Effects of space charge and nonlinearities on collective instabilities of a long bunch

We start with discussion of the effects of space charge and nonlinearities on the transverse microwave instability. A possibility of Landau damping with octupole correctors, using an example of the SNS ring, is explored. We also discuss the required strength of such nonlinearities for a bunched beam in the presence of the space-charge tune spread, as well as their effect on dynamic aperture and emittance dilution.