The Compton positron source of a future linear collider must obtain the target bunch population by accumulating a large number of positron packets, arriving either in a number of bursts from a ‘Compton ring’, with intermediate damping of the scattering electron beam, or quasicontinually from a ‘Compton energy recovery linac’. We present simulation results for the longitudinal stacking of Compton positrons in the ILC damping ring (DR) and the CLIC pre-damping ring (PDR), discussing parameter optimization, stacking efficiency, possible further improvements, and outstanding questions

Antoniou, F

Chehab, R

Kuriki, M

Omori, T

Papaphilippou, Y

Rinolfi, L

Urakawa, J

Variola, A

Vivoli, A

Yakimenko, V

Zimmermann, F

International audienceThe Compton positron source of a future linear collider must obtain the target bunch population by accumulating a large number of positron packets, arriving either in a number of bursts from a “Compton ring”, with intermediate damping of the scattering electron beam, or quasi-continually from a “Compton energy recovery linac”. We present simulation results for the longitudinal stacking of Compton positrons in the ILC damping ring and the CLIC pre-damping ring, reporting parameter optimization, stacking efficiency, possible further improvements, and outstanding questions

Zimmermann, F.

Papaphilippou, Y.

Rinolfi, L.

Antoniou, F.

Chehab, R.

Kuriki, M.

Omori, T.

Urakawa, J.

Variola, A.

Vivoli, A.

Yakimenko, V.

Hal-Diderot

Stacking Simulations for Compton Positron Sources of Future Linear Colliders

CERN Document Server

STACKING SIMULATIONS FOR COMPTON POSITRON SOURCES OFFUTURE LINEAR COLLIDERSF. Zimmermann, Y. Papaphilippou, L. Rinolfi, A. Vivoli, CERN; V. Yakimenko, BNL;M. Kuriki, HU/AdSM Hiroshima; R. Chehab, IN2P3 IPNL Villeurbanne;T. Omori, J. Urakawa, KEK; A. Variola, LAL & U. Paris Sud; F. Antoniou, NTU AthensAbstractThe Compton positron source of a future linear collidermust obtain the target bunch population by accumulatinga large number of positron packets, arriving either in anumber of bursts from a ‘Compton ring’, with interme-diate damping of the scattering electron beam, or quasi-continually from a ‘Compton energy recovery linac’. Wepresent simulation results for the longitudinal stacking ofCompton positrons in the ILC damping ring (DR) and theCLIC pre-damping ring (PDR), discussing parameter op-timization, stacking efficiency, possible further improve-ments, and outstanding questions.INTRODUCTIONA conceptual design of a polarised positron source basedon laser Compton scattering in a dedicated “Compton ring”was first proposed at the Snowmass’05 workshop [1] forthe International Linear Collider (ILC). Updates & im-provements were obtained and documented in the courseof several successive workshops [2], at which a Comptonsource for the Compact Linear Collider (CLIC) has alsobeen studied, and various scenarios have emerged. As analternative to the original Compton Ring (CR), a ComptonEnergy Recovery Linac (CERL) is now being considered[3]. Such ERL based source would operate in cw mode,without transient effects, and with larger bunch spacings,with reduced charge per e− bunch, and at lower bunch fre-quency. A Compton ring, can or would, operate in a pulsedmode, where short periods of injecting e+ bunchlets arefollowed by longer damping intervals.The Compton sources considered produce positrons inthe following way. An electron beam of 1.3–1.8 GeV iscollided with a high-power laser pulse stored in an opticalcavity, with a laser wavelength of order 1 μm. The totalphoton yield is about 1 gamma per electron for six 600 mJcavities with a typical rms spot size of 5 μm at the electron-laser collision point. The Compton scattered photons arenext converted into e+e− pairs, of which the e+’s are se-lected and captured with a simulated yield per photon of or-der 1%. The total number of positrons produced per pulsein this type of scheme is about 50–1000 times smaller thanthe number of e+’s per bunch required in a future linearcollider. To reach the desired bunch charge, it is proposedto stack the positrons in an accumulation ring. For exam-ple, assuming 1010 electrons per bunch in the initial Comp-ton ring or CERL, yields about 108 positrons, which meansthat, for CLIC, at least 40–60 positron bunchlets must bestacked in the same bucket of an accumulator ring to obtainthe design bunch charge of about 4 × 109. A schematic ofa possible CLIC-CERL positron source is shown in Fig. 1.2.86 GeV Accumulator Ring (pre-DR)injection over 2800 turns makes312 bunches with 4.5x10 9   e+/ bunchwith 0.5 ns spacing;   then 16.3 ms for dampingafter stacking and damping,    extract beam and inject intodamping ring, 312 bunches2.4 GeV sc linac 50 Hz5 YAG Laser Pulse Stacking Cavities, 600 mJ each 6.7x10 7 pol. e +/turn/bunch1.8 GeV ERLNb=1x1010 ,20 ns spacing0.25 GeV cw linac10 10  γ's  /turn/bunchFigure 1: Schematic of CLIC CERL Compton source in-cluding typical yields at various steps of the e+ generation.There are significant differences between ILC and CLICwith regard to a Compton source: (1) CLIC has a 5 timessmaller bunch charge and about 10 times less bunches perpulse than ILC. (2) The CLIC bunch spacing is 0.5 ns in-stead of about 3 or 6 ns for the ILC DR, which means that atCLIC one cannot stack on every turn in every bucket, bute.g. on every 40th turn with a 20-ns CR/CERL e− spac-ing. (3) The CLIC DR needs to produce a beam with anextremely small emittance and is limited in dynamic aper-ture. Therefore, a PDR is required. This PDR can be usedand optimized for stacking the polarized positrons from theCR or CERL source. Alternatively, for CLIC, an efficientstacking could also be performed in two dedicated smallstacking rings operated in alternation [4, 5]. The ILC DRhas a large circumference to store the much higher numberof bunches. Adding a PDR is neither required, nor practi-cal. Therefore, we assume that for ILC the stacking is donein the DR proper. It will be necessary to optimize the pa-rameters of the CLIC PDR and the ILC DR for maximumstacking efficiency. With or without such optimization, theILC DR has a larger bucket area and a higher synchrotrontune, both facilitating the stacking. (4) The higher CLICrepetition rate of 50 Hz compared to the 5 Hz for ILC canbe outweighed by a more than 10-times shorter PDR damp-ing time.In the following we report on studies of positron stackingfor the ILC and CLIC, considering both CR and CERL con-figurations. The input parameters describing the positronsto be stacked were taken from simulations, which con-MO6RFP064 Proceedings of PAC09, Vancouver, BC, Canada512Sources and InjectorsT02 - Lepton Sourcessidered 5 optical cavities of 600 mJ each and an electronbunch population of 1010, and showed a yield of 6.65×107positrons per pulse, a longitudinal edge emittance (roughly10 times the rms emittance) of 0.72 meV-s at 200 MeV, anda transverse normalized edge emittance of 0.63 m-rad [6].STACKING SIMULATIONSWe consider positron stacking in the longitudinal phasespace. Efficient stacking requires the size of the RF bucketto be much larger than the longitudinal edge emittance ofthe injected positrons. Stacking simulations have the fol-lowing ingredients: sinusoidal RF, linear and second-ordermomentum compaction factors, radiation damping, quan-tum excitation, a nonzero synchronous phase, realistic pa-rameters for the injected positron bunchlets, and the equi-librium beam distribution. It is assumed that the injectionseptum is placed at a location with large dispersion, andthat the thickness of the septum blade is much smaller thanthe transverse beam size, so that losses on the septum bladecan be ignored.CLIC Pre-Damping RingCLIC stacking simulations have been performed consid-ering injection and accumulation in the PDR, whose accep-tance we have increased with respect to the present base-line design [7], by doubling the RF voltage and increas-ing the field of the wigglers (or doubling their number),and through a ten-fold reduction in the momentum com-paction factor αc,1 (the latter could be increased to its orig-inal value after the stacking process, e.g. to stabilize thedamped beam). Figure 2 illustrates the bucket size for thedesign parameters and for the stacking-optimized version.The optimized parameters are listed in Table 1.-0.06-0.04-0.02 0 0.02 0.04 0.06-0.04 -0.02  0  0.02  0.04δ [1]z [m]nominal PDR, Vrf=10 MV, α1=0.0038, U0 =3.3 MeV-0.06-0.04-0.02 0 0.02 0.04 0.06-0.04 -0.02  0  0.02  0.04δ [1]z [m]optimized PDR, Vrf=20 MV, α1=0.00038, U0 =6.5 MeVFigure 2: Longitudinal phase space of the CLIC PDR de-sign (left) and stacking-optimized version (right).Similar to the case of CLIC, the ILC-CR stacking effi-ciency was optimized by additional DR wigglers for twotimes faster damping, and a 1.5 times larger RF voltage(see Table 1). Alternatively, one could consider stackinge+ for only 50 ms simultaneously in both the electron andpositron DRs.The ILC-DR final vertical rms emittance should beγy,f = 17 nm. For an initial positron emittance of γy,0of 6 mm, the minimum store time Tstore required, afterstacking, follows from y,f exp(2Tstore/τy) ≤ y,0, whichyields Tstore ≥ 6.4τy = 79.4 ms, leaving 120 ms for stack-ing (this number would be 60 ms for the original wigglerstrength and/or number of ILC-DR wigglers).Table 1: Key parameters for the stacking-optimized CLICPDR and ILC DR. The momentum compaction factor α isexpanded as αc = αc,1 + αc,2δ + . . ., which defines α2.parameter CLIC PDR ILC DR#bunches/train 312 2625bunch spacing 0.5 ns 6.2 nsfinal #e+/bunch 4.2× 109 2.0× 1010circumference 397.74 m 6695 mRF frequency 2 GHz 650 MHzRF Voltage 20 MV 36 MVαc,1 0.00038 0.00042αc,2 0.00088 0.0beam energy 2.86 GeV 5 GeVlongit. damping time 0.58 ms 6.4 mseq. momentum spread 0.1% 0.09%synchrotron tune 0.033 0.084eq. bunch length 0.9 mm 5.2 mmbucket area / π 28 meV-s 41 meV-sCLIC CERL/CR SchemeFor CLIC the number of stacking turns is small, less than100, and we can, therefore, consider the same stacking pro-cess for both the CR and CERL scenarios, where on ev-ery 40th turn positron bunchlets are injected into the samePDR bucket. Accordingly a 20-ns bunch spacing is con-sidered for the CERL or CR electron beams, and a suitableCR/CERL-cicumference difference with respect to a mul-tiple of 20 ns is assumed, e.g. 0.15 m corresponding to aninjection shift by 0.5 ns from turn to turn. Over 2800 turnsor 3.7 ms, 70 injections would be realized, providing thetarget number of positrons. Following the stacking periodwould be 12225 turns (16.3 ms) of damping. As the longi-tudinal damping time is only 0.56 ms, a significant reserveexists, which could be used for lowering the laser power bya factor of 3–5, or the number of collision points, increasingthe capture efficiency. The beam is injected with a constantphase offset zoﬀ = 0.01 m , and with an optimized constantmomentum offset δ of 4% from the center of the bucket, asis illustrated in Fig. 3. The maximum stacking efficiency isabout 89%. Snapshots taken during the simulated stackingprocess are presented in Fig. 4.A fast orbit bump at the septum ensures that newly in-jected positrons do not hit the septum on the turn follow-ing the injection. The bump amplitude chosen, Abump =Dseptumδbump, corresponds to 4 times the initial energyspread (δbump = 4σδ,0), which is taken to be 2.9 MeV andaccompanied by an initial bunch length of 7.3 mm, as maybe obtained after energy pre-compression [6].If either the synchrotron tune or the energy loss fromsynchrotron radiation per turn were very high one couldavoid the fast septum bump. In the latter case the condi-tion for avoiding the bump is that the energy loss per turnbe larger than the magnitude of the fast septum bump, orΔESR > 4σδ,0. In our example the energy loss is about6 MeV per turn, which is half of the 12 MeV bump ampli-Proceedings of PAC09, Vancouver, BC, Canada MO6RFP064Sources and InjectorsT02 - Lepton Sources 5130204060801000 2 4 6stacking efficiency [%]offset ? [%]Figure 3: Simulated stacking efficiency for the CLIC-PDRvs. the momentum offset at injection, δoﬀ , for zoﬀ =10 mm. Each bunchlet is represented by 5 macroparticles.-0.06-0.04-0.02 0 0.02 0.04 0.06δ [1]1st turn, 1 bunchseptum blade-0.06-0.04-0.02 0 0.02 0.04 0.06δ [1]400th turn, 10 bunchesseptum blade-0.06-0.04-0.02 0 0.02 0.04 0.06δ [1]2400th turn, 60 bunchesseptum blade-0.06-0.04-0.02 0 0.02 0.04 0.06δ [1]16.3 ms after last injectionseptum bladeFigure 4: Phase-space snapshots for CLIC-PDR stackingprocess: first bunchlet on first turn (top left), 10 bunchletson turn 400 (top right), 60 bunches on turn 2400 (bottomleft), and 16.3 ms after last injection (bottom right). Theblue line indicates the location of the septum blade.tude. Therefore, with a two times stronger damping thanassumed here the fast bump could be omitted.ILC CR SchemeSince 4–5 times more bunchlets need to be injected, thestacking scheme considered here consists of several periodsof injections, with intermediate damping. Between succes-sive injections in one injection period the orbit at the sep-tum is monotonically varied with fast bumper magnets and,at the same time, the energy of the injected beam is rampedsuch that the transverse septum position is always separatedby the equivalent of 2σδ,0 from the injected beam centroid.We propose a scheme where bunchlets are injected ev-ery second turn (80 MHz) into the same RF bucket of thedamping ring, 30 times in total. This is followed by a wait-ing time of 10 ms (equal to about 450 turns, or 1 dampingtime) and the entire process is repeated 9 times. The to-tal number of injections per bucket is 300. Such burstingmode of operation still needs to be demonstrated for an op-tical Fabry-Perot cavity at high finesse.Injecting with a constant longitudinal offset zoﬀ =0.45 m and with a momentum offset that is minimum atthe start of an injection period, δmin = 5.7 × 10−3, andthen increases linearly by δstep = 0.175 × 10−3 per turn,the simulated stacking efficiency is about 95%.ILC Compton ERLFor the CERL scheme, instead of cycles, we considercontinuous stacking. We choose a bunch frequency ofabout 32 MHz (implying 18 MW power in the optical cav-ities). A period of 1020 continuous injections over 5100turns (injecting into the same bucket on every 5th turn) isfollowed by 3853 turns (about 86 ms) of damping with adamping time of 6.4 ms. The stacking efficiency is opti-mized by adjusting the injection momentum offset and in-jection phase, which are held constant throughout the pro-cess. equal to zoﬀ = 0.10 m, and δoﬀ = 1.5%. For the ILCthe synchrotron phase advance per turn is so high that nofast orbit bump is required at the septum, especially withproperly optimized injection phase. The simulated stack-ing efficiency is 94.2%.CONCLUSIONS AND OUTLOOKWe presented stacking schemes for CLIC and ILCCompton positron sources based either on an energy-recovery linac or a Compton ring. The parameters of theCLIC PDR and of the ILC DR were optimized for efficientstacking (Table 1). The stacking processes are summarizedin Table 2. Stacking efficiencies of about 90% or higherare obtained with off-momentum off-phase injection for allschemes. There is quite some flexibility in the design as-sumptions. Nevertheless a few challenges remain, for ex-ample related to the off-momentum dynamic aperture ofthe stacking rings. Stacking is helped by a short dampingtime, a small energy spread of the injected positrons (possi-bly with energy pre-compression), a large ring momentumacceptance (small αc,1, low αc,2, large RF voltage, higherharmonic rf), and a sufficiently long store time.Table 2: Stacking Processes and Simulated Efficienciesparameter CLIC ILCCR/CERL CR CERL#injections/bucket 70 330 1020e−/bunch [109] 10 10 3.4total injection time 3.7 ms 100 ms 114 msremaining time 16.3 ms 100 ms 86 mssimulated efficiency 89% 95% 94%e+/bunch [109] 4.2 21 22REFERENCES[1] S. Araki et al, 2005 Snowmass, physics/0509016.[2] POSIPOL 2006 Geneva, POSIPOL 2007 Paris, POSIPOL2008 Hiroshima, and CLIC2008.[3] A. Variola, C. Bruni et al, MO6RFP068, these proceedings.[4] T. Omori, private communication, Tsukuba, April 2009.[5] L. Rinolfi et al, WE6RFP065, this conference.[6] A. Vivoli, Pulse Stacking Meeting, LAL, 1 February 2008.[7] F. Antoniou et al, WE6PFP107, this conference.MO6RFP064 Proceedings of PAC09, Vancouver, BC, Canada514Sources and InjectorsT02 - Lepton Sources

Stacking Simulations for Compton Positron sources of Future Linear Colliders

HAL-IN2P3

Stacking Simulations for Compton Positron Sources ofFuture Linear CollidersF. Zimmermann, Y. Papaphilippou, L. Rinolfi, F. Antoniou, R. Chehab, M.Kuriki, T. Omori, J. Urakawa, A. Variola, A. Vivoli, et al.To cite this version:F. Zimmermann, Y. Papaphilippou, L. Rinolfi, F. Antoniou, R. Chehab, et al.. StackingSimulations for Compton Positron Sources of Future Linear Colliders. Particle AcceleratorConference (PAC09), May 2009, Vancouver, Canada. Triumf Vancouver, pre-press version,pp.MO6RFP064, 2009. <in2p3-00382135>HAL Id: in2p3-00382135http://hal.in2p3.fr/in2p3-00382135Submitted on 13 Jan 2010HAL is a multi-disciplinary open accessarchive for the deposit and dissemination of sci-entific research documents, whether they are pub-lished or not. The documents may come fromteaching and research institutions in France orabroad, or from public or private research centers.L’archive ouverte pluridisciplinaire HAL, estdestine´e au de´poˆt et a` la diffusion de documentsscientifiques de niveau recherche, publie´s ou non,e´manant des e´tablissements d’enseignement et derecherche franc¸ais ou e´trangers, des laboratoirespublics ou prive´s.STACKING SIMULATIONS FOR COMPTON POSITRON SOURCES OFFUTURE LINEAR COLLIDERSF. Zimmermann, Y. Papaphilippou, L. Rinol, A. Vivoli, CERN; V. Yakimenko, BNL;M. Kuriki, HU/AdSM Hiroshima; R. Chehab, IN2P3 IPNL Villeurbanne;T. Omori, J. Urakawa, KEK; A. Variola, LAL & U. Paris Sud; F. Antoniou, NTU AthensAbstractThe Compton positron source of a future linear collidermust obtain the target bunch population by accumulatinga large number of positron packets, arriving either in anumber of bursts from a ‘Compton ring’, with interme-diate damping of the scattering electron beam, or quasi-continually from a ‘Compton energy recovery linac’. Wepresent simulation results for the longitudinal stacking ofCompton positrons in the ILC damping ring (DR) and theCLIC pre-damping ring (PDR), discussing parameter op-timization, stacking efciency, possible further improve-ments, and outstanding questions.INTRODUCTIONA conceptual design of a polarised positron source basedon laser Compton scattering in a dedicated “Compton ring”was rst proposed at the Snowmass’05 workshop [1] forthe International Linear Collider (ILC). Updates & im-provements were obtained and documented in the courseof several successive workshops [2], at which a Comptonsource for the Compact Linear Collider (CLIC) has alsobeen studied, and various scenarios have emerged. As analternative to the original Compton Ring (CR), a ComptonEnergy Recovery Linac (CERL) is now being considered[3]. Such ERL based source would operate in cw mode,without transient effects, and with larger bunch spacings,with reduced charge per e− bunch, and at lower bunch fre-quency. A Compton ring, can or would, operate in a pulsedmode, where short periods of injecting e+ bunchlets arefollowed by longer damping intervals.The Compton sources considered produce positrons inthe following way. An electron beam of 1.3–1.8 GeV iscollided with a high-power laser pulse stored in an opticalcavity, with a laser wavelength of order 1 µm. The totalphoton yield is about 1 gamma per electron for six 600 mJcavities with a typical rms spot size of 5 µm at the electron-laser collision point. The Compton scattered photons arenext converted into e+e− pairs, of which the e+’s are se-lected and captured with a simulated yield per photon of or-der 1%. The total number of positrons produced per pulsein this type of scheme is about 50–1000 times smaller thanthe number of e+’s per bunch required in a future linearcollider. To reach the desired bunch charge, it is proposedto stack the positrons in an accumulation ring. For exam-ple, assuming 1010 electrons per bunch in the initial Comp-ton ring or CERL, yields about 108 positrons, which meansthat, for CLIC, at least 40–60 positron bunchlets must bestacked in the same bucket of an accumulator ring to obtainthe design bunch charge of about 4 × 109. A schematic ofa possible CLIC-CERL positron source is shown in Fig. 1.2.86 GeV Accumulator Ring (pre-DR)injection over 2800 turns makes312 bunches with 4.5x109   e+/ bunchwith 0.5 ns spacing;   then 16.3 ms for dampingafter stacking and damping,    extract beam and inject intodamping ring, 312 bunches2.4 GeV sc linac 50 Hz5 YAG Laser Pulse Stacking Cavities, 600 mJ each 6.7x10 7 pol. e +/turn/bunch1.8 GeV ERLNb=1x1010 ,20 ns spacing0.25 GeV cw linac10 10  γ's  /turn/bunchFigure 1: Schematic of CLIC CERL Compton source in-cluding typical yields at various steps of the e+ generation.There are signicant differences between ILC and CLICwith regard to a Compton source: (1) CLIC has a 5 timessmaller bunch charge and about 10 times less bunches perpulse than ILC. (2) The CLIC bunch spacing is 0.5 ns in-stead of about 3 or 6 ns for the ILC DR, which means that atCLIC one cannot stack on every turn in every bucket, bute.g. on every 40th turn with a 20-ns CR/CERL e− spac-ing. (3) The CLIC DR needs to produce a beam with anextremely small emittance and is limited in dynamic aper-ture. Therefore, a PDR is required. This PDR can be usedand optimized for stacking the polarized positrons from theCR or CERL source. Alternatively, for CLIC, an efcientstacking could also be performed in two dedicated smallstacking rings operated in alternation [4, 5]. The ILC DRhas a large circumference to store the much higher numberof bunches. Adding a PDR is neither required, nor practi-cal. Therefore, we assume that for ILC the stacking is donein the DR proper. It will be necessary to optimize the pa-rameters of the CLIC PDR and the ILC DR for maximumstacking efciency. With or without such optimization, theILC DR has a larger bucket area and a higher synchrotrontune, both facilitating the stacking. (4) The higher CLICrepetition rate of 50 Hz compared to the 5 Hz for ILC canbe outweighed by a more than 10-times shorter PDR damp-ing time.In the followingwe report on studies of positron stackingfor the ILC and CLIC, considering both CR and CERL con-gurations. The input parameters describing the positronsto be stacked were taken from simulations, which con-Proceedings of PAC09, Vancouver, BC, Canada MO6RFP064Sources and Injectors T02 - Lepton Sources1sidered 5 optical cavities of 600 mJ each and an electronbunch population of 1010, and showed a yield of 6.65×107positrons per pulse, a longitudinal edge emittance (roughly10 times the rms emittance) of 0.72 meV-s at 200 MeV, anda transverse normalized edge emittance of 0.63 m-rad [6].STACKING SIMULATIONSWe consider positron stacking in the longitudinal phasespace. Efcient stacking requires the size of the RF bucketto be much larger than the longitudinal edge emittance ofthe injected positrons. Stacking simulations have the fol-lowing ingredients: sinusoidal RF, linear and second-ordermomentum compaction factors, radiation damping, quan-tum excitation, a nonzero synchronous phase, realistic pa-rameters for the injected positron bunchlets, and the equi-librium beam distribution. It is assumed that the injectionseptum is placed at a location with large dispersion, andthat the thickness of the septum blade is much smaller thanthe transverse beam size, so that losses on the septum bladecan be ignored.CLIC Pre-Damping RingCLIC stacking simulations have been performed consid-ering injection and accumulation in the PDR, whose accep-tance we have increased with respect to the present base-line design [7], by doubling the RF voltage and increas-ing the eld of the wigglers (or doubling their number),and through a ten-fold reduction in the momentum com-paction factor αc,1 (the latter could be increased to its orig-inal value after the stacking process, e.g. to stabilize thedamped beam). Figure 2 illustrates the bucket size for thedesign parameters and for the stacking-optimized version.The optimized parameters are listed in Table 1.-0.06-0.04-0.02 0 0.02 0.04 0.06-0.04 -0.02  0  0.02  0.04δ [1]z [m]nominal PDR, Vrf=10 MV, α1=0.0038, U0 =3.3 MeV-0.06-0.04-0.02 0 0.02 0.04 0.06-0.04 -0.02  0  0.02  0.04δ [1]z [m]optimized PDR, Vrf=20 MV, α1=0.00038, U0 =6.5 MeVFigure 2: Longitudinal phase space of the CLIC PDR de-sign (left) and stacking-optimized version (right).Similar to the case of CLIC, the ILC-CR stacking ef-ciency was optimized by additional DR wigglers for twotimes faster damping, and a 1.5 times larger RF voltage(see Table 1). Alternatively, one could consider stackinge+ for only 50 ms simultaneously in both the electron andpositron DRs.The ILC-DR nal vertical rms emittance should beγ#y,f = 17 nm. For an initial positron emittance of γ#y,0of 6 mm, the minimum store time Tstore required, afterstacking, follows from #y,f exp(2Tstore/τy) ≤ #y,0, whichyields Tstore ≥ 6.4τy = 79.4 ms, leaving 120 ms for stack-ing (this number would be 60 ms for the original wigglerstrength and/or number of ILC-DR wigglers).Table 1: Key parameters for the stacking-optimized CLICPDR and ILC DR. The momentum compaction factor α isexpanded as αc = αc,1 + αc,2δ + . . ., which denes α2.parameter CLIC PDR ILC DR#bunches/train 312 2625bunch spacing 0.5 ns 6.2 nsnal #e+/bunch 4.2× 109 2.0× 1010circumference 397.74 m 6695 mRF frequency 2 GHz 650 MHzRF Voltage 20 MV 36 MVαc,1 0.00038 0.00042αc,2 0.00088 0.0beam energy 2.86 GeV 5 GeVlongit. damping time 0.58 ms 6.4 mseq. momentum spread 0.1% 0.09%synchrotron tune 0.033 0.084eq. bunch length 0.9 mm 5.2 mmbucket area / pi 28 meV-s 41 meV-sCLIC CERL/CR SchemeFor CLIC the number of stacking turns is small, less than100, and we can, therefore, consider the same stacking pro-cess for both the CR and CERL scenarios, where on ev-ery 40th turn positron bunchlets are injected into the samePDR bucket. Accordingly a 20-ns bunch spacing is con-sidered for the CERL or CR electron beams, and a suitableCR/CERL-cicumference difference with respect to a mul-tiple of 20 ns is assumed, e.g. 0.15 m corresponding to aninjection shift by 0.5 ns from turn to turn. Over 2800 turnsor 3.7 ms, 70 injections would be realized, providing thetarget number of positrons. Following the stacking periodwould be 12225 turns (16.3 ms) of damping. As the longi-tudinal damping time is only 0.56 ms, a signicant reserveexists, which could be used for lowering the laser power bya factor of 3–5, or the number of collision points, increasingthe capture efciency. The beam is injected with a constantphase offset zoff = 0.01 m , and with an optimized constantmomentum offset δ of 4% from the center of the bucket, asis illustrated in Fig. 3. The maximum stacking efciency isabout 89%. Snapshots taken during the simulated stackingprocess are presented in Fig. 4.A fast orbit bump at the septum ensures that newly in-jected positrons do not hit the septum on the turn follow-ing the injection. The bump amplitude chosen, Abump =Dseptumδbump, corresponds to 4 times the initial energyspread (δbump = 4σδ,0), which is taken to be 2.9 MeV andaccompanied by an initial bunch length of 7.3 mm, as maybe obtained after energy pre-compression [6].If either the synchrotron tune or the energy loss fromsynchrotron radiation per turn were very high one couldavoid the fast septum bump. In the latter case the condi-tion for avoiding the bump is that the energy loss per turnbe larger than the magnitude of the fast septum bump, or∆ESR > 4σδ,0. In our example the energy loss is about6 MeV per turn, which is half of the 12 MeV bump ampli-MO6RFP064 Proceedings of PAC09, Vancouver, BC, CanadaSources and Injectors2T02 - Lepton Sources0204060801000 2 4 6stacking efficiency [%]offset ! [%]Figure 3: Simulated stacking efciency for the CLIC-PDRvs. the momentum offset at injection, δoff , for zoff =10 mm. Each bunchlet is represented by 5 macroparticles.-0.06-0.04-0.02 0 0.02 0.04 0.06δ [1]1st turn, 1 bunchseptum blade-0.06-0.04-0.02 0 0.02 0.04 0.06δ [1]400th turn, 10 bunchesseptum blade-0.06-0.04-0.02 0 0.02 0.04 0.06δ [1]2400th turn, 60 bunchesseptum blade-0.06-0.04-0.02 0 0.02 0.04 0.06δ [1]16.3 ms after last injectionseptum bladeFigure 4: Phase-space snapshots for CLIC-PDR stackingprocess: rst bunchlet on rst turn (top left), 10 bunchletson turn 400 (top right), 60 bunches on turn 2400 (bottomleft), and 16.3 ms after last injection (bottom right). Theblue line indicates the location of the septum blade.tude. Therefore, with a two times stronger damping thanassumed here the fast bump could be omitted.ILC CR SchemeSince 4–5 times more bunchlets need to be injected, thestacking scheme considered here consists of several periodsof injections, with intermediate damping. Between succes-sive injections in one injection period the orbit at the sep-tum is monotonically varied with fast bumper magnets and,at the same time, the energy of the injected beam is rampedsuch that the transverse septum position is always separatedby the equivalent of 2σδ,0 from the injected beam centroid.We propose a scheme where bunchlets are injected ev-ery second turn (80 MHz) into the same RF bucket of thedamping ring, 30 times in total. This is followed by a wait-ing time of 10 ms (equal to about 450 turns, or 1 dampingtime) and the entire process is repeated 9 times. The to-tal number of injections per bucket is 300. Such burstingmode of operation still needs to be demonstrated for an op-tical Fabry-Perot cavity at high nesse.Injecting with a constant longitudinal offset zoff =0.45 m and with a momentum offset that is minimum atthe start of an injection period, δmin = 5.7 × 10−3, andthen increases linearly by δstep = 0.175 × 10−3 per turn,the simulated stacking efciency is about 95%.ILC Compton ERLFor the CERL scheme, instead of cycles, we considercontinuous stacking. We choose a bunch frequency ofabout 32 MHz (implying 18 MW power in the optical cav-ities). A period of 1020 continuous injections over 5100turns (injecting into the same bucket on every 5th turn) isfollowed by 3853 turns (about 86 ms) of damping with adamping time of 6.4 ms. The stacking efciency is opti-mized by adjusting the injection momentum offset and in-jection phase, which are held constant throughout the pro-cess. equal to zoff = 0.10 m, and δoff = 1.5%. For the ILCthe synchrotron phase advance per turn is so high that nofast orbit bump is required at the septum, especially withproperly optimized injection phase. The simulated stack-ing efciency is 94.2%.CONCLUSIONS AND OUTLOOKWe presented stacking schemes for CLIC and ILCCompton positron sources based either on an energy-recovery linac or a Compton ring. The parameters of theCLIC PDR and of the ILC DR were optimized for efcientstacking (Table 1). The stacking processes are summarizedin Table 2. Stacking efciencies of about 90% or higherare obtained with off-momentum off-phase injection for allschemes. There is quite some exibility in the design as-sumptions. Nevertheless a few challenges remain, for ex-ample related to the off-momentum dynamic aperture ofthe stacking rings. Stacking is helped by a short dampingtime, a small energy spread of the injected positrons (possi-bly with energy pre-compression), a large ring momentumacceptance (small αc,1, low αc,2, large RF voltage, higherharmonic rf), and a sufciently long store time.Table 2: Stacking Processes and Simulated Efcienciesparameter CLIC ILCCR/CERL CR CERL#injections/bucket 70 330 1020e−/bunch [109] 10 10 3.4total injection time 3.7 ms 100 ms 114 msremaining time 16.3 ms 100 ms 86 mssimulated efciency 89% 95% 94%e+/bunch [109] 4.2 21 22REFERENCES[1] S. Araki et al, 2005 Snowmass, physics/0509016.[2] POSIPOL 2006 Geneva, POSIPOL 2007 Paris, POSIPOL2008 Hiroshima, and CLIC2008.[3] A. Variola, C. Bruni et al, MO6RFP068, these proceedings.[4] T. Omori, private communication, Tsukuba, April 2009.[5] L. Rinol et al, WE6RFP065, this conference.[6] A. Vivoli, Pulse Stacking Meeting, LAL, 1 February 2008.[7] F. Antoniou et al, WE6PFP107, this conference.Proceedings of PAC09, Vancouver, BC, Canada MO6RFP064Sources and Injectors T02 - Lepton Sources3

Stacking Simulations for Compton Positron sources of Future Linear Colliders

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