Boltzmann Equation Theory of Charged Particle Transport in Neutral Gases: Perturbation Treatment

Abstract

This paper examines the formal structure of the Boltzmann equation (BE) theory of charged particle transport in neutral gases. The initial value problem of the BE is studied by using perturbation theory generalised to non-Hermitian operators. The method developed by Résibois was generalised in order to be applied for the derivation of the transport coecients of swarms of charged particles in gases. We reveal which intrinsic properties of the operators occurring in the kinetic equation are sucient for the generalised diffusion equation (GDE) and the density gradient expansion to be valid. Explicit expressions for transport coecients from the (asymmetric) eigenvalue problem are also deduced. We demonstrate the equivalence between these microscopic expressions and the hierarchy of kinetic equations. The establishment of the hydrodynamic regime is further analysed by using the time-dependent perturbation theory. We prove that for times t ? &tgr;₀ (&tgr;₀ is the relaxation time), the one-particle distribution function of swarm particles can be transformed into hydrodynamic form. Introducing time-dependent transport coecients ? _*^(p) (^?q,t), which can be related to various Fourier components of the initial distribution function, we also show that for the long-time limit all ? _*(^p) (^?q,t) become time and ^?q independent in the same characteristic time and achieve their hydrodynamic values.