1. LC-ABD: WP2.3 (robust spin polarisation) and WP5.1 (helical undulator). Helical Collaboration I.R. Bailey, P. Cooke, J.B. Dainton, L.J. Jenner, L.I. Malysheva (University of Liverpool / Cockcroft Institute) D.P. Barber (DESY / Cockcroft Institute) P. Schmid (DESY) G.A. Moortgat-Pick (IPPP, University of Durham / CERN / Cockcroft Institute) A. Birch, 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, A. Lintern, J. Rochford (CCLRC Rutherford Appleton Laboratory) WP2.3 - Robust Spin Polarisation Status EUROTeV: WP3 (damping rings) and WP4 (polarised positron source). Leo Jenner, University of Liverpool on behalf of

2. WP2.3 Aims and Overview Developing reliable software tools that will allow us to make optimum use of polarisation for maximising the ILC physics output. Aiming to carry out full cradle-to-grave spin transport simulations. Currently carrying out simulations of depolarisation effects in damping rings, beam delivery system and during bunch-bunch interactions. Developing simulations of spin transport through the positron source (in collaboration with DESY, Zeuthen). Soon to extend 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.

3. Both stochastic spin diffusion through photon emission and classical spin precession in inhomogeneous 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

4. UndulatorCollimator / TargetCapture Optics Physics Process ElectrodynamicsStandard ModelT-BMT (spin spread) Packages SPECTRA, URGENT GEANT4, (EGS4)ASTRA 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

5. 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 Layout of ILC with undulator at 150GeV position in main linac.

6. 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) Target spin transfer Pre-release GEANT4 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 10MeV photons Simulations using SPECTRA

7. Positron Source Capture Optics Design Two coil superconducting magnet gives focussing solenoid field (Adiabatic Matching Device) z z V.S.Kashikhin, FNAL T-BMT

8. Runge-Kutta Integrator Scheme Let an initial value problem be specified as follows. initial value problem Then, the RK4 method for this problem is given by the following equation: where Thus, the next value (y n+1 ) is determined by the present value (y n ) plus the product of the size of the interval (h) and an estimated slope. The slope is a weighted average of slopes:slope k 1 is the slope at the beginning of the interval; k 2 is the slope at the midpoint of the interval, using slope k 1 to determine the value of y at the point t n + h/2 using Euler's method;Euler's method k 3 is again the slope at the midpoint, but now using the slope k 2 to determine the y-value; k 4 is the slope at the end of the interval, with its y-value determined using k 3. Andriy Ushakov, DESY

9. Boris’ Numerical Integration Scheme 1.Advance w by vector term b a half-step 2.Advance w by M a full step 3.Advance w by b a half-step Jeff Smith, Cornell

10. Boris 2 nd order Preserves conserved quantities 1 calculation per step R-K 4 th order 4 calculations per step Speed! R-K vs Boris Will try both!

11. Beam-Beam Simulations Survey of CAIN bunch-bunch depolarisation theoretical uncertainties complete.  Results presented at EPAC 2006.  Studies of possible ILC beam parameters:  Theoretical work ongoing into  validity of T-BMT equation in strong fields  validity of equivalent photon approximation (EPA) for incoherent pair production processes  higher-order processes  macro-particle non-conservation

12. Beam-Beam Simulations (2) Large Y During Interaction Before Interaction After Interaction Spread in Polarisation Low Q Before Interaction During Interaction After Interaction Depolarisation dependent on bunch charge density, as expected.

13. Beam-Beam Simulations (3) Background incoherent pair-production processes in beam-beam interactions and their EPA equivalents in CAIN: Breit Wheeler Collaboration with Tony Hartin Second-order QED processes with Spin Density Matrices Beithe-Heitler and Landau-Lifshitz Polarization of photons needs to be included (LC-ABD 2) Bremsstrahlung EPA not valid for ILC energies! Has to be rederived including leading-logarithmic terms (LC-ABD 2)

14. SLICKTRACK Simulations Beam Delivery System –The 2-mrad beam line selected –BDS2-OPTIC created and analysed –Beam parameters verified against MAD –Just completed first results for BDS with misalignments –Effect of misalignments on polarisation small (as expected) –Effect on emittance is drastic (as expected) Damping Rings –A new lattice OCS(6.6km) description available Conversion to new platforms –MAP2 cluster at Liverpool –Converting NAG library calls in SLICKTRACK to CERN library calls

15. 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 Copy from BDS ILC@SLAC presentation

16. Milestones Milestones for the coming period 1.7 Include spin-tracking algorithms into ASTRADecember 2006 1.9 Adapt SLICKTRACK for MAP2 October 2006 2.4 Implement higher-order corrections in CAIN September 2006 3.6 Initial linac simulations using SLICKTRACK November 2006

17. WP2.3 Status and Plans  Our work will be presented at the SPIN’06 conference in Kyoto  First SLICKTRACK studies of BDS complete  SLICKTRACK study of main linac expected by end of year  Work on the ASTRA code for modelling positron source capture optics starting  CAIN theoretical analyses ongoing and updates to CAIN simulation code will follow.  Full cradle-to-grave simulations delayed until end of year, but additional staff effort is now in place at the University of Liverpool and DESY to help fill in the missing pieces!