COMMENT ON FTI METHOD AND TRANSPORT COEFFICIENT DEFINITIONS FOR CHARGED-PARTICLE SWARMS IN GASES

The kinetic theory of charged particle swarms in gases is based upon s olution of the space and time dependent Boltzmann's equation for the p hase space distribution function f(r, c, t). Hydrodynamic transport co efficients 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 w ith the spatially independent form of the Boltzmann equation, which th ey solve iteratively as in path-integral methods, and define transport coefficients in terms of the 'starting rate distribution', rather tha n f itself. Ikuta's procedure has come to be known as the 'flight time integral' (FTI) method and the discrepancies between numerical calcul ations based upon this and the more commonly known DGE procedure have generated a deal of controversy in recent times. The purpose of this p aper is to point out that the respective definitions of the transverse diffusion coefficient D-T coincide only for light swarm particles und ergoing collisions for which the differential cross section is isotrop ic, and that the particular technique used for solving Boltzmann's equ ation, be it a path-integral or a multi-term method, has nothing to do with the numerical discrepancies which are observed when scattering i s anisotropic. In particular, it is shown that Ikuta's definition of D -T is inconsistent with even the well established result for constant collision frequency.