LONGITUDINAL PHASE SPACE DISRUPTION
IN MAGNETIC BUNCH COMPRESSORS
T. Limberg and Ph. Piot
Deutsches Elektronen Synchrotron-DESY 22603 HAMBURG, GERMANY
Abstract
It is now well-established [2, 3] that high-charge ultra-shortbunches can radiate coherently on curved trajectories (coherent synchrotron radiation). The two main consequencesof such an effect are (1) an energy redistribution within
the bunch, (2) a potential transverse emittance dilution in
the bending plane. This effect is especially important in
the foreseen next generation of free-electron laser driverlinacs and linear colliders. In this paper after briefly discussing the general aspects of coherent synchrotron radiation (CSR), we report on recent experimental results obtained at the Tesla Test Facility I and compare them withnumerical simulations. Schemes for reducing the impactof CSR on the beam dynamics are also discussed in theframe of the TESLA X-ray FEL project.

1INTRODUCTION

φWhen electrons travel on curved trajectory, e.g. in bending
magnets, they emit synchrotron radiation. Radiation emitted at a retarded time can overtake the bunch on a straightline and interact with electrons ahead in the bunch. Thistype of bunch “self-interaction” is relevant when the path
length in the bend is comparable to the so-called overtaking length defined as (24 s 2 )1=3 , where s is the rms
bunch length and  the bending radius. This is the regimeof coherent synchrotron radiation (CSR) – the power radiated [1] is / N 2 (N being the number of electrons in thebunch). This effect is favored in magnetic bunch compressors employed in FEL’s and linear colliders, where short(ps-level) and highly charged (Q ' 1 nC) bunches travel
through magnets with small bending radii (  1 m). TheCSR longitudinal wake function scales as [2]c

Wjj =Q
4=3 2=3
0 (2 )3=2 31=3 s,(1)

0 being the electric permittivity for vacuum.

Eqn (1)assumes the bunch has a Gaussian charge density. For
the bending radius of the bunch compressor dipoles usedat the Tesla Test Facility (TTF I),  = 1:6 m, we have
4=3
[eV/nC/m].
Wjj ' 3:64  sc2produces bunches of  s '2.7 mm that are compressed
down to s '750 m by the mean of a magnetic bunch
compressor installed downstream of the first accelerating TESLA-module (module 1), at an energy of approximately 135 MeV. The beam is then accelerated in a second TESLA-module (module 2). Further downstream,in a spectrometer transport line, a beam profile monitor(OTR) provides a beam energy measurement. The rateof compression is tuned by adjusting the RF-phase ofmodule 1, thus adjusting the amount of correlated energyspread. Module 2 is always operated for maximum energy
gain. The magnetic compressor consists of a four-dipole
achromatic chicane, the deflection angle of the dipoles being 18 deg yielding a momentum compaction R 56 =(@s)=(@Æ ) =18:04 cm. Preliminary experiment on

RECENT EXPERIMENT AT TTF I

The TTF I [4] driver-accelerator (see Fig. 1) consists ofa superconducting RF-linac capable of accelerating electron bunches up to 300 MeV. A 17 MeV photoinjector
 Philippe.Piot@desy.deE~135 MeV
E=17MeVAcc. Module 1

φAcc. Module 2

Bunch Compressor

High energy
Undulator Spectrometer FELe-E~230 MeV

OTR

Dump

Figure 1: Overview of the TTF I experiment (the red solid
circle represents locations of beam profile monitors).

bunch compression were performed [5] and it was reproducibly observed that the energy profile fragments in thevicinity of maximum compression. A typical energy profile measurement for maximum compression is presented
in Fig. 2 (top): the energy distribution splits into principally two main peaks, the characteristic energy separation
being '3 MeV. To understand such phenomenon we considered several effects: geometric wake in TESLA-cavity,
possible charge modulation due to imperfection in the photocathode drive laser, bunch self-interaction via CSR effect within the compressor. Only the latter of these considerations produces effects that are comparable to thoseobserved (see Fig. 2 (bottom)) while both former effects
could not yield any fragmentation of the energy profile.
The CSR-induced effects were calculated using the tracking program TraFiC 4 [6] which incorporates bunch selfinteraction due to retardation effects. The simulations include both the compressor and the spectrometer dipoles [7].
The latter, which has a bending angle comparable to thecompressor dipoles can locally over-compress the beam sothat CSR-induced effects are not negligible as shown inFig. 2 (bottom).

Population [a.u.]

the incoming pulse is essentially given by the photocathodedrive-laser (a Gaussian pulse of 8 ps), and is not easy to reduce.

10.025−20246δ

01

spectro exit
bc exit0−2024∆ E [MeV] (zero arbitrary)0−0.025

0.5

56Figure 2: Example of measured (top) and simulated (bottom) energy profiles. The simulations correspond to the energy profiles downstream of the compressor (dashed lines)
and at the measurement location (solid lines). The measurements are presented in Ref. [5].

3 LESSONS FROM TTF I ANDIMPLICATIONS ON TESLA X-FEL
It was pointed out [8] that local charge concentration within
the bunch can significantly enhance the CSR-wake function. In our case such a charge concentration originatesfrom the nonlinear distortion of the longitudinal phasespace at the compressor entrance: the bunch, being rather
long at the entrance of module 1, accumulates some RFcurvature during its acceleration in module 1. The compression of such distorted longitudinal phase space (seeFig. 3), produces a local peak of 25 m (rms) containing
approximately half of the bunch charge (i.e. 0.5 nC). Simple estimates of the CSR-wake amplitude using Eqn (1)gives 2.5 MeV/m, a number close to (supposing a selfinteraction length of 1 m) the measurement value. The longitudinal phase space and charge density downstream of thecompressor obtained with TraFiC 4 are presented in Fig. 4with and without CSR. It is worthwhile to note that the CSReffect, in this example, enhances the peak current. Thisleads to an increase in the energy disruption in the spectrometer magnet (see Fig. 2 (bottom)). CSR-induced gradient would lengthen the bunch if it passes through a simple
four-dipole chicane as in TTF I (R 56 < 0). However, if theenergy gradient is generated inside the chicane, and a single spectrometer magnet follows downstream, the effective
R56 now results from the dipoles and quadrupoles magnets between the point where the energy correlation was induced and the point of observation. For instance, the effective R56 between the third dipole of the chicane in TTF 1,
where the CSR-effect is expected to be the strongest, andthe end of the spectrometer is ' +0:40 cm. This has
the proper sign and magnitude to even over-compress thebunch locally, i.e. in region of the phase space where theCSR-induced gradient is significant. In the case of TTF I,

1500
Peak curr. [A]Population [a.u.]

0.5

15Population [a.u.]

1000

CSR OFFCSR ON

500
0−0.0001

100.0009

0.0019Figure 3: Impact of CSR effect on the longitudinal phasespace downstream of the bunch compressor. The simulation corresponds to the TTF I compressor of Fig. 2.
We have studied how to reduce the impact of CSR-driven
effects in for the TESLA X-ray FEL [10] injector [11].
In the driver-accelerator, the bunch is compressed in threestages to reach a final peak current, at the undulator entrance, of 5 kA. The injector is required to deliver bunchwith peak current of approximately 400-500 A. Optimization of the photoinjector parameters yields a minimum tolerable bunch length at the gun exit of ' 1:7 mm (to minimize the transverse emittance). Thus the first stage compression has to reduce the bunch from 1.7 mm down toapproximately 0.250 mm – the adopted compressor consists of a chicane similar to TTF I with a lower momentum
compaction of R 56 = 10:0 cm. We have investigated theimpact of two types of incoming distributions: Gaussianand Uniform (both with the same rms value of 1.7 mm).
In Fig. 4, we present the charge density and longitudinal
phase space for these two cases. For both cases, the upstream linac is operated so that the shortest bunch length isobtained. The Gaussian density yields a higher charge concentration that the Uniform one, which results in stronger
CSR-effects in particular on the energy profile. This dependence on the incoming profile suggests that tailoring anincoming longitudinal distribution might be a way of reducing the CSR impact. Practically this is not an easy task:
the longitudinal density is generally chosen to be as close
as possible to a uniform distribution in order to reduce nonlinear space charge forces at low energy.
Another mechanism for reducing the impact of CSR
wake field is to correct for the longitudinal phase space
nonlinear distortions. The principal advantages of thisscheme are that (1) the bunch shape does not change and0.05

δ

δ

0.05

0−0.0505s [m]Peak Curr. [A]2500

10x 100−0.050510Population [a.u.]−420001500

way of reducing the impact of CSR on the beam dynamics. Because the vacuum chamber acts as an electromagnetic waveguide, only frequency components of the radiation spectrum beyond the cut off frequency, !  c= (2=h)3=2 (h being the vacuum chamber height), can propagate. Simulations were performed with TraFiC 4, using
metallic plates separated by h = 8 mm. In Fig. 6 we
present the impact of shielding on the longitudinal emittance development along the chicane compared to the freespace case.

1000150
B1005s [m]10x 10−4Figure 4: Comparison of magnetic compression impact on
the beam for a Uniform (solid) and Gaussian (dashed) incoming charge density.
the generation of highly charged peaks is avoided, and (2)maximum compression is not required anymore to achievebunch length of ' 250 m. Such technique is indeed
foreseen for the TESLA X-ray FEL. The photoinjector isforeseen to incorporate a 3.9 GHz RF accelerating section [12] whose purpose is to “linearize” the longitudinal
phase space. This 3.9 GHz section has to be operated ina decelerating mode. As a consequence the beam looses
about 10% of its energy during this correction mechanism.
In Fig. 5 we compare the phase space upstream and downstream of the compressor. In this example the incoming
longitudinal phase space is obtained from multi-particle
simulations of the photoinjector and includes the correction
using TESLA cavities scaled to 3.9 GHz. It can be seen thatthe compression process does not significantly impact theshape of the beam profiles.
0.04

0.04

0.02

0.02

δ

δ

0−0.02−20s [m]2−3x 10

0.02

0.04

Population [a.u.]

400

Peak Curr. [A]B3

B4

free space100

shielded
50002

4Distance [m]68Figure 6: Effect of shielding with 8 mm parallel plates vacuum chamber on the longitudinal emittance growth along
the compressor beamline. The labels B1,...,B4 correspondto the location of the chicane dipoles.

4REFERENCES[1] Nodvick J.S., Saxon D.S., Phys. Rev. 96, p. 180 (1954)[2] Y. Derbenev, J. Roßbach, E. Saldin, V. Shitlsev, reportTESLA-FEL 95-05 (1995)[3] Murphy J.B, Krinsky S., Gluckstern R.L., Part. Acc. 57, pp.
9-64 (1997)[5] Hüning M., Piot, Ph., Schlarb H., “Observation of energy
fragmentation at TTF”, proc. of FEL 2001 Duke N.C. USA(to be published in NIM)

0−0.040B2[4] Edwards D.A. (Editor), Tesla Test Facility CDR, reportTESLA-1995-01 (1995)

−0.02

−0.04

Long. Emittance [mm−keV]

500[6] Dohlus M., Kabel A., Limberg T., Nucl. Instr. Meth. A445, p.
338-342 (2000)

300[7] Limberg T., Piot Ph., Schneidmiller E.A, “Analysis of energy
fragmentation at TTF”, Ibid [5]200[8] Li R., proc. of EPAC-2000 Vienna, p. 1312-1314 (2000)

100[9] Limberg T., Piot Ph., to be presented at PAC’01 Chicago

0−20s [m]2−3x 10Figure 5: Phase space before (solid) and after (dash) the1st stage compression stage in the TESLA X-ray FEL.
Finally, avoiding the CSR-field to propagate is also a[10] Technical Design Report of TESLA, report TESLA-FEL-0104 (2001)[11] Ferrario M., Flöttmann K, Grygorian B., Limberg T., PiotPh., report TESLA-FEL-01-03 (2001);[12] Flöttmann K, Limberg T., Piot Ph., report TESLA-FEL-0106 (2001); the method was experimentally demonstrated inDowell D. Nucl. Instr. Meth. A398, p.273 (1997);