We report about generic halo and tail simulations and estimates. Previous studies weremainly focused on very high energies as relevant for the beam delivery systems of linear colliders. We have now studied, applied and extended these simulations to lower energies as relevant for the CLIC drive beam

Adli, E

Ahmed, I

Burkhardt, H

Dalena, B

Fitterer, M

Latina, A

Müller, S

Rumolo, G

Schulte, D

CERN Document Server

HALO AND TAIL SIMULATIONS WITH APPLICATION TO THE CLICDRIVE BEAMMiriam Fitterer∗, Anke-Susanne Mu¨ller, Universita¨t Karlsruhe (TH), GermanyErik Adli, Helmut Burkhardt, Barbara Dalena, Giovanni Rumolo, Daniel Schulte,CERN, Geneva, Switzerland, Andrea Latina, FNAL, USA, Ijaz Ahmed, NCP, Islamabad, PakistanAbstractWe report about generic halo and tail simulations and es-timates. Previous studies were mainly focused on very highenergies as relevant for the beam delivery systems of linearcolliders. We have now studied, applied and extended thesesimulations to lower energies as relevant for the CLIC drivebeam.INTRODUCTIONHalo and Tail GenerationHalo particles can be a major source of beam losses andradiation and can therefore lead to performance limitationsof future accelerators. If the amplitude of a core particleincreases significantly, it becomes a halo particle. The in-crease of the amplitude can be caused by the following par-ticle processes:• Beam gas scattering: elastic scattering (Mott scatter-ing), inelastic scattering (Bremsstrahlung), multiplescattering• Scattering of thermal photons (Compton scattering)• Touschek effect• Intrabeam scattering• Electron and Ion cloud effects• Space charge effects• Synchrotron radiationThe most relevant processes for halo generation are usu-ally beam gas scattering and multiple scattering, whichcan be simulated with the halo and tail generation packageHTGEN [1]. In addition to the scattering processes, op-tics related effects like mismatch, coupling, dispersion andnonlinearities can enlarge the halo. These as well as the ef-fect of synchrotron radiation are fully included in the track-ing code PLACET [2], which can be used in combinationwith HTGEN. Previous studies using PLACET-HTGENwere done for high energy beams like the 250 GeV beamof the ILC [3]. In the following we will describe the exten-sion of PLACET-HTGEN to low energy beams with highintensity like the CLIC drive beam decelerator.∗ at CERNCLIC Drive Beam DeceleratorThe CLIC Drive Beam decelerator will extract X-bandRF power from a 100 A Drive Beam. The focussing andalignment systems must ensure transport of particles of allenergies through the decelerator sectors, ensuring minimallosses. A short summary of relevant beam parameters isgiven in Table 1 and a more detailed description can befound in [4].Table 1: CLIC drive beam decelerator parametersParameter Unit ValueDrive beam sector length m 1053numb. of part. per bunch 109 52.5numb. of bunches per train 2928mean initial beam energy GeV 2.40mean final beam energy GeV 0.40N,y,initial μm 150N,y,final μm 334THEORYElastic ScatteringThe electron is deflected by the Coulomb potential of theparticles in the residual gas. Taking the spin of the electroninto account the differential cross section is given by [5]:dσdΩ=(Zre2γβ2)2 1− β2 sin2 θ2sin4 θ2(1)where Z is the charge of the nucleus, re the classical elec-tron radius, γ the Lorentz factor E/mc2 of the electron andβ the velocity of the electron in units of the speed of light.Relevant for halo production are only scattering angles ex-ceeding the beam divergence, so roughly:θ > θmin =√N,y/(γβy) (2)where N,y is the normalized emittance and βy the lo-cal vertical beta function. Integration over the solid angleyields the total cross section:WE6PFP085 Proceedings of PAC09, Vancouver, BC, Canada2700Lepton AcceleratorsA03 - Linear Collidersσ = π(Zreγβ2)2(1 + cos θmin1− cos θmin + β2 ln(1− cos θmin2))(3)In the relativistic limit β ≈ 1 and for small scattering an-gles θmin < 0.1 the terms except (1 + cos θmin)/(1 −cos θmin) can be neglected.σ = 2π(Zreγ)2 ( 11− cos θmin)(4)This is used in HTGEN. Because the electron mass is verysmall, β ≈ 1 also for low energies, so Eq. 4 is still validfor low energy electron beams. Assuming a constant nor-malized emittance, the cross section scales with the inverseof the beam energy, hence Mott scattering becomes morerelevant for low energies.Inelastic ScatteringIn the Bremsstrahlung process the electron interacts withthe field of the residual gas nucleus and radiates photons.At high energies the cross section can be approximated inthe “complete screening case” [6] by:dσdk=ANAX01k(43− 43k + k2)(5)where k is the photon energy in units of the beam energy,NA the Avogadro constant and X0 the radiation length. Acompact fit of the radiation length after Dahl of Tsai’s for-mula gives values better than 2.5% accuracy for all ele-ments except Helium, where the result is 5% to low [7]:X0 =A4αr2eNAZ(Z + 1) ln (287/√Z)(6)Integration of (5) over k from k = kmin to k = 1 yieldsthe total cross section:σ =ANAX0(−43ln kmin − 56 +43kmin − k2min2)(7)A good value for kmin is 0.01. Note that the cross sectionis energy independent. A more accurate approximation ofthe Bremsstrahlung cross section is given by GEANT4. Forenergies lower than 1 GeV GEANT4 uses a fit to the EEDLdata set [8] and above 1 GeV the exact Tsai formula. Theerror of the parameterisation is estimated to be smaller than5 % for energies bigger than 1 MeV [9].SIMULATION TECHNIQUEWith ∼ 1010 particles per bunch the CLIC drivebeam is a rather high intensity beam and therefore asliced beam model is used in the simulation. Thehalo generation requires a particle beam model, becausethe simulation is done by scattering of individual parti-cles. We have extended interface and tracking routines ofPLACET-HTGEN, so that a sliced beam model can be usedfor the beam and a particle beam model for the halo. Due tothe high particle density of the CLIC drive beam collectiveeffects like wake fields become important. To get a realistichalo tracking we have implemented the effect of transversewake fields of the beam on the halo.DISCUSSION FOR THE CLICDECELERATORAnalytical EstimatesWe expect to have the largest halo generation in thelongest decelerator, for which we performed the simula-tions. For the analytical estimates of beam gas scatteringand Compton scattering we assumed a residual gas con-stitution of 40% H2O, 40% H2 and the remaining 20%shared among CO,N2,CO2, a total pressure of 10 nTorrand a temperature of 300 K. As minimal scattering angleθmin we used the beam divergence and as minimal pho-ton energy with respect to the beam energy kmin = 0.01.The beam divergence and the beam energy were calculatedfrom the simulation results. We based our calculations forCompton scattering on [10]. The results are presented inTable 2. Elastic scattering is the dominant process and in-creases along the beamline. The energy spread caused byCompton scattering stays below 0.25% and is negligiblecompared to the energy spread due to the deceleration ofthe beam. The total scattering probability integrated overthe whole decelerator is 7.69 · 10−9. Therefore we expecta very small halo generation due to beam gas and Comp-ton scattering. The cross sections for beam gas scatteringTable 2: Analytical estimates for beam-gas scattering andCompton scattering. ρ is the molecule density in the caseof beam gas scattering and the photon density in the caseof Compton scattering, Pinit and Pfinal the initial and finalscattering probabilityProcess ρ [m−3] Pinit [m−1] Pfinal [m−1]Mott 3.22 · 1014 7.96 · 10−12 4.21 · 10−11Brems. 3.22 · 1014 1.11 · 10−13 1.11 · 10−13Comp. 5.45 · 1014 3.63 · 10−14 3.63 · 10−14change slightly, when the effect of ionization of the residualgas is taken into account. Our analytical estimates show,that the ionization level stays below 3%, so no extension ofour model is required.The total number of intra-beam-scattering events per unittime scales with 1/β4 [11], where β is the velocity in unitsof speed of light, and increases with the particle density,which shows that intrabeam scattering as well as Touschekeffect become more relevant for low energy beams with asmall beamsize. In the CLIC decelerator the Touschek ef-Proceedings of PAC09, Vancouver, BC, Canada WE6PFP085Lepton AcceleratorsA03 - Linear Colliders 2701fect could be more important than in comparable linear ac-celerators without decelerating sections, because beam par-ticles, which have performed Touschek scattering and lostlongitudinal momentum, could lose almost all their longi-tudinal momentum during the deceleration and get lost.As the drive beam is a negatively charged beam, only ioncloud effects are important. Ion cloud effects are knownfrom ring accelerators, but also in linear accelerators an in-stability can occur - the fast ion instability. We have per-formed analogous analytical studies for the decelerator asfor the CLIC long transfer lines [12]. To ensure the stabil-ity of the beam, the number of rise-times should stay belowone. Taking the inital beam parameters it lies between 1.9and 5.7 and taking the final beam parameters between 0.5and 1.6, which might indicate an eventual appearance ofthe fast ion instability.Simulation ResultsIn the simulations we used a sliced beam model with areduced number of bunches per train. We included align-ment errors as well as an initial beam offset in the verticaland horizontal plane. For simplicity we performed the sim-ulation with a gas equivalent consisting of pure nitrogen.Our tracking results are shown in Fig. 1 and Fig. 2. If theamplitude of a particle exceeds the aperture of the elementit is considered as lost.We find that only a very small fraction of particles of 10−7x[μm]-8000 -4000 0 4000 8000N11010101010y[μm]-10000 -5000 0 5000 100001101010101010101010234562345678910Figure 1: Transverse Beam profiles at the exit of the CLICdeceleratoris lost. Most of these are low energy particles with largescattering angles, which are lost at the end of the beamline.SUMMARY AND OUTLOOKWe have extended the simulation capabilities ofPLACET-HTGEN to low energy, high intensity beams,performed simulations for the CLIC drive beam deceleratorand presented the results together with analytical estimates.We have started to apply PLACET-HTGEN to the TestBeam Line drivebeam [4] and intend to perform simula-tions for other low energy linear accelerators like for exam-ple TBONE [13]. To provide an even more complete sim-Figure 2: Vertical beam position along the complete CLICdecelerator and along an extract. Halo particles are shownin black, beam particles in redulation of low energy beams, we consider to include also asimple model of the Touschek effect. An extension of thefast-ion simulation code FASTION [14] for the CLIC drivebeam is in progress.REFERENCES[1] H. Burkhardt, L. Neukermans, ”Haloand Tail generator package HTGEN”,http://hbu.home.cern.ch/hbu/HTGEN.html.[2] A. Latina, E. Adli, H. Burkhardt, Y. Renier, G. Rumolo, D.Schulte, R. Tomas, ”Recent Improvements in the TrackingCode PLACET”, EUROTeV-Report-2008-043[3] H. Burkhardt, L. Neukermans, A. Latina, D. Schulte,I.Agapov, G.A. Blair, F. Jackson, ”Halo Estimates and Sim-ulations for Linear Colliders”, PAC’07,Albuquerque, USA[4] E. Adli et. al, ”Beam Dynamics of the CLIC Decelerator”,To be published in proceedings of the X-Band RF Structureand Beam Dynamics Workshop 2008, The Cockcroft Insti-tute, United Kingdom[5] B. Povh, K. Rith, Ch. Scholz, F. Zetsche, ”Particles and Nu-clei”, Springer, 1999, edition 4[6] Y. Tsai, ”Pair production and Bremsstrahlung of chargedleptons”, Rev. Mod. Phys., 1974, Rev.Mod.Phys. 46, p. 815-851[7] Particle Data Group, ”Passage of particles through matter”,Review of Particle Physics, 2008[8] S.T. Perkins, D.E. Cullen, S.M. Seltzer, ”EEDL”, UCRL-50400, 1991, vol. 31[9] Geant 4, ”Physics Reference Manuel”, 2008, p. 120-134[10] V.I. Telnov, ”Scattering of electrons on thermal radiationphotons in electron-positron storage rings”, Nucl. Inst.Meth., 1987, vol. A260, p. 304-308[11] A. Piwinski, ”The Touschek Effect in Strong Focusing Stor-age Rings”, DESY, 98-179, 1998[12] J.B. Jeanneret, E. Adli, A. Latina, G. Rumolo, D. Schulte, R.Tomas, ”Beam Dynamics Issues in the CLIC Long TransferLines”, EPAC’08, Genoa, Italy, 2008[13] A.-S. Muller et al., ”Ultra-fast High-Power Coherent THz toMid-IR Radiation Facility”, these proceedings[14] G. Rumolo, D. Schulte, ”Fast Ion Instability in the CLICTransfer Line and Main Linac“, EPAC’08, Genoa, Italy,2008WE6PFP085 Proceedings of PAC09, Vancouver, BC, Canada2702Lepton AcceleratorsA03 - Linear Colliders

Halo and tail simulations with applications to the CLIC drive beam

Halo and tail simulations with applications to the CLIC drive beam

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