Transverse beam instability in a 50 GeV×50 GeV muon-collider ring

The transverse beam instability due to a broad-band impedance in a 50 GeV×50 GeV muon-collider ring is numerically investigated. It is shown that the transverse beam size is increased by a factor of five when the impedance, Z||/n, is 1.7 Ω. The transverse instability is shown to be cured by introducing tune spreads, such as BNS damping, chromaticity, amplitude-dependent tune shift, and beam–beam interaction. It is shown that any one of these tune spreads limits the growth of the beam size to less than 20%.