1. Beam-beam effects in eRHIC and MeRHIC
Y. Hao, V.N.Litvinenko, E.Pozdeyev, V.Ptitsyn

2. Beam-beam in linac-ring scheme
For the ring-ring eRHIC design option maximum achievable luminosity is limited by the beam-beam interactions. The beam-beam parameter limits are reached for both electron and proton beams.
The linac-ring scheme (main design option of eRHIC now) allows to go far beyond standard beam-beam limit for electrons: from 0.08(ring-ring) to 0.59 (linac-ring) in terms of electron beam-beam parameter.
05/29/09
EIC/ENC Workshop

3. Features of beam-beam interaction of linac-ring scheme
Compared with “standard” beam-beam interactions in collider rings, the linac-ring collision scheme brings on very specific effects:
Electron beam disruption.
Fluctuation of electron beam parameters.
Kink instability of the proton beam.
Effect of electron beam pinch on the incoherent proton beam emittance growth.
Those effect have been studied in details using a dedicated simulation code (Y.Hao)
05/29/09
EIC/ENC Workshop

4. ERL-based eRHIC Parameters: e-p mode
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
1.2
Beam current, mA
420
260
Normalized 95% emittance, p mm.mrad 6
460
570
Rms emittance, nm
3.8 4 19
16.5
b*, x/y, cm 26 25 30
beam-beam for p /disruption for e
0.015
5.9
3.9
Rms bunch length, cm 20 1
Polarization, % 70 80
Peak Luminosity, 1.e33 cm-2s-1
Aver.Luminosity, 1.e33 cm-2s-1
2.6
0.53
0.87
0.18
Luminosity integral /week, pb-1
530
105

5. MeRHIC parameters for e-p collisions
not cooled
pre-cooled
high energy cooling p e
Energy, GeV
250 4
Number of bunches
111
Bunch intensity, 1011
2.0
0.31
Bunch charge, nC 32 5
Normalized emittance, 1e-6 m, 95% for p / rms for e 15 73 6 29
1.5
7.3
rms emittance, nm
9.4
3.8
0.94
beta*, cm 50
rms bunch length, cm 20
0.2
beam-beam for p /disruption for e
1.5e-3
3.1
3.8e-3
7.7
0.015
Peak Luminosity, 1e32, cm-2s-1
0.93
2.3
9.3
05/29/09
EIC/ENC Workshop 5

6. Electron pinching beta*=0.2m, s*=0m e beta*=0.2m, s*=0.2m
From results of the IR optics
parameter study for eRHIC
Issues coming with the pinch effect:
Luminosity increase due to smaller beam size compared with the design
Increase of the proton beam-beam parameter (proton beam lifetime)
Electron beam disruption (one still needs to transport and decelerate electron beam)
05/29/09
EIC/ENC Workshop

7. Deformation of the electron distribution
Example for eRHIC
beta*=1m
The electron beam distribution is deformed by the nonlinear beam-beam force and deviates from Gaussian form: longer tails, dense core.
It enhances the effective beam-beam parameter of the proton beam further and enhances the emittance growth of the proton beam.
The distribution deformation depends on the IR optics choice and initial beam emittance.
Again, smaller beta* (larger emittance) are preferable.
beta*=0.2m
05/29/09
EIC/ENC Workshop

8. Effect of the Electron Pinch on Protons
Source
The electron beam is focused by strong beam-beam force.
Enhanced beam-beam parameter value.
Main Factors under Consideration
Working Points for protons (avoid nonlinear resonance )
Electron optics and initial emittance
Reduce synchrotron-betatron oscillation
For beta*=1m:
The maximum beam-beam parameter of protons is as large as 0.19
The average beam-beam parameter of protons is
05/29/09
EIC/ENC Workshop

9. The proton beam emittance growth for different IR optics choices in eRHIC. Smaller design beta* is preferred for the electron beam.
05/29/09
EIC/ENC Workshop

10. Electron beam disruption
From eRHIC calculations
Two effects:
Linear mismatch caused by the beam-beam interaction increases the effective emittance in the design lattice (without beam-beam). Lower b* -> less mismatch.
The geometric emittance increase due to non-linear beam-beam force.
05/29/09
EIC/ENC Workshop

11. Geometric emittance disruption in eRHIC
Design β* = 1m at IP
Initial emittance 1nm
Design β* = 0.25m at IP
Initial emittance 4nm
Geometric emittance increase is minimal at beta*=0.25m
05/29/09
EIC/ENC Workshop

12. Beamsize and Emittance evolution of electron beam in MeRHIC
(Electron beam comes from right)
Initial Emittance:
9.4 nm-rad
beta*: m
s*: m (at IP)
Luminosity:
1.2×1032 cm-2s-1 e
30% luminosity
enhancement by
the beam-beam !
Effective emittance growth during collision due to mismatch between the electron distribution and design lattice. This is main effect compared with the geometric emittance growth due to the beam-beam nonlinear field.
05/29/09
EIC/ENC Workshop

13. The choice of electron emittance and beta* in MeRHIC is made on
the basis of minimizing geometric
and effective emittance and maximizing
the luminosity.
The further reduction of the effective emittance can be done by modification of IR optics after collision point to match the beam shape into the recirculation pass optics.
The luminosity (solid lines) and final effective emittance (dot lines) are optimized at around s=0, which is IP.
18.8nm-rad m beta*
4.7nm-rad m beta*
9.4nm-rad m beta *
05/29/09
EIC/ENC Workshop 13

14. The amount of beam loss for different beam pipe apertures (MeRHIC case)
beta=5m
For both initial Beer-Can and Gaussian (4-σ cutoff) distributions
Position
Energy
Aperture
Beer-Can
Gaussian
Lowest Energy at arc
750 MeV
2.9 mm
4mm
The exit of main linac
100 MeV
7.8 mm
10mm
Entrance of Beam dump
5 MeV
(Dump All)
35 mm
53mm
05/29/09
EIC/ENC Workshop

15. MeRHIC case
Phase space of Beer-Can
Phase space of Gaussian
For Beer-Can distribution, if the optics after collision is matched to the beam emittance shape, the required aperture will be largely reduced.
05/29/09
EIC/ENC Workshop

16. Kink instability eRHIC case
Proton emittance growth caused by transverse
instability. The head of the proton bunch affects
the tail through the interactions with the electron
beam. Includes synchrotron oscillations.
Without tune spread (zero chromaticity) the
instability threshold is at 1.6e10 proton per bunch.
The tune spread stabilizes the instability.
Required chromaticity: >3 units.
Nonlinearity character of the beam-beam
interactions also helps.
05/29/09
EIC/ENC Workshop

17. Proton beam kink instability for MeRHIC case
In both cases, the beam parameters are above the threshold of kink instability for proton beam. Proper energy spread is needed to suppress the emittance growth.
Not Cooled p-beam
Chromaticity=1 is needed
Pre Cooled p-beam
Chromaticity=4 is needed
The rms energy spread is 5e-4
05/29/09
EIC/ENC Workshop 17

18. Summary
Several features of the beam-beam interactions, specific to the linac-ring collision scheme have been under consideration.
The beam-beam study are essential for the understanding achievable luminosity and for defining the magnet aperture (at lower electron energy).
Both electron beam disruption and the minimization of the proton beam-beam parameter depends strongly on the choice of the electron b*, s* and emittance. The corresponding optimization of those parameter has been done for both eRHIC and MeRHIC.
The kink instability is stabilized for the design beam intensities by the proper (and reasonable) choice of the chromaticity.
05/29/09
EIC/ENC Workshop

19. Subjects of further studies
Proton beam-beam limits in “parallel” operation mode of eRHIC:
one e-p + two p-p collisions
Proton beam lifetime: combined effect of the beam-beam and machine errors.
Electron beam transport with the combination of the beam-beam and machine errors.
Electron beam parameters fluctuations (intensity, emittance) for eRHIC and MeRHIC with realistic noise spectrum.
05/29/09
EIC/ENC Workshop