Generalized Pearson distributions for charged particles interacting with an electric and/or a magnetic field

TL;DR

This paper derives a generalized distribution function for charged particles under electric and magnetic fields using the Boltzmann and Fokker-Planck equations, linking kinetic theory with transport phenomena.

Contribution

It introduces a new class of generalized Pearson distributions for charged particles in external fields, extending previous models with detailed physical cases.

Findings

Derived the distribution function using Boltzmann and Fokker-Planck equations

Established equivalence with electron transport in phonon backgrounds

Provided physically meaningful special cases

Abstract

The linear Boltzmann equation for elastic and/or inelastic scattering is applied to derive the distribution function of a spatially homogeneous system of charged particles spreading in a host medium of two-level atoms and subjected to external electric and/or magnetic fields. We construct a Fokker-Planck approximation to the kinetic equations and derive the most general class of distributions for the given problem by discussing in detail some physically meaningful cases. The equivalence with the transport theory of electrons in a phonon background is also discussed.