K. V. Brushlinskii, V. V. Kriuchenkov, E. V. Stepin
{"title":"On the Stability of Strict Equilibrium of Plasma in Two-Dimensional Mathematical Models of Magnetic Traps","authors":"K. V. Brushlinskii, V. V. Kriuchenkov, E. V. Stepin","doi":"10.1134/S1064562424601653","DOIUrl":null,"url":null,"abstract":"<p>Known from previous works, instabilities in a two-dimensional mathematical model of plasma configuration equilibrium are analyzed using a Galatea-belt toroidal magnetic trap straightened into a cylinder and possessing plane symmetry. It is established that the previously observed large values of the two-dimensional perturbation velocity in the plane of the cylinder cross section arise at the periphery of the configuration near its conventional boundary. They do not grow with time and are caused by arbitrarily small values of density, which is not determined by the idealized model of strict equilibrium. By varying the density, it is possible to influence stability. Three-dimensional (corrugated along the axis of the cylinder) perturbations grow with time in accordance with traditional Lyapunov instability. The dependence of its quantitative characteristics on problem parameters is determined in calculations.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"408 - 411"},"PeriodicalIF":0.5000,"publicationDate":"2025-01-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424601653","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On the Stability of Strict Equilibrium of Plasma in Two-Dimensional Mathematical Models of Magnetic Traps
Known from previous works, instabilities in a two-dimensional mathematical model of plasma configuration equilibrium are analyzed using a Galatea-belt toroidal magnetic trap straightened into a cylinder and possessing plane symmetry. It is established that the previously observed large values of the two-dimensional perturbation velocity in the plane of the cylinder cross section arise at the periphery of the configuration near its conventional boundary. They do not grow with time and are caused by arbitrarily small values of density, which is not determined by the idealized model of strict equilibrium. By varying the density, it is possible to influence stability. Three-dimensional (corrugated along the axis of the cylinder) perturbations grow with time in accordance with traditional Lyapunov instability. The dependence of its quantitative characteristics on problem parameters is determined in calculations.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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