Emittance Growth of Beams Close to the Space Charge Limit

In linear devices the effective phase space volume occupied by a beam can grow rapidly if the beam intensity is sufficiently close to the space charge limit and if a source of instability is available, like a periodic variation of the focusing force and/or considerable anisotropy between different phase planes. Results from analytic work and computer simulation are compared and shown to support each other. Regimes are defined in terms of tunes and tune depressions, where no emittance growth should occur; special emphasis is given to the coupling instability in case of considerably different energy content in two phase planes. The amount of transfer is found to depend critically on the strength of tune depression. The nonlinearity required for coupling is shown to arise from instability, which grows out of arbitrarily small initial fluctuations.