CONTROL OF LONGITUDINAL COLLECTIVE BEHAVIOR IN THE MUON COLLIDER RINGS

The longitudinal single bunch collective effects in a Muon Collider [1] ring are theoretically examined. The situation involves an intense bunch, a short bunch, a small momen-tum compaction, a rather large impedance compared with the stability threshold criterion, and a luminosity life time limited by muon decay to a thousand turns. Qualitative de-scriptions of stability are given and a scaling law for the in-stability threshold is derived. Numerical simulation results for the impedance-related instabilities are given for two cases of current interest- a 250 GeV 250 GeV demon-stration machine and a 2 TeV 2 TeV high energy ma-chine. The results of these simulations are in good agree-ment with the predictions of the scaling law and show that the longitudinal collective effects are controllable with