Beam dynamics in crab collision

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.
• E7 TeV.
• Bunch population 1.15x1011
• Bunch spacing 25 ns, wRF400.8 MHz.
• Number of bunch 2808 I 0.584 A
• L26,016m

4
Crabbing voltage

• Deflecting RF voltage, f half crossing angle
• b0.5m b 4000 m, fRF400 MHz
• V2.8 MV is required for f 0.15 mrad.
• V75 MV for 4 mrad

5
KEKB type crab cavity

• TM110 500 MHz
• TM010 324 MHz
• V1.44 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)L13 kW.GHz/cav.
• Z(w)T0.025 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_at_injection
• t Growth time (sec)
• Transverse
• Zt,peak (KEKB) 0.025 MW/m/cav,
• t 1.5 sec /cav (KEKB) _at_injection,
• Zt,peak (TESLA) gt 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, zDx/z,
  (hDx/pz).
• Symplectic diffusion is enhanced by the optics
  error, with the result that the luminosity
  degrades in 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
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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, ltxxgtcltxxgtz2ltzzgt. Note that the
luminosity is higher.
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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
• dx1.6 mm for dj5 degree (dz1 cm) and f 0.15
  mrad. Note sx17 mm.
• Correlation of the fluctuation.
• ltdx(n) dx(nm)gte-m/t, where n, m are turn.
• dz1, 0.5, 0.2, 0.1 cm at t1, 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 dxz dz induced by the
crab cavity.
16
Diffusion rate given by the simulation

• sx2sx02Dt t turn
• D1.4x10-3 dx2 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

• Dx1.7 mm and dz1 cm (dx 1.7 mm)
• Similar diffusion rate
• L
  sx

Coherent motion is induced by the noise.
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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)

Ddx2
20
Diffusion rate due to offset noise. (round beam)
21
Comparison with the simulation

• DJ(a1)ltDJ2gt1.5x10-25 m2/turn for dx1.7 mm and
  t100.
• DJ(sim)2DJJ2 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 dx1.7 mm (df5 degree) and t100,
• D1.4x10-3 dx2 m2, where sx2sx02Dt, t
  turn.
• Tolerance is dx0.017 mm(s/1000), df 0.05 degree
  for t100, and dx0.0017 mm (s/10000), 0.005
  degree for t1, if luminosity life time 1 day
  is required.
• We extrapolate the diffusion rate using dx2
  scaling. Simulation for noise s/1000 requires
  gt106 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.

dEb1/2 dk/E0 E03.5 GeV
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Speculated beam noise for the kicker noise
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Effect on the beam-beam performance of the phase
jitter of cavity and crab RFs 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 Q200,000 and H5120, 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, t100, may be optimistic.
• Luminosity degradation due to the noise (mainly
  due to feedback noise) has been observed in many
  machines, KEKB, DAFNE, HERA, RHIC.