RUNAWAY PARTICLES FOR A BOLTZMANN-LIKE TRANSPORT EQUATION

Abstract

In this paper we consider the linear Boltzmann equation which describes the evolution of one species of charged particles, electrons or ions, in a single component neutral gas. Collisions among charged particles are neglected and the acceleration field is dependent on time. We investigate a necessary condition on the behavior of both collision frequency and acceleration field so that the time-dependent solution relaxes towards a steady-state. Under suitable conditions on the acceleration field, an asymptotic behavior similar to a travelling wave in velocity space is pointed out. Various examples with different behaviors of the acceleration field for large times are given, in the simple context of the BGK model.