Recent experiments [1] have explored the use of a free-electron laser (FEL)
as a buncher for a microwave two-beam accelerator, and the subsequent driving
of a standing-wave rf output cavity. Here we present a deeper analysis of the
longitudinal dynamics of the electron bunches as they are transported from the
end of the FEL and through the output cavity. In particular, we examine the
effect of the transport region and cavity aperture to filter the bunched
portion of the beam.
  [1] T. Lefevre, et. al., Phys. Rev. Lett. 84 (2000), 1188.Comment: 3 pages, 8 figures. Submitted to XX Int'l LINAC Conferenc

Donohue, J. T.

Gardelle, J.

Gouard, P.

Lefevre, T.

Lidia, S.

Rullier, J. L.

Vermare, C.

English

arXiv

Recent experiments have explored the use of a free-electron laser (FEL) as a buncher for a microwave two-beam accelerator, and the subsequent driving of a standing-wave rf output cavity. Here the authors present a deeper analysis of the longitudinal dynamics of the electron bunches as they are transported from the end of the FEL and through the output cavity. In particular, the authors examine the effect of the transport region and cavity aperture to filter the bunched portion of the beam

Donohue, J.T.

Rullier, J.L.

UNT Digital Library

Analysis of Longitudinal Bunching in an FEL Driven Two-Beam AcceleratorS. Lidia, LBNL, Berkeley, CA USAJ. Gardelle, T. Lefevre, CEA/CESTA, Le Barp, FranceJ.T. Donohue, CENBG, Gradignan, FranceP. Gouard, J.L. Rullier, CEA/DIF, Bruyeres le Chatel, FranceC. Vermare, LANL, Los Alamos, NM USAAbstractRecent experiments [1] have explored the use of a free-electron laser (FEL) as a buncher for a microwave two-beam accelerator, and the subsequent driving of a standing-wave rf output cavity. Here we present a deeper analysis ofthe longitudinal dynamics of the electron bunches as theyare transported from the end of the FEL and through theoutput cavity. In particular, we examine the effect of thetransport region and cavity aperture to filter the bunchedportion of the beam.1 INTRODUCTIONSince 1995, free-electron laser (FEL) experiments at theCEA/CESTA facility have addressed the problem of thegeneration of a suitable bunched drive beam for a two-beamaccelerator using linear inductionaccelerator technology.In these trials, a 32 period long bifilar-helix wiggler is cou-pled with a 35GHz, 5kW magnetron to provide an effectiveFEL interaction with the beam. Early experiments [2], [3]demonstrated optical diagnostic techniques to show bunch-ing of the beam at the 35GHz FEL resonant frequency.In the first cavity experiments [1], the induction linac’PIVAIR’ was utilized, since its design energy of 7.2MeVis near optimum for a Ka-band two-beam accelerator basedupon the relativistic-klystron mechanism [4]. During op-eration, PIVAIR delivered a 6.7MeV, 3kA, 60ns (FWHM)electron beam. The emittance out of the injector is approx-imately 1000 mm mrad, and the energy spread is lessthan 1% (rms) over the pulse length. The full current iscollimated to 830 30A at the FEL entrance. Two 6-period adiabatic sections are used to inject the beam intothe proper helical trajectory inside the wiggler, and then torelease the beam back into the transport line afterwards.After the wiggler follows a short transport beamline tocapture and focus the beam through a narrow-aperture (4-mm ID), 35GHz, single-cell rf output cavity [5]. The beam-line consists of a section of stainless steel pipe (39mm ID,1.2m long) with a set of solenoid magnets to provide fo-cusing through the rf cavity. The rf power generated bythe beam in the cavity is collected and analyzed, while thebeam itself is dumped. This set-up is shown in Figure 1.The work at LBNL was performed under the auspices of the U.S. De-partment of Energy by University of California Lawrence Berkeley Na-tional Laboratory under contract No. AC03-76SF00098.Figure 1: Schematic of downstream transport beamline,and rf diagnostics.Figure 2: FEL power and bunching evolution in the wig-gler, measured versus period number.2 SIMULATION CODESTwo separate numerical simulation codes are used to modelthe system behavior. The first is the steady-state, 3-D FELcode, SOLITUDE [6]. The evolution of the FEL modepower, both as measured and as calculated bySOLITUDE,is shown (circles and solid line, respectively) in Figure 2.Also shown is the calculated value of the bunching param-eter (dashed line) [7]. Not shown is the evolution of thebeam current during transport through the wiggler. Exper-imentally, the current exiting the wiggler was observed tobe 250 A. This value was reproduced in the FEL simula-tions [8].The RKS code [9] is then used to propagate the beamfrom the end of the wiggler through the cavity, and to cal-024681012141618200 0.2 0.4 0.6 0.8 1 1.2 1.4z [m]RMS Envelopes [mm]Solenoid Field [kG]Beam Pipe Radius [mm]RF Cavity Radius [mm]x yFigure 3: Simulation results of beam transport from thewiggler exit through the rf cavity.00.10.20.30.40.50.60.70 0.2 0.4 0.6 0.8 1 1.2 1.4z [m]Bunching ParameterBunch Current [kA]CavityWiggler ExitFigure 4: Simulation results of current and bunching pa-rameter transport.culate the interaction of the beam with the rf output struc-ture. The 6D particle distribution of the beam at the end ofthe wiggler, as calculated bySOLITUDE, is used as input toRKS. The evolution of the beam rms envelopes are shownin Figure 3. The cavity acts as a collimator, reducing thebeam current, as can be seen in Figure 4. This degree ofcurrent loss was observed experimentally. The calculatedpower developed in the rf cavity is also comparable to thatobserved experimentally [1].3 FILTERING AND BUNCHENHANCEMENTThe interesting feature to observe in Figure 4, is the discon-tinuous growth of the bunching parameter, and simultane-ous current loss, as the beam is partially focused throughthe cavity. This is preceded by the gradual loss of cur-rent, and the gradual increase in the bunching parameterin the transport region between the end of the wiggler andthe entrance to the rf cavity. As was pointed out in [1],1213141516-4 -3 -2 -1 0 1 2 3 4γs = c * t [mm]Figure 5: Longitudinal phase space distribution at wigglerexit.the transport line and cavity appear to act as a filter thatpreferentially selects the bunched portion of the beam fortransmission. We seek to analyze this behavior in terms ofthe dynamics of the beam in the transport line following thewiggler.The longitudinal phase space of the bunches near themiddle of the beam pulse at the exit of the wiggler areshown in Figure 5. As shown, there is significant initialbunching (b 0.4) as well as ’tilt’ (energy-phase correla-tion). The presence of this tilt arises from the fortuitousextraction of the beam at an appropriate synchrotron oscil-lation phase in the ’saturated’ regime of the FEL interac-tion. This tilt contributes to continued bunching in a bal-listic transport line. The effect of space charge forces upondebunching are limited by the low current (250 A) and highkinetic energy (6.7 MeV), and significant debunching willonly appear after several meters [10]. This tilt canaccountfor a modest rise in the bunching parameter, from 0.4 to0.5, as discussed below.In addition to the energy tilt, the bunches emerging fromthe wiggler exhibit nonuniform bunching over the trans-verse distribution. This is shown in Figure 6. Displayed arecontours of constant bunching parameter as a function oftransverse position. The transverse position coordinate hasbeen normalized by the appropriate rms transverse beamsize (x or y). While the average value of the bunchingparameter is0.4, there is a large degree of variation withthe high-brightness, central core more strongly bunchedthan the outlying edges. Collimation of the beam can thenstrip away the less-bunched regions, resulting in an overallenhancement of the average bunching parameter.The origin of the transverse variation can be related tot e variation of the electromagnetic signal co-propagatingwith the beam in the waveguide of the FEL. Optical guid-ing studies [11] show that both the beam density and theelectromagnetic mode amplitude decrease with increasingtransverse distance from the beam axis. There is, then, a0.70.40.1-6 -4 -2 0 2 4 6x / σ-6-4-20246y / σyxFigure 6: Transverse distribution of bunching parameter atwiggler exit.00.10.20.30.40.50.60.70 0.2 0.4 0.6 0.8 1 1.2 1.4Current [kA], Bunchingz [m]BunchingCurrent10mm10mm19.5mm19.5mm30mm30mm45mm45mmFigure 7: Evolution of beam current and bunching param-eter with varying beam pipe diameters.smaller coupling between the beam and the mode at dis-tances from the beam axis, with the subsequent decrease inthe forces responsible for bunching.A series of simulations were performed in which thebeam pipe radius of the transport line between the wigglerand rf cavity was varied. The purpose of this was to ex-plore the relative influence of the two bunching effects de-scribed above. The results are shown in Figure 7, showingevolution of beam current and bunching parameter alongthe beamline. As shown, the smaller pipes act as collimat-ing agents, while the larger pipes transmit nearly 100% ofthe beam current from the wiggler to the entrance of thecavity. In the simulations, the smaller beam pipes allowedthe less-bunched portions of the beam to be intercepted,thereby increasing the average bunching parameter. How-ever, all simulations demonstrated ballistic bunching due tothe energy-phase tilt. At the end of the transport line liesthe cavity with a 2mm bore radius, which acts as a finalcollimator and limits drastically the percentage of transmit-ted current, while also stripping away the unbunched por-tions from the highly-bunched core. The final transverse0.8 0.60.1-6 -4 -2 0 2 4 6x / σ-6-4-20246y / σxyFigure 8: Transverse distribution of bunching parameter atcavity exit.distribution of the bunching parameter is shown in Figure8, taken at the exit plane of the cavity. This distributionexhibits a broader central plateau with a greater degree ofbunching than seen in Figure 6.4 CONCLUSIONSWe have presented results of simulations to assist in theanalysis of experimental measurements of current andbunching transport in a high-frequency, two-beamccel-erator prototype experiment. We have shown that the aver-age degree of longitudinal bunching in a beam that exits anFEL amplifier can be improved by collimation. However,this may also be accompanied by significant loss of current.5 REFERENCES[1] T. Lefevre, et. al.,Phys. Rev. Lett.84 (2000), 1188.[2] J. Gardelle, et. al.,Phys. Rev. Lett.76 (1996), 4532.[3] J. Gardelle, et. al.,Phys. Rev. Lett.79 (1997), 3905.[4] G. Westenskow, et. al., Proceedings of the VIII Interna-tional Workshop on Linear Colliders, Frascati (1999).[5] S.M. Lidia, et. al.,Proceedings of the XIX InternationalLinear Accelerator Conference, Chicago (1998), 97.[6] J. Gardelle, et. al.,Phys. Rev. E50 (1994), 4973.[7] The bunching parameter is defined asb = jhexp (i )ij,where = kwz   ! (z=c  t) is the usual phase variableof an electron in the bunch, and wherehi denotes the bunchensemble average.[8] S.M. Lidia, et. al.,Proceedings of the1999 IEEEParticle Accelerator Conference, New York (1999), 1797.[9] S.M. Lidia, Proceedings of the1999 IEEE Particle Ac-celerator Conference, New York (1999), 2870.[10] J. Gardelle, et. al.,Proceedings of the XIXInternational Linear Accelerator Conference, Chicago(1998), 794.[11] A. Bhattacharjee, et. al.,Phys. Rev. Lett.60 (1988),1254.

Analysis of longitudinal bunching in an FEL driven two-beam accelerator

Recent experiments have explored the use of a free-electron laser  (FEL) as a buncher for a microwave two-beam accelerator, and the subsequent  driving of a standing-wave rf output cavity. Here we present a deeper analysis  of the longitudinal dynamics of the electron bunches as they are transported  from the end of the FEL and through the output cavity. In particular, we  examine the effect of the transport region and cavity aperture to filter the  bunched portion of the beam

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Analysis of longitudinal bunching in an FEL driven two-beam 
accelerator

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Analysis of longitudinal bunching inan FEL driven two-beam accelerator

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