On two models for charged particle systems: the cometary flow equation and the Shockley-Read-Hall model

Abstract

In this work we are considering two models of charged particles; first model is a kinetic transport model which describes wave-particle interaction in cometary flows, and the second model describes the flow of electrons and holes through the trapped state. In Chapter 1 we are investigating the Cometary flow equation:<br />\partial_t f+v abla_x f=Q(f)=P(f)-f The particle distribution function f(t,x,v) is a nonnegative function, which depends on time, space and on velocity. We denote with Q(f) the collision operator, with a nonlinear projection operator P onto the set of distribution functions isotropic around the mean velocity u (S {d-1} is the unit sphere of R d).<br />The set of equilibrium distributions satisfying Q(f)=0 is infinite dimensional, and consists of all velocity distributions isotropic around an arbitrary mean velocity. There are infinitely many collision invariants, but out of those only three produce macroscopic conservation laws. As a consequence, we restrict our attention on the linearized version of the cometary flow equation, and for this flow equation we apply the entropy-entropy dissipation approach developed by Desvillettes and Villani.<br />In Chapter 2 we are considering a model which describes the statistics of recombination and generation of holes and electrons in semiconductors occuring through the mechanism of trapping. We prove existence of solutions, and rigorously justify the quasistationary limit for both drift diffusion and the kinetic SRH model.