Systematic solution of the Vlasov-Poisson equations for charged particle beams

Rapidly oscillating solutions of the Vlasov-Poisson equations are required when external forces are rapidly oscillating, as occurs in focusing systems for charged particle beams. Such systems are treated using a Hamiltonian a veraging technique carried out to third order. As a result one can deal wit h the problems of matching, stability, and transient time evolution using t he well-established techniques previously used for simpler, time-independen t systems. (C) 1999 American Institute of Physics. [S1070-664X(99)03203-6].