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Beam-beam R&D for eRHIC Linac-Ring Option. Yue Hao Collider-Accelerator Department Brookhaven National Laboratory Dec. 7, 2007. Outline. Main consideration in eRHIC beam-beam R&D study. Electron Disruption effect and mismatch Aperture of energy recovery path
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Beam-beam R&D for eRHIC Linac-Ring Option Yue Hao Collider-Accelerator Department Brookhaven National Laboratory Dec. 7, 2007
Outline • Main consideration in eRHIC beam-beam R&D study. • Electron Disruption effect and mismatch • Aperture of energy recovery path • Proton beam transverse instability with interaction with electron bunch. • Electron beam jitter • Countermeasure • Conclusion
Beam-Beam field For a transverse Gaussian distribution, (+/-4 sigma cut-off) Bassetti-Erskine formular For round beam case, the field have simple form Near axis, the field is linear.
Electron Disruption The nonlinear beam-beam force will cause the electron beam geometric emittance growth. The focusing force will attract the electron to center and form the effect so called ‘pinch effect’
Mismatch The mismatch due to beam-beam effect also plays a important role. It can enlarge the effective emittance in additional to the geometric emittance growth. Need 4e-7 m-rad admittance to ensure all electron from losing in design optics. Average electron beam size is 19 microns. Minimum electron beam size is 8 microns.
Vary the electron emittance, the optics (beta alpha function) at IP point before collision Compromise to get higher luminosity, smaller emittance after collision, and larger average electron beam size.
After Optimization Graph shows the case that electron waist offset is zero. Need 1.7e-7 m-rad admittance to ensure all electron from losing in design optics. And the average electron beam size at interaction region is 24 microns and minimum electron beam size is 16 microns.
Power Loss calculation With assumption beta=50m Courtesy of V. Ptitsyn
Beam-Beam effect on Proton beam • Tune shift and tune spread • Need proper working point. • (0.672, 0.678) is used in simulation. • May introduce single bunch transverse instability (Kink instability). • Beam-beam force acts as wake field. • Threshold • Possible way to suppress the emittance growth
Kink instability Use 2-Particle model to illustrate kink instability, The two particles have same synchrotron amplitude but opposite phase. Let T be the synchrotron period. p p p e p e p p p e p e e p e p p p e p e p p p After T/2, the head and tail exchange there positions p Unstable Stable p p e p e Candidacy Seminar
Threshold and modes For fixed electron intensity (1.2e11 per bunch), the threshold of proton intensity for kink instability is about 1.6e10 proton per bunch. The longitudinal snapshot shows mode 1 pattern.
Increase tune spread to suppress emittance growth With Energy spread 1e-3
Electron parameter fluctuation Assuming beam-beam force is linear, the electron beam can be considered as a thin special quadrupole which focuses in both transverse directions. The shot to shot noise of electron beam will cause proton beam size to grow exponentially. Courtesy of E.Pozdeyev
Conclusion • From the beam-beam study, the Linac-ring option of eRHIC is a promising scheme. • The aperture of electron energy recovery path required by beam-beam interaction is achievable. • The kink instability can be suppressed by proper chromaticity. • The fluctuation of Electron beam parameter must be controlled within certain level.
