1. Gear Changing Issues for MEIC: Outline
Framing the problem
Hao/Litvinenko/Ptitsyn paper
Dipole modes
Quadrupole modes
Things missing…
RF knockout
Path forward

2. Framing the Problem
One solution for synchronization is different number of bunches in MEIC collider rings
Two different numbers of bunches in collider rings: N1, N2
Beam-beam collisions precess
All bunch combinations cross if N1, N2 are incommensurate
Can create linear and nonlinear instabilities
Analysis similar to coupled bunch instabilities driven by impedance
But flat frequency dependence

3. Hao/Litvinenko/Ptitsyn Paper (and others)
2014 PRST:AB paper: Hao, Litvinenko, Ptitsyn
PRST:AB 17, , 2014
Extends previous work by Hirata/Keil
Matrix approach reproduces H/K dipole mode result
Extends to quad modes, bunch gaps, luminosity evolution
Motivated by potential RHIC asymmetric operations, EIC ring-ring synchronization
Some (simple) simulation results

4. Dipole Modes
Fig 1: HLP paper, N=(3,4), Q2=0.4
Q1=0.22
Dipole mode analysis shows extended spectrum of sum/difference resonances
Effective tunes/eigenmodes
Instability occurs when eigenmodes merge
Number of eigenmodes, possibility of eigenmode mixing scales as LCM(N1,N2)
Tune space becomes densely packed with resonances for large N
Q1=0.35

5. Dipole Modes: Simulation
I wrote a simple linear beam-beam simulation to validate these results and explore some parameter space
Indeed:
I could quickly reproduce H/L/P Fig 1 results
Naïve scaling with N is bad (see next slide)
It was difficult to find ANY region of tune space that was stable for MEIC parameters
But tracking quickly becomes tedious
Instability timescale also scales as number of bunches
Noted in H/L/P paper as motivation for dipole damper
Will probably be resolved by Landau/nonlinear damping

6. Dipole Modes: Simulation Results
Raising number of bunches in linear simulation quickly produced instabilities – as low as N=(10,11)!
A verification but of course many details left out

7. Quadrupole Modes
Fig 3: HLP paper, N=(3,4), Q2=0.4
H/L/P extended to linear quadrupole mode matrix analysis
Evaluates for linear quadrupole mode instabilities
Eigenvalue analysis less clear but appears more stringent
Eigenvalues merge and separate: regions of instability
H/L/P includes supporting multi-bunch simulations
1D linear transport, full beam-beam, no dipole mode
Generally support this analysis
Q1=0.22
Fig 5: HLP paper

8. Things Missing… In principle this doesn’t look good for MEIC BUT
MEIC is strong focusing (transverse and longitudinal, e and p)
Landau damping may damp instabilities faster than even the pessimistic growth rates
Typical damping times are o(1/σQ) (chromatic dominates nonlinear)
Hadron rebunching should be performed without e- beam
Nonlinear beam-beam tune spread may help
Many dynamical effects were not included in H/L/P paper
Nonlinear beam transport
6D effects (e.g. chromatic tune spread, tune modulation)
Higher order moment instabilities
Assumed only round beams

9. RF Knockout
S. Myers, PAC’79,
Occurs if bunches precess at non-harmonic frequency of bunch spacing
Bunch trains create many precession sidebands
Observed at RHIC and ISR (!)
RHIC: equal d-Au rigidities, circumferences; unequal frev
Beam-beam effect during injection, deuterons and Au with same rigidity
Δfrf = 44 kHz, vertical separation was 10 mm (~ 10σ) in all interaction regions
Pseudo-random dipole kicks lead to emittance increase
MEIC concern: strong longitudinal focusing, synchrobetatron sidebands (see Myers ISR paper)
Fig. 3
Au beam
VERY modest beam intensities
From May 2005 RHIC dAu
Experience talk
d beam

10. Path Forward
This could be (but is unlikely to be) a show stopper for incommensurate bunch numbers in MEIC
Simple H/L/P simulations were verified
Simple simulation also showed (simple) problems for MEIC baseline parameters
Many important decoherence effects not included
These decoherence effects save other colliders from non-gear-changing coherent beam-beam instabilities
More simulations needed -- H/L/P paper: