1. Beam-beam R&D for eRHIC Linac-Ring Option
Yue Hao
Collider-Accelerator Department
Brookhaven National Laboratory
Dec. 7, 2007

2. 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

3. eRHIC parameter High energy setup Low energy setup p e Energy (GeV)
250 10 50 3
Number of bunches
166
Bunch spacing (ns) 71
Bunch intensity (1011)
2.0
1.2
Beam current (mA)
420
260
95% normalized emittance
(π·mm·mrad) 6
115
RMS emittance (nm)
3.8
1.0 19
3.3
β*(cm), x/y 26
100
150
Beam-beam parameters, x/y
0.015
2.3
RMS bunch length (cm) 20 1
Polarization(%) 70 80
Peak Luminosity (1.e33 cm-2s-1)
2.6
0.53

4. 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.

5. 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’

6. 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.

7. 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.

8. 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.

9. Power Loss calculation
With assumption beta=50m
Courtesy of V. Ptitsyn

10. The revised parameter table
High energy setup
Low energy setup p e
Energy (GeV)
250 10 50 3
Number of bunches
166
Bunch spacing (ns) 71
Bunch intensity (1011)
2.0
1.2
Beam current (mA)
420
260
95% normalized emittance
(π·mm·mrad) 6
460
565
RMS emittance (nm)
3.8 4 19
16.5
β*(cm), x/y 26 25 30
Beam-beam parameters, x/y
0.015
0.58
0.47
RMS bunch length (cm) 20 1
Polarization(%) 70 80
Peak Luminosity (1.e33 cm-2s-1)
2.6
0.53

11. 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

12. After T/2, the head and tail exchange there positions
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 e p 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 e p p e
3/6/2007
Candidacy Seminar

13. Proton emittance growth due to kink instability

14. 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.

15. Increase tune spread to suppress emittance growth
With Energy spread 1e-3

16. 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

17. 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.

20. Histogram of electron beam after beam-beam interaction

21. Optimum Waist Position.