1. Software Tools Beam-Beam TESLA damping ring As part of a study to choose the optimum damping ring configuration for the ILC, the depolarisation effects in two damping ring lattices were analysed: the 6 km OCS ring, and the 17 km TESLA ring (figures on right). The depolarisation was estimated using a Monte-Carlo tracking algorithm which simulates stochastic photon emission. The bottom left-hand figure shows the results of a simulation using the SLICKTRACK software package for the OCS ring at 4.8 GeV. The bottom right-hand figure shows that if the initial polarisation vector is initially tilted from vertical then, contrary to the common expectation, there is no complete decoherence of the projections of the spin on the horizontal plane. This result is in good agreement with analytical calculations. Radiative depolarisation in the damping rings was found to be negligible even with beam emittances ten times greater than those planned for the ILC. Damping Rings After production, the electrons and positrons pass through damping rings containing wiggler magnets which act to radiatively ‘cool’ the beams. Although it expected that in a damping ring that has been well designed and sufficiently well aligned the depolarisation will be negligible, this expectation should be checked since the enhancement of synchrotron radiation by the wigglers has the potential to cause spin depolarisation. Mean square angular deviation from the equilibrium direction mrad**2 Turns The mean square angle of tilt away from vertical vs. turns in the OCS ring at 4.8 GeV. Mean square angular deviation from the equilibrium direction mrad**2 Turns The mean square angle of tilt away from vertical vs. turns in the OCS ring at 5.066 GeV for spin initially at 100 mrad from vertical. OCS damping ring The Cockcroft Institute The Cockcroft Institute is a newly created international centre for Accelerator Science and Technology (AST) in the UK. It is a joint venture of Lancaster University, the Universities of Liverpool and Manchester, the Council for the Central Laboratory of the Research Councils (CCLRC at the Daresbury and Rutherford Appleton Laboratories), the Particle Physics and Astronomy Research Council (PPARC), and the North West Development Agency (NWDA). The heLiCal collaboration J.A. Clarke +, O.B. Malyshev +, D.J. Scott + CCLRC ASTeC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, UK E. Baynham, T. Bradshaw, A. Brummitt, S. Carr, Y. Ivanyushenkov, J. Rochford CCLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK I.R. Bailey +, P. Cooke, J.B. Dainton +, L. Malysheva + Department of Physics, University of Liverpool, Oxford St., Liverpool, L69 7ZE, UK D.P. Barber + DESY-Hamburg, Notkestraße 85, 22607 Hamburg, Germany G.A. Moortgat-Pick + Institute of Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, UK, and CERN, CH-1211 Genève 23, Switzerland + 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. Large Y During Interaction Before InteractionAfter Interaction Spread in Polarisation Low Q Before InteractionDuring InteractionAfter Interaction Overview  High intensity polarized e - and e + beams are needed for realising the full physics potential of the ILC.  Polarized e - source is already in ILC baseline design, and baseline e + source is easily upgraded to give polarized beam.  Precision physics requires 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 Beam Delivery System After acceleration to 250 GeV, the electron and positron beams are prepared for collision by the beam delivery system via bending and focusing magnets. For a 250 GeV electron beam undergoing the total of 11 mrad of bend, the spin precession is approximately 332°. Preliminary calculations using the SLICKTRACK software package in a single-pass mode indicate there is no significant loss of polarization, confirming earlier work carried out at Cornell using BMAD. Summary  Damping rings  Depolarization for carefully corrected orbits is negligible (as expected).  A rolling study to include extra effects and new lattices will be continued.  Beam delivery system  First SLICKTRACK simulations completed.  With good alignment there is no noticeable depolarization.  Further studies of misalignments are required.  Beam-beam interactions  The maximum depolarization is ~0.2% (‘large Y’ and ‘low P’ scenarios)  The minimum depolarization is <0.1% (‘low Q’ scenario).  Theoretical uncertainty due to use of the Equivalent Photon Approximation being investigated.  Validity of the T-BMT equation for strong fields being investigated.  On track to provide full cradle-to-grave simulations for the ILC.  We are developing reliable software tools to optimise the ILC for polarisation delivery as well as luminosity.  Currently simulating damping rings, beam delivery system, bunch-bunch interactions and positron source. UndulatorCollimator / TargetCapture Optics Physics Process ElectrodynamicsStandard ModelT-BMT (spin spread) Packages SPECTRAGEANT4, (EGS4)ASTRA Damping ringMain Linac / BDSInteraction Region Physics Process T-BMT (spin diffusion) T-BMTBunch-Bunch Packages SLICKTRACK, (Merlin) Merlin / SLICKTRACK CAIN2.35 (Guinea-Pig) Spin Tracking at the ILC Classical spin precession in inhomogeneous external fields: T-BMT equation. Stochastic spin diffusion 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 ILC parameter sets: ‘low Q’  ‘low charge’ ‘large Y’  ‘wide flat beams’ ‘low P’  ‘low current’ The largest depolarisation effects in the ILC are expected to occur during the beam-beam interactions. The interactions have been simulated using the CAIN software package for the ILC parameter sets shown in the table on the right. The results of simulations carried out for 100% polarised beams colliding head-on are shown on the left. The table underneath shows the different contributions to depolarisation from classical and radiative processes. The theoretical uncertainties in CAIN are under investigation. Incoherent pairs are only implemented in the soft photon approximation (problems with bremsstrahlung!), and the form of the anomalous magnetic moment in the T-BMT equation only applies for low fields.

2. The Cockcroft Institute The Cockcroft Institute is a newly created international centre for Accelerator Science and Technology (AST) in the UK. It is a joint venture of Lancaster University, the Universities of Liverpool and Manchester, the Council for the Central Laboratory of the Research Councils (CCLRC at the Daresbury and Rutherford Appleton Laboratories), the Particle Physics and Astronomy Research Council (PPARC), and the North West Development Agency (NWDA). The heLiCal collaboration J.A. Clarke +, O.B. Malyshev +, D.J. Scott + CCLRC ASTeC Daresbury Laboratory, Daresbury, Warrington, Cheshire WA4 4AD, UK E. Baynham, T. Bradshaw, A. Brummitt, S. Carr, Y. Ivanyushenkov, J. Rochford CCLRC Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire OX11 0QX, UK I.R. Bailey +, P. Cooke, J.B. Dainton +, L. Malysheva + Department of Physics, University of Liverpool, Oxford St., Liverpool, L69 7ZE, UK D.P. Barber + DESY-Hamburg, Notkestraße 85, 22607 Hamburg, Germany G.A. Moortgat-Pick + Institute of Particle Physics Phenomenology, University of Durham, Durham DH1 3LE, UK, and CERN, CH-1211 Genève 23, Switzerland + 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. Beam Delivery System IR1 20 mrad IR2 2 mrad e-e+ 11 mrad NLC-style Big Bends 2 mrad (L* = 4.5 m) dump lines 20 mrad ILC FF9 (x 2) 2 mrad ILC FF (x 2) 20 mrad (L* = 6 m) dump lines IP separation: 138.4 m (Z), 20.4 m (X) Path length difference (to IR2): 3 × 400 1.3 GHz periods = 276.7315 m Fig.5 Layout of BDS ( Copy from BDS ILC@ SLAC presentation) After acceleration to 250 GeV, the electron and positron beams are prepared for collision by the beam delivery system. Initial studies show that the depolarisation due to synchrotron radiation in the total of 11 mrad of horizontal bends is negligible, but further careful evaluation is still needed. Plans We will maintain the rolling study for DR to include extra effects as necessary. It is clear that the effects of misalignments for BDS will require careful further study. Fig.2 TESLA damping ring As part of a study to choose the optimum damping ring configuration for the ILC, the depolarisation effects in two damping ring lattices were analysed: the 6 km OCS ring, and the 17 km TESLA ring (figures 1 and 2). The depolarisation was estimated using a Monte-Carlo tracking algorithm which simulates stochastic photon emission. In figure 3 the results of a simulation using the SLICKTRACK software package for the OCS ring at 4.8 GeV are presented. Figure 4 shows that if the initial polarisation vector is initially tilted from vertical then, contrary to the common expectation, there is no complete decoherence of the projections of the spin on the horizontal plane. This result is in good agreement with analytical calculations. Radiative depolarisation in the damping rings was found to be negligible even with beam emittances ten times greater than those planned for the ILC. Damping Rings After production, the electrons and positrons pass through damping rings containing wiggler magnets which act to radiatively ‘cool’ the beams. Although it expected that in a damping ring that has been well designed and sufficiently well aligned the depolarisation will be negligible, this expectation should be checked since the enhancement of synchrotron radiation by the wigglers has the potential to cause spin depolarisation. Mean square angular deviation from the equilibrium direction mrad**2 Turns Fig.3 The mean square angle of tilt away from vertical vs. turns in the OCS ring at 4.8 GeV. Mean square angular deviation from the equilibrium direction mrad**2 Turns Fig.4 The mean square angle of tilt away from vertical vs. turns in the OCS ring at 5.066 GeV for spin initially at 100 mrad from vertical. Fig.1 OCS damping ring Large Y During Interaction Before InteractionAfter Interaction Spread in Polarisation Low Q Before InteractionDuring InteractionAfter Interaction (polarized) sources spin rotators damping rings beam delivery system beam-beam interaction spin rotators