{"title":"Analytic Solution of the System of Integro-Differential Equations for the Plasma Model in an External Field","authors":"S.I. Bezrodnykh, N.M. Gordeeva","doi":"10.1134/S1061920823040039","DOIUrl":null,"url":null,"abstract":"<p> We study a system of two integro-differential equations that arises as the result of linearization of Boltzmann–Maxwell’s kinetic equations, where the collision integral is chosen in the Bhatnagar–Gross–Krook approximation, and the unperturbed state of the plasma is characterized by the Fermi–Dirac distribution. The unknown functions are the linear parts of the perturbations of the distribution function of the charged particles and the electric field strength in plasma. In the paper, an analytical representation for the general solution of this system is found. When deriving this representation, some new results were applied to Fourier transforms of distributions (generalized functions). </p><p> <b> DOI</b> 10.1134/S1061920823040039 </p>","PeriodicalId":763,"journal":{"name":"Russian Journal of Mathematical Physics","volume":"30 4","pages":"443 - 452"},"PeriodicalIF":1.7000,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Russian Journal of Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1134/S1061920823040039","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
Abstract
We study a system of two integro-differential equations that arises as the result of linearization of Boltzmann–Maxwell’s kinetic equations, where the collision integral is chosen in the Bhatnagar–Gross–Krook approximation, and the unperturbed state of the plasma is characterized by the Fermi–Dirac distribution. The unknown functions are the linear parts of the perturbations of the distribution function of the charged particles and the electric field strength in plasma. In the paper, an analytical representation for the general solution of this system is found. When deriving this representation, some new results were applied to Fourier transforms of distributions (generalized functions).
摘要 我们研究了波尔兹曼-麦克斯韦动力学方程线性化后产生的两个积分微分方程系，其中碰撞积分按巴特那加-格罗斯-克罗克近似选取，等离子体的未扰动状态用费米-狄拉克分布表征。未知函数是等离子体中带电粒子分布函数和电场强度扰动的线性部分。本文找到了该系统一般解的解析表示。在推导这一表示时，一些新结果被应用于分布（广义函数）的傅立叶变换。 doi 10.1134/s1061920823040039
期刊介绍：
Russian Journal of Mathematical Physics is a peer-reviewed periodical that deals with the full range of topics subsumed by that discipline, which lies at the foundation of much of contemporary science. Thus, in addition to mathematical physics per se, the journal coverage includes, but is not limited to, functional analysis, linear and nonlinear partial differential equations, algebras, quantization, quantum field theory, modern differential and algebraic geometry and topology, representations of Lie groups, calculus of variations, asymptotic methods, random process theory, dynamical systems, and control theory.
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