Application of the lie transform perturbation method to stochastic ion heating phenomena in a plasma

Abstract

In this thesis, Lie transform perturbation theory is used to examine stochastic ion heating process in a plasma. The system considered is composed of one monochromatic electrostatic wave propagating perpendicularly to a uniform magnetic field which is directed along z-direction. It is shown that, with the spatially varying wave amplitude, there exists non-stochastic acceleration mechanism which greatly enhances stochastic ion heating rate. For rational wave frequencies of the form ν =r/s, where r and s are relatively prime integers, it is shown in detail that acceleration ion dynamics arises along the separatirx skeleton in the case of s=1 (superharmonic resonance), while this process nearly vanishes when s ≥ 2 (subharmonic resonance) due to the presence of secular terms.