Comment on FTI Method and Transport Coefficient Definitions for Charged Particle Swarms in Gases

Abstract

The kinetic theory of charged particle swarms in gases is based upon solution of the space and time dependent Boltzmann's equation for the phase space distribution function f(r, c, t). Hydrodynamic transport coefficients are defined in connection with a density gradient expansion (DGE) of f(r, c, t) and it is believed that these are the quantities measured in experiment. On the other hand, Ikuta and coworkers start with the spatially independent form of the Boltzmann equation, which they solve iteratively as in path-integral methods, and define transport coefficients in terms of the 'starting rate distribution', rather than f itself. Ikuta's procedure has come to be known as the 'flight time integral' (FTI) method and the discrepancies between numerical calculations based upon this and the more commonly known DGE procedure have generated a deal of controversy in recent times. The purpose of this paper is to point out that the respective definitions of the transverse diffusion coefficient DT coincide only for light swarm particles undergoing collisions for which the differential cross section is isotropic, and that the particular technique used for solving Boltzmann's equation, be it a path-integral or a multi-term method, has nothing to do with the numerical discrepancies which are observed when scattering is anisotropic. In particular, it is shown that Ikuta's definition of DT is inconsistent with even the well established result for constant collision frequency.