Decoherence of beam oscillation in a 2 TeV x 2 TeV muon-collider ring

Abstract

The decoherence behavior of betatron-oscillation motion of a beam after a transverse kick is examined by a multiparticle tracking method. When a beam is displaced transversely, it undergoes a betatron oscillation and the oscillation decays in time because of decoherence among the oscillations of different particles. The rate of decoherence depends on the spread of betatron frequencies as well as the strength of wakefields. The impedances of a broad-band resonator model and rf cavity are adopted. Operation of the ring with a slippage factor eta (1) similar or equal to -10(-6) in the 2 TeV x 2 TeV muon-collider ring may lead to beam breakup-like instability. It is explicitly shown that the decoherence due to betatron-tune spreads results in a transition from beam breakup-like instability to stable beam oscillation. Emittance growth due to a strong wakefield is also shown to be suppressed by tune spreads.