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

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

Hao/Litvinenko/Ptitsyn Paper (and others) 2014 PRST:AB paper: Hao, Litvinenko, Ptitsyn PRST:AB 17, 041001, 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

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

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

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

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

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

RF Knockout S. Myers, PAC’79, http://epaper.kek.jp/p79/PDF/PAC1979_3574.PDF 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

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: