issues related to crossing angles

1. issues related to crossing angles Frank Zimmermann

2. Super-KEKB crab cavity scheme 2 crab cavities / beam / IP

3. voltage of crab cavities tolerance on IP offset jitter translates into tolerance on left-right crab-cavity phase and crab-main-rf phase

4. R12 & R22(R11) from MAD nominal LHC optics |R12,34|~30-45 m |R22,44|~1 (from crab cavity to IP)

5. voltage required for Super-LHC

6. crab cavity voltage for different qc’s & rf frequencies

7. tolerance on R22 z-dependent additional crossing angle corresponding Piwinski angle should be small not a problem [for qc=1 mrad, sx=12 mm, R12=30 m, sz=7.55 cm]

8. K. Ohmi, HHH-2004 ~1.5 MV@500 MHz KEKB crab cavity • Squashed cell operating in TM2-1-0 (x-y-z) • Coaxial coupler is used as a beam pipe • Designed for B-factories (1〜2A) ~1.5 m Courtesy K. Akai

9. longitudinal space & crab frequency longitudinal space required for crab cavities scales roughly linearly with crab voltage; desired crab voltage depends on rf frequency); achievable peak field also depends on rf frequency; 2 MV ~ 1.5 m, 20 MV ~ 15 m frequency must be compatible with bunch spacing; wavelength must be large compared with bunch length; 1.2 GHz probably too high; 400 MHz reasonable; 800 MHz perhaps ok

10. noise amplitude noise introduces small crossing angle; e.g., 1% jitter translates into 1%qc/2 crossing angle – not critical phase noise causes beam-beam offset; → tight tolerance on left-right crab phase and on crab-main-rf phase differences

11. p emittance growth due to random offsets emittance growth from turn-by-turn random offsets Dx SuperLHC: b*x,y=0.25 m, nIP=2, xHO=0.005, g=7500, ge=3.75 mm requiring less than 10%/hr emittance growth Dxrms<12 nm ~ 10-3s* Df <0.012o at qc=1 mrad & 500 MHz Df <0.04o at qc=0.3 mrad & 500 MHz

12. K. Ohmi, HHH-2004 diffusion rate from strong-strong simulation with BBSS • sx2=sx02+Dt t: turn • D~1.4x10-15Dx[mm]2 dz= 0 0.005 0.01

13. K. Ohmi, HHH-2004 tolerance from Ohmi san’sstrong-strong simulation • For Dx=1.6 mm (df=5 degree) and t=100, D~1.4x10-15Dx[mm]2, wheresx2=sx02+Dt, t: turn. • Tolerance is Dx=0.016 mm, Df= 0.05 degree for t=100, and Dx=0.0016 mm, 0.005 degree for t=1, for luminosity life time ~ 1 day slightly worse than my “pessimistic estimate”!? for 300 mrad crossing angle and 400 MHz

14. analytic theory of b-b diffusion (T. Sen et al., PRL77, 1051 (1996)M.P.Zorzano et al., EPAC2000) • Diffusion rate due to offset noise. (round beam) K. Ohmi, HHH-2004

15. K. Ohmi, HHH-2004 comparison with the simulation } 3 orders of magnitude discrepancy! • D(a=1)=<DJ2>=1.5x10-25 m2/turn • D(sim)=(s-s02)2/b2 =10-28 m2/turn Need to check analytical diffusion rate from Sen-Ellison-Zorzano model even much larger!!

16. impedance of crab cavities transverse impedance is an issue due to large beta function rise time due to 1 crab cavity = rise time from ~10 normal rf cavities with the same voltage

17. dispersion correction if large crossing angles are realized by placing single D1 dipoles first, and the triplet between D1 and 2, the dispersion correction could be an issue to be studied

18. minimum crossing angle from LR b-b “Irwin scaling” coefficient from simulation note: there is a threshold - a few LR encounters may have no effect! (2nd PRST-AB paper with Yannis Papaphilippou) minimum crossing angle with wire compensator need dynamic aperture of 5-6 s and wire compensation not efficient within 2 s from the beam center