Transverse stability with nonlinear space charge

Transverse stability with nonlinear space charge is studied within the context of coasting beams. For bare tune spreads originating from chromaticity or frequency slip, the space charge tune spread has a fairly small effect and the incoherent space charge force is well modeled by a transverse capacitance. For tune spreads due to octupoles or fringe fields, beams are more stable when the bare tune increases with betatron amplitude.