Alfv en{Wave Particle Interaction in Finite-Dimensional Self-Consistent Field Model

A low{dimensional Hamiltonian model is derived for the acceleration of ions in nite amplitude Alfv en waves in a nite pressure plasma sheet. The reduced low{dimensional wave{particle Hamiltonian is useful for describing the reaction of the accelerated ions on the wave amplitudes and phases through the self{consistent elds within the envelope approximation. As an example, it is shown that for a single Alfv en wave in the central plasma sheet of the Earth's geotail, modeled by the linear pinch geometry called the Harris sheet, the time variation of the wave amplitude during the acceleration of fast protons. PACS numbers: 52.40.Db, 52.35.Mw, 96.50.Ci, 94.30.Tz, 94.20.Rr.