Analytical and semi-analytical solutions to the kinetic equation with Coulomb collision term and a monoenergetic source function

TL;DR

This paper derives comprehensive analytical and semi-analytical solutions to the kinetic equation with Coulomb collisions and a monoenergetic source, improving accuracy in plasma modeling and diagnostics.

Contribution

It presents the first complete solutions using a practical dimensionless form that accounts for particle conservation and Maxwellization, surpassing simplified models.

Findings

Solutions conserve particle number and accurately describe high energy tails.

The approach captures Maxwellization process naturally in low energy regions.

Results are applicable to nuclear processes and advanced plasma diagnostics.

Abstract

Complete and physically adequate analytical and semi-analytical solutions have been obtained using a practical dimensionless form of kinetic equation assuming azimuthal symmetry and Maxwellian distributions of target plasma species. Formerly considered simplified equations with truncated Coulomb collision term do not conserve the number of particles, are inapplicable to describe high energy distribution tails, and are also essentially unable to demonstrate the Maxwellization process naturally observed in the low energy region of correct distributions. The results may be useful in numerical modeling and in experimental data analysis, especially concerning nuclear processes and advanced localized, angle-resolved suprathermal particle diagnostics.