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Beam-beam effect with an external noise in LHC

Beam-beam effect with an external noise in LHC. K. Ohmi (KEK) LHC LUMI 2006 Oct. 16-20, 2006, Valencia Thanks to W. Hofle and F. Zimmermann. Introduction. Nonlinear system with noise Beam-beam, beam-electron cloud interactions

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Beam-beam effect with an external noise in LHC

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  1. Beam-beam effect with an external noise in LHC K. Ohmi (KEK) LHC LUMI 2006 Oct. 16-20, 2006, Valencia Thanks to W. Hofle and F. Zimmermann

  2. Introduction • Nonlinear system with noise • Beam-beam, beam-electron cloud interactions • Weak-strong and strong-strong effects (single particle issue and coherent motion) • Analyze the effects using a weak-strong and strong-strong simulations. • High statistics simulation to be sensitive for the emittance growth with the rate, De/e~1x10-9 (1day decay rate). • Crab cavity noise, RF cavity noise • Bunch by bunch feedback system

  3. Two types of noise have been studied • Orbit fluctuation at collision point • Orbit diffusion and damping d: random, but unique for every particles.

  4. 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.

  5. Bunch by bunch feedback system of LHC (W. Hofle) • 14 bit resolution, 214=16384. • Covered area is Dx=+-2 mm at b=100-150 m, resolution is dxmon=0.001s. • Effect of kick error is the same contribution, if an oscillation with Dx is damped by the damping rate of G with 14 bit system. • G: damping rate of the feedback system (feedback gain). • Beam fluctuation without beam-beam

  6. Weak-strong effectDiffusion rate due to offset noise (T. Sen et al., PRL77, 1051 (1996), M.P.Zorzano et al., EPAC2000)

  7. Strong-strong effect Y.I. Alexahin, NIM391, 73 (1996) • Kick  Oscillation (s and p modes)  Decoherence  Emittance growth • dx: Kick error of the feedback system, ~G times monitor read error.

  8. Simulation for the first type of noise • Orbit fluctuation at collision point • Use both of the weak-strong and strong-strong simulation. • My previous simulation was wrong. There was a mistake for the noise implementation.

  9. Weak-strong simulation • This simulation is available for studying only the weak-strong effect. • The correlation time of the noise (tcor) is 1 turn.

  10. Emittance growth rate and luminosity decrement in the weak-strong simulation • The correlation time of the noise (tcor) is 1 turn. • Hour-1=2.5x10-8 turn-1. Day-1=1x10-9 turn-1. • Tolerance is dx/sx=0.2% for one day decrement.

  11. Strong-strong simulation, tcor= 1 turn • Dipole amplitude • Emittance growth • Luminosity decrement

  12. Strong-strong simulation, tcor= 100 turn • Dipole amplitude • Emittance growth • Luminosity decrement

  13. Emittance growth and luminosity decrement in the strong-strong simulation • The tolerance is more severe than that given by the weak-strong simulation. • The tolerance is slight less than 0.1% for tcor=1, but is 1% for tcor=100. • Build-up of the dipole oscillation is seen. • Bunch by bunch feedback may help the build-up of the dipole motion, therefore tolerance may be expected to be similar as that of weak-strong simulation.

  14. Comparison with the simulation • DJ(a=1)=<DJ2>=2.3x10-27 m2/turn for dx=0.2 mm (0.012s) and t=100. De/e=4.5x10-9 (Tanaji’s formula). • The simulation gives De/e=2x10-9 at the same condition, dx=0.2 mm (0.012s) and t=100. • The agreement is good.

  15. I have to apologize my mistake • Tolerance for Crab cavity noise is 10 times larger (easier). • Tolerance is now dx=0.2 mm(0.012s), df= 0.5 degree for t=100, and dx=0.02 mm (0.0012s), 0.05 degree for t=1, if luminosity life time ~ 1 day is required.

  16. 2nd type of noise • Orbit diffusion and damping • If the beam-beam effect is week,

  17. Residual dipole amplitude and emittance growth • dx=0.012 sx.

  18. dx=0.006 sx.

  19. dx=0.003 sx.

  20. dx=0.0012 sx.

  21. Residual dipole moment • <x2>~dx2/2G • Beam-beam interaction little affects the residual dipole motion.

  22. Emittance growth rate and luminosity decrement in the strong-strong simulation • For G=0.1 and dxmon=0.1%s, dxkick=0.0002s, the luminosity life time is 1day.

  23. Comparison with analytic theory • Agreement with the formula (Y. Alexahin) is very good. • Note: the decrement, 1e-9, is hard for simulation, because of the statistics.

  24. Summary • Tolerance of crab cavity phase is dx=0.2 mm (0.012s) for tcor=100 turn, and dx=0.02 mm (0.0012s) for tcor=1 turn. • The effects of feedback noise is sensitive, but the resolution with14 bit system is sufficient. • Theory and simulation had good agreement.

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