Elementary Theory of Transport Phenomena in Charged-Particle System under Electric Field

Abstract

A method to evaluate the transport coefficients of charged particles under an electric field is developed. Two velocity-distribution functions ψ s ( v 0 ) and ψ c ( v ') are introduced in addition to the usual velocity-distribution function f ( v ). Here, ψ s ( v 0 )d v 0 and ψ c ( v ')d v are the probabilities of a charged particle starting a new flight with a velocity in the range v 0 , d v 0 , and making a collision at a velocity in the range v ', d v ', respectively. The velocity-dispersion functions through flight, H ( v ', v 0 ), and through scattering, S ( v ' 0 , v ') are used to determine ψ s ( v 0 ). Since H ( v ', v 0 ) includes the full information on the flight of charged particles, the transport coefficients defined in real space have to be expressed directly by ψ s ( v 0 ). The velocity-distribution function f ( v ) and the transport coefficients defined in velocity space are also expressed by ψ s ( v 0 ). This method is simple but is applicable to anisotropic systems.