1. Ian Bailey University of Liverpool / Cockcroft Institute Depolarization Effects and Other Aspects

2. heLiCal collaboration L.I. Malysheva 1,2, I.R. Bailey 1,2, D.P. Barber 3,2,1, E. Baynham 6, A. Birch 1,5, T. Bradshaw 6, A. Brummitt 6, S. Carr 6, J.A. Clarke 1,2,5, P. Cooke 1,2, J.B. Dainton 1,2, Y. Ivanyushenkov 6, L.J. Jenner 1,2, A. Lintern 6, O.B. Malyshev 1,5, G.A. Moortgat-Pick 1,4, J. Rochford 6, P. Schmid 3 and D.J. Scott 1,2,5 1 Cockcroft Institute, 2 Department of Physics, University of Liverpool, 3 DESY, Deutsches Electronen Synchrotron, 4 Institute of Particle Physics Phenomenology, University of Durham, 5 CCLRC ASTeC Daresbury Laboratory. 6 CCLRC Rutherford Appleton Laboratory

3. Talk Overview Accelerator Physics Issues (GigaZ) on behalf of Gudi Moortgat-Pick Status of Robust Spin Transport simulations by HeLiCal collaboration and colleagues.

4. m Z = 91.1876+/- 0.0021 GeV  Z =2.4952 +/-0.0023 GeV => undulator at 147.5 GeV position?

7. Robust Spin Transport Developing reliable software tools that allow the machine to be optimised for spin polarisation as well as luminosity. Aiming to carry out full cradle-to-grave simulations. Currently carrying out simulations of depolarisation effects in damping rings, beam delivery system and during bunch- bunch interactions. Currently extending simulations to main linac, etc. Energy spectrum and circular polarisation of photons from helical undulator. Trajectories of electrons through helical undulator. Example of SLICKTRACK simulation showing depolariation of electrons in a ring. Collaborating with T. Hartin (Oxford) P. Bambade, C. Rimbault (LAL) J. Smith (Cornell) S. Riemann, A. Ushakov (DESY)

9. Both stochastic spin diffusion through photon emission and classical spin precession in inhomogeneous magnetic fields can lead to depolarisation. 1 mrad orbital deflection  30° spin precession at 250GeV. Largest depolarisation effects are expected at the Interaction Points. Depolarisation Processes Photon emission Spin precession

10. UndulatorCollimator / TargetCapture Optics Physics Process ElectrodynamicsStandard ModelT-BMT (spin spread) Packages SPECTRA, URGENT GEANT4, FLUKAASTRA Damping ringMain Linac / BDS Interaction Region Physics Process T-BMT (spin diffusion) T-BMTBunch-Bunch Packages SLICKTRACK, (Merlin) SLICKTRACK (Merlin) CAIN2.35 (Guinea-Pig) Packages in parentheses will be evaluated at a later date. e + source Software Tools

11. Positron Source Simulations  Polarisation of photon beam Ongoing SPECTRA simulations (new version from SPRING-8) Benchmarked against URGENT (F77 code) Depolarisation of e - beam Analytic studies eg Perevedentsev etal “Spin behavior in Helical Undulator.” (1992) c.f. trajectory simulations Target spin transfer GEANT4 (v 8.2) with polarised cross-sections provided by Andreas Schaelicke, DESY (E166 experiment) Installed and commissioned at University of Liverpool Capture Optics Adding Runge-Kutta and Boris-like T-BMT integration routine to ASTRA

12. Bunch-Bunch Simulations  Opposing bunches depolarise one another at the IP(s).  Studies of different possible ILC beam parameters (see table on right).  Much work ongoing into theoretical uncertainties. Large Y During Interaction Before Interaction After Interaction Spread in Polarisation Low Q Before Interaction During Interaction After Interaction CAIN simulatons

13.  Theoretical work ongoing into  validity of T-BMT equation in strong fields (checked by Gudi)  higher-order QED processes  spin correlations in pair-production processes  validity of equivalent photon approximation (EPA) for incoherent pair production processes Bunch-Bunch Simulations (2) Dominant at ILC energies

14. Tony Hartin, Oxford

17. Damping rings In ideal Damping Ring depolarising effects are expected to be negligible Enhancement of synchrotron radiation (wigglers) might lead to the depolarisation effects Two out of seven reference lattices were selected: OCS 6km (circle) and TESLA 17 km (dogbone) Two energies: 5.066GeV and 4.8 GeV (close to resonance) SLICKTRACK: Monte-Carlo simulation of the effects of synchrotron radiation, i.e. evolution of the spin distribution over a few damping times including full 3-D spin motion

18. OCS Spin Diffusion at 5.066GeV for spins initially at 100 mrad from n 0 Spread of the projections of spins on a horizontal plane reaches equilibrium (25 0 ) : Longitudinal polarisation can survive DR!!! Direction of polarisation vector depends on time.

19. OCS Spin Diffusion at 4.8 GeV and 5.066 GeV for all spins parallel to n 0 The loss of polarisation is negligible

20. SLICKTRACK Simulation Summary Loss of the vertical component of polarisation in DR is insignificant. Contrary to common belief there is little decoherence of the horizontal components of spin, thus the direction of the horizontal component polarisation vector depend on time at which the kickers are fired Our results are in excellent agreement with simple analytical model ( see http://www.desy.de/~mpybar/mypapers.html and arXiv:physics/9709025) http://www.desy.de/~mpybar/mypapers.html Spin rotators before DR required Loss of polarisation in BDS is negligible confirming earlier work (J.Smith, Cornell) Future plans We will maintain a rolling study to include extra effects as necessary Include non-linear optics (Collaboration with E. Forest) Linac simulations (started)

21. MERLIN development as a cross-check of main results Non-linear orbital maps interfaced to SLICKTRACK –Modelling sextupoles, octupoles, undulator, etc Integrated positron source simulations –Rolling study Beam-beam theoretical uncertainties –Incoherent pair production and EPA, T-BMT validity, etc… –Comparison with GUINEA-PIG Novel polarisation flipping in positron source –Flipping polarity of source without spin rotators (cost saving) Polarimetry and polarisation optimisation (University of Lancaster) –Developing techniques to optimise polarisation at the IP Optimising use of available computing resources at DL, Liverpool and on the GRID Further Spin Transport Activities