1. Software Tools The heLiCal collaboration J.A. Clarke +, N.A. Collomb, O.B. Malyshev +, N.C. Ryder, D.J. Scott +, B.J.A. Shepherd + STFC ASTeC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, UK E. Baynham, T. Bradshaw, A. Brummitt, S. Carr, Y. Ivanyushenkov, A. Lintern, J. Rochford STFC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK I.R. Bailey +, P. Cooke, J.B. Dainton +, K. Hock +, L. Jenner +, L. Malysheva +, L. Zang + Department of Physics, University of Liverpool, Oxford St., Liverpool, L69 7ZE, UK D.P. Barber +, DESY-Hamburg, Notkestraße 85, 22607 Hamburg, Germany S. Hesselbach, G.A. Moortgat-Pick + Institute of Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, UK A. Hartin, John Adams Institute, Oxford University Physics, Oxford, OX1 3RH, UK. A.Bungau, University of Manchester, Manchester, UK + Cockcroft Institute, Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, UK Work supported by the Commission of the European Communities under the 6 th Framework Programme “Structuring the European Research Area”, contract number RIDS-011899. Our activities:  High intensity polarized e - and e + beams needed to exploit full ILC physics potential ( Phys.Rept.460 (2008), 131-243. )  Polarized e - source in ILC baseline design.  Baseline e + source can also provide ~30% polarization, upgradeable to ~60%.  High precision physics requires determination of beam polarization at interaction point with ~0.1%.  We therefore need full cradle-to-grave spin tracking. (polarized) sources spin rotators damping rings beam delivery system beam-beam interaction spin rotators Sources of depolarisation Spin depolarisation mechanisms Further Work of heLiCal  An ongoing rolling study of the full spin dynamics in the ILC from source to the interaction region will be maintained, and results updated periodically as the design of the lattice evolves.  The SLICKTRACK computer code will be extended to include non-linear orbital motion, which will allow a detailed study of spin motion in non-linear elements such as the helical undulator in the ILC positron source and sextupoles in the damping rings.  Studies of polarized positron production in the positron source will be extended to include details such as electron beam jitter, and the modular design of the helical undulator.  Current analytical studies predict there will be no appreciable depolarisation of the ILC electron beam in the helical undulator  Investigations into the decoherence of horizontal components of spin vectors in the ILC damping rings will be extended to include injected bunch length effects.  Development of reliable software tools to optimise the polarisation delivery as well as luminosity at the ILC.  Spin-tracking for damping rings, main linac, beam delivery system, bunch-bunch interactions and at positron source.  Here: new developments concerning description of beam- beam effects and depolarization UndulatorCollimator / TargetCapture Optics Physics Process ElectrodynamicsStandard ModelT-BMT (spin spread) Packages SPECTRA, URGENT GEANT4, FLUKAASTRA Damping ringMain Linac / BDSInteraction Region Physics Process T-BMT (spin diffusion) T-BMTBunch-Bunch Packages SLICKTRACK, (Merlin) SLICKTRACK (Merlin) CAIN2.35 (Guinea-Pig) Depolarization and Beam-Beam Effects at the LC Classical spin precession in inhomogeneous external fields: T-BMT equation. Stochastic spin-flips from photon emission: Sokolov- Ternov effect, etc.  Polarization of an ensemble of particles is defined as L  left-handed helicity state, R  right-handed helicity state Positron Source Incoherent Pair Production Beam-Beam Effects In general, two effects influence the spin motion in elec.magn. Fields: spin precession described by the Thomas- Bargmann-Michel-Telegdi (T-BMT) equation and b) spin-flip Sokolov-Ternov (S-T) processes. In addition two kinds of background processes occur: the production of coherent and of incoherent e+/e- pairs. Coherent Pair Production Incoherent pair production processes Breit-Wheeler (  +  → e + + e - ) Bethe-Heitler (e ± +  → e ± + e + + e - ) Landau-Lifshitz (e + + e - → e + + e - + e + + e - ) Bremsstrahlung (e + + e - → e + + e - +  ) are dominant at the ILC. The production of incoherent pairs depends strongly on the polarization state of the initial photons. At present the Breit-Wheeler production cross-section in CAIN is approximated by an expression that only takes into account the circular polarizations of the initial photons. A comparison is shown between the CAIN approximation and the full cross-section for different ILC parameter sets (left figure). A 10% to 20% reduction in the number of incoherent pairs produced is observed using the full cross-section, whilst there is no discernible change in collision luminosity. Coherent pair production is suppressed at the ILC due to small beamstrahlung. For the CLIC design with high beamstrahlung and higher energie, these processes are the dominant background process. The coherent production of pairs via the first order interaction between a beamstrahlung photon and the beam field is included already in CAIN. The second order stimulated Breit-Wheeler process (shown above) also takes place in the presence of the bunch fields. The bunch field has the effect of allowing the second order cross-section to reach the mass shell which means that the stimulated Breit-Wheeler cross-section can exceed the first order coherent process cross-section. The second order process is currently being added to CAIN. Feynman Diagrams for the second order coherent Breit-Wheeler process. The double lines represent solutions to the Dirac equation in an external field. T-BMT Equation in Strong Fields The T-BMT and the S-T depolarization effects have been simulated using the CAIN software Usually the spin precession effect is dominant, but at higher energy the depolarization due to the S-T effect increases, as can be seen below. Expected Depolarization The other processes are treated in equivalent photon approximation that is only valid if full polarization of the virtual photons have been included. The corresponding updates for CAIN are in progress. Numerical results for the ILC baseline and the parameter set of the CLIC-G design are given: Description of QED processes in external fields A semi-classical method has been used so far to describe the S-T and T-BMT effects in external fields, called ‘operator method’ (Baier, Katkov et al.). Another more quantum field theoretical approach is to use the bound interaction picture (so called ‘Furry representation’: a solution for an electron in an external field A e is given by the Volkov solution, composed by the product of the free field Dirac spinor and a function that describes the full effect of the external field on the electron wave function. Sokolov-Ternov Effect in external fields Assuming that the bunch field can be described by a constant crossed electromagnetic field, work is in progress to describe the S-T process with general parameters, applicable for strong external fields. Spin precession is described by the T-BMT equation which depends on the anomalous magnetic moment (AMM) of the electron a: In a quasiclassical approximation the AMM gets corrections from the external fields: ( Baier, Katkov) The AMM is given in QED by radiative corrections to the e-e- photon vertex: A complementary field theoretical calculation using the furry representation is in progress.