Bailey IR

Barber DP

Baynham Elwyn

Bradshaw Thomas William

Brummitt A

Bungau A

Carr FS

Clarke JA

Dainton J

Hartin AF

Hesselbach S

Hock KM

Jenner LJ

Lintern A

Malyshev Oleg B

Malysheva LI

Moortgat-Pick GA

Rochford J

Ryder NC

Scott Duncan

Shepherd Ben

Zang L

English

ePubs: the open archive for STFC research publications

DEPOLARIZATION AND BEAM-BEAM EFFECTS AT THE LINEARCOLLIDER∗I.R. Bailey1,2, A.F. Hartin3, G.A. Moortgat-Pick1,4∗∗, J.A. Clarke1,2,5, D.P. Barber1,6,E. Baynham7, T.W. Bradshaw7, A. Brummitt7, A. Bungau1,8, F.S. Carr7, N.A. Collomb5,J. Dainton1,2, S. Hesselbach1,4, K.M. Hock1,2, L.J. Jenner1,2, A. Lintern7, O.B. Malyshev1,5,L.I. Malysheva1,2, J. Rochford7, N.C. Ryder1,5,9, D.J. Scott1,5, B.J.A. Shepherd1,5, L. Zang1,2.1 Cockcroft Institute, Daresbury Science and Innovation Campus, Warrington, UK2 Department of Physics, University of Liverpool, Liverpool, UK3 John Adams Institute, Oxford University Physics, Oxford, UK4 Institute of Particle Physics Phenomenology, University of Durham, Durham, UK5 STFC Daresbury Laboratory, Warrington, UK6 DESY, Hamburg, Germany7 STFC Rutherford Appleton Laboratory, Didcot, Oxfordshire, UK8 University of Manchester, Manchester, UK9 Department of Physics, University of Bristol, Bristol, UKAbstractThe clean environment of a lepton linear collider allowshigh-precision measurements for physics analyses. In or-der to exploit this potential, precise knowledge about thepolarization state of the beams is also required. In this pa-per we concentrate on depolarization effects caused by theintense beam-beam interaction, which is expected to be thedominant source of depolarization. Higher-order effects, aswell as critical analyses of the theoretical assumptions usedin the past and theoretical improvements in the derivationof suitable equations, are given. Updates on existing sim-ulation programs are reported. Numerical results for thedesign of the International Linear Collider (ILC) are dis-cussed.BASELINE ILC SOURCESThe full physics potential of the ILC can be realized onlywith polarized e− and e+ beams [1]. Polarized e− with adegree of polarization between 80% and 90% are foreseenfor the baseline machine design. The electron source con-sists of a circularly polarized high-power laser beam anda high-voltage DC gun with a semiconductor photocath-ode [2], and a helical undulator based positron source [2]has been chosen as the most reliable solution for producingthe required flux of order 1014 positrons per second.The positron source undulator operates on the mainILC e− beam generating circularly-polarized photons. Anoverview of a suitable full-scale superconducting undula-tor module is given in [3]. Polarized positrons are pro-duced via an electromagnetic shower instigated by the cir-cularly polarized synchrotron radiation striking a thin tar-get. The production target has to be carefully designed tocope with the high heat load and strong thermal stresses,∗Cockcroft Institute Report No. Cockcroft-08-17 and EUROTeV-Report-2008-026. This work is supported by the Commission of the Eu-ropean Communities under the 6th Framework Programme “Structuringthe European Research Area”, contract number RIDS-011899.∗∗g.a.moortgat-pick@durham.ac.uksee [4]. Using the ILC baseline undulator a e+ polarizationof about 30% to 40% should be acheivable and could beused to enhance physics at the ILC interaction point (IP).The source can be readily upgraded by extending the un-dulator length to produce positrons with about 60% polar-ization. The undulator-based method has previously beenexperimentally verified by the E166 experiment [5].DEPOLARIZATION EXPECTATIONSThe characteristics of the physics processes at the IP de-pend on the luminosity-weighted polarization of the beams.As the polarimeters can only measure the polarization ei-ther side of the IP, it is mandatory to model the depolariza-tion processes expected during the beam interaction.In the following sections we first list the possible depo-larization effects in the interaction region and give numeri-cal depolarization results obtained from the CAIN programfor both the ILC and CLIC designs. Later in the paper wereport on recent theoretical progress in the description ofthe depolarization effects and incoherent and coherent pairproduction during beam-beam interactions.Effects during beam-beam interactionsIn general, two effects influence the spin motion in elec-tric and magnetic fields: a) spin precession governed bythe Thomas–Bargmann-Michel-Telegdi (T-BMT) equationand b) the spin-flip Sokolov-Ternov (S-T) effect via syn-chrotron radiation emission. Usually the spin precessioneffect is dominant, but at higher energy the depolariza-tion due to the S-T effect increases [6]. The analytically-based program CAIN [7] models both of these depolar-ization effects. In addition models of the two kinds ofbackground processes that occur during beam-beam inter-actions, the production of incoherent and coherent e+/e−pairs, are also included with certain approximations that arediscussed later.MOPP024 Proceedings of EPAC08, Genoa, Italy03 Linear Colliders, Lepton Accelerators and New Acceleration Techniques598A03 Linear CollidersThe difference between the initial beam polarization andthe luminosity-weighted beam polarization of the beamshave been evaluated for the ILC baseline parameters [2]and the CLIC-G design [8], cf. Table 1, using CAIN and areshown in Table 2. In the ILC design, the predicted low val-ues of the field strength parameter, Υ, result in very smalleffects from the coherent first-order background pairs. Athigher energy and also for the CLIC-G design with muchhigher beamstrahlung, significant contributions from thecoherent pairs are expected.Table 1: Parameters sets for the ILC and the CLIC design.More details can be found in [2, 8]ILC baseline CLIC-G√s/GeV 500 3000N /1010 2 0.37nB 2625 312β∗x/mm 20 4β∗y /mm 0.4 0.09σ∗x/nm 640 40σ∗y /nm 5.7 ∼1σz /μm 300 45Dx 0.17Υ 0.048L/1034cm−2s−1 2 2Table 2: Comparison of the luminosity-weighted depo-larizing effects in beam-beam interactions for the ILCbaseline with both 100% polarized and partially polarizedbeams, and for the CLIC-G parameter set with 100% po-larized beams. T-BMT (S-T) denotes effects due to spinprecession (synchrotron radiation)Parameter set Depolarization ΔPlwILC 100/100 ILC 80/30 CLIC-GT-BMT 0.17% 0.14% 0.10%S-T 0.05% 0.03% 3.4%incoherent 0.00% 0.00% 0.06%coherent 0.00% 0.00% 1.3%total 0.22% 0.17 % 4.8%Investigations of the sensitivity of the depolarization pre-dictions on the form of the T-BMT model in CAIN havebeen carried out by scaling the field strength used in themodel by a factor of 2, and similar investigations of the S-T effect have been carried out by scaling the ratio of initialand final state energies, ζ, by a factor of 2. From these stud-ies, the expected depolarization at the ILC IP is predictedto be 0.21%± 0.01%± 0.03%. where the first uncertaintyis indicative of the sensitivity of the result to variations inthe T-BMT model and the second uncertainty is indicativeof the sensitivity to variations in the S-T model. For CLICthe analagous result is 4.8%± 0.1% ± 1.5%, highlightingthe dominance of the S-T effect at high energies.DESCRIPTION OF DEPOLARIZATIONAND BACKGROUND EFFECTSSpin precessionSpin precession is described by the Thomas-Bargmann-Michel-Telegdi (T-BMT) equation:d~Sdt= − emγ[(γa + 1) ~BT + (a + 1) ~BL−γ(a + 1γ + 1)β~ev ×~Ec]× ~S, (1)where a describes the anomalous magnetic moment of theelectron given by the higher-order corrections to the eeγvertex. In the environment of strong colliding beams, how-ever, the usual perturbation theory cannot be applied, andmodified expressions for the anomalous magnetic momentin a medium have been derived in the literature [9]. Theexpressions have been evaluated in the no-scattering caseand using the quasi-classical approximation that impliesthat the change in the momentum due to the strong fieldshas to be sufficiently slow. This condition is fulfilled ifthe Larmor radius of the particle motion due to the ex-isting magnetic field in the bunches is much larger thanthe particle wavelength. Even in the strong field environ-ment of the ILC such a quasi-classical approximation canbe used and the T-BMT equation can be applied to describethe spin precession sufficiently accurately [7, 9]. However,the Furry representation (bound interaction picture), is alsobeing studied [10], as it allows the contributions to be cal-culated separately. The dependence of the anomalous mag-netic moment on the field parameter Υ previously derivedusing ‘by-consistency’ arguments [9] can thereby be red-erived and cross-checked with this technique [10].Spin-flip processesUsually the S-T spin flip process is expected to lead to asmall depolarization of about 0.05%, cf. [11, 6], but thisdepolarization increases with energy as seen in Table 2.This effect is normally described quasi-classically, usingthe operator method of [12] for ultra-relativistic electronsin external fields. However real collisions may include lessideal bunches containing lower energy leptons. In addition,much higher field strengths at the IP, Υ, are planned forCLIC, and a more general calculation of the S-T processallowing for quantised motion of the leptons is required.Such a calculation is provided by using the Furry repre-sentation in which the bunch field (Aeμ) is included at La-grangian level in the description of the fermion. For thiscalculation to proceed, the solution of the bound Dirac fieldequation is required.[(p− eAe)2 −m2 − ie2 F eμνσμν]ψV (x, p) = 0where F eμν = kμ ∂Aν∂φ − kν ∂Aμ∂φ , φ = kμxμ(2)The solution is obtained [13] by writing it generally as aproduct of the Dirac bispinor uS(p) and a function F (φ)whose explicit form is to be determined by substitution intoProceedings of EPAC08, Genoa, Italy MOPP02403 Linear Colliders, Lepton Accelerators and New Acceleration Techniques A03 Linear Colliders599the field Eq. (2)ψV (x, p) = uS(p)F (φ). (3)Expansion of operator products in Eq. 2 and substitution ofthe general solution ψV (x, p) yields a first order differentialequation in F (φ). The solution is obtained by expanded inpowers of photon momentum k and external field A e andusing the Lorentz gauge condition (k.Ae) = 0ψV (x, p) = [1 +e2(kp)6k 6Ae]e[F (k,Ae)]e−ipxuS(p). (4)The bunch field can be described by a constant crossedelectromagnetic field. Work is in progress to calculate theS-T process using this description with general parameters.More comprehensive details can be found in [10].Incoherent pair productionThe production of background pairs is strongly depen-dent on the polarization state of the initial photons. Thesephotons are either real (beamstrahlung) or virtual and theirspecific momenta and polarization depend on the interac-tion with the bunch electromagnetic fields. For the caseof real initial photons the Breit-Wheeler cross-section forspecific particle polarization states is required in order tocalculate the contribution. In CAIN this cross-section waswritten down only for the product of circular polarizationsof initial photons. The full cross-section is a sum over spe-cific functions of 4-momenta products and the polarizationvector components [14]. Since the Breit-Wheeler processcontributes only a small portion of the background pairsthe effect of including full polarizations is likewise small.Initial simulations predict a slight increase in overall pairnumbers. Final results will require inclusion of the full po-larization in the virtual photon processes.The other incoherent processes, Landau-Lifshitz, Bethe-Heitler and the Bremsstrahlung process are calculated us-ing the equivalent photon approximation (EPA). In generalthis approximation is only valid [15] if the polarization ofthe virtual photons has been included in the calculations.The corresponding updates for CAIN are in progress.Coherent pair productionThe coherent production of pairs via the first order inter-action between a beamstrahlung photon and beam field isincluded already in CAIN. However the second order stim-ulated Breit-Wheeler process also takes place in the pres-ence of the bunch fields. The cross-section calculation forthis process involves products of four Volkov solutions.Naively, in comparison to the first order coherent pro-cess, the second-order cross-section is diminshed by an or-der of the fine structure constant. However the bunch fieldhas the effect of allowing the bound virtual lepton to reachthe mass shell. The resulting resonances are rendered finiteby inclusion of the electron self-energy in the external fieldand the stimulated Breit-Wheeler cross-section can exceedthe first order coherent process. A detailed investigation isrequired to gauge the effect on produced pairs [10].CONCLUSIONSAn analysis of depolarization and higher-order processesduring the beam-beam interaction at a linear collider hasbeen carried out. In line with previous studies, the ILC ispredicted to display a depolarization of about 0.2% duringeach bunch crossing. For the current CLIC-G parameters,a much higher depolarization of around 4.8% is expecteddue to the strong beamstrahlung and higher Υ parameter.The current CAIN implementation now includes updatesallowing for full polarization of coherent background pairsas well as for the incoherent pairs for the case of real initialphotons. The inclusion of additional processes is ongoing.New theoretical studies are currently underway for thedescription of the T-BMT and S-T effect in strong field en-vironments during the beam-beam interaction. Both theanomalous magnetic moment as well as the spin-flip ef-fects are being evaluated using the Volkov solution for theparticle wave function in an external field. These studiesbecome particularly relevant at higher energies and for ahigh beamstrahlung parameter.REFERENCES[1] G. A. Moortgat-Pick et al., Phys. Rept. 460 (2008) 131[arXiv:hep-ph/0507011].[2] ILC Reference Design Report, available via webpagehttp://www.linearcollider.org/cms/.[3] J.A. Clarke et al., Construction of a full scale superconduct-ing undulator module for the International Linear ColliderPositron Source, these proceedings.[4] I.R. Bailey et al., A prototype target wheel for the ILCpositron source, these proceedings; L.R. Jenner et al., ”Astudy of mechanical and magnetic issues for a prototypepositron source, these proceedings.[5] G. Alexander et al., Phys. Rev. Lett. 100 (2008) 210801.[6] G. A. Moortgat-Pick et al., Spin tracking at the ILC,EUROTeV-Report-2006-037.[7] K. Yokoya, P. Chen, SLAC-PUB-4692, 1988; K. Yokoya,“User’s Manual of CAIN”, Version 2.35, April 2003.[8] H. Braun et al., CLIC 2008 parameters, CLIC Note 764;see also preliminary parameters on webpage: http://clic-meeting.web.cern.ch/clic-meeting/clictable2007.html.[9] V. N. Baier and V. M. Katkov, Phys. Lett. A 280 (2001) 275;V. N. Baier and V. M. Katkov, Phys. Rept. 409 (2005) 261.[10] I. Bailey, A. Hartin, G. Moortgat-Pick, et al., in preparation.[11] K. A. Thompson, SLAC-PUB-8716; A.W. Weidemann,Int. J. Mod. Physics A, 2537 (2000).[12] V. N. Baier and V. M. Katkov, On basic concepts of thequasiclassical operator approach, arXiv:hep-ph/9910202;V. N. Baier, V. M. Katkov and V. M. Strakhovenko, Elec-tromagnetic processes at high energies in oriented singlecrystals, Singapore, World Scientific (1998) 568 pp.[13] D.M. Volkov, Zeit. f. Phys. 94 (1935) 250.[14] V. N. Baier and A. G. Grozin, arXiv:hep-ph/0209361.[15] V. M. Budnev, I. F. Ginzburg, G. V. Meledin and V. G. Serbo,Phys. Rept. 15 (1974) 181.MOPP024 Proceedings of EPAC08, Genoa, Italy03 Linear Colliders, Lepton Accelerators and New Acceleration Techniques600A03 Linear Colliders

A prototype target wheel for the ILC positron source, these proceedings; L.R. Jenner et al., ”A study of mechanical and magnetic issues for a prototype positron source, these proceedings.

Construction of a full scale superconducting undulator module for the International Linear Collider Positron Source, these proceedings.

ILC Reference Design Report, available via webpage http://www.linearcollider.org/cms/.

Moortgat-Pick et al.,

Moortgat-Pick et al., Spin tracking at the ILC,

On basic concepts of the quasiclassical operator approach, arXiv:hep-ph/9910202;

Physics A,

Depolarization and beam-beam effects at the Linear Collider

Depolarization and beam-beam effects at the Linear Collider

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