Self-consistent beam distributions with space charge and dispersion in a circular ring lattice

The interplay between dispersion and space charge in circular accelerators or storage rings is investigated by looking for self-consistent, stationary solutions of the Vlasov-Poisson equation in the form of generalized Kapchinsky-Vladimirsky (KV) distributions. The smooth approximation is assumed. The results show a growth of the rms quantities describing the beam distribution with the longitudinal momentum spread, and the tune depression. This growth, however, is modest for realistic values of these parameters in strong focusing systems.