Collective instabilities of the 50-50 GeV muon collider

Abstract

Single bunch instabilities for the 50-50 GeV muon collider are discussed. An impedance budget for the collider is estimated. An |/spl eta/|=1/spl times/10/sup -6/ is desired to avoid excessive RF systems. Potential-well distortion can be compensated by RF cavities. Longitudinal microwave growth can be reduced by smoothing the bunch distribution before injection. Transverse microwave instability can be damped by chromaticities and octupoles. Beam breakup can be cured by BNS damping in principle, but is nontrivial in practice.