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Beam dynamics in crab collision

Beam dynamics in crab collision. K. Ohmi (KEK) IR2005, 3-4, Oct. 2005 FNAL. Thanks to K. Akai, K. Hosoyama, K. Oide, T. Sen, F. Zimmermann. Contents. Introduction of crab cavity Effect on the Beam-beam performance. Crossing angle and symplectic diffusion

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Beam dynamics in crab collision

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  1. Beam dynamics in crab collision K. Ohmi (KEK) IR2005, 3-4, Oct. 2005 FNAL Thanks to K. Akai, K. Hosoyama, K. Oide, T. Sen, F. Zimmermann

  2. Contents • Introduction of crab cavity • Effect on the Beam-beam performance. Crossing angle and symplectic diffusion Luminosity degradation due to noise

  3. 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

  4. Crabbing voltage • Deflecting RF voltage, f: half crossing angle • b*=0.5m b =4000 m, fRF=400 MHz • V=2.8 MV is required for f =0.15 mrad. • V=75 MV for 4 mrad

  5. KEKB type crab cavity • TM110 500 MHz • TM010 324 MHz • V=1.44 MV • Need 2x2 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. • Impedance of KEKB crab cavity wZ(w)L=13 kW.GHz/cav. Z(w)T=0.025 MW/m/cav.

  6. KEKB type single cell • TESLA type multi-cell

  7. Coupled bunch instability caused by the parasitic modes • Longitudinal f ZL,peak (KEKB) =13 [kW GHz/cav] , t =1.5 sec /cav@injection t : Growth time (sec) • Transverse Zt,peak (KEKB) =0.025 [MW/m/cav], t =1.5 sec /cav (KEKB) @injection, Zt,peak (TESLA) > 1 [MW/m/cav],

  8. Effect of the crab cavity on beam-beam performance (Symplectic diffusion) • Optics error at the collision point determines the beam-beam performance in lepton colliders with high beam-beam parameter. • Crossing angle is a kind of optics error, z=Dx/z, (h=Dx/pz). • Symplectic diffusion is enhanced by the optics error, with the result that the luminosity degradesin lepton colliders. • Is optics error at the collision point important for hadron colliders? If important, crab cavity may improve the beam-beam performance. • Crab cavity always compensate the geometrical reduction.

  9. Vertical dispersion (KEKB) Gaussian approx. • Diffusion behavior due to dispersion in a system without synchrotron radiation. • Luminosity and beam size are degraded. PIC simulation

  10. X-y coupling (KEKB) Gaussian approx. • Diffusion due to x-y coupling. • Luminosity and beam size degradation. PIC simulation

  11. Crossing angle (KEKB) • Crossing angle is equivalent to x-z coupling. • Diffusion and luminosity degradation due to crossing angle Gaussian approx. PIC simulation

  12. Is the Symplectic diffusion important for LHC? • Not seen in the short time tracking. • How about long turn tracking? It is difficult to distinguish with diffusion due to artifact in computer. L sx The beam size with crab is larger, but is pretense, <xx>c=<xx>+z2<zz>. Note that the luminosity is higher.

  13. Effect on beam-beam performance of the crab cavity - Fluctuation in collision due to the crab cavity and cavity noise - • Noise of RF system. Deviation of RF phase, dj. • Phase error between two crab cavities.

  14. 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.

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

  16. Diffusion rate given by the simulation • sx2=sx02+Dt t: turn • D~1.4x10-3dx2 [m2] dz= 0 0.005 0.01

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

  18. 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 Coherent motion is induced by the noise.

  19. 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) *** D~dx2

  20. Diffusion rate due to offset noise. (round beam)

  21. Comparison with the simulation • DJ(a=1)=<DJ2>=1.5x10-25 m2/turn for dx=1.7 mm and t=100. • DJ(sim)=2DJJ=2 D e/b=2x3.5x10-15x5x10-10/0.5 =7x10-24 m2/turn. (missed at HHH04). • This value is somewhat larger than analytical estimation. Coherent motion and chaotic (resonance) behavior seem to make enhance the diffusion.

  22. Tolerance • For dx=1.7 mm (df=5 degree) and t=100, D~1.4x10-3dx2 [m2], wheresx2=sx02+Dt, t: turn. • Tolerance is dx=0.017 mm(s/1000), df= 0.05 degree for t=100, and dx=0.0017 mm (s/10000), 0.005 degree for t=1, if luminosity life time ~ 1 day is required. • We extrapolate the diffusion rate using dx2 scaling. Simulation for noise s/1000 requires >106 macro-particle.

  23. Luminosity degradation due to noise in KEKB-Feedback noise and beam-beam effect- • In 2005 spring operation, luminosity boosted up 1.35x1034 to 1.58x1034 cm-2s-1. • It is due to that the gain of the transverse bunch-by-bunch feedback system was optimized (weakened but kept a sufficient strength to suppress the coupled bunch instability).

  24. Specific luminosity and feedback gain (Funakoshi) 0dB -1.5dB -3dB 0dB 1.5dB 3dB 4.5dB Specific luminosity

  25. External diffusion: Vertical offset noise(simulation) • Since the beam-beam system is chaotic, such noise enhances the diffusion of the system. • Luminosity degradation for the noise without correlation between turns.

  26. Orbit offset (static) (simulation) • Static vertical offset. Tolerance is easier than the fast noise. • For slower variation than radiation damping time, emittance can be an adiabatic invariant. 1/20 compare than that for fast noise

  27. Estimation of feedback noise(Hiramatsu, K.O. & Tobiyama) • Twp-tap filter and vector composition with two position monitors • Phase space position at kicker, vector composition with two position monitor • Offset noise due to kicker error (dE) and monitor error(dP(dX1,dX2)))

  28. Kicker noise measurement (LER) • (7/14/05) Kicker output depending on feedback gain. dE=b1/2dk/E0 E0=3.5 GeV

  29. Speculated beam noise for the kicker noise

  30. Effect on the beam-beam performance of the phase jitter of cavity and crab RF’s in KEKB • Luminosity and beam size as functions of dx. • Correlation time of the jitter, 1 or 10 turns, is important for the degradation. • Since Q=200,000 and H=5120, the correlation time will be larger than 10 turns. • Tolerance is 0.05 degree.

  31. Summary • Crab cavity is expected to reduce the sympletic diffusion in KEKB. • The symplectic diffusion seems to be weak for hadron machines with low beam-beam parameter. Since there is no damping mechanism, it is difficult to conclude whether the crab cavity improve luminosity more than the geometrical effect. • 800 MHz crab cavity may be possible if geometrical loss is small. • Tolerance for collision offset noise induced by RF phase modulation is severe. • The correlation time, t=100, may be optimistic. • Luminosity degradation due to the noise (mainly due to feedback noise) has been observed in many machines, KEKB, DAFNE, HERA, RHIC.

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