Asymptotic Transition from Kinetic to Adiabatic Electrons along Magnetic Field Lines

Abstract

Plasma dynamics is known to involve several time- and space scales, a fact which renders its study particularly challenging from an analytical as well as a numerical point of view. In this work we focus on the electron dynamics, studied on the time scale of ion thermal motion, leading to a quasi-adiabatic response of the electrons in this regime. Starting from a bikinetic model with intra- and interparticle collision operators, we establish via a scaling procedure the nondimensional equations, suitable for the kinetic-to-adiabatic electron transition as the asymptotic parameter $\varepsilon \rightarrow 0$. Our studies are done in one space and one velocity dimension, modeling electron motion along (straight) magnetic field lines (no cyclotron motion or drifts). We introduce two numerical schemes for solving the electron Vlasov-BGK equation along the transition $\varepsilon\to0$ (Boltzmann relation), in a uniformly stable way with respect to $\varepsilon$. Our approach is based on micro-macro techniques, s...