LC-ABD WP2.3 (robust spin polarisation) and WP5.1 (helical undulator) form the heLiCal collaboration. Ian Bailey on behalf of the Helical Collaboration I.R. Bailey, P. Cooke, J.B. Dainton, L.I. Malysheva (University of Liverpool / Cockcroft Institute) D.P. Barber (DESY / Cockcroft Institute) G.A. Moortgat-Pick (IPPP, University of Durham / CERN / Cockcroft Institute) J.A. Clarke, O.B. Malyshev, D.J. Scott (CCLRC ASTeC Daresbury Laboratory / Cockcroft Institute) E. Baynham, T. Bradshaw, A. Brummit, S. Carr, Y. Ivanyushenkov, J. Rochford (CCLRC Rutherford Appleton Laboratory) ILC Spin Tracking Overlaps with EUROTeV WP3 (damping rings) and EUROTeV WP4 (polarised positron source).

Aims and Overview Developing reliable software tools to simulate e - /e + spin transport through each region of ILC. Aiming to carry out full cradle-to-grave simulations to facilitate optimisation of ILC for spin polarisation as well as luminosity. Currently carrying out simulations of positron source, damping rings and bunch-bunch interactions. In the process of extending simulations to cover BDS, main linac, etc. Aiming to address issues such as impact of tunnel curvature, positions of polarimeters, etc. In process of recruiting new staff and actively seeking new collaborators. 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.

UndulatorCollimator / TargetCapture Optics Physics Process ElectrodynamicsStandard ModelT-BMT (spin spread) Packages SPECTRAGEANT4, EGS4ASTRA Damping ringMain Linac / BDS Interaction Region Physics Process T-BMT (spin diffusion) T-BMTBunch-Bunch Packages SLICKTRACK, (Merlin) Merlin / SLICKTRACK CAIN2.35 (Guinea-Pig) Packages in parentheses will be evaluated at a later date. Software Tools Overview e + source

Conversion Target (0.4X 0 Ti) Polarised Positrons (≈ 5 MeV) Helical Undulator (≈ 100 m) Photon Collimator Photons(≈ 10 MeV ) Electrons (150 GeV) Undulator-Based Positron Source Baseline layout of ILC with undulator at 150GeV position in main linac.

Structure: bifilar helical undulator Period: 12 mm Field on axis:0.75 T Vacuum Bore: > 4mm Beam pipe: Cu / Al / StSteel / Cu plated StSteel Field quality: - 1 st integral10 -4 Tm - peak-to-peak £ 1% - number of periodsodd - end structurefield increase Module: - length 4 m - two undulators per module  Desirable to  Increase beam pipe radius.  Decrease undulator period.  Maintain high on-axis field.  Challenges materials and engineering. Long Superconducting Module Prototype NB heLiCal has already developed two short (20 period) undulator prototypes - one superconducting and one using permanent magnets.

Amanda Brummitt, RAL Cryostat length – 4000 mm Undulator length (incl. ends) – 3576 mm (89%) Undulator effective length – 3480 mm (87%) Superconducting Module Prototype Design

Models photon beam polarisation Models electron beam trajectory Doesn’t model B field off-axis Doesn’t track spin of electron beam SPECTRA Undulator field quality: Tm  < 0.1 μrad e - beam deviation

Structure of SLICKTRACK

Damping Ring Simulations  Leading the ILC Damping Ring group’s depolarisation task.  Results presented at the ILC DR workshop at CERN in November and form part of ILC DR report (Cockcroft ).  Studies of TESLA (17km dogbone) and OSC (6km ring) designs show negligible radiative depolarisation effects giving variances of up to (radians) 2.  Angle of the polarisation vector of the injected bunches is however critical and must be carefully controlled by the spin rotators.  The mean square angle (mrad 2 ) of tilt away from the radiationless equilibrium direction (n 0 ) versus ‘turns’ in the OCS ring at 4.8GeV. The spins are initially aligned along n 0. The mean square angle (mrad 2 ) of tilt away from the radiationless equilibrium direction (n 0 ) versus ‘turns’ in the OCS ring at 5.066GeV. The spins are initially aligned 100 mrad away from n 0.

Current Work –Apply CAIN to variety of ILC parameter sets at 500 GeV and 1 TeV. –Critical review of theoretical uncertainties. –Add further higher-order / full spin correlations to CAIN. Non-Gaussian beam profiles. Spin correlations in incoherent processes. Preliminary indications –Large relative difference between beam depolarisation obtained using different ILC parameter sets. –Small absolute difference… Future –Compare with Guinea-Pig CAIN

Before interactionDuring interactionAfter interaction TESLA parameters low Q parameters P INIT =1.0 CAIN Simulations

Use of curved tunnel geometry? –Expect approximately 560 bends of 5.7mrad (after energy upgrade to 500 GeV beam). –Will lead to spin precession 100°±0.1° along main linac. –Effect of additional spin diffusion deemed small. –More sophisticated calculation to follow… Main Linac

Recent Progress Successful application of the SLICKTRACK software program to the ILC damping ring designs. Initial assessment of CAIN bunch-bunch depolarisation with LC bunch structure complete (details to be presented at EPAC 2006). Larisa Malysheva joined Liverpool as a PhD student in September and Dr Mari Berglund will fill a related Liverpool RA position in March New milestones recently adopted to explicitly cover depolarisation of the electron beam in the helical undulator in the positron source and the implementation of high-order corrections in the CAIN code.

Plans for 2006  Initial commissioning of the MERLIN code is underway.  Further development of SLICKTRACK now in progress to adapt the code for use in modelling the ILC beam delivery system. Initial simulations expected June  Work on the ASTRA code for modelling positron source capture optics should also begin in Spring  CAIN theoretical uncertainties being assessed (e - anomalous moment in T-BMT equation, spin correlations in incoherent processes, …). Expected complete June  First cradle-to-grave simulations expected in second half of 2006.