KV-beam in a dispersive channel

The interplay between dispersion and space charge in circular accelerators or storage rings is investigated by looking for self-consistent solutions of the Vlasov-Poisson equation that generalize the KV-distribution to the case where dispersion is present. The results show a growth of the rms quantities describing the beam distribution with the momentum deviation and tune depression. The growth, however, is modest for realistic values of these parameters.