Transverse instability in a 50 GeV/spl times/50 GeV muon collider ring

The intense bunch which is called for in the muon collider design will be subject to transverse instability. It has been suggested that tune spread due to BNS damping be used to control the instability. The transverse dynamics in a 50 GeV/spl times/50 GeV muon collider ring is examined numerically using a broad-band impedance. In addition to the BNS damping, tune spreads due to chromaticity, amplitude dependent tune shift and the beam-beam interaction are taken into account. It is shown that each of these tune spreads adequately stabilize the transverse dynamics.