Semiclassical approach to the nonlocal kinetic model of metal vapor active media

TL;DR

This paper develops a semiclassical method based on the WKB-Maslov approach to analyze the kinetic ionization equation in dense plasma of metal vapor active media, transforming a nonlinear nonlocal problem into a linear PDE for easier analysis.

Contribution

It introduces a novel semiclassical asymptotic technique for solving nonlinear nonlocal kinetic equations in dense plasma media, enabling analytical solutions and qualitative analysis.

Findings

Derived asymptotic solutions for plasma relaxation in metal vapor media.

Transformed nonlinear kinetic equations into linear PDEs for simplified analysis.

Provided qualitative insights into plasma behavior using higher transcendental functions.

Abstract

A semiclassical approach based on the WKB-Maslov method is developed for the kinetic ionization equation in dense plasma with approximations characteristic of metal vapor active media excited by a contracted discharge. We develop the technique for constructing the leading term of the semiclassical asymptotics of the Cauchy problem solution for the kinetic equation under the supposition of weak diffusion. In terms of the approach developed, the local cubic nonlinear term in the original kinetic equation is considered in a nonlocal form. This allows one to transform the nonlinear nonlocal kinetic equation to an associated linear partial differential equation with a given accuracy of the asymptotic parameter using the dynamical system of moments of the desired solution of the equation. The Cauchy problem solution for the nonlinear nonlocal kinetic equation can be obtained from the solution of the associated linear partial differential equation and some algebraic equations for the coefficients of the linear equation. Within the developed approach, the plasma relaxation in metal vapor active media is studied with asymptotic solutions expressed in terms of higher transcendental functions. The qualitative analysis of such the solutions is given.