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Crab cavity option at LHC

Crab cavity option at LHC. K. Ohmi (KEK) HHH04, 8-11, Nov. 2004 CERN. Thanks to K. Akai, K. Hosoyama, T. Sen, F. Zimmermann. Introduction. Half crossing angle 0.15 mrad. Other possibilities are 0.225, 0.5 and 4 mrad. E=7 TeV. Bunch population 1.15x10 11

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Crab cavity option at LHC

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  1. Crab cavity option at LHC K. Ohmi (KEK) HHH04, 8-11, Nov. 2004 CERN Thanks to K. Akai, K. Hosoyama, T. Sen, F. Zimmermann

  2. Introduction • Half crossing angle 0.15 mrad. • Other possibilities are 0.225, 0.5 and 4 mrad. • E=7 TeV. • Bunch population 1.15x1011 • Bunch spacing 25 ns, wRF=400.8 MHz. • Number of bunch 2808 I = 0.584 A • L=26,016m

  3. Crabbing voltage • Deflecting RF voltage, f: half crossing angle • b*=0.5m b =150 m, fRF=500 MHz • V=11.6 MV is required for f =0.15 mrad.

  4. KEKB type crab cavity • TM110 500 MHz • TM010 324 MHz • V=1.44 MV • Need 8x2 cavities for f = 0.15 mrad. • Need more cavities 0.225, 0.5 and 4 mrad. How is multi-cell cavity? Coupled bunch instability issue.

  5. Original 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

  6. Why squashed cell shape cavity? TM110 TM010 TM110 - like Mode TM010 - like Mode 500MHz 324MHz 500MHz 413.3MHz B E Crab Mode 650.5 MHz / 677.6MHz Crab Mode TE111 720MHz Unwanted Mode Unwanted Mode TM110 500MHz 700MHz The squashed cell shape cavity scheme was studied extensively at Cornell in 1991 and 1992 for CESR-B under KEK-Cornell collaboration. Courtesy of K.Hosoyama & K. Akai

  7. Transverse coupling impedance t~1 sec (inj) Zx /cav Zy/cav f ZL /cav t~1 hour (inj) Courtesy of K. Akai

  8. High current type for super KEKB Damped structure with wave guides. Impedance~1/10. Courtesy of K. Akai

  9. Coupled bunch instability caused by the parasitic modes • Longitudinal f ZL,peak=17.8 /t kW GHz @injection =152 /t kW GHz @top t : Growth time (sec) • Transverse Zt,peak=1.37 /t [MW/m] @injection, =21 /t [MW/m] @top

  10. Cryostat for KEKB Crab Cavity (Top View) ~ 3 m Courtesy of K. Hosoyama

  11. Road Map to Beam Test (Feb 2004) 2003 2004 2005 Dec. Jan. Dec. Jan. Dec. Jan. Jan. Crab Cavity #1 Design E.P. Crab Cavity Cold Test Cryostat Crab Cavity Prototype Coaxial Coupler Cold Test Ｃｒｙｏｓｔａｔ　(Prototype) Assembling Installation Coaxial Coupler (Prototype) Assembling Nb-Cu R&D Cold Test Beam Test Vac. RF Cryogenics Control Vac. RF Cryogenics Control Courtesy of K. Hosoyama

  12. Effect on the beam-beam performance(preliminary) • Noise of RF system. Deviation of RF phase, dj. • Phase error between two crab cavities.

  13. Fluctuation in collision due to the crab cavity noise • Random fluctuation of beam offset at the collision point. • Example to sketch rough behaviors • dx=1.6 mm for dj=5 degree (dz=1 cm) and f =0.15 mrad. Note sx=17 mm. • Correlation of the fluctuation. <dx(n) dx(n+m)>=e-m/t, where n, m are turn. • dz=1, 0.5, 0.2, 0.1 cm at t=1, 100 were examined. • A Strong-strong simulation was executed including the fluctuation.

  14. 3D algorithm, Longitudinal slicing Strong-strong Weak-strong • Strong bunch is divided into some slices. • Particles in the weak beam is tracked slice by slice. • A bunch is divided into some slices which include many macro-particles. • Collision is calculated slice by slice.

  15. Synchro-beam mapping (Hirata) • Weak-strong s1 s2 • Beam envelope of the strong beam slice is transferred to collision point. • Since the interaction depends on z, energy kick occurs.

  16. Extension to strong-strong simulation • Potential is calculated at sf and sb. • Potential is interpolated to si between sf and sb. sf sf sb sb si si • Since the interaction depends on z, energy kick should be taken into account df/dz. • We repeat the same procedure exchanging particle and slice.

  17. All particles in i-th slice are kicked by φcp Interpolation Convergence for the slice number How many slices do we need? Disruption parameter of each slice should be smaller than 1.

  18. Noise free - no diffusion • L sx The beam size with crab is larger, but is pretense, <xx>c=<xx>+z2<zz>. Note that the luminosity is higher.

  19. Diffusion due to RF phase error, dz • L sx dx is raised by dispersion dx=z dz induced by the crab cavity.

  20. Diffusion rate given by the simulation • sx2=sx02+Dt t: turn • D~1.4x10-15dx[mm]2 dz= 0 0.005 0.01

  21. No crab cavity、RF phase error • Diffusion without crab cavity was weak. • Noise of transverse offset is origin of the diffusion. L sx

  22. Diffusion due to phase error of crab cavity • Dx=1.7 mm and dz=1 cm (dx =1.7 mm) • Similar diffusion rate L sx

  23. Correlation time, t • dx=1.6 mm, t=100 and dx=0.16 mm t=1 was similar behavior. M.P.Zorzano and T. Sen

  24. Analytic theory of beam-beam diffusion (T. Sen et al., PRL77, 1051 (1996), M.P.Zorzano et al., EPAC2000) • Diffusion rate due to offset noise. (round beam)

  25. Comparison with the simulation • D(a=1)=<DJ2>=1.5x10-25 m2/turn • D(sim)=(s-s02)2/b2 =10-28 m2/turn Need to check

  26. Tolerance • 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, if luminosity life time ~ 1 day is required.

  27. Crab crossing in e+e- colliders • Flat beam, small by, ey<<ex<<ez . • High beam-beam parameter, x>0.05. • High disruption f=(4pxsz/ by)1/2~1. • Radiation damping and diffusion. • Symplectic diffusion is caused by crossing angle and lattice errors at collision point • Final beam-beam limit after removing all diffusion sources is determined by the radiation excitation.

  28. Diffusion for various crossing anglegiven by the weak-strong simulation (Gauss) • Vertical equilibrium size obtained by the weak-strong simulation and the ratio of the diffusions for the rad. damping. • Diffusion rate

  29. Diffusion due to x-y coupling (Gaussian) • X-y coupling is characterized by r1-r4. • Diffusion caused by r1 and r2 is shown. The diffusion rate is proportional to r1 and r2.

  30. Luminosity behavior with x-y coupling in 2D and 3D simulation • X-y coupling seems to affect 2D dynamics. • Luminosity behavior depends on 2D or 3D simulation, namely include z or not.

  31. Diffusion due to vertical dispersion • Gaussian beam

  32. Diffusion in the head-on collisionsymplectic diffusion is removed • Radiation excitation enhances beam enlargement. • In Gaussian model, enlargement is small. • Accuracy of PIC is excellent as far as diffusion. Distorted distribution : PIC Gaussian:PIC Gaussian:Exact solution

  33. Beam-beam parameter for zero and finite crossing angle Strong-strong Gauss model PIC * Present KEKB parameter

  34. Discussions • Do crab cavities contribute luminosity upgrade of LHC? • Is the symplectic diffusion caused by crossing angle dominant? If yes, crab cavity works. • Do diffusion limit the LHC luminosity? What determine the beam-beam limit in LHC? • What is dominant diffusion source in LHC? • Parasitic collision is weakened by large crossing angle.

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