It is now well-established [2, 3] that high-charge ultra-short bunches can radiate coherently on curved trajectories (coherent synchrotron radiation). The two main consequences of 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 driver linacs 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 with numerical simulations. Schemes for reducing the impact of CSR on the beam dynamics are also discussed in the frame of the TESLA X-ray FEL project

Limberg, T

Piot, P

Limberg, T.

Piot, P.

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Longitudinal Phase Space Disruption in Magnetic Bunch Compressors

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LONGITUDINAL PHASE SPACE DISRUPTIONIN MAGNETIC BUNCH COMPRESSORST. Limberg and Ph. PiotDeutsches Elektronen Synchrotron-DESY 22603 HAMBURG, GERMANYAbstractIt is now well-established [2, 3] that high-charge ultra-shortbunches can radiate coherently on curved trajectories (co-herent synchrotron radiation). The two main consequencesof such an effect are (1) an energy redistribution withinthe bunch, (2) a potential transverse emittance dilution inthe bending plane. This effect is especially important inthe foreseen next generation of free-electron laser driverlinacs and linear colliders. In this paper after briefly dis-cussing the general aspects of coherent synchrotron radi-ation (CSR), we report on recent experimental results ob-tained 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.1 INTRODUCTIONWhen electrons travel on curved trajectory, e.g. in bendingmagnets, they emit synchrotron radiation. Radiation emit-ted 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 pathlength in the bend is comparable to the so-called overtak-ing length defined as (24s2)1=3, where sis the rmsbunch length and  the bending radius. This is the regimeof coherent synchrotron radiation (CSR) – the power radi-ated [1] is / N 2 (N being the number of electrons in thebunch). This effect is favored in magnetic bunch compres-sors employed in FEL’s and linear colliders, where short(ps-level) and highly charged (Q ' 1 nC) bunches travelthrough magnets with small bending radii (  1 m). TheCSR longitudinal wake function scales as [2]cWjj=Q0(2)3=231=34=3s2=3, (1)0being the electric permittivity for vacuum. Eqn (1)assumes the bunch has a Gaussian charge density. Forthe bending radius of the bunch compressor dipoles usedat the Tesla Test Facility (TTF I),  = 1:6 m, we havecWjj' 3:64  4=3s[eV/nC/m].2 RECENT EXPERIMENT AT TTF IThe TTF I [4] driver-accelerator (see Fig. 1) consists ofa superconducting RF-linac capable of accelerating elec-tron bunches up to 300 MeV. A 17 MeV photoinjectorPhilippe.Piot@desy.deproduces bunches of s'2.7 mm that are compresseddown to s'750 m by the mean of a magnetic bunchcompressor installed downstream of the first accelerat-ing TESLA-module (module 1), at an energy of approxi-mately 135 MeV. The beam is then accelerated in a sec-ond 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 energygain. The magnetic compressor consists of a four-dipoleachromatic chicane, the deflection angle of the dipoles be-ing 18 deg yielding a momentum compaction R56=(@s)=(@Æ) =  18:04 cm. Preliminary experiment onφφE=17MeVE~230 MeVUndulatorHigh energySpectrometer FELDumpE~135 MeVBunch CompressorAcc. Module 2Acc. Module 1OTRe-Figure 1: Overview of the TTF I experiment (the red solidcircle represents locations of beam profile monitors).bunch compression were performed [5] and it was repro-ducibly observed that the energy profile fragments in thevicinity of maximum compression. A typical energy pro-file measurement for maximum compression is presentedin Fig. 2 (top): the energy distribution splits into princi-pally two main peaks, the characteristic energy separationbeing '3 MeV. To understand such phenomenon we con-sidered several effects: geometric wake in TESLA-cavity,possible charge modulation due to imperfection in the pho-tocathode drive laser, bunch self-interaction via CSR ef-fect within the compressor. Only the latter of these con-siderations produces effects that are comparable to thoseobserved (see Fig. 2 (bottom)) while both former effectscould not yield any fragmentation of the energy profile.The CSR-induced effects were calculated using the track-ing program TraFiC4 [6] which incorporates bunch self-interaction due to retardation effects. The simulations in-clude 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).−2 0 2 4 600.51Population [a.u.]−2 0 2 4 600.51Population [a.u.]∆ E [MeV] (zero arbitrary)spectro exitbc exit     Figure 2: Example of measured (top) and simulated (bot-tom) energy profiles. The simulations correspond to the en-ergy profiles downstream of the compressor (dashed lines)and at the measurement location (solid lines). The mea-surements are presented in Ref. [5].3 LESSONS FROM TTF I ANDIMPLICATIONS ON TESLA X-FELIt was pointed out [8] that local charge concentration withinthe bunch can significantly enhance the CSR-wake func-tion. In our case such a charge concentration originatesfrom the nonlinear distortion of the longitudinal phasespace at the compressor entrance: the bunch, being ratherlong at the entrance of module 1, accumulates some RF-curvature during its acceleration in module 1. The com-pression of such distorted longitudinal phase space (seeFig. 3), produces a local peak of 25 m (rms) containingapproximately half of the bunch charge (i.e. 0.5 nC). Sim-ple estimates of the CSR-wake amplitude using Eqn (1)gives 2.5 MeV/m, a number close to (supposing a self-interaction length of 1 m) the measurement value. The lon-gitudinal phase space and charge density downstream of thecompressor obtained with TraFiC4 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 spec-trometer magnet (see Fig. 2 (bottom)). CSR-induced gra-dient would lengthen the bunch if it passes through a simplefour-dipole chicane as in TTF I (R56< 0). However, if theenergy gradient is generated inside the chicane, and a sin-gle spectrometer magnet follows downstream, the effectiveR56now results from the dipoles and quadrupoles mag-nets between the point where the energy correlation was in-duced and the point of observation. For instance, the effec-tive R56between 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 hasthe 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,the incoming pulse is essentially given by the photocathodedrive-laser (a Gaussian pulse of 8 ps), and is not easy to re-duce.−0.0001 0.0009 0.0019050010001500CSR OFFCSR ON−0.02500.0255 10 15Peak curr. [A]Population [a.u.]δ Figure 3: Impact of CSR effect on the longitudinal phasespace downstream of the bunch compressor. The simula-tion corresponds to the TTF I compressor of Fig. 2.We have studied how to reduce the impact of CSR-driveneffects 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 en-trance, of 5 kA. The injector is required to deliver bunchwith peak current of approximately 400-500 A. Optimiza-tion of the photoinjector parameters yields a minimum tol-erable bunch length at the gun exit of ' 1:7 mm (to min-imize the transverse emittance). Thus the first stage com-pression has to reduce the bunch from 1.7 mm down toapproximately 0.250 mm – the adopted compressor con-sists of a chicane similar to TTF I with a lower momentumcompaction of R56=  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 longitudinalphase space for these two cases. For both cases, the up-stream linac is operated so that the shortest bunch length isobtained. The Gaussian density yields a higher charge con-centration that the Uniform one, which results in strongerCSR-effects in particular on the energy profile. This de-pendence on the incoming profile suggests that tailoring anincoming longitudinal distribution might be a way of re-ducing the CSR impact. Practically this is not an easy task:the longitudinal density is generally chosen to be as closeas possible to a uniform distribution in order to reduce non-linear space charge forces at low energy.Another mechanism for reducing the impact of CSRwake field is to correct for the longitudinal phase spacenonlinear distortions. The principal advantages of thisscheme are that (1) the bunch shape does not change and0 5 10x 10−4−0.0500.05s [m]δ0 5 10−0.0500.05δPopulation [a.u.]0 5 10x 10−405001000150020002500s [m]Peak Curr. [A]Figure 4: Comparison of magnetic compression impact onthe beam for a Uniform (solid) and Gaussian (dashed) in-coming 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 indeedforeseen for the TESLA X-ray FEL. The photoinjector isforeseen to incorporate a 3.9 GHz RF accelerating sec-tion [12] whose purpose is to “linearize” the longitudinalphase space. This 3.9 GHz section has to be operated ina decelerating mode. As a consequence the beam loosesabout 10% of its energy during this correction mechanism.In Fig. 5 we compare the phase space upstream and down-stream of the compressor. In this example the incominglongitudinal phase space is obtained from multi-particlesimulations of the photoinjector and includes the correctionusing TESLA cavities scaled to 3.9 GHz. It can be seen thatthe compression process does not significantly impact theshape of the beam profiles.−2 0 2x 10−3−0.04−0.0200.020.04s [m]δ−2 0 2x 10−30100200300400s [m]Peak Curr. [A]0 0.02 0.04−0.04−0.0200.020.04δPopulation [a.u.]Figure 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 away of reducing the impact of CSR on the beam dynam-ics. Because the vacuum chamber acts as an electromag-netic waveguide, only frequency components of the radia-tion spectrum beyond the cut off frequency, !  c= (2=h)3=2 (h being the vacuum chamber height), can prop-agate. Simulations were performed with TraFiC4, usingmetallic plates separated by h = 8 mm. In Fig. 6 wepresent the impact of shielding on the longitudinal emit-tance development along the chicane compared to the free-space case.0 2 4 6 8Distance [m]050100150Long. Emittance [mm−keV] free spaceshieldedB1 B2 B3 B4Figure 6: Effect of shielding with 8 mm parallel plates vac-uum chamber on the longitudinal emittance growth alongthe compressor beamline. The labels B1,...,B4 correspondto the location of the chicane dipoles.4 REFERENCES[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)[4] Edwards D.A. (Editor), Tesla Test Facility CDR, reportTESLA-1995-01 (1995)[5] Hu¨ning M., Piot, Ph., Schlarb H., “Observation of energyfragmentation at TTF”, proc. of FEL 2001 Duke N.C. USA(to be published in NIM)[6] Dohlus M., Kabel A., Limberg T., Nucl. Instr. Meth. A445, p.338-342 (2000)[7] Limberg T., Piot Ph., Schneidmiller E.A, “Analysis of energyfragmentation at TTF”, Ibid [5][8] Li R., proc. of EPAC-2000 Vienna, p. 1312-1314 (2000)[9] Limberg T., Piot Ph., to be presented at PAC’01 Chicago[10] Technical Design Report of TESLA, report TESLA-FEL-01-04 (2001)[11] Ferrario M., Flo¨ttmann K, Grygorian B., Limberg T., PiotPh., report TESLA-FEL-01-03 (2001);[12] Flo¨ttmann K, Limberg T., Piot Ph., report TESLA-FEL-01-06 (2001); the method was experimentally demonstrated inDowell D. Nucl. Instr. Meth. A398, p.273 (1997);

Longitudinal phase space disruption in magnetic bunch compressors

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