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Semiclassical Approach to the Nonlocal Kinetic Model of Metal Vapor Active Media

Author

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  • Alexander V. Shapovalov

    (Department of Theoretical Physics, Tomsk State University, 1 Novosobornaya Sq., 634050 Tomsk, Russia
    International Laboratory of Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics, 40 Lenina av., 634050 Tomsk, Russia
    These authors contributed equally to this work.)

  • Anton E. Kulagin

    (Laboratory of Quantum Electronics, V.E. Zuev Institute of Atmospheric Optics, Siberian Branch of the Russian Academy of Sciences, 1 Academician Zuev Sq., 634055 Tomsk, Russia
    Division for Electronic Engineering, Tomsk Polytechnic University, 30 Lenina av., 634050 Tomsk, Russia
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Alexander V. Shapovalov & Anton E. Kulagin, 2021. "Semiclassical Approach to the Nonlocal Kinetic Model of Metal Vapor Active Media," Mathematics, MDPI, vol. 9(23), pages 1-17, November.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:23:p:2995-:d:685572
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    References listed on IDEAS

    as
    1. V. V. Belov & A. Yu. Trifonov & A. V. Shapovalov, 2002. "The trajectory-coherent approximation and the system of moments for the Hartree type equation," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 32, pages 1-46, January.
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    Cited by:

    1. Anton E. Kulagin & Alexander V. Shapovalov, 2023. "Analytical Description of the Diffusion in a Cellular Automaton with the Margolus Neighbourhood in Terms of the Two-Dimensional Markov Chain," Mathematics, MDPI, vol. 11(3), pages 1-18, January.
    2. Hari Mohan Srivastava, 2022. "Higher Transcendental Functions and Their Multi-Disciplinary Applications," Mathematics, MDPI, vol. 10(24), pages 1-3, December.
    3. Anton E. Kulagin & Alexander V. Shapovalov, 2024. "A Semiclassical Approach to the Nonlocal Nonlinear Schrödinger Equation with a Non-Hermitian Term," Mathematics, MDPI, vol. 12(4), pages 1-22, February.

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    1. Anton E. Kulagin & Alexander V. Shapovalov, 2024. "A Semiclassical Approach to the Nonlocal Nonlinear Schrödinger Equation with a Non-Hermitian Term," Mathematics, MDPI, vol. 12(4), pages 1-22, February.

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