Collimation Depth Calculations for ILC BDS

1. Collimation Depth Calculations for ILC BDS Frank Jackson

2. Latest Versions ILC-BDS • ‘FF9’ deck available at SLAC • http://www.slac.stanford.edu/~mdw/ILC/Beam_Delivery/20050316/ • 20 mrad and 2 mrad x-ing angle schemes • Include energy spectrometers • Bandwidth has been optimised • Different designs for 2 mrad extraction • SLAC-EU collaboration, under development

3. Collimation Depth Calculation • SR must pass through all apertures close to IR • IP beampipe, extraction quadrupoles or the facing final doublet • Use semi-analytic linear calculation routine DBLT by Oliver Napoly (SACLAY) • Calculates SR fan as function of collimation depth • Constrain the fan to pass through IR apertures, solve for collimation depth

4. DBLT (O. Napoly) Assumptions and Method • Assumes minimal 2-phase collimation • Collimators in phase and 90O out of phase with IP • Assumes mono-energetic halo particles • Track corners of collimated phase space at IP back through final doublet • Use many SR emission points in final doublet x’ x Collimated halo phase space at IP

5. DBLT Solutions SR profiles y • Aperture constraint satisfied by ellipse of solutions in Nx, Ny space • A different ellipse for every SR emission point in FD • ‘Smallest’ ellipse defines collimation depth Aperture x Possible coll. depth solutions for one emission point Ny X marks solution for square SR profile at aperture For more details see 15 Oct 04 talk http://www.astec.ac.uk/ap/collider/collimmeet05Oct04/index.html Nx

6. 20 mrad Collimation Issues Aperture list http://www.slac.stanford.edu/xorg/lcd/ipbi/lcws05/maruyama_backgrounds.ppt Last extraction quad is at 47m from IP, 71 mm aperture.

7. 20 mrad Collimation Issues • Extraction quads extend to ~50m from IP. • How far from IP should SR cleanly pass? • Don’t have good feeling for background effects/back scattering • For depth calculation choose 3 apertures for SR clearance • VTX beampipe at IP • QFEX1A exit (12mm, 5.71 m from IP) • QFEX1C exit (24mm, 9.73 m from IP)

8. 20 mrad Collimation Solutions VTX beampipe QFEX1A exit QFEX1C exit QFEX1A exit solution Nx = 8.82 xNy= 68.89 y Compare with estimation by optics rescaling from NLC (A. Drozhdin), Nx = 8 x Ny = 57 y Corresponds to spoiler gaps of ax = 1mm, ay = 0.5 mm

9. 20 mrad SR Fan Envelope • Plot SR fan envelope for 8.82x x 68.89y collimated halo • Demonstrates SR clearance of constraining aperture • Rays are not straight lines in r vs. s space! FD VTX QFEX1-5

10. 2mrad Collimation Depth • Now non-symmetrical problem • SR fan passes through one or more non-symmetrical apertures, then will hit beam pipe eventually QD0 SR fan centroid IP QD0 Extracted Beam

11. 2mrad Extraction (Daresbury/Orsay) 500 GeV • What collimation depth to clear QD exit? • Treat as symmetric problem and constrain SR fan with 22 mm symmetrical aperture – to do QD 5.4 m 31 mm Ignore everything afterwards 1.6 mrad 8.8mm SR fan centroid Distance of closest approach ~ 22 mm QD

12. Other Issues • SR from last bend before final focus may also constrain coll. depth • Have been ignoring effect of local chromaticity correction sextupole • Have been ignoring energy spread of beam halo

13. Conclusion and Future Work • DBLT gives quick evaluation of collimation depth • Can use as first approximation for spoiler gaps • Fine tuning of collimation depth requires simulation • For example, BDSIM cross check of DBLT incorporating halo energy spread • Broader collimation questions • Collimation performance of whole lattice (STRUCT/BDSIM) • Machine protection issues