{"title":"Calculation of Plasma Heating by Charged Products of Thermonuclear Reactions Based on the Simplified Fokker–Planck Equation","authors":"K. V. Khishchenko, A. A. Charakhch’yan","doi":"10.1134/s0965542524700295","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A two-level time scheme for solving the simplified Fokker–Planck kinetic equation is created as applied to the transport of charged products of a thermonuclear reaction, which includes an interpolation procedure in a four-dimensional grid space. The instability of this scheme is discovered at low values of the particle velocity and a special choice of the particle deceleration rate in the ion field, which is included in the kinetic equation as a parameter. It is shown that the thermalization condition, which prohibits solving the kinetic equation for particles with an energy less than the average ion energy significantly limits the number of thermonuclear reactions in which instability can manifest itself. This scheme is tested on the problem of relaxation to a stationary state and on the problem with a given time dependence of the thermonuclear reaction rate, for which an exact solution to the kinetic equation can be found.</p>","PeriodicalId":55230,"journal":{"name":"Computational Mathematics and Mathematical Physics","volume":"39 1","pages":""},"PeriodicalIF":0.7000,"publicationDate":"2024-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Mathematics and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1134/s0965542524700295","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
A two-level time scheme for solving the simplified Fokker–Planck kinetic equation is created as applied to the transport of charged products of a thermonuclear reaction, which includes an interpolation procedure in a four-dimensional grid space. The instability of this scheme is discovered at low values of the particle velocity and a special choice of the particle deceleration rate in the ion field, which is included in the kinetic equation as a parameter. It is shown that the thermalization condition, which prohibits solving the kinetic equation for particles with an energy less than the average ion energy significantly limits the number of thermonuclear reactions in which instability can manifest itself. This scheme is tested on the problem of relaxation to a stationary state and on the problem with a given time dependence of the thermonuclear reaction rate, for which an exact solution to the kinetic equation can be found.
期刊介绍：
Computational Mathematics and Mathematical Physics is a monthly journal published in collaboration with the Russian Academy of Sciences. The journal includes reviews and original papers on computational mathematics, computational methods of mathematical physics, informatics, and other mathematical sciences. The journal welcomes reviews and original articles from all countries in the English or Russian language.
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