Skin Effect Problem with Diffusion Boundary Conditions in Maxwell Plasma

TL;DR

This paper develops an analytical method to solve boundary problems in Maxwell plasma considering diffusion reflection, providing exact solutions for electron behavior, electric fields, and surface impedance.

Contribution

It introduces a novel eigenfunction decomposition approach to solve Vlasov-Maxwell boundary problems with diffusion boundary conditions.

Findings

Exact solutions for electron distribution and electric fields in Maxwell plasma.

Derived explicit expression for surface impedance.

Validated the eigenfunction method for boundary value problems.

Abstract

The analytical method of solving the boundary problems for a system of equations describing the behaviour of electrons and an electric field in the Maxwell plasma half-space is developed. Here the diffusion reflection of electrons from the surface as a boundary condition is supposed. The exact solution for boundary value problem of the Vlasov-Maxwell equations through the eigenfunctions of the discrete spectrum and the continuous spectrum is obtained. The method of decomposition by eigenfunctions of discrete and continuous spectrum is used. The exact expression for the surface impedance also is obtained.