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.
Highlights
Studies of kinetics of metal vapor active media (MVAM) are motivated by their wide application in the development of laser systems
In a number of works, active media were investigated, where neon acted as a buffer gas, and vapors of copper and its halides did as an active substance
The approach for constructing a spacetime kinetic model of active media on copper vapor was developed in [22,23,24] where the model equations were studied mainly numerically
Summary
Studies of kinetics of metal vapor active media (MVAM) are motivated by their wide application in the development of laser systems. The properties of active media that are useful for applications appear when the upper resonance energy level of metal atoms is effectively pumped In such the conditions, the degree of ionization is small, i.e., nneut (~x, t) ni (~x, t),. The active component of the resistance prevails This parameter significantly depends on time within the pump pulse period and it is a complex function of the temperature and electron concentration. The approach for constructing a spacetime kinetic model of active media on copper vapor was developed in [22,23,24] where the model equations were studied mainly numerically.
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