonator (êªÉ zÉ . yxD¸ ¾ is thetotal round-trip power reflectivity). The oscillator energy
buildup is shown in Fig. 4.
1 Simulations carried out in the time domain model.
2 Simulations carried out in the space-frequency approach.

FEL Theory

489

WEPPH058

Proceedings of FEL 2007, Novosibirsk, Russia[4] G.H.C. van Werkhoven, Dissertation, TU Eindhoven (1995)
Fabry−Perot
Nrt=1

2

10

[5] M. Tecimer, Dissertation, Tel Aviv University (2004)

Nrt=2[6] L.R. Ellias and J.C. Gallardo, Appl. Phys. B 31 (1983) 229.

dW/df [nJ/GHz]

Nrt=3
Nrt=5

[7] N. S. Ginzburg et al., “Dispersion effects in short pulse
waveguide FEL”. Proc. of the 28th International FEL Conf.,
2006, Berlin, Germany, p. 378.

N =10

1

10

rt

0

[8] Y. Pinhasi, Y. Lurie, A. Yahalom, Nucl. Instr. Meth. Phys.
Res. A 528 (2004) 62.

10[9] A. Doria et al., Phys. Rev. Lett. 80 (1998) 2841.

−1

10

274.55274.6

274.65274.7[10] Yu. Lurie and Y. Pinhasi, Phys. Rev. ST Accel. Beams 10(2007) 080703.

274.75f [GHz][11] Y. Pinhasi, Yu. Lurie, Phys. Rev. E 65 (2002) 026501.

Figure 3: Oscillations build-up at the first round-trips.
Evolution of the radiation build-up process when thebunches with uncorrelated energy spread are injected wasconsidered in the time domain model. Comparison of results of Fig. 4 and 5 reveals significant reduction of opticalpulse energy at the last case. The difference is explained by
the enhancement of coherent emission due to energy-phasecorrelation, as described in [10].






 

 






þÿ 






ú û üý

CONCLUSIONSö ÷ øù

In the paper we presented two approaches for simulating excitation and buildup of FEL radiation in an oscillator configuration. Using the models, a study of a FEL operated at the sub-millimeter wavelengths was carried out.
The models consider dispersion effects in the waveguidewhen a highly slippage radiation pulses are excited by atrain of short electron bunches produced by rf-linac.

ì í~í

î~ïï

ð~ññ

òóó

ôõõ

 !#"%$!&  ' ()"*)+-,.
/10 2

m n o p7m o-q
gUh i j7k i-l
a\b c d7e c-f
wxyuv

Z\[ ] ^7_ ]-`r st

REFERENCESë

SUT V W7X V-Y[1] M.Tecimer et al., “A design study of a FIR/THz FEL forhigh magnetic field research”. Proc. of the 28th International
FEL Conf., 2006, Berlin, Germany, p. 327.

Q%R Q
35476987:9;=<?>7@BA C=CED F GEH I=JEK L7MEN O7P
z7{}| ~ | -%#  #~ #

[2] Y. Pinhasi, V. Shterngartz and A. Gover, Phys. Rev. E 54
(1996) 6774.

 ¶\· ¸ ¹7º ¸!»[3] Y. Pinhasi, Yu. Lurie, A. Yahalom, Phys. Rev. E 71 (2005)
036503.

¯\° ± ²7³ ´!µ©\ª « ¬7­ «!®
ÁÂÃ
¿À

0

¼ ½¾

tot

W

7 ¡7 !¢%  7 !
% 


−2

10

−3

10

0

5

10

15

20

25

30

35

40

Number of round−trips

Figure 4: Evolution of the total stored intracavity energy.
FEL Theory490£7¤ ¥ ¦7£ §!¨

−1

10

w

( z = L ) [µJ]

10

=
 7
Ä=ÅÆ Ç ÈÆ È-É%Ê#Ë ÌÍ Î#Ç È#Ï#Ð =

Figure 5: Evolution of the intracavity optical pulse energy
with round-trips, and the radiation power shape at small
signal gain (a) and at the beginning of the exponential gain(b) regimes, respectively (time domain simulations with an
uncorrelated Gaussian beam energy spread).

Proceedings of FEL 2007, Novosibirsk, Russia

THAAU01

EXPERIENCE AND PLANS OF THE JLAB FEL FACILITY AS A USER
FACILITY*
Michelle D. Shinn # , Thomas Jefferson National Accelerator Facility, 1200 Jefferson ave., Newport
News, VA 23606, USA
Abstract

Jefferson Lab’s IR Upgrade FEL building wasplanned from the beginning to be a user facility, andincludes an associated 600 m2 area containing sevenlaboratories. The high average power capability(multikilowatt-level) in the near-infrared (1-3
microns), and many hundreds of watts at longer
wavelengths, along with an ultrafast (~ 1 ps) high
PRF (10’s MHz) temporal structure makes this laser aunique source for both applied and basic research. In
addition to the FEL, we have a dedicated laboratory
capable of delivering high power (many tens ofwatts) of broadband THz light. After commissioning
the IR Upgrade, we once again began delivering
beam to users in 2005. In this presentation, I will
give an overview of the FEL facility and its current
performance, lessons learned over the last two years,
and a synopsis of current and future experiments.

INTRODUCTION
The Free-electron laser (FEL) User Facility at
Jefferson Lab (JLab) saw first light in 1998, and ran
as a User Facility from 1999-2001. We thendecommissioned our first FEL, the IR Demo, so we
could install the IR Upgrade, which had almost anorder of magnitude higher output and a larger tuning
range. We once again began providing light to users
in 2005. Previous reports [1,2] provide details of theuniqueness of the FEL driver accelerator, so this will
be touched on only briefly. Along with the capabilityof the IR Demo to produce high average power, areother unique properties for a laser source (evencompared to other FELs) in the mid-IR. To exploit
the IR Demo the building that houses it was designed
to be a user facility. An earlier report [3] gave someof the details of the facility while it was being built.
This paper updates the current status of the facility,
including measured values of the laser output, anddiscusses some of the infrastructure needed to run auser facility efficiently and safely. We then consider
some of the interesting applied and basic researchwhich is being done, and conclude with future plans
for the facility.
________________________________*Work supported by the Commonwealth of Virginia and DOE
Contract DE-AC05-06OR23177#
shinn@jlab.org
Notice: Authored by Jefferson Science Associates, LLC under U.S.
DOE Contract No. DE-AC05-06OR23177. The U.S.
Government retains a non-exclusive, paid-up, irrevocable,
world-wide license to publish or reproduce this manuscriptfor U.S. Government purposes.

THE IR UPGRADE FEL
The Electron Accelerator
The driver accelerator of the IR Upgrade FEL uses
SRF accelerator technology consisting of a 10 MeV
injector (containing a DC photocathode gun driven bya Nd:YLF laser) and a SRF linac (whose total
accelerating voltage may be as high as ~ 150 MeV) to
produce an electron beam with an average current of~ 10 mA at a PRF of 74.85 MHz. More than one
percent of the electron beam power is converted tooutcoupled laser radiation.
The beam is thentransported back through the linac where it isdecelerated and most of the kinetic energy increase
due to the linac is converted back into RF power.
The use of an energy-recovering linac (ERL) greatly
reduces the utility demands and installed RF powerand has an added benefit that the waste beam isdumped at an energy below the giant photonuclear
resonance threshold, eliminating activation of thebeam dump.
This type of FEL was first demonstrated at theJefferson Lab in the spring of 1999 and, its design
and performance has been the subject of a number of
papers. [4,5] The FEL is housed in the vault of theuser facility [3] and has delivered several thousand
hours of laser beam time to users. Given our desire
to develop the FEL as an industrial tool, a generous
amount of this beam time was delivered to users
working on potential industrial applications. [6,7]The advantage of ERL FELs is the ability to scale
the output power to very high levels, many 10’s of
kW in the IR, without greatly increasing the spacerequired to house it. This is because the FEL output
power scales with electron beam power, which can bevaried either with electron beam current or energy.
Another advantage is the ability to lase at
wavelengths that aren’t accessible with conventionallaser sources and at higher output powers. A
disadvantage is that FELs are larger and more
complex than conventional laser sources, however, anindustrial version could be built which is morecompact, and we have already demonstrated highavailability (approaching 95% over 80 hours).

FEL operation

491

THAAU01

Proceedings of FEL 2007, Novosibirsk, Russia

Figure 1 Layout and purpose of user labs in the JLab FEL Facility

The Optical Cavity and Transport
The optical cavity of the FEL is based on a nearlyconcentric resonator design of 32.016m length.
Mirrors for up to 4 different wavelength regions canbe installed in the mirror vessels; operators can
switch wavelengths, and be lasing again in about 15
minutes. Some of the design features of the cavity
are available in another publication [8].
Currently, the IR Upgrade currently uses apermanent magnet, variable gap wiggler. The highest
output at several wavelengths is shown in Table 1.
Outcoupling is through a partially reflecting cavity
mirror, where it is then collimated and transported
upstairs first into the room where the optical
diagnostics are located, and then onto the User Labs.
(Fig. 1)
Diagnosis and beam delivery are
simultaneous, only ~0.05% of the laser power isdelivered to the diagnostics, giving us the ability toprovide realtime information on power, wavelength,
and pulselength to our users.
Table 1: IR Upgrade FEL Output Power at several
wavelengths.
Average Power (kW)Wavelength (μm)
1.1
2.2
1.6
14.3
2.8
6.7
All mirrors in the cavity and transport are watercooled to minimize thermally-induced surface
aberrations that would degrade the wavefront, andshielded to minimize absorption of stray light on themounting hardware that cause beam steering.
Presently, all mirrors in the transport are silicon withprotected silver coatings. The choice of metal
coatings allows us to transport the wide tuning rangeof the IR Upgrade without changing mirrors. Whenlasing on the fundamental, the FEL still produces
harmonics with powers in the μW to mW range,
which can be used as probes or for alignment
FEL operation492

purposes. A down side to this choice of coating is theloss of ~ 25% of the laser output to absorption andscatter. The beam is transported in a high vacuum (at~ 10-7 Torr), to avoid absorption by the atmosphere.
In order to send beam into any one lab there is amirror cassette, an assembly containing mirrors on alinear translation stage. Currently, every mirror
cassette contains a metal reflector, eventually two
more mirrors will be added, each with dielectric
coatings for higher reflectivity at a particular
wavelength. There is also a home position, where thebeam traverses the cassette without intersecting amirror The mirror cassette diverts the beam into a
short line containing an insertable mirror that directs
the beam into a water-cooled dump; this serves as alocal shutter for the user. When withdrawn, the beamthen exits into the lab through a calcium fluoride or
fused silica Brewster window.

The THz Beamline
As shown in Fig. 1, there is a THz lab located near
the center of the laboratory area. As discussed
elsewhere [9,10] we take advantage of themultiparticle coherence of our electron beam to
extract broadband radiation in the THz region of thespectrum and transport it into a lab. The lower power(~ 100 W) of the THz beam makes it unnecessary tocool the optics in the beamline. Transport is also in
vacuum, with a diamond window placed at a point
where the beam is imaged to a waist, and is thus
small. From there the beam continues in vacuum, but
at a higher pressure (mTorr) than the initial part ofthe beamline. The beam exits into a hutch within thelab through a second diamond window, where it can
travel through evacuated chambers containing theexperiment, or in air.

Laser Personnel Safety System (LPSS)
Transport of a beam with such high power requires
safety procedures and controls to protect personnel aswell as equipment. This was implemented throughProceedings of FEL 2007, Novosibirsk, Russia

PLC-based hardware (with status passed to thecontrols software) to prevent inadvertent transport ofbeam into an area that has not been properlyinterlocked. Several different modes exist. For
delivery of the FEL to a lab, either the entire lab can
be interlocked (exclusionary mode) or the experimentis enclosed in an interlocked hutch (hutch mode).
When a lab’s LPSS in made up, a maglock energizes.
Entry (when permitted) is by a “smart card” systemthat allows access only to personnel and users that areaware of the FEL and other hazards in a particularroom.
Recognizing that for many types ofexperiments, e.g., pump-probe, alignment is criticaland difficult to optimize remotely, we have defined astate of operation known as “alignment mode”. In
this mode, the accelerator is locked into a state where
the laser produces a low duty factor pulsed beam
operating at 2 Hz with a pulsewidth of 250 μsec.
During this time users can be in what normally beconsidered an exclusionary lab, or a user can be in thehutch. In the usual mode of operation, known as“laser permit”, the lab is “swept”, that is, checked tomake sure that all personnel are outside the lab before
the interlocks are engaged. Failure of an interlock
causes the lab to become safe, inserting the local
shutter, an intracavity shutter to prevent lasing, andsetting the mirror cassette to the home position.
However, the accelerator remains on. This allows us
to maintain stable operations and more quickly
resume lasing after the problem is corrected.
Most labs also have Class 4 laser systems in them,capable of operating without the FEL. To allow FEL
beam delivery to one lab, and use of a laser system inanother lab, we have a “local laser” mode, whereby
the lab must still be swept and the interlocks madeup. However, FEL beam delivery is prevented inseveral ways.
FEL operators and users receive formal training,
through documentation and a walk-through by theLaser Systems Supervisor for the FEL. They are thengiven a test that must be passed before their badge
allows them into the lab they will be working in.
FEL operators are trained for all labs.

THAAU01

exposure to the beam. This latter document isevaluated by the laboratory safety professionals andan experiment cannot proceed without their approval.

APPLICATIONS
Ablative processing of materials
Carbon nanotubes are increasingly utilized invarious technologies. Demand for the single-wallvariety is such that the price for high-quality material
is currently about $500/gm, with pure material priced
at over $2K/gm [11]. Current techniques produce
about 0.2 gm/hr. [12] In comparison, worldwide
demand is of order of thousands of kilograms
annually. [13]. Using the IR Demo FEL anddelivering an average power of about 300 W onto thetarget, researchers obtained yields of 1.5 gm/hr, farhigher than competing techniques. [14] Work to
optimize yield and dimensions have continued using
the IR Upgrade FEL delivering about 1 kW of 1.6 μm
light into the reactor.
The processing of nonmetallic materials was alsostudied with the IR Demo FEL. One study [15],showed the benefits of wavelength tunability. In thisinvestigation polyimide (DuPont Kapton HN100)
was irradiated at two wavelengths, 3.1 μm (offresonance) and at 5.8 μm (on-resonance). Processing
at the shorter wavelength, where the material wastransparent, resulted in blackening of the material, asign that the polymer has been thermally degraded.
Tuning the laser to the longer wavelength resulted incleanly-drilled holes, indicating the processing was
nonthermal. This “cold-cutting” mode exhibited by
IR FELs has been noted in earlier studies [16],enabling PLD of polymers.

Surface Processing
Besides
ablative
processes,
thermal(orphysiochemical) processes can be employed toperform surface modifications. No material is lost,
merely melted and then resolidified, or while quite
hot, transformed by oxidation, nitriding, orFacility Administration
Formal training of staff and users is just one facetof the administration of a user facility. We havemodeled our procedures on those in place at thevarious synchrotron light sources in the UnitedStates; these have an experience based on over two
decades of operations. Potential users must submit arequest for beam time that is then reviewed externallyby a Program Advisory Committee (PAC) andinternally for feasibility. If accepted, users must
submit two other forms that state what beam
conditions and, possibly, changes to the hardware orsoftware that they require, and, an evaluation of any
hazards associated with the experiment, e.g., solvents
used, or toxic materials produced as a byproduct of

Fig. 2 Formation of dendrites of δ-TiNx after bursts of
FEL irradiation at 3.15 microns. From Ref 19

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Proceedings of FEL 2007, Novosibirsk, Russia

carburization. An example which is familiar to manyis the application of titanium nitride (TiN) on tool
bits. This gives the bit a distinctive gold color. TiN
is also used to improve the biocompatibility and wear
characteristics of replacement joints [17]. In a seriesof papers, P. Schaaf and coworkers from the
University of Göttingen have published the results forthe nitriding of Ti metal with the FEL. The FEL wasoperated at 3 μm, usually in a burst mode (alsoknown as a macropulse). Compared to other types oflaser nitrided titanium, the FEL-produced material
had a thicker and harder coating [18]. This appears tobe due to the formation of oriented (200) dendrites of
δ-TiNx, as shown in Fig. 2. While one might thinkthat this would result in a rough surface, in fact it isfairly smooth. [19]Medical Applications
With the wavelength and timing flexibility of the
IR Upgrade FEL, it is natural to use it in medical
applications. One such application is known as
selective photothermolysis, the selective heating oftissues with light.
By carefully choosing awavelength in the near infrared, researchers targeted
lipid-rich cells and heated them preferentially without
heating the surrounding tissue. This study [20] paves
the way for a laser treatment of acne, a condition
where a sebaceous gland is producing too much lipid.
Only the over-active glands, located a few
millimeters under the surface of the skin are killed by
the absorption of light, leaving the other cells
unaffected. This technique also shows promise in thetreatment of atherosclerosis, which if left untreatedleads to heart disease and stroke.

THz Applications
The spectral region covered by THz radiation,roughly 1 mm to 0.1 mm in wavelength, is absorbed
by transitions between electronic states and/or
vibrational states in matter. Because these states are
specific to a particular molecule, or ion,
spectroscopy, either in the time domain, or in thefrequency domain can be used for location andidentification. This makes the use of the THz regionof the spectrum attractive for applications such as
medical imaging or hazardous material detection andnondestructive testing. While the list of applications
is long, progress from the lab to the field has beenhampered by the lack of high average power (several
watts) sources. The THz source at JLab, is capable ofproducing high power, broadband, ultrashort pulsed
radiation to evaluate the utility of some of theseapplications. It was recently used to make full-field
video-frame rate images of a moving object [21]. We
anticipate exciting results from the research occurringin this lab.

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494

LESSONS LEARNED
While one might think that the user experiments
occurring over the last two years were simply acontinuation of the IR Demo user runs, with few new
lessons to learn, in fact, that wasn’t the case. The IR
Upgrade was built in part to make it more attractive
to users. And, we took the lessons learned from thefirst several years of operation to improve how wetreated beam delivery to the labs, particularly in theuse of hutches. By housing experiments in a hutch,
the users are in close proximity to their hardware,
making interfacing and sample changes far easier.
Since the hutch eliminates the need to wear laser
safety eyewear while the experiment is underway,
we’ve found that users prefer this mode of operation.
The preplanning of an experiment that is necessitatedby the proposal and approval process encourages a lotof dialog between the users and members of the
facility. This lessens the amount of time lost because
the experiment isn’t ready, time that is particularly ata premium when the users have come from a distanceand have a well-defined period during which theirexperiment is supposed to run.
Ultimately, when running a user facility, whatmakes it work is the attitude and aptitude of the staff.
The operators of the FEL are also its builders, andthus can respond to requests for unusual modes ofmachine operation.

CONCLUSIONS
Since the last paper on the JLab FEL User Facility[3], there have been a number of improvements to thefacility over and above the upgraded IR FEL. In
addition to outlining some of these improvements,
I‘ve highlighted some applications and experimentsthat an ERL-based FEL enables more readily thanother lasers. Even then, this is merely a sampling;
space does not permit me to discuss all theapplications currently envisioned for an IR FEL,
much less one that operates in the UV. Indeed, theprevailing view is that the best application for a FEL
has yet to be found.

ACKNOWLEDGEMENTS
I’d like to acknowledge my colleagues in the FEL
Division at Jefferson Lab, whom I have had theprivilege to work with. I would also like to thank ourusers for sharing their results and enthusiasm forworking at our facility

REFERENCES[1] C. L. Bohn, et al, "Performance of the Accelerator
Driver of Jefferson Laboratory's Free-Electron
Laser," Proceedings of the 18th Particle Accelerator
Conference (PAC 99), New York, NY, March 29April 2, 1999.

Proceedings of FEL 2007, Novosibirsk, Russia[2] G. R. Neil, et al., “Sustained Kilowatt Lasing in a
Free-Electron Laser with Same-Cell Energy
Recovery,” Phys. Rev. Lett. 84 (2000) pp 662-665.
[3] M. D. Shinn, et al., “The Jefferson Lab FEL User
Facility,” in Laser-Induced Damage in Optical
Materials: 1999, Gregory Exharos, Arthur Guenther,
Keith Lewis, M. J. Soileau, Editors, Proceedings of
SPIE 3902, (2000) pp. 355-360.
[4] Christopher Behre, Stephen Benson, George Biallas,
James Boyce, Christopher Curtis and Others, “First
Lasing of the IR Upgrade FEL at Jefferson Lab”,
Nuclear Instruments & Methods in Physics Research,
A528, (2004) pg 19.
[5] G. R. Neil, C. Behre, S. V. Benson, M. Bevins, G.
Biallas, J. Boyce, J.Coleman, L.A. Dillon-Townes, D.
Douglas, H. F. Dylla, R. Evans, A. Grippo, D. Gruber,
J. Gubeli, D. Hardy, C. Hernandez-Garcia, K. Jordan,
M. J. Kelley, L. Merminga, J. Mammosser, W.
Moore, N. Nishimori, E. Pozdeyev, J. Preble, R.
Rimmer, M.Shinn, T. Siggins, C. Tennant, R. Walker,
G. P. Williams, and S. Zhang, "The JLab High PowerERL Light Source", Nuclear Instr. & Methods A557
(2006) pg 9.
[6] M. D. Shinn, “High Average Power Free-Electron
Lasers - A New Laser Source for Materials
Processing,” in High Power Laser Ablation, Claude
A. Phipps, Editor, Proceedings of SPIE 4065, (2000)
pp 434-440.
[7] G. R. Neil, “Applications for Energy Recovering
Free-Electron
Lasers”,
paper
MOZBC03,
Proceedings of the 22nd Particle Accelerator
Conference (PAC07) Albuquerque, NM, June 25-29
2007.
[8] M. D. Shinn, G. R. Baker, C. P. Behre, S. V. Benson,
M. E. Bevins, L. A. Dillon-Townes, H. F. Dylla, E. J.
Feldl, J. F. Gubeli, R. D. Lassiter, F. D. Martin, and G.
R. Neil “Design of the Jefferson Lab IR Upgrade FEL
Optical Cavity,” Nuclear Instruments and Methods
A507, (2003) pp 196-199.
[9] G.P. Williams, “Far-IR/THz radiation from theJefferson Lab FEL Energy Recovered Linac”, Rev.
Sci. Instr. 73 (2002).1461.
[10] G.L. Carr, M.C. Martin, W.R. McKinney, K. Jordan,
G.R. Neil and G.P. Williams, “High Power Terahertz
Radiation from Relativistic Electrons”, Nature 420(2002) pp 153-156.

THAAU01[11] See Carbon Nanotechnologies Inc. web site:
http://www.cnanotech.com/pages/store/60_online_store.html .
[12] M.W. Smith, private communication 2003.
[13] J. Ouellette, “Building the Nanofuture with Carbon
Tubes,” The Industrial Physicist 8(6) 2002 pp18-21.
[14] P.C. Elkund, B.K. Pradhan, U.J. Kim, Q. Xiong, J.E.
Fischer, A.D. Friedman, B.C. Holloway, K. Jordan,and M.W. Smith, “Large-Scale Production of SingleWalled Carbon Nanotubes Using Ultrafast Pulses
from a Free Electron Laser,” Nanoletters 2, (2002) pp
561-566.
[15] M. Kelley, “Surface processing and micromachiningof polyimide driven by a high average power infrared free electron laser”, Mat. Res. Soc. Symp. (2000)
pg 617.
[16] D. Bubb et al, “Resonant infrared pulsed-laser
deposition of polymer films using a free-electron
laser”, J. Vac. Sci. Tech A19 2001 pp 2698-2702.
[17] E. Carpene, P. Schaaf, M. Han, K.-P. Lieb and M.
Shinn, “Reactive Surface Processing by Irradiation
with Excimer Laser, Nd:YAG Laser, Free-Electron
Laser and Ti: Sapphire Laser in Nitrogen
Atmosphere” Applied Surface Science 186 (2002) pp
195-199.
[18] E. Carpene, M.Shinn, and P. Schaaf, “Synthesis ofhighly oriented TiNx coatings by free-electron laser
processing of titanium in nitrogen gas”, Appl. Phys.
A247, (2005) pp 307-312.
[19] P.Schaaf, M. Shinn, E. Carpene, and J. Kaspar,“Direct Laser Synthesis of functional coatings by
FEL treatments”, Proceedings of the Third Intl WLTConf on Lasers in Manufacturing, (2005) pg 399.
[20] R. Rox Anderson, William Farinelli, Hans Laubach,
Dieter Manstein, Anna N. Yaroslavsky, Joseph
Gubeli III, Kevin Jordan, George R. Neil, Michelle
Shinn, Walter Chandler, Gwyn P. Williams, Steven
V. Benson, David R. Douglas, H.F. Dylla, “Selective
photothermolysis of lipid-rich tissues: A free electron
laser study”, Lasers in Surgery and Medicine 38,(10),pp 913-919[21] J. Michael Klopf, Matthew Coppinger, Nathan
Sustersic, James Kolodzey, and Gwyn P. Williams,“High-Power Terahertz Source Opens the Door for
Full-Field Video-Rate Terahertz Imaging”, preparedfor Nature.

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Proceedings of FEL 2007, Novosibirsk, Russia

EXPERIMENTAL STUDY OF VOLUME FREE ELECTRON LASERUSING A ”GRID” PHOTONIC CRYSTAL WITH VARIABLE PERIOD
V.G.Baryshevsky, N.A. Belous, A.A. Gurinovich, V.A. Evdokimov,
P.V. Molchanov ∗ , A.V. Oskin, P.F. Safronov
Research Institute for Nuclear Problems, 11 Bobryiskaya str., 220050, Minsk, Belarus
Theory of VFEL with spatially variable period was deAbstract
Experimental Study of Volume Free Electron Laser witha ”grid” resonator (”grid” photonic crystal) with changing
in space parameters are reported.

INTRODUCTION
Generators using radiation from an electron beam in aperiodic circuit (traveling wave tubes [1,2], backward wave
oscillators, free electron lasers) are now widespread [3].
All the above devices use one-dimensional feedback,which is formed by either two parallel mirrors placed on
the both sides of working area or a diffraction grating.
But there are some challenges that restrict applicationsof such devices: electrical endurance of resonator limits
radiation power and current of acceptable electron beam.
Conventional waveguide systems are essentially restrictedby the requirement for transverse dimensions of resonator,
which should not significantly exceed radiation wavelength.
The indicated problems can be overcome by the aidof volume (non-one-dimensional) multi-wave distributed
feedback [4–10]. New type of radiation generators using
volume multi-wave distributed feedback was called Volume Free Electron Laser (VFEL). Transverse dimensionsof VFEL resonator could significantly exceed radiation
wavelength. The electron beam and radiation power are
distributed over the large volume that is beneficial for electrical endurance of the system.
One of the VFEL types uses a ”grid” photonic crystal
that is formed by a periodically strained either dielectric or
metallic threads, which provides to weaken requirements
for beam guiding.
The ”grid” structure of dielectric threads was experimentally studied in [11], where it was shown that such”grid” photonic crystals have sufficiently high Q-factor(104 − 106 ).
Theoretical analysis [12, 13] showed that periodic metal
grid does not absorb electromagnetic radiation and the”grid” photonic crystal, made of metal threads, is almost
transparent for the electromagnetic waves in the frequency
range from GHz to THz. (In this range the skin depth δ isabout 1 micron or less for the most of metals (for example,
for 10 GHz δCu = 0.66 µm, δAl = 0.8 µm, δW = 1.16
µm and so on). Thus, in this frequency range the metallic
threads can be considered as perfect conducting.)∗ molchanov@inp.minsk.by

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496

veloped in [16, 17]. There it was shown that use of photonic crystal with variable period could provide significant
increase in radiation output. It was mentioned that diffraction gratings (photonic crystal) can be used for creation the
dynamical wiggler with variable period in the system. This
makes possible to develop double-cascaded FEL with variable parameters changing, which efficiency can be significantly higher that of conventional system.
In the present paper experimental study of Volume Free
Electron Laser with a ”grid” resonator (”grid” photonic
crystal) with changing in space parameters are considered.

EXPERIMENTAL SETUP
The ”grid” photonic crystal is built from tungsten threads
with the diameter 0.1 mm strained inside the rectangular
waveguide with the transversal dimensions a = 35 mm,
b = 35 mm and length 300 mm (see Fig.1). A pencillike electron beam with the diameter 32 mm, energy up to
200 keV and current about 2kA passes through the above
structure. The magnetic field guiding the electron beam is∼ 1.55−1.6 tesla. Period of ”grid” photonic crystal is chosen to provide radiation frequency ∼ 8.4 GHz. The ”grid”

Figure 1: The ”grid” diffraction grating placed inside thewaveguidestructure is made of separate frames each containing thelayer of 1, 3 or 5 parallel threads with the distance between
the next threads dy = 6 mm). Frames are joined to get the”grid” structure with the distance dz between layers.
Frequency range is evaluated by means of tunablewaveguide filters, which were tuned in the band 7.8 - 12.4
GHz with passbands 0.25 GHz, 0.5 GHz and 1 GHz. Attenuation of radiation in the suppressed band of this filter

Proceedings of FEL 2007, Novosibirsk, Russia

THAAU03is ∼ −25 dB.
Evaluation of ”grid” heating by electron beam action
provides to expect long-time stability. For example, changeof the thread temperature (tungsten threads of 100 µm diameter) due to action of the 250 keV electron beam withdiameter 32 mm, current 1 kA and pulse duration 100 nsec
can be estimated as ∆T < 125◦ . Experiments with VFEL
with the different ”grids” have demonstrated stability ofdeveloped photonic crystals to heating caused by electron
beam action.

EXPERIMENTAL RESULTS
In the experiments [14] generation in the ”grid” VFEL
was observed in BWO regime.
The sample oscillogram is shown in Fig.2, where signals
marked 1 and 2 are the signals obtained from microwave
detectors. Other two curves are the electron gun voltage
and electron beam current. Time scale is 80 ns.

Figure 2: The sample oscillogram
The radiation power is measured for photonic crystal
with 4, 6, 10, 12, 14 and 22 frames (period dz = 12.5mm) each containing five threads distant dy = 6 mm eachfrom other.
The result of these measurements is presented in Fig.3,
where the radiation power is normalized to the maximal detected power (10 kiloWatt). Dependence of the generated
radiation intensity on the ”grid” photonic crystal length isobtained. The solid curve in this figure shows the numerically simulated radiation power, which also normalized. It
can be seen from this Figure that for the photonic crystal
with more than 14 periods (∼ 3 · λ ) saturation is reached.

Figure 3: Dependence of the generation intensity on thelength of the ”grid” photonic crystal with 5 threads in theframe marked with squares and numerically simulated dependence of the wave amplitude on the ”grid” photonic
crystal length for the electron beam with the energy ∼200
keV and current density ∼ 2 kA/cm2
The next experiment uses ”grid” resonator made of two
photonic crystals with different periods. The ”grid” structure is made of separate frames each containing the layerof 5 parallel threads with the distance between the next
threads dy=6 mm), 12 frames were joined to get the ”grid’
photonic crystal with the period 12.5 mm and another 12
frames formed ”grid’ photonic crystal with the period 10.5mm . Total resonator length is 300 mm (the same as in theprevious experiment). Separate experiments with the first
photonic crystal (period 12.5 mm, 12 frames) were done
to determine how the electron beam energy reduces after
passing it. Period of the second photonic crystal is chosen
to provide for the electron beam, which have lost part of its
energy for radiation in the first photonic crystal, the sameradiation frequency. Distance between two photonic crystals is 25 mm. The typical oscillogram for this experimentis shown in Fig.4.
Two radiation peaks are apparent in this oscillogram.
Measurements of radiation frequency gives value close to
8.4 GHz for both peaks. Their intensities are also comparable and detected power is almost twice higher then that for
the experiments with ”grid” photonic crystal with 5 threads
in the frame and fixed period.
Experimental results confirmed conclusion that photonic
crystal with variable period could increase radiation output.
Experiments are in progress.
Several experiments with Volume Free Electron Laserwith the ”grid” photonic crystals in millimeter and submillimeter wavelength ranges are in preparation now.
In the experiment with 200 keV electron beam radiation in the range 4-5 mm is expected to be observed. This
experiment will be carried out in the Research Institutefor Nuclear Problems (INP, Minsk, Belarus) for the ”grid”
photonic crystal, built from periodically strained tungsten

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Proceedings of FEL 2007, Novosibirsk, Russia[6] V.G.Baryshevsky, K.G.Batrakov, I.Ya.Dubovskaya. ”Parametric (quasi-Cerenkov) X-ray free electron lasers”, J.Phys.
D, 24, pp.1250-1257 (1991).
[7] V.G.Baryshevsky, ”Volume Free Electron Lasers” NIM
A, 2000, vol.445, pp.281-282; LANL e-print archive
physics/9806039.
[8] V.G.Baryshevsky, K.G.Batrakov, A.A.Gurinovich, I. Ilienko,
A. Lobko, V. Moroz, P. Sofronov, and V. Stolyarsky, ”First
Lasing of Volume FEL (VFEL) at Wavelength Range λ ∼4 − 6 mm” NIM A, 2002, vol.483, pp.21-24.
[9] V.G.Baryshevsky, K.G.Batrakov, A.A.Gurinovich, I. Ilienko,
A. Lobko, V. Moroz, P. Sofronov, and V. Stolyarsky,”Progress of the Volume FEL (VFEL) experiments in millimeter range” NIM A, 2003, vol.507, pp.137-140.
[10] V.G.Baryshevsky, K.G.Batrakov, V.Mihalchik, V.P. Peftiev,
V.I.Stolyarsky. ”A process for generating electromagnetic radiation and volume free electron laser apparatus for carryingout the proces”, Eurasian patent EA 004665B1.
[11] V.G.Baryshevsky, K.G.Batrakov, I.Ya.Dubovskaya, et al.,”Volume Quasi-Cherenkov FEL in mm-Spectral Range”, inProceedings of FEL 1996, p.II-75, Elsevier Science B.V.
(1997).

Figure 4: Typical oscillogram for ”grid” resonator made oftwo photonic crystals with different periods
threads in the waveguide.
Joint experiment is being prepared now by INP and Joint
Institute for Nuclear Research (JINR, Dubna, Russia) at
LINAC-800, where 6 MeV electrons will be used for generation of radiation with mm and mm (150 GHz and 1 THz,
respectively).
Realization of VFEL with dynamical wiggler (and conventional wiggler) with spatially varied period is also in ournearest plans.

CONCLUSION
Experimental results confirmed conclusion that photonic
crystal with variable period could increase radiation output.
Experiments are in progress.

REFERENCES[1] R.Kompfner, ”The traveling wave valve” Wireless World,
1946, vol.52, pp.369-372.
[2] R.Pierce, ”Theory of the beam-type traveling-wave tube”
Proc. IRE, 1947, vol.35, pp.111-123.
[3] V.L.Granatstein, R.K.Parker and C.M.Armstrong, ”Vacuum
electronics at the dawn of the twenty-first century,” in Proceedings of the IEEE, 1999, vol.87, no.5, pp.702-716 .
[4] V.G.Baryshevsky and I.D.Feranchuk.”Parametric beam instability of relativistic charged particles in a crystal”, Phys.Lett.
A, 102, pp.141-144 (1984).
[5] V.G. Baryshevsky. ”Surface parametric radiation of charged
particles”, Doklady Akademy of Science USSR 299, pp.6-9(1988).

FEL operation

498[12] V.G.Baryshevsky, A.A.Gurinovich, ”Electrodynamical
properties of a ”gri” volume resonator” LANL e-printarchive: physics/0409107.
[13] V.G.Baryshevsky, A.A.Gurinovich, ”Spontaneous and induced parametric and Smith-Purcell radiation from electrons
moving in a photonic crystal built from the metallic threads”
NIM B, 2006, vol.252, pp.92-101.
[14] V.G. Baryshevsky, K.G. Batrakov, N.A. Belous, A.A. Gurinovich, A.S. Lobko, P.V. Molchanov, P.F. Sofronov, and
V.I. Stolyarsky, ”First observation of generation in the backward wave oscillator with a ”grid” diffraction grating andlasing of the volume FEL with a ”grid” volume resonator”
LANL e-print archive: physics/0409125.
[15] V.G. Baryshevsky,
N.A.Belous,
A.A.Gurinovich,
A.S.Lobko, P.V.Molchanov, and V.I.Stolyarsky ”Experimental study of a volume free electron laser with a ”grid”
resonator” in Proceedings of FEL 2006, BESSY, Berlin,
Germany, p331-334, LANL e-print arXiv: physics/0605122.
[16] V.G.Baryshevsky, A.A.Gurinovich. ”Generation of radiation in free electron lasers with diffraction gratings(photonic crystal) with the variable spacial period”arXiv:
physics/0608068.
[17] V.G.Baryshevsky, A.A.Gurinovich. ”Electrodynamical
Properties of a Volume Free Electron Laser with a ”Grid”
Resonator” in Proceedings of FEL 2006, BESSY, Berlin,
Germany, pp.335-339 (2006).

Proceedings of FEL 2007, Novosibirsk, Russia

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RESEARCH HIGHLIGHTS FROM FLASHR. Treusch and J. Feldhaus, DESY, Hamburg, Germany
Abstract
The Free electron LASer in Hamburg (FLASH) has
started regular user operation in summer 2005, providing XUV radiation pulses with pulse energies in the 10–100 µJ range and pulse durations of 10–50 fs. The science
programme at FLASH covers a broad range of novel applications including fundamental studies on atoms, ions,molecules and clusters, creation and characterisation ofwarm dense matter, diffraction imaging of nanoparticles,
spectroscopy of bulk solids and surfaces, investigation of
surface reactions and spin dynamics, and the developmentof advanced photon diagnostics and experimental techniques. So far, 16 science projects have been pursued involving approximately 200 scientists from 11 countries.
Some of the research highlights were presented in the talk.
Most of the presented results are presently in the publishingprocess. Hence the reader is kindly referred to the selectionof already published research at FLASH as listed below.

SELECTED PUBLICATIONS ON
RESEARCH AT FLASH
1. V. Ayvazyan et al.,First operation of a Free-Electron Laser generating
GW power radiation at 32 nm wavelength,
Eur. Phys. J. D, 37, 297-303 (2006)
2. S. Düsterer et al.,Spectroscopic characterization of vacuum ultraviolet
free electron laser pulses,
Opt. Lett. 31, 1750-1752 (2006)
3. A.A. Sorokin et al.,Multi-photon ionization of molecular nitrogen by femtosecond soft x-ray FEL pulses,
J. Phys. B: At. Mol. Opt. Phys. 39,L299-L304 (2006)
4. H.N. Chapman et al.,Femtosecond diffractive imaging with a soft-X-ray
free-electron laser,
Nature Physics 2, 839-843 (2006)

7. N. Stojanovic et al.,Ablation of solids using a femtosecond extreme ultraviolet free electron laser,Appl. Phys. Lett. 89, 241909 (2006)
8. A.R.B. de Castro et al.,Spectroscopy of rare gas clusters using VUV lightfrom a free-electron-laser,
J. Electron Spectrosc. Relat. Phenom. 156158, 25-29(2007)
9. M. Kirm et al.,Time resolved luminescence of solids excited by femtosecond VUV pulses and synchrotron radiation,phys. stat. sol. (c) 4, No. 3, 870876 (2007)
10. S. Cunovic et al.,Time-to-space mapping in a gas medium for the temporal characterization of vacuum-ultraviolet pulses,
Appl. Phys. Lett. 90, 121112 (2007)
11. P. Radcliffe et al.,Single-shot characterization of independent femtosecond extreme ultraviolet free electron and infraredlaser pulses,
Appl. Phys. Lett. 90, 131108 (2007)
12. S.P. Hau-Riege et al.,Damage threshold of inorganic solids under freeelectron laser irradiation at 32.5 nm wavelength,
Appl. Phys. Lett. 90, 173128 (2007)
13. S.P. Hau-Riege et al.,Subnanometer-Scale Measurements of the Interactionof Ultrafast Soft X-Ray Free-Electron-Laser Pulses
with Matter,
Phys. Rev. Lett. 98, 145502 (2007)
14. S.W. Epp et al.,Soft x-ray laser spectroscopy on trapped highly
charged ions at FLASH,
Phys. Rev. Lett. 98, 183001 (2007)

5. M. Meyer et al.,Two-color photoionization in xuv free-electron andvisible laser fields,
Phys. Rev. A 74, 011401(R) (2006)

15. J. Chalupský et al.,Characteristics of focused soft X-ray free-electron
laser beam determined by ablation of organic molecular solids,
Optics Express 15, 6036-6043 (2007)

6. A.A. Sorokin et al.,
Method based on atomic photoionization for spot-size
measurement on focused soft x-ray free-electron laser
beams,
Appl. Phys. Lett. 89, 221114 (2006)

16. A.A. Sorokin et al.,
X-ray-laser interaction with matter and the role ofmultiphoton ionization: Free-electron-laser studies
on neon and helium,
Phys. Rev. A 75, 051402(R) (2007)

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17. M. Nagasono et al.,Resonant two-photon absorption of extreme ultraviolet FEL radiation in Helium,
Phys. Rev. A 75, 051406(R) (2007)
18. R. Moshammer et al.,Few-photon Multiple Ionization of Ne and Ar by
Strong Free-Electron-Laser Pulses,
Phys. Rev. Lett. 98, 203001 (2007)
19. H.B. Pedersen et al.,Crossed Beams Photodissociation Imaging of HeH+
with Vacuum Ultraviolet Free Electron Laser Pulses,
Phys. Rev. Lett. 98, 223202 (2007)
20. W. Ackermann et al.,Operation of a Free Electron Laser in the Wavelength
Range from the Extreme Ultraviolet to the Water Window,
Nature Photonics 1, 336-342 (2007)
21. A. Föhlisch et al.,High-brilliance free-electron-laser photoionizationof N2 : Ground-state depletion and radiationfieldinduced modifications,Phys. Rev. A 76, 013411 (2007)
22. H.N. Chapman et al.,Femtosecond Time-Delay X-ray Holography,
Nature 448, 676-680 (2007)

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MILLIMETER WAVES SENSING BEHIND WALLS - FESEABILITYSTUDY WITH FEL RADIATION*
B.Kapilevich, M.Einat, A.Yahalom, M.Kanter, B.Litvak, The Israeli FEL Knowledge Center,
the Ariel University Center of Samaria, Ariel, 44837, Israel
A.Gover, Tel Aviv University, Israel
Abstract
Design of through-wall imaging (TWI) system needs
the knowledge of constitutive parameters of different
building materials. The paper describes the results ofmeasurements of the effective attenuation constant of
typical building materials such as concrete bricks, wood,tiles, sand, gypsum, etc. on mm-waves using powerfulpulse FEL radiation. Since the Rayleigh criterion forsurface roughness cannot be satisfied for majority ofmeasured building materials on mm waves, the increased
measured attenuation in comparison with bulky material
is taken place. Additional experiments were performed toestimate a role of these effects using quasi-noise mmwave source and wide-band mm-wave receiver.

INTRODUCTION
The through-wall imaging (TWI) systems provide
unique possibility to detect and image objects behind thewalls, door and other opaque medium [1, 2]. Basically,
through-wall imaging (TWI) systems operate in 1.99 –10.6 GHz or below 960 MHz [3]. The penetration
capability at these frequencies is characterized by rather
small attenuation caused by building material as shown in
Fig.1 [4]. However, the spatial resolution of TWI systems
is degraded when the operating frequency is relatively
low. On the other hand, a majority of building materials
demonstrate increased losses as the frequency increases.
As a result, higher RF power from the source is requiredfor quality TWI process.
The Israeli mm-wave FEL provides unique opportunity
to solve the above TWI problem delivering an output
power of 100-1000W at 85-105 GHz. But design of TWI
system operating on mm-waves needs comprehensive
study of constitutive parameters of different building
materials that must be measured in real pulse operation
FEL conditions. The paper describes the experimental
setup assembled for measurements of the effective
attenuation constant of typical building materials such asconcrete bricks, wood, tiles, sand, gypsum, etc. on mmwaves using powerful FEL radiation. Since the Rayleighcriterion for surface roughness at mm-waves cannot besatisfied for majority of measured materials, the measured
attenuation is different in comparison with bulky material.
Additional experiments were performed to estimate acontribution of this effect into the measured attenuation.
The special W-band quasi-noise sensor has been designed
and assembled to carry out such experiments.

Figure 1: Illustration of penetration capabilities ofdifferent building materials as a function of frequency [4].

EXPERIMENTAL SETUP AND
CALIBRATION PROCEDURE
The block-diagram of the experimental setup used formeasurement of effective attenuation constant is shown in
Fig.2. The pulse mm-wave FEL radiation (5-10 μs)
propagating in the corrugated wave guide line excites the
Tx standard rectangular horn antenna that transforms it toplane wave. This wave partially penetrates though thesample of the tested material and is captured by a similar
Rx antenna coupled with the W-band programmableattenuator and DXP-10 detector (Millitech). A similar
detector is coupled with the directional couplers providing
a total coupling level of -64dB. Both detected signals are
independently recorded by the Tektronix digital scope.

Figure 2: The block-diagram of the experimental setup.

___________________________________________*Work was partly supported by the Israeli Ministry of Science.

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Several detectors were preliminary compared in orderto choose the two maximally identical units. A generalview of the experimental setup is shown in Fig.3.

CHARACTERIZATION OF BULDING
MATERILAS USING MM-WAVE PULSERADIATION OF THE FEL
The effective attenuation of various building materials
has been measured using mm-wave pulse radiation of the
FEL as described in the previous section. Various
materials were tested. Some selected results are presented
in the Table.1 for cement plate, gypsum board and woodboard.

Figure 3: A general view of the experimental setup.

Figure 4: Examples of the detected signals recorded by
the digital scope in process of calibration (channel 2 - Rx
detector, channel 3 - Tx detector).
Calibration of the setup shown in Fig. 2 was done using
free space conditions. Typical detected signals recordedby the digital scope in channel 2 and channel 3 aredepicted in Fig. 4 for receiving and transmitting detectors
correspondently. Based on this calibration, we have foundout that the RF peak power at the FEL output is 150W in
the vicinity of 100GHz. When material under test isinserted between Rx and Tx antennas, the detected signal
is reduced depending on material transmittance. By
adjusting the variable attenuator we can restore theoriginal amplitude of the signal in the Rx channel. The
difference of the attenuator readings corresponding to thetwo situations gives directly the effective attenuation.
The only factor that must be taken into account is thevariation of the FEL’s radiated power from pulse to pulse.
However, suitable correction can be easily introduced into
the measurements since the Tx detector in channel 3
continuously controls this parameter.

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Table 1: Measured effective attenuation of the selectedbuilding materials
Type of theEffective
Comments
material
attenuation[dB]
one layer of-19
Horizontal
wood board,polarization
2cm
one layer of-20.4
Verticalwood board,polarization
2cm
two layers of-41.6
Both are inwood board,
Vertical
4cm
polarization
one layer of- 3.5--gypsum board,
1.2cm
one plate of-39.3
Verticalcement tile,polarization
2.5cm
one plate of-39.5
Horizontal
cement tile,polarization
2.5cm
All samples of materials under test were examined inboth orthogonal polarizations – horizontal and vertical.
Most of building materials have a texture and demonstratepolarization sensitivity of the measured attenuation.
However, the gypsum plate is quite uniform andinsensitive to the polarisation of the radiated wave.

CHARACTERIZATION OF BULDING
MATERILAS USING MM-WAVE QUASINOISE ILLUMINATION
Basically, constitutive parameters of many building
materials are characterized using coherent illumination.
However, TWI systems operate with UWB signals that
leads to uncertainty in estimation of their real penetration
capabilities if a frequency domain. The best way to solve
this problem is to measure an attenuation applying
incoherent (quasi-noise) illumination. We have developed
and assembled a wide band mm-wave sensor forexperiments with quasi-noise signals schematically
depicted in Fig. 5.

Proceedings of FEL 2007, Novosibirsk, Russia
The sensor is based on heterodyne circuitry consistingof the receiving antenna connected with the W-band pindiode modulator that provides 1 KHz pulse modulation of
the received signal. Then the signal comes to W-band
LNA (gain about 15 dB) and down-converted by mixer
with IMPATT LO operating at 94GHz. The IF signal isamplified about 70 dB by IF LNA with 6 GHz bandwidth
so that the total double-side bandwidth of the received
signal is about 12 GHz. The wideband HP-423A detector,
post detector’s video-amp and Tektronix Digital Scopeare employed for recording the signals propagating
through the material under test. Full W-band FARRAN
noise generator has been used as the source of incoherent
illumination of the container with materials undermeasurements. The general view of the setup used forquasi-noise characterization of building materials isshown in Fig. 6. W-band FARRAN noise generator isplaced beneath container and invisible.

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W-bandnoise sensor

Rx antenna

Container
with sandunder test
Absorbingbox
Figure 6: The general view of the setup used for quasinoise characterization of building materials.

dB
Figure 5: Schematic of the wide band mm-wave sensor.
The setup depicted in Fig.6 was employed formeasurement of an attenuation of the sand samples withdifferent thickness. To estimate the role of depolarisation
effects the container with sand was rotated and theeffective attenuation has been measured for different
angular orientations of the sand sample.
Typical measured attenuation as a function of sand’slayer thickness is shown in Fig. 7 for the four angular
position of container: ooo - 0 deg, xxx – 90 deg, ◊ ◊ ◊ 180 deg and □□□ – 270 deg. The averaged result isplotted by the solid line.
The same samples of sand have also been tested using
coherent illuminations by means of Agilent W-band
network analyzer at the frequency 100 GHz. The effective
attenuation is depicted in Fig. 8 as a function of the
thickness for the four angular position of the container as
was done in previous experiments. We observed highvariations of the measured attenuation as a function of
thickness. It can not explained by properties of bulky
material. The most realistic interpretation of such
behaviour is interference on boundaries sand-air, surface
roughness and possible depolarisation effects.

Figure 7: Measured attenuation for quasi-noise
illumination in W-band as a function of sand’s layer
thickness for the four angular position of container: ooo 0 deg, xxx – 90 deg, ◊ ◊ ◊ - 180 deg and □□□ – 270 deg.
The solid line corresponds to the averaged result.

CONCLUSION
The paper has presented the results of measurements ofeffective attenuation of various building materials using
powerful FEL radiation on mm-waves.

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dB

ACKNOWLEDGEMENTS
Authors would like to thank D.Hardon for his valuable
coordinating efforts, M.Harpaz for his assistance in
conducting FEL’s experiments and A.Konevsky forparticipating in experiments with the W-band quasi-noise
sensor.

REFERENCES

Figure 8: Measured attenuation for coherent
illumination at 100 GHz as a function of sand’s layer
thickness for the four angular position of container: ooo 0 deg, xxx – 90 deg, ◊ ◊ ◊ - 180 deg and □□□ – 270 deg.
Comparison of the measured losses for coherent andincoherent illuminations has revealed essential
differences. The noise-like illumination suppresses
interference and depolarization effects due to natural
averaging in frequency domain. That can berecommended for characterization of building materials toprovide more realistic data needed for design mm-wave
TWI systems. The short pulse FEL generating a wideband spectrum is a good candidate for this purpose.

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504[1] D.D.Ferris Jr. and N.C. Curie, “A Survey of Current
Technologies for Through-the-Wall Surveillance(TWS)”, Proc. SPIE, 1998, Vol.3577, pp.62-72.
[2] F.Ahmad, M.Amin, and S.Kassam, “Synthetic
Aperture Beamformer for Imaging through aDielectric Wall”, IEEE Trans, AES, January 2005,
Vol.41, No.1, pp.271-283.
[3] Revision of Part 15 of the Commission’s Rules Regarding Ultra-Wideband Transmission Systems, the FCC
order of 4-22-2002, www.fcc.gov.
[4] L.M.Frazier, “Radar Surveillance trough Soled
Materials”, SPIE Photonics East Conference, Boston
MA, November 1996, paper 2938-20.

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SOURCES OF RADIATION ON ARC-EN-CIEL PROPOSAL
M. E. Couprie, C. Benabderrhamane, C. Bruni, O.Chubar, M. Labat, G. Lambert, A. Loulergue,
O. Marcouillé, Synchrotron-SOLEIL, Saint-Aubin, France
L. Giannessi, ENEA, Frascati, Italy.
Abstract
The ARC-EN-CIEL project [1] proposes a panoply oflight sources for the scientific community. The choice tobase the FEL sources on HGHG (High Gain Harmonic
Generation) radiation and their Non Linear Harmonics
seeded with the High order Harmonics generated in Gas(HHG) is further confirmed with the successful
demonstration experiment of such a scheme at SCSS
Prototype Accelerator in Japan [2]. In phase 1 (220 MeV),
the radiation extends down to 30 nm, phase 1’ (800 MeV)
and phase 2 (1 GeV), the radiation reaches 1 nm, with 30100 fs pulses. The first FEL “LEL1” utilizes in-vacuum
undulators of period 26 mm for the modulator, and
APPLE-type radiators of period 30 mm, close to thestandard SOLEIL insertion devices. The second FEL
branch “LEL2” uses in-vacuum planar U18 undulators asradiator. In addition, THz radiation from the magnets ofthe compression chicanes will be provided and has been
calculated using SRW. ARC-EN-CIEL Phase 3 adds ERL
loops at 1 GeV and 2 GeV where undulators emit
conventional synchrotron radiation above 10 keV fromshort period in-vacuum undulators and soft X ray using avariable polarisation undulator. An FEL oscillator in the
40-8 nm spectral range is installed in the 1 GeV loop. The
HHG seeded “LEL4” uses the electron beam from the 2
GeV loop and further accelerated to 3 GeV for producing
coherent light production below 1 nm. Recent
calculations and optimisations are presented.

INTRODUCTION
ARC-EN-CIEL (Accelerator-Radiation for Enhanced
Coherent Intense Extended Light) aims at providing theuser community with coherent femtosecond light pulses
covering from UV to soft X ray spectral range in France[2]. It is based on a CW 1.3 GHz superconducting linear
accelerator delivering high charge, subpicosecond, lowemittance electron bunches at high repetition rate. The
completion of ARC-EN-CIEL relies on different phases,
according to the electron beam energy, the average
current and the light sources available for the users. Phase
1 uses a 1 kHz high charge, short bunch electron beam,reaching an energy of 220 MeV with 3 cryomodules, anda first bunch compressor delivered by a modified Zeuthen
RF gun [3], illuminated by a Ti:Sa laser. LEL1 is based on
a FEL seeded with HHG with an APPLE-II typeundulator as a radiator for adjustable polarisation
radiation. Phase 1 (220 MeV, 30 nm) is now extended to
800 MeV (Phase1’) with an additional bunch compressor
and five cryomodules, and fits in the tunnel of the ALS(Accelerateur Linéaire de Saclay) allowing LEL1
radiation to be extended to shorter wavelengths for users
applications. With two additional cryomodules on the
Linac leading to 1 GeV (Phase 2), the FEL source“LEL2” will be installed, allowing stronger radiation to
be achieved in the 1 nm range. Then, with the installationof an additional high average current gun (AES/JLab type[4]) illuminated by a Ytterbium diode pump fiber laser,
two ERL loops at 1 and 2 GeV will be added. On the 1
GeV loop is planned LEL3 and FEL oscillator taking
advantage of the mirror development for lithography, andan APPLE-II for subpicosecond radiation synchrotron
radiation. On the 2 GeV loop, 6 in vacuum U20 (period of
20 mm) will be installed for hard X ray spontaneousemission. When the 2 GeV beams is not energy recovered
but once again accelerated up to 3 GeV, it is sent to“LEL4”, an FEL seeded with HHG and using cryogenic
undulators. THz radiation is also produced in the bending
magnets of the compression chicanes and of the arcs. The
general scheme of ARC-EN-CIEL is shown in fig. 1.
Table 1: List of radiation sources on ARC-EN-CIEL.
Phase: P. M for Modulator and R for Radiator. SR:
Synchrotron Radiation. CSR: Coherent Synchrotron
Radiation. BC Bunch Compressor. E: Energy. N: numberof periods. Conf: configuration. BL: beam line.
P
FEL radiation
LEL1
1, 1’,
Planar 2
helicalbranchLEL2 2
Planarbranch

E
GeV

Type

M/R, N

Spectral
range

0.22
-1

HGHG
conf 1-1
1-3
HHG seed
HGHG,
conf 1-1
et 1-3
HHG seed
HGHG
conf
13and 1-5
HHG seed
FEL
oscillator

M :U26200
R : HU30,
N2=700
M : U26,
N1=500
R : U18
N2=500
M :U35,N1=700
R :U18,N2=1000
HU30,
N=350

200-1.5
nm

SR

HU30

0.2-4 keVSR

U 20, 100

1-20 keV

CSR

BC1, 2, arc

0.1-10THz

0.81.2

LEL4 3planarbranch

3

LEL3

1

3

Spontaneous emission
VUV 3
1
BL
X BL 3
2
THz Radiation
1-1’
2, 3

10-0.5nm2-0.2 nm

40-8 nm

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Fig. 1: General scheme of ARC-EN-CIEL, with the different phases and FEL sources

THE CONSTITUTING ELEMENTS
The different parts of the FEL and SR sources are here
described, including accelerator parameters, insertion
devices, HHG seed for LEL1, LEL2, LEL4 and optics.

The accelerator
A scheme of implementation of Phase1’ in the ALS
tunnel, showing the different accelerator components, isshown in fig. 2. Another site, the so-called “Mare duVivier” at Saint-Aubin nearby SOLEIL and Orme desMerisiers, the French third generation synchrotron lightsource, is considered for Phases 2 and 3. The radiationfrom a SOLEIL beamline could be coupled to ARC-ENCIEL radiation.
The beam dynamics has been studied starting from thegun using ASTRA, CSR-Track and TRAFFIC-4 for Phase
1 and 2, and using BETA and BU for Phase 3 [5]. The
beam parameters taken for the FEL and radiation
simulations are presented in Table 2.
The ERL mode relaxes the constraints with respect to thecompression. In such a case, the beam will not go throughthe second bunch compressor bunch but will travel in astraight vacuum chamber installed at this position. ARCEN-CIEL Phase 3 aims at achieving high average
currents. Typically, 1 mA can be obtained for a repetition
rate of 5 MHz. Two regimes depending on the charge
level are envisaged, leading to different values of theemittance and peak current as shown in table 2. Higher
average currents can be reached in enhancing therepetition rate up to 100 mA.
ARC-EN-CIEL should provide simultaneous electron
beams in the accelerators for feeding the light sources forthe users: the 1 kHz high peak current for LEL1 andLEL2 should coexist with the high repetition rate (1-100
MHz) recirculated beam in the ERL loops. Such an
operation requires the electron beams to be recombined at
low energy at the loop entrance and the beams to be
separated at the exit of the accelerating structures thanks
to kicker magnets.
The operating mode between the different phases relieson the temporal structure illustrated in figure 3.

Fig. 2: Possible implementation of ARC-EN-CIEL phase 1’ in the tunnel of the former Accelerateur Linéaire de
Saclay (Linear Accelerator of Saclay) situated at Orme des Merisiers.

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506Proceedings of FEL 2007, Novosibirsk, Russia
Table 2: ARC-EN-CIEL beam parameters. Total and slice
energy spread σγ/γtot, and σγ/γslice, total and slice beamemittance εtot and εslice.
Phase

1

2

Energy(Gev)
Rep. rate(kHz)
Charge(nC)∆T(fs rms)

0.2

1

1-10

1-10

1

1

5006001-10200300
1-10

0.8
1
2.4

<I> (μA)
Ipeak (kA)
Ipeak,slice(kA)
εtot( mm
mrad)
εslice ( mm
mrad)
σ/tot(%rms)σ/slice(%rms)

3,
mode 1
1-2

3,mode 2
1-2

3

103 –
105
0.2//1103 –
105
0.2//11500600103-105

200

1.5
2
1.6

500600103105
0.2
1
2

1
1
6

1.5

1

1.2

1

5

1.2

0.1

0.1

0.1

0.2

0.04

0.04

0.04

0.08

3

0.75

0.02

Fig. 3: Simultaneous operation of the electron beams inthe different phases of ARC-EN-CIEL.

The undulators
Thanks to the experience on insertion devices acquired
at SOLEIL [6], the choice of the undulators tends to selectsolutions not very different from the ones adopted at
SOLEIL. For LEL1, 2, and 4, a conventional HGHG
scheme comporting a modulator, a dispersive section anda radiator has been chosen. Different configurations areforeseen, from the 1-1 (modulator and radiator tuned on
the seed wavelength), 1-2 (radiator tuned to the second
harmonic of the modulator resonant wavelength), 1-3, 15 and harmonic cascade (resonant wavelength of theradiator equal to the resonant wavelength of themodulator multiplied by a ratio of integer numbers [7]).
The resonant wavelength versus the undulator period has
been calculated for different beam energies and thedeflection parameter K values in planar and helicalconfiguration. The accessible magnetic field B versus gap
for a given undulator period o has been evaluated using
the analytical expression for NdFeB of remanent field
1.2T: B=a·exp(b·gap/o + c·(gap/o)2) where the

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coefficients a, b and c are derived for different cases ofundulators types [8]. Further optimisations have been
done then specifically with RADIA software [9], as in theexample of the APPLE-II HU30. Such an undulator isadopted for the radiator of LEL1 and for the undulator of
the FEL oscillator LEL3. At SOLEIL, after the
installation of three HU80 on the ring, different APPLE-II
types undulators are under construction or to be built,
with periods ranging between 60 down to 34 mm. Since
the vacuum chamber should be as wide in the horizontal
direction and the vacuum constraints are soften withrespect to storage ring, a period of 30 mm seems quite
reasonable. Further analysis during the TDR phase will
investigate the possible use of APPLE-III type undulators[10] and designs of in-vacuum APPLE-II undulators.
Standardization with respect to the different undulators
sections of ARC-EN-CIEL and small deviations from thesolutions adopted at SOLEIL are aimed. SOLEIL has
already built several in vacuum U20 undulators, which
type of insertion device has been adopted as the ones for
the X ray synchrotron light sources on the 2 GeV loop.
Further final adjustments will be made later according to
the user requests. The periods for the in-vacuum
undulators at SOLEIL range between 20 and 26 mm. An
U26 has been chosen as a modulator for LEL1 and LEL2,
allowing efficient bunching by the seed for theconfiguration 1-3 for example. The use of a short periodhigh magnetic field in vacuum undulator allows the total
length to be reduced and the system to be more compact.
LEL2 aiming at operating even below 1 nm on the nonlinear harmonics, the magnetic field has been pushed inthis case with a radiator of 18 mm period.
Recent development in cryogenics undulators permit toenhance the peak magnetic field by a factor 1.3 using a
specific magnet variety operated at low temperature(typically 140 K). First proposed at SPring-8 [11], realadvances have been achieved so far in particular at
SPring-8, ESRF [12] and BNL [13]. R&D is launched on
this subject at SOLEIL. So far, it has been demonstrated
that the shimming can be done at normal temperature andthe magnetic field properties remain at low temperature,
as far as the girders mechanics is not modified. The
cooling of the magnets can be performed either via
cryocoolers or nitrogen circulation. The magnetic typeallowing the highest magnetic field can not be baked forreaching low vacuum pressure, but this is less limiting on
a Linac than on a storage ring. So cryogenic undulators
are adopted for LEL2 and LEL4 of ARC-EN-CIEL
project.
Table 3 summarizes the characteristics of theundulators considered for the simulations of the lightsources. Mainly, simulations have been performed using
PERSEO Time Dependent [14] considering a filling
factor [15] of 0.1 in order to take into account thetransverse overlap between the seed and the electron
beam, considering average betatron functions of 2.6 m.
The undulators are to be built in 2 meters length segmentswith a FODO lattice in between two segments. Comparedto the values given in Table 3, the length will be slightly

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increased for being a multiple of the segment length.
After each undulator module will be placed Optical
Transition Radiator screens, Beam Position Monitors.
These further optimizations (lattice, segmentations) willtake place during the TDR phase of the project. Eachsegment comports four correctors for adjustment of thevertical and horizontal trajectories at its entrance and exit.
After checking the magnetic axis, the module effect on
the orbit will be measured versus gap and compared withthe magnetic measurements. The natural focusing and theone resulting from defects of magnetic fields will be
studied thanks to the quadrupoles located between twosegments. In a further step, the radiation will be measured
versus the electron beam position using a zone plate
selecting the spatial distribution at a given energy, such as
the DIAGON type measurements performed at SOLEIL[16].
Table 3: Undulators for ARC-EN-CIEL sources, M for
Modulator and R for radiator, * for cryogenic undulators.
In-vac for in-vacuum.
o Kmax
Gapmin Lengt
FEL
Type
mm
h (m)
LEL1-M In-vac
26
3.2
3.5
5.2
LEL1-R
Apple30
P:2.16 10
21
II
H:1.5
8
LEL2-M In-vac
26
3.2
3.5
13
LEL2-RIn-vac* 18
3.1*
3.7
9
LEL3
Apple30
P:3.36 6
10.5
II
H:1.5
8
LEL4-M In-vac * 35
4.8
3.5
24.5
LEL4-RIn-vac * 18
3.1*
3.7
18
VUV
Apple30
P:1.1
15.5
2
II
H:0.7
X
In-vac
20
1.9
5.5
2x6

temporal [21] and spatial [22] coherence, emitting very
short pulses (attosecond pulses in a femtosecond
envelope) in a small divergence (1 to 10 mrad), with arelatively high repetition rate (up to few kHz). The High
Harmonics generated in Gas cover presently a wide
spectral range with already significant intensities, aspresented in fig. 4. Presently, in the short wavelength
range, one can rely on a 10 fs pulse with peak powers of
10 MW at 30 nm, 1 MW at 10 nm, 1 kW at 4 nm (withfurther improvement foreseen in the next 3-4 years up to
10 kW) [23].

Fig. 4: Peak power and energy per pulse provided byHigh Harmonics generated in Gas.

Seeding optics and FEL oscillator mirrors

Simulations consider a dispersive section compression
factor R56 of 1.5 μm maximum. The R56 can be expressed
in
terms
of
magnetic
field
as:
⎡

R = L ⎢1+56

D
2γ ⎢⎣ L

e

2

LD

⎤

⎤

D

2 2

D

2

⎡s

∫ ⎢ ∫ B (u)du⎥⎦ ds⎥⎥where LD is the
mc ⎣
0

0

⎦

dispersive section total length, m the mass of the electron,c the speed of light, BD the magnetic field of thedispersive section and s the longitudinal coordinate. Sucha dispersive section can be realised with permanent
magnets and modelised with RADIA [9]. In an example,
R56 ranging between 33 μm at 500 MeV to 6 μm at 1.2
GeV, and 0.9 μm at 3 GeV were found.

HHG seed
The harmonic generation in gas results from the strong
non-linear polarisation induced on the rare gases atoms,
such as Ar, Xe, Ne and He, by the focused intenseelectromagnetic field ELaser of a "pump" laser [17]. The
radiation spectrum is tunable in the VUV-XUV region byfrequency-mixing techniques applied on the pump laser.
High order harmonics are linearly polarised sources from
266 nm down to the water window [18, 19, 20], of high
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Fig. 5: Normal incidence reflectivity of multilayer
mirrors.
The HHG seed can be injected inside the modulator via
a set of two spherical mirrors for being able to adjust thefocusing inside the undulator, and two periscope mirrors
for introducing the light on axis on a dogleg of theaccelerator. One can also consider using toroidal andgrazing incidence mirrors. For the first, third and fifth
harmonics, high reflectivity multilayer mirrors (oxides
and fluorides) can be employed. In the VUV, Al metallic
and then SiC mirror can be used. In the soft X ray, X ray
multilayers are available [24]. In normal incidence, theperformances of multilayers around 13 nm benefit fromthe development carried out for lithography and highProceedings of FEL 2007, Novosibirsk, Russia
reflectivity has been achieved. Such reflectors, currently
developed at Institut d’Optique, will be employed for
LEL3 (see fig. 5).

Power and Spectral range
The spectral range covered by LEL1, LEL2 and LEL4
of ARC-EN-CIEL is shown in fig. 6. In seeded FEL
sources, different wavelengths will be provided via
various electron beam energies: a kicker will extract the
500 MeV beam after Bunch Compressor 2 for being sent
to LEL1 for example, the phase tuning of the LINAC
allows the energy to be varied between 0.8 and 1.2 GeV
for LEL2 and the 3 GeV will be obtained after the 2 GeV
loop after a further injector. A slow adiabatic change ofthe energy in operating the different beams produced by
the two guns will be studied in details in the TDR phase.
Fine tuning will result from a simultaneous gap change ofthe undulators and wavelength modification of the Ti-Sa
laser illuminating the gas cell for the HHG production,
coupled to a change in the monochromators for allowing
the users to scan the energy during the measurements on
their samples. Compared to the usual “gap scan” onsynchrotron radiation facilities, the coupling with thechange of the Ti-Sa laser should be added. At shortwavelength, the wavelength of the harmonics produced ingas are very close (they are separated by 0.3 nm at 10nm), a relatively small change wavelength is required topass from one to the other. Spectral tuneability performedby means a combined chirp on the laser and the electron
beam can also be applied [29].

9

1 GeV

8

10

Peak Power (W)After comparisons of saturation lengths were performed
between PERSEO and GENESIS in the steady state
regime, the design, characteristics evaluation of the ARCEN-CIEL FEL sources has been mainly performed using
PERSEO Time Dependent adapted to the ARC-EN-CIEL
case. Such a code present the advantage of providing also
the radiation on the odd non linear harmonics in theplanar undulator case. A Filling factor of 0.1 was appliedin the modulator in order to approximate the transverse
overlap between the electron and the seed beam. Specificcalculations (such as short wavelength case, emittanceeffects) were also studied with GENESIS1.3 (without thenon linear harmonics) [25] coupled to SRW [26]. The
GENESIS-SRW combination permits the further
propagation of the FEL wavefront to the beamlines anddeeper insight on transverse coherence issues. Non linear
harmonics in the helical undulator configuration and evenharmonics produced on the UVSOR-II FEL seeded with a
1 kHz Ti:Sa laser [27] are under analysis with MEDUSA[28]. Following these studies, one plans to proceed tosimulations of even harmonics and non linear harmonics
produced in the helical configuration for ARC-EN-CIEL
FEL sources.

10

10

3 GeV

7

10

6

10

220 MeV5

10

500 MeV4

10

750 MeV

3

H1
H3
H5

10

1.2 GeV

2

10

1

10

0.1

1

10
Wavelength (nm)100

Fig. 6. Spectral range covered by the HHG seeded FEL
sources of ARC-EN-CIEL on the fundamental (black),
third (red) and fifth (green) harmonics of the radiator.
A closer zoom of the radiation produced by LEL 1 inthe short wavelength region for planar and helicalconfiguration is shown in fig. 7. Saturation length
depends on the seed wavelength, the number of undulator
modules or the dispersive section which can be adjusted.
10

Peak power (W)ARC-EN-CIEL SEEDED FEL SOURCES10FRAAU01

10

10

8

10

6

10

4

10

2

10

0

1

2

3

4

5

6

Wavelength (nm)

7 8 9

10

Figure 7: Radiation produced by LEL1 in ARC-EN-CIEL
Phase 2. Calculations with 1.5 kA. Seeding power is 30
kW, 50 fs-fwhm, U26 Modulator (100 to 200 periods,
depending on seeded wavelength); HU30 Radiator: in (x)planar and (o) helical configuration (400 to 700 periods).
LEL2 allows the spectral range to be extended below 1
nm in the linear polarisation case, as illustrated in fig. 8.
Note that in both cases, the calculations were performed
with a conservative peak power of 1.5 kA.
LEL4 is more prospective. It allows the spectral range
to be extended down to 0.2 nm in the linear polarisationcase in configuration 1-5, as illustrated in fig. 9. It
exploits the energy enhancement in the loops and theaccelerating structures up to 3 GeV and cryogenic
undulators technology. The seed ranges between 6.3 and 4
nm, with 30 kW as expected in a near future.

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Peak power (W)10

Proceedings of FEL 2007, Novosibirsk, Russia

10

10

8

10

6

10

4

10

2

10

0
4

5

6 7 8 9

1

2

3

4

5

6 7 8 9

10

Wavelength (nm)pulse duration than the main central pulse. When theheated electrons refresh, the radiation can start again fromthe center. The behaviour on the harmonics is similar,
with a larger number of bifurcation when the harmonic
number is higher. The change of slope in the evolution
diagram here results the process of saturation of theelectrons in the middle of the pulse. The pulse in themodulator appears as a vertical line since slippage here issmall with respect to the pulse duration. For this reason
the process appears different the one previously observedin the case of a super-radiant regime [30].

Fig. 8 : Peak power delivered by LEL 2 in ARC-ENCIEL Phase 2. Seeding power is 50 kW, 50 fs fwhm.
Beam parameters of phase 2 with 1.5 kA and (x) E=1
GeV, (Δ) E=1.2 GeV. U26 Modulator (400 to 500
periods), U18 Radiator (400 to 500 periods).

Peak power (W)

10

10

10
10
10
10
10

8

6

4

2

0

0.0

0.2

0.4

0.6

0.8

1.0

Wavelength (nm)

1.2

1.4

Figure 9: Radiation produced by LEL4 in ARC-EN-CIEL
Phase 3. Seeding power is 30 kW, 50 fs-fwhm. U35
Modulator (up to 700 periods), cryogenic U18 radiator(1000 periods).

Fig. 10: Evolution of the radiation longitudinal
distribution along the position in the modulator (top) andradiator (bottom) for the fundamental (H1), the third (H3)and the fifth harmonic. Case of LEL1, seed at 12.3 nm, 50
fs and 50 kW.

Longitudinal dynamics, pulse duration andlinewidth
Fig. 10 shows the longitudinal dynamics of the FEL
radiation followed using evolution diagrams showing thepulse temporal distribution along the progression in theundulators. In the modulator, the seeded fundamental
wavelength radiates strongly, with a short, nearly Fouriertransformed limited pulse. The non-linear harmonics
radiation in contrast are very noisy, wide spectrally andtemporally and weak in intensity. The energy modulationof the electrons due to the seed interaction can be seen inphase space, it is transformed into density modulation
after the dispersive section. The electrons rotate in phasespace when the end of the radiator is reached and some ofthem escape the separatrix.
At the entrance of the radiator in fig. 10, the radiation
first results from the one emitted in the modulator, shifted
towards the head of the bunch because of slippage. Then,the emission from the bunched electrons starts andreaches an asymmetric bifurcation, where the light slips
along the electron bunch mainly in the forward direction.
The electrons situated where the radiation was previously
emitted are strongly heated (as seen on phase space
analysis) and the radiation starts from the lateral electrons
which still have sufficient bunching, exhibiting a thiner
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Fig.11 : Temporal and spectral profiles of LEL2 (caseof fig. 11) after 6 m in the radiator : H1 : 26 fs rms,
0.014%, 0.38 mJ, H3 : 25 fs, 0.009%, 1.2 μJ, H5 : 20 fs,
0.006%, 30.5 nJ, 2 MW. After 5.1 m in the radiator: H1 :23 fs fwhm, 0.015%, 0.15 mJ, H3 : 16 fs, 0.0075%, 0.56
μJ, H5 : 14 fs, 0.0054%, 3.7 nJ.
Pulse duration and width decrease along the path in theradiator and start to increase again after saturation. The
minimum of pulse duration is reached earlier on theProceedings of FEL 2007, Novosibirsk, Russia
harmonics than on the fundamental. The FEL pulse
duration and spectral width does not vary significantly
when the seed pulse is changed from 150 fs to 50 fs.

Tolerances Sensitivity to parameters
The sensitivity to the different parameters (electron
beam, seed) has been studied in order to evaluate
tolerances. They have been mainly carried out in the caseof LEL2, more sensitive than LEL1.
The influence of the emittance has been studied with
GENESIS coupled to SRW, and is illustrated in fig. 11. Incase of peak current, the peak power drops by one orderof mzagnitude from 1.5 kA to 2 kA. Higher peak current
permit a more efficient power extraction on theharmonics. An increase of energy spread leads to asignificant reduction of the peak power, in particular on
the non linear harmonics (from 0.06% to 0.08%, oneorder of magnitude is lost on H1, more than 1 on H2 and2 on H5).

FRAAU01

ARC-EN-CIEL FEL OSCILLATOR
SOURCEThe length of the optical resonator is given by thesynchronism condition with the electron bunch spacing(d=c/2f) with f frequency of the electrons. A 34 m longresonator corresponds to a repetition rate of 4.5 MHz forthe 1 GeV loop. In fact, two series of electrons bunches(from the first pass in the 1 GeV loop or from the return
pass from the 2 GeV loop in the 1 GeV one) will generate
two FELs. For the calculations presented here, amacropulse of 10 ms is considered.
The optical resonator consists of two spherical mirrors
with a hole for extraction of the radiation (10 % efficiency
assumed for the calculations). For a symmetrical cavity,
the waist wo which minimises the volume of mode along
the undulator of length Lond is wo = Lond λ / 2π 3 with the wavelength. For LEL3 at 10 nm, it is of the order of

100 μm, leading to mirror radius of curvature of 16 m at
10 nm. The corresponding mode divergence θ = λ is 35
πwo

QuickTime™ et undécompresseur TIFF (non compressé)sont requis pour v isionner cette image.

Fig. 11: GENESIS study on the influence of theemittance on the LEL1 on fundamental radiation peak
power and pulse duration. LEL1 seeded at 12 nm in the 11 configuration.
A change of synchronisation between the seed and theelectron bunch leads to a reduction of the saturation
length and to a deformation of the pulse shape. At given
undulatro length, a tolerance of ±35 fs is found for a 10%change in peak power, while temporal and spectral
distribution remain similar.
The maximum of peak power is obtained when the seedwavelength is slightly higher than the undulator resonant
one. The influence of the spectral detuning is not
symmetrical and becomes much more drastic at shortwavelength. Tolerances for 10% peak power change are±0.025 nm @38 nm, ±0.022 nm (resp. ±0.012nm )@14
nm for a 1-1 (resp. 1-3) configuration.

μm at 10 nm. A slight asymmetry of the resonator isbetter in order to reduce the heat load on the front mirror,
so radii of curvature of 16 and 20 m are taken. PERSEO
calculations have been carried out for this configuration
with the two modes (low and high charge) of operation at
1 GeV. The HU30 undulator allows variable polarisation
to be produced. At 1 GeV, the spectral range in circularpolarisation on the fundamental covers from 20 to 8.5 nm,with peak power of 120 MW and average power of 90550 W. In planar polarisation, the spectral range covers
from 40 to 10 nm, with peak powers of 50 MW andaverage power of 200 MW. The absorbed power by the
mirrors has been limited to 2 kW, assuming cryogenic
cooling as usually done on the SOLEIL beamlines. The
use of deformable mirrors is foreseen. Further
optimisation of the duty cycle, cavity length and mirror
position will be performed during the TDR phase forenhancing the extracted power. Indeed, a longer cavity
length allows the mirror to handle a larger laser spot andthe power density to be reduced. Pulses are typically 300
fs and 0.5% spectral width. LEL3 is complementary to
LEL1, since it provides to the users a source with higher
average and lower peak power.

ARC-EN-CIEL SYNCHROTRONRADIATION SOURCES
Radiation from the spontaneous emission undulator
sources has been calculated using SRW. The peakbrilliance is plotted in fig. 12.

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Proceedings of FEL 2007, Novosibirsk, Russia

Fig. 12 : Peak Brillance by LEL1 operated at 10 kHz andthe spontaneous emission sources for 20 mA in the loops.

ARC-EN-CIEL THZ SOURCES
Figure 13 presents the spectral energy per pulse and theaverage spectral power of the terahertz emission,
calculated for angular apertures of 60 mrad (H) x 40 mrad(V) for three different phases of ARC-EN-CIEL.

Fig. 13: Pulse energy spectra of terahertz range emission
collected by 60 mrad (H) x 40 mrad (V) aperture ports.

REFERENCES[1] M. E. Couprie et al., “The ARC-EN-CIEL FEL
proposal”, FEL06, Berlin, Aug 2006, p. 146-149
http://www.jacow.org[2] G. Lambert et al, “First lasing in seeding
configuration at 160 nm using High order Harmonic
Generated in gas on the FEL of the SCSS Prototype
Accelerator”, FEL07, Novosibirsk, Aug 2007,
http://www.jacow.org.
[3] J.H. Han et al, ”Conditioning and High Power Test of
the RF Guns at PITZ”, EPAC04, 357[4] T. Rao et al, ”Photoemission Studies on
BNL/AES/JLab all Niobium, Superconducting RF
Injector”, PAC05, 2556.
[5] C. Bruni “ARC-EN-CIEL project electron beam
dynamics” these proceedings[6] C. Benabderrahmane et al, « Commissioning of theFirst Insertion Devices at SOLEIL » PAC07,
Albuquerque, New Mexico, USA, p. 929-931[7] L. Giannessi, P. Musumeci, The free-electron laser
harmonic cascade, New Jour. Phys. 8, 294(2006)
FEL projects

512[8] P. Elleaume, J. Chavanne, B. Faatz, “Design
Considerations for a 1Å SASE Undulator” Nucl.
Instrum. Meth. A 455, 503 (2000)[9]http://www.esrf.eu/Accelerators/Groups/InsertionDevic
es/Software/Radia, P. Elleaume, O. Chubar, J.
Chavanne, "Computing 3D Magnetic Field from
Insertion Devices", PAC97, 3509-3511 ; O. Chubar,
P. Elleaume, J. Chavanne, "A 3D Magnetostatics
Computer Code for Insertion devices", SRI97,
August 1997, J. Synchrotron Rad. (1998). 5, 481-484[10] J. Bahrdt, W. Frentrup, A. Gaupp, B. Kuske, A.
Meseck, M. Scheer, Undulators for the BESSY softX-Ray FEL, Proceed. FEL2004, JACoW, 610-613[10] T. Hara, T. Tanaka, H. Kitamura, J. Bizen, X.
Maréchal, T. Seike, “Cryogenic Permanent Magnet
Undulators”, Phys. Rev. Special Topics Acc. &Beams 7, 050702 (2004), H. Kitamura, Proceed.
Synch. Rad.Inst. 2006, SRI May, Daegu, Korea[12] C. Kitegi “Development of a cryogenic permanent
magnet cryogenic undulator at ESRF”, Edimburg,
EPAC 06, 3559
[13] T. Tanabe et al., X-25 Cryo-ready In-vacuum
Undulator at the NSLS, AIP Conference Proceedings
879, 283 (2007)[14] http://www.perseo.enea.it/, L. Giannessi, Overview
of PERSEO, a system for simulating FEL dynamics in
Matcad, proceedings of FEL, 91 (2006)[15] W. Colson P. Elleaume Appl. Phys. B 29, (1982)10[16] http://www.synchrotron-soleil.fr[17] P. Salières et al., Adv. At., Mol., Opt. Phys. 41, 83(1999)[18] Z. Chang et al, Phys. Rev. Lett. 79 (1997), n°16,
2967[19] Seres, J. et al. Nature. 433, 596 (2005).
[20] E. Gibson et al. Phys. Rev. Lett. 92 (03), 3001 (4)(2004).
[21] H. Merdji et al, Phys. Rev. A 74 (2006) 043804[22] L. Le Déroff et al, Phys. Rev. A61 (2000), n°19,
43802[23] H. Merdji, private communication[24] P. Zeitoun et al, Appl. Phys. B 78, 983 (2004), F.
Delmotte, “Applications des sources accordables
VUV-X fs combinant accélérateurs et lasers ; slicing
à SOLEIL et le projet ARC-EN-CIEL “, Feb. 2004,
Orsay[25] GENESIS, S. Reiche, NIM A 429, (1999) 243[26] O. Chubar et al, “Numerical Propagation Simulations
and Coherence Analysis of SASE Wavefronts” thisconference[27] M. Labat, “Even harmonic production on UVSOR-II
storage ring” this conference[28] H.P. Freund et al., IEEE J. Quantum Electron. 36,
275 (2000).
[39] S. Biedron et al., NIM A475, 401; T. Shaftan, PRE
71, 2005, 046501[30] R. Bonifacio et al., Phys. Rev. A40, 4467 (1989), L.
Giannessi et al., Jour. Appl. Phys. 8, 294 (2006); T.
Watanabe et al., Phys. Rev. Lett. 98, 03402 (2007)

Proceedings of FEL 2007, Novosibirsk, Russia

FRAAU02STATUS OF THE FEL TEST FACILITY AT MAX-LAB *Mathias Brandin, Filip Lindau, Nino Cutic, Sara Thorin, Sverker Werin#, MAX-lab, Lund, Sweden
Johannes Bahrdt, Kathrin Goldammer, Michael Abo-Bakr, Dmytro Pugachov, BESSY GmbH,
Berlin, Germany
Anne L’Huillier, Lund University, Lund, Sweden
Abstract
An FEL test facility is built on the existing MAX-lab
linac system in collaboration between MAX-lab and
BESSY. The goal is to study and analyse seeding,harmonic generation, beam compression and diagnostic
techniques with the focus of gaining knowledge andexperience for the MAX IV FEL and the BESSY FEL
projects. The test facility will in the first stage be using
the 400 MeV linac beam to generate the third harmonic at
88 nm from a 266 nm Ti:Sapphire seed laser.
The optical klystron is installed and magnetic system,
gun and seed laser systems are currently being finalised.
Start-to-end simulations have been performed andoperation modes for bunch compression defined. The
linac and beam transport system is already in operation.

INTRODUCTION
The BESSY FEL project [1] and the MAX IV proposal[2] are both focused on seeded FEL sources as part of the
facilities. In the aim of improving the designs a decision
was made to build a test facility for harmonic generation
at MAX-lab.
By utilising the gun, injector and linac system alreadyavailable at MAX-lab a test facility for seeded
FEL/Harmonic generation could be accomplished byrelative low additional funding. Contacts had been takenwith BESSY and with the application for the EUROFEL
collaboration the project was started. The focus of theactivities is to explore ideas of harmonic generation andgain experience with the FEL technology, test diagnostics
and working with short pulses.

OVERVIEW OF THE PROJECT
The project is built in one major phase (I) with two
improvement phases (phase II: an improved gun systemand phase III: HHG seeding). The starting point is theinjector built at MAX-lab in the first years of thismillennium which was designed to be flexible and also
allow accelerator development. A linac system waschosen together with a flexible gun mounting systemequipped with a thermionic RF-gun. The source is used
for injection into the storage rings (MAX I, II, III) and in
the intermediate time this source is one of few available
sites for tests of FEL operation at these energies.
An optical klystron system and a seed laser at 266 nm
will produce the 3rd and 5th harmonic at 88 and 53 nm
respectively using the 400-450 MeV electron beam. The
radiator undulator in the optical klystron is not enough for
amplification, and thus the activities are focused on
harmonic generation. BESSY is providing the undulator
and chicane system while MAX-lab is providing theelectron beam and the laser system.
The aim is to study several features in the design andoperation of this kind of facility. On the electron beam
side: bunch compression, electron beam transport(especially with low emittance), beam stability,
synchronisation and stability. On the FEL side: Harmonic

See
Seed
d laser

Gun laser

Gun

Optical KlystronDog-leg

Recirculator
Previously existing system

Fig 1. Overview of the accelerator systems and test FEL.
* This work has been partially supported by the EU
Commission in the Sixth Framework Program, Contract
No. 011935 – EUROFEL and the Swedish ResearchCouncil# sverker.werin@maxlab.lu.se
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Proceedings of FEL 2007, Novosibirsk, Russia

Generation, laser systems, control of overlap of the
optical mode to electron beam focus, modelling,simulations and beam handling.

BASIC LAYOUT & COMPONENTS
The layout out the system is shown in fig 1.

The accelerator system
The accelerator for the FEL test facility utilises theinjector system [3] for the storage rings at MAX-lab.
These facilities are available during the majority of time
as injections are only scheduled for a few instances a day.
The system is built around two 5.2 m long linac
structures. These are equipped with SLED cavities [3] andpowered by one 35 MW klystron each, thus being able toprovide up to 125 MeV each. The electron beam is passed
via a recirculation system through the linacs twice andthus reach routinely an energy of 400 MeV. (The design
value is 500 MeV.)
The electron source is a RF-gun [4] consisting of ½+½1
cells. The cathode is BaO and is used in two modes.
Either as a thermionic source operated at 900 C, mainly
aimed for storage ring injection, and in a gated mode witha 5 ns laser to be able to fill bucket-by-bucket into thestorage rings. In the latter mode the cathode temperatureis reduced just below thermal emission, around 600 C,
and the electrons are gated by the laser system.
For the FEL operation the temperature will be reduced
further and a more powerful laser system providing 10 ps
pulses will generate the electrons.
The electron gun provides 2 MeV and the beam ispassed through a magnetic energy filter bending 120
degrees before entering the linac system.
The transport system from the linac to the FEL is theone used for injections into the MAX II storage ring. It
consists of mainly a dog-leg moving the beam from thebasement up to ground floor level. This dog-leg has
proven a good solution for bunch compression.
Table1: Parameters of the undulators and the chicane
Modulator
Period length
Number of periods
Minimum gap
Maximum K-parameter

48 mm
30
10 mm
4.3

Radiator
Period length
Number of periods
Minimum gap
Maximum K-parameter

56 mm
30
12 mm
4.3

ChicaneNumber of magnets
Type of magnet
Gap
Maximum field
Distance between magnets

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4
H-frame, electromagnet
15 mm
0.2 T
400 mmThe optical klystronThe optical klystron is built around two re-used
undulator structures. A pure permanent magnet (PPM)
structure has been loaned from the ESRF to be used in themodulator. The radiator will be equipped with the APPLE
structure of the BESSY UE56-1. The devices have been
re-measured, re-shimmed and equipped with newcarriages [5]. The chicane system is a newly constructedsystem. The parameters are summarized in table 1.

Laser system and transport optics
A combined laser system for the gun and the seeding of
the HG-FEL has been purchased from Thales SA. The
system comprises a common oscillator system locked to
the RF of the accelerators to better than 1 ps andsynchronization by optical fibre. The gun laser branch
consists of a pulse shaper, amplifier and harmonic
generation. The seed laser system is similar, but without
the pulse shaper. The layout of the system is shown in fig
2.
The system should deliver 500 μJ in a 10 ps pulse at
266 nm to the RF gun and 100 μJ in a 300 fs pulse at 266
nm to the seeding.
Gun laser
Seed laser

Pump

3 GHz
Synchroclock

P
u
m
p

Oscillator

Stretcher
Regen.
amplifierDazzler
Compressor

Compressor

Regen.
amplifier

THG

Pre
amplifier

P
u
m
p

THG
Seed

265 nm
100 uJ<500 fs

265 nm
500 uJ
10 ps

Gun

Fig 2. The laser system

Diagnostics
The start up of the system will mainly rely on OTR
screens for alignment and beam diagnostics. A calibrated
current monitor will be installed, but the response is not in
the range of the short pulses accelerated. Beamloss
monitors [6] are already installed along the undulators,
which will allow a rough estimate of beam position.
Energy distribution will be available on a screen at adispersion point by the beam dump. Alignment of thelaser beam to the electron beam will be made by opticalmethods using the spontaneous emission in the modulator
undulator and the laser beam. Temporal overlap between
seed laser and electron bunch will be achieved by several
techniques: photodiodes for the >ps range, detecting theTHz signal from the fraction of the electron bunchinteracting with the seed laser [6], detecting increased
energy, spread due to seed laser, at the beam dump.
Emittance measurements will be done by quadrupole
scans and 1-to-1 imaging of an OTR screen signal. Bunch
length measurements will be done both with CTR pulses

Proceedings of FEL 2007, Novosibirsk, Russia
measured in a Michelson interferometer [7] and byelectro-optical techniques using the seed laser as probe
pulse [8].

TARGET PERFORMANCE
The performance of the system in the first phase has
been calculated. The basic operation has been establishedin the injector, but the performance outlined below has
not been verified in detail.

FRAAU02

final acceleration which increases the final energy spread,but possibly reduces the timing jitter. An achromatic
dogleg consisting of two 15 degree bends with 5
quadrupoles in between performs the compression. The
dogleg provides an R56 of 5.5 cm which gives maximum
compression for an accelerating linac RF phase of 30 deg.
This however leads to a very high energy spread (since
compression happens after full acceleration). AfterFig 3. Simulations of the beam performance from the current gun system at the entrance to the optical klystron.

Electron beam
The electron beam is extracted from an RF gun
delivering around 2 MeV. In normal thermionic mode
there is a strong bunching right at the cathode surface. As
the energy is low the space charge effects significantly
increase the emittance. By gating at a later phase angle
the effect is reduced. For the FEL tests it will be used as aphotocathode gated gun. The gun laser will provide a 10
ps pulse which can be tuned to an optimal phase, around30 degrees, to reduce space charge effects. The gun
structure though was not optimised for low emittance
operations and thus the extracted charge has to be
reducedto ~0.1 nC to meet the demands of FEL tests.
The electrons are then accelerated in the reciruclated
linac system to >400 MeV. Compression is done after

optimizing the accelerating phase to give maximum peakcurrent while maintaining low emittance and energy
spread it was found that 8 deg gives the best electron
properties.
The beam has been traced through the system using thecodes Parmela [9], ASTRA [10] and elegant [11]. At theentrance of the optical klystron a peak current of 50 A, anormalised emittance around 3.5 mm mRad and an
energy spread of 0.04% can be achieved in a time windowof 300 fs (fig 3). The total charge in the window definedby the seed laser (time and transverse dimensions) is only
0.01 nC. The pulse has a long tail with lower current
which will not interact with the seed laser.
The pulse is stable in tracking and the peak current ismatched in time to the lowest emittance and energy
spread.

Fig 4. The beam at the optical klystron entrance in improved mode with a new gun. (not optimised results)
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Proceedings of FEL 2007, Novosibirsk, Russia

Coherent output

Phase 3 HHG source

The coherent enhancement and the sensitivity toemittance and energy spread have been calculated by a
1D model. In the 300 fs seed-laser-window the power is
0.2 MW (60 nJ) in the third harmonic at 88 nm. The
coherent enhancement is 6*104 over the incoherent
emission in the window. The total incoherent pulse shouldhave an energy of 6 pJ. A 1D model should in this context
be regarded as an “optimum performance”.
To increase the power an improved gun structure has
been designed.

The third phase will use a HHG (High Harmonic
Generation) chamber on the seed laser system to seed the
FEL process at a lower wavelength down to 100 nm. The
drive laser for the seed pulse will be equipped with anadditional amplifier and a High Harmonic Generation gas
jet chamber. This chamber can provide a tunable seedpulse down to 30 nm range. The electron energy willthough limit shortest seeding wavelength in the modulator
undulator to around 100 nm.
The gas jet chamber is system is developed and inoperation at the Lund Laser Center [14] and an adaptedchamber system will be built for the seeding. This part ofthe project still awaits funding.

STATUS
The project is at the moment (summer 2007)
developing quickly with the goal of taking the phase 1
into operation in the fall 2007.

Parts in operation
The complete injector and electron beam transportsystem are in operation. The electron gun is operating inboth thermionic mode and in laser gated mode with a longpulse, 5 ns, laser system. The undulator systems are
installed and in operation.

Parts installed
The laser systems are being installed/are installed.
Laser beam transport and optics will be installed afterlaser system acceptance tests. The magnetic and vacuum
system around the undulators are being installed at the
moment. Basic diagnostic systems are currently being
installed.

DEVELOPMENT OF THE SYSTEM
The system is planned to be developed in two new phases.

Phase 2 New gun
The second phase contains a new electron gun [12]allowing operation at higher bunch charges while
retaining the emittance. This system is an adapted
BNL/SLAC type RF gun with an emittance compensating
solenoid system [13].
The simulations of the beam performance with the new
gun system can be found in fig 4. The current at amaintained emittance is considerably increased allowing
for higher output power. The compression of the bunch istrickier in this high charge case and the energy spread
tends to increase. In start-to-end simulations it can beseen that the HG-process chooses to operate at a part ofthe bunch where the current is not the maximum but theenergy spread is slightly lower. In the third harmonic at
88 nm a power of 11 MW in < 100 fs is shown and at the
5th harmonic at 53 nm 1.4 MW is shown. The results
shown here are not the final optimisations (which await
publication).

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REFERENCES[1] D. Kraemer et al., BESSY TDR, 2004.
[2] MAX IV Conceptual Design report, MAX-lab, 2006.
[3] S. Werin et al., Commissioning of the 500 MeV
injector for MAX-lab, proceedings EPAC 2004
[4] B. Anderberg, A. Andersson, M. Demirkan, M.
Eriksson, L. Malmgren, S. Werin, The design of a
3GHz thermionic RF-gun and energy filter for MAXlab, Nucl. Instr. and Meth. A 491 (2002) 307[5] J. Bahrdt et al., Undulators for a Seeded HGHG-FEL
at MAX-lab, EPAC 2006.
[6] J. Bahrdt et al., Status of the undulator system of theseeded HGHG-FEL test bench at MAX-lab, theseproceedings.
[7] M. Brandin et al, Measurements and diagnostics on
the MAX recirculator, proceedings EPAC 2006
[8] P. J. Phillips et al., Single Shot Longitudinal Bunch
Profile Measurements by Temporally Resolved
Electro-Optical Detection, proceedings DIPAC07.
[9] PARMELA, K.R. Crandall, J.H. Billen, et al., Los
Alamos National Laboratory, USA.
[10] K. Flöttman “ASTRA User Manual”, September 18,
2000, www.desy.de/~mpyflo[11] M. Borland, “Elegant: A flexible SDDS-Compliant
Code for Accelerator Simulation”, APS LS-287,
2000.
[12] S. Werin, et al., Design of a new preinjector for the
MAX recirculator to be use din EUOREL,
Proceedings of EPAC 2006, Edinburgh, Scotland[13] R. Boyce, D.H. Dowell, J. Hodgson, J.F. Schmerge,
N. Yu, Design Considerations for the LCLS RF Gun,LCLS TN 04-4 (2004)[14] A. L’Huillier, F. Krausz, High-Order Harmonic
Generation, Handbook of Lasers and Optics (ed. F.
Träger), Springer, New York (2007) p. 219

Proceedings of FEL 2007, Novosibirsk, Russia

FRAAU03

COMPACT RING FEL AS A SOURCE OF HIGH POWER INFRARED
RADIATION
O.A. Shevchenko# , A.N. Matveenko, N.A. Vinokurov,
Budker Institute of Nuclear Physics, 11 Acad. Lavrentyev Prosp., 630090, Novosibirsk, Russia
Abstract
Ring FELs [1] were proposed mainly to improve thequality of radiation of x-ray FELs. Their main advantage
is the absence of mirrors. It appears that this advantage isalso useful for high power FELs. Another reason to build
infrared ring FEL is the proof-of-principle for shorter
wavelength FELs. Therefore we considered the scheme ofinfrared ring FEL which requires ERL with beam energy
50 MeV. Using extensive simulations we developed
requirements for electron beam parameters and magnetic
system of ring FEL. In spite of rather compact design
such FEL may provide more than 10 kW average power.

INTRODUCTION
The further development of FELs towards the region ofshort wavelengths and high powers is limited by theabsence of mirrors with appropriate parameters. Thereexist different approaches to the solution of this problem.
One of them is based on the fact that the beam
microbunching which appears in undulator can be partlyconserved in the specially designed isochronous bend.
Electron outcoupling may be considered as the simplest
scheme which utilizes this idea [2-3].
The further evolution of this approach leads to thescheme of the ring FEL which has been proposed in [1].
The lattice of the ring FEL consists of straight undulator
sections and isochronous bends which compose a ring. At
the bends radiation is lost. The signal between adjacentundulator sections is transferred trough microbunching.
Radiation from the last undulator produces energy
modulation of the new coming beam inside the first
undulator and amplification goes on till saturation. The
basic advantage of this scheme is that it has a feedback
which is realized without any mirrors.
High power ring FEL implies CW operation mode.
Therefore one has to use energy recovery linac (ERL) as asource of electron beams for such FEL. The present stateof the art of ERLs allows for producing the beams withrequired parameters which makes the ring FEL project
feasible.
The main problem of the ring FEL which becomes very
essential for the short wavelength is that it requires
isochronous bends to conserve microbunching. The
problem of creating of such bend is discussed in detail in[4]. To demonstrate the feasibility of the ring FEL
concept it is desirable to build first the small-scale model
for longer wavelength which may be interesting itself as asource of high power infrared radiation.
In this paper we consider the possible design of___________________________________________#

O.A.Shevchenko@inp.nsk.su

compact high power infrared ring FEL. We present thepossible lattice of the bends, required electron beam
parameters and results of simulation of FEL operation.

RING FEL SCHEME AND ELECTRONBEAM PARAMETERS
The schematic layout of the ring FEL is presented inFig. 1. It includes two undulator sections. One of themplays the role of “modulator” where the energy
modulation takes place. The other one may be called“radiator”, here the FEL radiation is generated. In the longwavelength case the debunching of the beam is not very
severe problem. Therefore one can use 360 degrees bend
and additional undulator sections are not required.

Figure 1. Schematic layout of the ring FEL.
The total 360 degrees bend in the proposed layout iscomprised of two 180 degrees isochronous bend sections
and a straight section with matching quadrupoles. The
lattice of the isochronous bend is presented in Fig 2. It
includes three bending magnets with different curvature
sign, quadrupoles which are required to focus transversal
dispersion and sextupoles which correct the second orderaberrations.

Figure 2. Magnetic lattice of the isochronous bend.
The beam and undulator parameters used in simulations
are listed in Table 1.

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Undulator period, m

0.06

Undulator deflection parameter

1.5

Electron energy, MeV

50

Beam charge, nC

1

Peak current, A

50/100Relative r.ms. energy spread, %0.1

Normalized emittance, mm×mrad

5

The beam parameters presented in this table do notmake any problems for contemporary accelerators. In
principle one can assume shorter bunch length and higher
peak current but in this case the wake field created bycoherent synchrotron radiation (CSR) significantly
reduces electron efficiency.

PARAMETERS OF OPTIMIZATION AND
SIMULATION RESULTS
We used different codes to simulate the ring FEL
operation. In this paper we present the results ofsimulations obtained by the code GENESIS [5] which is
widely accepted in the FEL community for simulations ofconventional FELs. Strictly speaking it was not pure
GENESIS simulation as this code is not adapted for the
ring FEL lattice. We used GENESIS to simulate
amplification of the FEL signal in the undulator sections.
The particle tracking in the bends including second-orderaberrations and CSR effects was done by external
homemade code.
To obtain the best performance of the FEL first of all
we optimized the bend lattice. The purpose of thisoptimization was to achieve the minimal value of beam

50 A peak current case
Setting of the stationary state in the ring FEL for theconsidered set of parameters requires approximately 50
passes as it is illustrated in Fig 3. Here one can see thedependence of electron efficiency (which is determined as
the ratio of radiation energy to electron bunch energy) on
the pass number.
0,3

0,2

0,1

0,0
0

10

20
30
Pass number

40

50

Figure 3. Dependence of the electron efficiency on thepass number in ring FEL for beam current 50 A. Dottedcurve corresponds to ideal case without CSR effects.
The dotted curve corresponds to CSR free case. It isseen that CSR effects do not reduce significantly electron
efficiency in this case.
16

0,6

12

0,4

8

(here ω0 is radiation

0,2

4

frequency and τ i - time delay of the i-th electron at the

0,0

iω τ

debunching factor 1− e 0 iexit from the bend). Adjusting the sextupoles it waspossible to make debunching less then 4 %.
The other optimization parameters were the lengths ofundulator sections which determine the single-pass gain
and saturation power. Length of the last undulator section
has to be large enough for the radiation power to reachsaturation level, but on the other hand increasing of its
length leads to the increase of the gain. It worth noting,that the gain does not have to be too large, otherwise thelasing may become unstable. The gain value can be
adjusted either by modulator length or by overlap degree
between new-coming beam in modulator and illuminatingradiation from radiator.
The optimal beam current is limited by CSR effects.
Further we present the simulation results for two cases. In
the first case the beam current is assumed to be 50 A andCSR effects are tolerable. In the second case of 100 A
current the CSR effects become very significant.
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Bunching

0,8Peak power, MW

Table 1: Undulator and electron beam parameters

Electron efficiency, %FRAAU03

0
0

1

2

3

4

5

z, m
Figure 4. Dependence of the beam bunching factor(green) and peak radiation power (red) on the longitudinalcoordinate in the last undulator section (dotted curves –CSR effects are not included).
Dependence of the beam bunching factor and peakradiation power on the longitudinal coordinate in the lastundulator section is shown in Fig. 4. Radiation power
almost reaches saturation level by the end of undulator(one can probably slightly increase its length yet) and thebunching starts dropping down. It is interesting that thewake created by CSR can increase peak power.

Proceedings of FEL 2007, Novosibirsk, Russia

12

0,4

8

0,2

4

0,0

0
4

6

8

10

0,3

s, mm

0,1

0,0

The output beam bunching and radiation power
distributions corresponding to stationary state are shownin Fig. 5. One can also see here the beam current
distribution (dashed violet curve).
10

2,0

8

1,6

6

1,2

4

0,8

2

0,4

0

10

20
30
Pass number

40

50

Figure 7. Dependence of the electron efficiency on thepass number in ring FEL for beam current 100 A. Dottedcurve corresponds to ideal case without CSR effects.

Bunching

Figure 5. Stationary beam bunching (green) and radiation
power (red) distributions at the exit from the lastundulator section (dotted curves – CSR effects are notincluded, dashed violet curve – beam current profile).

Power, a.u.

0,2

0,8

28

0,6

21

0,4

14

0,2

7

0

0,0
0
6,4

6,5

6,6

6,7

6,8

6,9

0,0
7,0

λ, μm

Figure 6. Spectral distribution of the output radiation
power (dotted curve – CSR effects are not included).
The output radiation power spectrum is plotted in Fig.
6. From this plot one can see that CSR effects
significantly increase the bandwidth.
Table2: Parameters of the output radiation
Wavelength, μm~ 6.6

Peak power, MW~ 10

Pulse duration, ps~ 10Electron efficiency, %0.15Power, MW

2

Increasing the peak current one can increase theradiation peak power but unfortunately in this case thewake field created by CSR effects significantly decreases
electron efficiency. This fact is illustrated in Fig. 7-8.
Electron efficiency, %0,6Power, MW

Bunching

100 A peak current case

16

0,8

FRAAU03

1

2

3

4

5

s, mm
Figure 8. Stationary beam bunching (green) and radiation
power (red) distributions at the exit from the lastundulator section (dotted curves – CSR effects are notincluded, dashed violet curve – beam current profile).
One can see from Fig 8. that although the radiation
peak power is larger then in CSR free case radiation pulse
becomes shorter due to CSR. In this case radiation isformed in the region where the energy chirp created by
CSR is small as it is shown in Fig. 9.

Parameters of the output radiation are summarized inTable 2.
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Proceedings of FEL 2007, Novosibirsk, Russia

0,6

120

0,4

100

0,2

80

0,0

60

-0,2

40

-0,4

20

CONCLUSION

Peak current, A

δγ/γ0, %FRAAU03

0

-0,6
1

2

3

4

5

s, mm
Figure 9. Beam current distribution (violet) and electronenergy deviation created by CSR (pink). Dotted curves
illustrate the beam bunching (green) and radiation power(red) distributions.
It should be noted that CSR wake field depends on thederivative of the beam current. In our simulations weassumed Gaussian current distribution. In the case of flattop distribution CSR effects may be smaller.

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We have shown theoretically the feasibility of thecompact high power ring FEL for the infrared region. At
that we have considered the problem of beam debunchingin the bends and CSR effects. The option to install
additional undulator into the free straight section exists.
Then all requirements (magnet tolerances, peak current,
emittances, etc.) will be even more relaxed. Moreover, theuse of this auxiliary undulator may decrease thelinewidth.
The next step would be the building of such FEL anddemonstrating the feasibility of the ring FEL concept inpractice.

REFERENCES[1] N.A. Vinokurov, O.A. Shevchenko, NIM A528
(2004) 491-496.
[2] 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.
[3] N. A. Vinokurov, NIM A375 (1996) 264.
[4] A.N. Matveenko, O.A. Shevchenko, N.A. Vinokurov,
Proc. Of the 2004 FEL Conference, p. 629[5] S. Reiche, NIM A429, (1999) 243.

Proceedings of FEL 2007, Novosibirsk, Russia

FRAAU04

RE-COMMISSIONING OF THE FAR-INFRARED FREE ELECTRONLASER FOR STABLE AND HIGH POWER OPERATION AFTER THE
RENEWAL OF THE L-BAND LINAC AT ISIR, OSAKA UNIVERSITY
R. Kato, S. Kashiwagi,T. Igo, Y. Morio, G. Isoyama#
Institute of Scientific and Industrial Research, Osaka University, Osaka, Japan
Abstract
The far-infrared FEL at the Institute of Scientific andIndustrial Research (ISIR), Osaka University, which was
operated in the wavelength region from 32 to 150 µm andwas suspended since 1998, is being commissioned forstable and high power operation. The FEL is based on the
L-band electron linac constructed in 1978, but it waslargely remodelled for higher stability and reproducibilityof operation as well as for long pulse operation for FEL.
The long pulse mode has been successfully commissioned
using a feed forward control system, which can stabilize
the amplitude and the phase of the 1.3 GHz RF power inthe macropulse within 0.5 % in amplitude and 0.3º inphase. The FEL system is the same as before except forthe strong focusing wiggler based on the edge-focussing
scheme, which was recently introduced. The FEL
experiment is all set up and we are waiting for the next
machine time and lasing.

INTRODUCTION
We have been developing a far-infrared FEL since late1980s based on the 40 MeV, L-band electron linac at theInstitute of Scientific and Industrial Research (ISIR),
Osaka University. The first lasing was obtained at 32~40µm in 1994 [1] and since then we progressively modified
the FEL system and continued experiment in between to
expand the wavelength region toward the longer
wavelength side beyond 100 µm. We finally obtainedlasing at 150 µm in 1998 [2], which was, at that time, thelongest wavelength obtained with FELs based on RF
linacs. We could not obtain power saturation because themacropulse duration is 2 µs, though the RF pulse is 4 µs
long, due to a long filling time of the acceleration tube of
the L-band linac and the number of amplification times islimited to 50 only. The linac was constructed
approximately 30 years ago and it was not suitable forstable and high power operation of FEL, so that wesuspended the development of the FEL.
In 2002, we had an opportunity to remodel the linac
largely for higher stability and reproducibility ofoperation. We also added a new operation mode for FEL
in which the macropulse duration can be extended to 8 µs.
I took time to remodel the linac and commission it, but
finally the operation mode for FEL is beingcommissioned and we are resuming the FEL again after
the long suspension. We will report the progress and thecurrent status of the re-commissioning of the FEL.
___________________________________________#

isoyama@sanken.osaka-u.ac.jp

RENEWED LINAC
The linac is comprised of a thermionic electron gun, athree-stage sub-harmonic buncher system with two 108
MHz RF cavities and a 216 MHz cavity, a pre-buncher, abuncher, and a 3 m long accelerating tube. The last threecomponents are excited by a single klystron of the 1.3
GHz frequency, the maximum peak output power of 30
MW, the pulse duration of up to 8 µs, and the repetition
frequency of 60 Hz. The main parameters of the linac arelisted in Table 1. A klystron modulator, which provides
high voltage pulses to the klystron, has two operation
modes; one is the normal mode with the pulse duration of
4 µs and the repetition rate of 60 pps and the other is thelong-pulse mode with 8 µs and 30 pps. The operation
modes can be changed manually but easily in a short time.
The maximum output power of the klystron is limited
to 25 MW in the long pulse mode, so that the maximum
beam energy in the multi-bunch mode used for FEL isslightly lower than 40 MeV.
Stability and reproducibility of linac operation are
essential for advanced studies with the linac, including
FEL and all the possible measures have been taken in theremodelling to reduce fast fluctuations and long-term
drifts. Most influential power supply for the stability is
the klystron modulator and it is designed and fabricated toreduce pulse-to-pulse fluctuations less than 0.1 %. Voltage
ripples on the flat top of the square pulse applied to the
klystron should be less than 0.1 % in order to make theamplitude and the phase of the output power from theTable 1: Main Parameters of the L-Band Linac
Acceleration frequency

1.3 GHz

Sub-harmonic buncher

108

Accelerating structures

Prebuncher×1, Buncher×1,
Accelerating tube×1

MHz×2,

216MHz×1

λ/4 coaxial resonators
Travelling wave, 2π/3 mode

Electron gun

Thermionic cathode (EIMAC
YU-156), DC 100 kV

Operation modes, peakcurrents or maximum
charge, and pulse
durations

Transient: 1.9 A, 8 ns

Single bunch: 91 nC, 20 ps
Steady: 1.9 A, 4 µs
Multi-bunch: 1.9 A, 8 µs

Repetition rate

≤ 60 pps

Klystron

30 MW×1

Total length10.5 m

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Proceedings of FEL 2007, Novosibirsk, Russia

klystron constant over the macropulse duration. Figure 1
shows a voltage pulse applied to the klystron with the
klystron modulator in the normal mode and a histogram
showing the intensity fluctuation in longer than two hours.
The undulation of the flat top in the normal mode ismeasured to be 0.21 % (peak to peak) over the time
period of 3.5 µs, which is twice as large as the design goal,
but it is much less in the latter third, while the fluctuationof the peak voltage is 0.06 % (two standard deviations) in
two hours, which meets the specifications.
Most popular operation modes of the linac are thetransient mode used for the pulse radiolysis study in thenanosecond region and the single bunch mode for pulse
radiolysis in the sub-picosecond region as well as SASE
experiment in the far-infrared region, and hence they are
first commissioned to resume the joint-use of the linac.

MULTI-BUNCH MODE FOR FELIn FEL experiments, the linac is operated in the multibunch mode, in which the second 108 MHz and the 216
MHz cavities of the sub-harmonic buncher system areswitched on and the 1.3 GHz RF power of 8 µs duration
is provided to the accelerating structures so that the multibunch beam with time intervals of 9.25 ns between
bunches, which is the inverse of 108 MHz is accelerated.
In order to make the peak of the energy spectrum of themulti-bunch beam sharp and to make intervals between
bunches precisely equal, the amplitude and the phase of

Klystron voltage [kV]

(a)
0

-100

-200

-300
-5

0

5
Time [µ s]1015

the RF power must be constant over the macropulse
period. It is said that the amplitude and the phase of theoutput power from a klystron do not vary in a pulse
provided that the flat top of the high voltage pulse applied
to the klystron is flat and constant. As the first step forcommissioning of the multi-bunch mode for FEL, webegan with the steady mode with the macropluse durationof 4 µs, in which the sub-harmonic buncher system is notturned on. Although the condition is met in our case, we
could not make the peak of the energy spectrum for thesteady mode sharp. We, therefore, measured theamplitude and the phase of the RF pulse from the klystronin the normal mode and found that the amplitude varied
by 3.1 % for the most flat part of 2.9 µs and the phasealso varied by ~12 degrees in 3.4 µs, both of which aremuch larger than our expectation of < 1 % in amplitudeand < 1 degree in phase.
Since reproducibility and stability of the high-voltage
pulse from the klystron modulator are high andaccordingly those of the amplitude and the phasevariations of the RF power from the klystron are also high,we have adopted the feed-forward method to compensate
for these variations. Figure 2 shows a block diagram of
the compensation system for the amplitude and the phaseof the 1.3 GHz RF power provided from the klystron to
the accelerating structures of the linac. We, for the
moment, adopt an analogue phase shifter with PIN diodes
for phase control and an I-Q modulator for amplitudecontrol. A part of the RF power is taken at a directional
coupler on a waveguide from the klystron to the linac.
The amplitude of the RF power is measured with a diodedetector and the phase is measured with a phase detector,
both of which have sufficiently fast response times, andthe output signals are analysed with a digital oscilloscope.
A personal computer calculates waveforms to be applied
to the phase shifter and the variable attenuator so thatboth amplitude and phase variations becomes constantand flat over the RF pulse. Among the various
components in the RF line, the phase shifter and the ABclass transistor amplifier, which is denoted by 300W
amplifier in Fig. 2, have relatively long response times. In
order to compensate for the slow response time, we use
overdrive technique and the equation

4000
(b)

∆ =0.06%

σ =0.027%

Counts

3000

2000

1000

0
99.5

100
Normalized klystron voltage [%]100.5

Fig. 1. High voltage pulse provided to the klystron in
the normal mode and a histogram showing the peakintensity fluctuation.
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522

Fig. 2. Block diagram of the compensation system for theamplitude and the phase of the 1.3 GHz RF power fromthe klystron.

Proceedings of FEL 2007, Novosibirsk, Russia

dVc (t )(1)
dt
is used to calculate the waveform generated with thefunction generator and applied to the control devices,where Vc is the control voltage for the ideally fast
responding system, τ the response time of the system, ∆t
is the delay time in the control and measurement system,
and Vin the actual control voltage. The response time andthe delay time are measured with the actual system andthey are τ = 50 ns and ∆t = 540 ns for the amplitudecontrol and τ = 780 ns and ∆t = 640 ns for the phase
control. Figure 3 shows the amplitude and the phasevariations of the 1.3 GHz RF power in the long pulse
mode before and after the compensation. The amplitudevaries by 14.8 % in 7.4 µs and the phase by 13.5º before
the compensation and they are reduced to 0.5 % and 0.3º,
respectively, after compensation iteratively made several
times.
Another problem we ran up against in thecommissioning of the multi-bunch mode is that a correctenergy spectrum could not be measured due to a digitalcurrent meter used for a Faraday cup in the momentum
analyser, which is newly introduced in the upgrade of thelinac in place of an old analog current meter, because it
does not measure a correct current for an electron beam
longer than a microsecond. It took time to find the current
meter responsible for it. The long pulse electron beam isaccelerated with the corrected RF power and energy
spectra are measured with another momentum analyser
with a fluorescent plate and a CCD camera. Figure 4
Vin (t − ∆t ) = Vc (t ) + τ

Amplitude [a.u.]

(a)
-0.04

14.8%
-0.0450.5%7.2µ s-0.05

Phase [deg]

(b)

100
13.5deg90

0.3deg7.4µ s

80

0

5

10

Time [µ s]1520

Fig.3. Amplitude and the phase of the 1.3 GHz RF
power for the linac before and after the compensation.
The panel (a) shows the amplitude and (b) the phase,
while the red and the blue lines before and after
compensation, respectively.

FRAAU0424.43µ sIntensity [a.u]1.53.69µ s2.95µ s12.21µ s0.5

1.48µ s0.74µ s0

Fig. 4. Energy spectra of electron beams with several time
durations in the long pulse mode without the SHB system.
shows energy spectra of electron beams with several
different time durations accelerated in the long pulse
mode without the SHB system, which we call the steadymode. The filling time of the accelerating tube isapproximately 2 µs and energy spectra for the electron
beams with pulse durations shorter than it have broader
peaks due to the transient effect, while the sharp peaks
grow up on the lower energy side in the energy spectra ofelectron beams longer than the filling time or 2 µs. The
electron beam is easily conditioned in the multi-bunchmode with the SHB system being on and thus the multibunch mode for FEL is successfully commissioned.

FEL SYSTEM
The infrared FEL system, main parameters of which arelisted in Table 2, is the same before the suspension except
for the wiggler. The multi-bunch beam accelerated with
the L-band linac is transported through the beam transportline consisting of two bending magnets and several
quadrupole magnets to the wiggler. We used aconventional planar wiggler, but the magnet arrays were
replaced with new ones that can not only wiggle theelectron beam but also focus it both horizontally andvertically [3.] Figure 5 shows the magnetic field and thefield gradient in the vertical direction measured along thebeam axis of the strong focus wiggler at the magnet gapof 3 cm. The period length is 6 cm and the number of
periods is 32, which are the same as before. The
maximum peak magnetic field is 0.39 T at the minimum
gap of 3 cm, which is slightly higher than before because
permanent magnet materials advanced in the meanwhile.
The FODO structure is adopted for the double focusing sothat the electron beam of any energy accelerated with thelinac can be focused even at larger wiggler gaps. The
wiggler consists of four FODO cells and the cell length is
0.48 m. The focusing and the defocusing units are single
wiggler periods with edge angles ±5º and the drift space isfour normal wiggler periods. The maximum field
gradients are ±3.2 T/m at the gap of 3 cm. The new
wiggler was developed and installed for SASE
experiments in the far-infrared region being conducted

FEL projects

523

FRAAU04

Proceedings of FEL 2007, Novosibirsk, Russia

Table 2: Main Parameters of the Infrared FEL
Wiggler

0.4

Permanent magnet

Ne-Fe-B

Period length

6 cm

Number of periods

32

Magnet gap

12 – 3 cm-0.2

Peak magnetic field

0.39 T-0.4

Krms-value

0.013 – 1.556

Total length10.5 mFocusing type

Strong focus with the edgefocusing scheme

Maximum field gradient

3.2 T

Length of FODO cell

0.48 mNumber of FODO cells

4-2

Optical resonator-3

By [T]

0.2
0LengthConcentric resonator withspherical mirrors
5.531 m

-500

0
z[mm]

-1000

-500

0

500

1000

4
dBy/dx [T/m]

3
2
1
0

-1

-4

Type

-1000

500

1000

Fig. 5. Magnetic field and the field gradient in thevertical direction measured along the beam axis of thestrong focus wiggler at the magnet gap of 3 cm.

Mirrors
Type

Spherical copper mirrors coatedwith gold

Curvature radii

3.358 m (upstream), 2.877 m(downstream)

Diameter

8 cm

Rayleigh range

1m

Output coupling

3φ hole at the center of the
upstream mirror

SUMMARY
After a long period of suspension, the infrared FEL at
ISIR, Osaka University is being commissioned. The linac
has been largely remodelled, so that the FEL is expected
to operate stably at the saturation power level, which was
not possible before. The optical resonator and themeasurement system have been aligned, the experiment is
all set up, and we are waiting for the machine time for
FEL.

REFERENCES
with the wiggler, but the FEL gain will be enhanced with
it.
The optical resonator is a concentric resonatorconsisting of two spherical mirrors with different
curvature radii. It is 5.531 m long and four optical pulses
bounce back and forth in the cavity. The two mirrors are
installed asymmetrically to the wiggler due to limitations
by the magnets and other components in the FEL beamline and the curvature radii are chosen so that the waist of
the stored light is located at the center of the wiggler. The
FEL light is taken out through a hole at the center of the
upstream mirrors and it is led with mirrors to themeasurement room through the evacuated opticaltransport line, where the low vacuum in the opticaltransport line is separated with a synthetic diamondwindow from the high vacuum in the FEL beam line. The
FEL light is analysed with a grating monochromator anddetected with a Ge:Ga photoconductive detector cooledwith liquid helium.

FEL projects

524[1] S. Okuda, Y. Honda, N. Kimura, J. Ohkuma, T.
Yamamoto, S. Suemine, T. Okada, S. Ishida, T.
Yamamoto, S. Takeda, K. Tsumori, and T. Hori,
Nucl. Instr. And Meth. A358 (1995) 244.
[2] R. Kato, S. Kondo, T. Igo, T. Okita, T. Konishi, S.
Suemine, S. Okuda, and G. Isoyama, Nucl. Instr. And
Meth. A445 (2000) 169.
[3] G. Isoyama, R. Kato, S. Kashiwagi, T. Igo, Y. Kon, T.
Yamamoto, S. Suemine, “Performance of theRenewed L-band Linac and Recent Progress ofDevelopment FEL and SASE at Osaka University,
APAC’07, Indore, India, January-February 2007,
TUPMA68.