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ON THE STABILITY OF STRICT EQUILIBRIUM OF PLASMA IN TWO-DIMENSIONAL MATHEMATICAL MODELS OF MAGNETIC TRAPS
- Authors: Brushlinskii K.V.1, Kriuchenkov V.V.2, Stepin E.V.1
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Affiliations:
- Keldysh Institute of Applied Mathematics
- National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
- Issue: Vol 519, No 1 (2024)
- Pages: 3-6
- Section: MATHEMATICS
- URL: https://kazanmedjournal.ru/2686-9543/article/view/647995
- DOI: https://doi.org/10.31857/S2686954324050015
- EDN: https://elibrary.ru/XFBYTG
- ID: 647995
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Abstract
The article presents an analysis of instabilities known from previous works in a two-dimensional mathematical model of plasma configuration equilibrium using the example of a toroidal magnetic trap “Galatea–Belt” straightened into a cylinder and possessing plane symmetry. It is established that the previously observed large values of the two-dimensional velocity of disturbances in the plane of the cylinder cross-section arise on the periphery of the configuration near its conventional boundary, do not grow with time, and are due to 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) disturbances grow with time in accordance with the traditional Lyapunov instability. Calculations allow us to determine the dependence of its quantitative characteristics on the problem parameters.
About the authors
K. V. Brushlinskii
Keldysh Institute of Applied Mathematics
Email: brush@keldysh.ru
Moscow, Russia
V. V. Kriuchenkov
National Research Nuclear University MEPhI (Moscow Engineering Physics Institute)
Email: kriuchenkov.viacheslav@mail.ru
Moscow, Russia
E. V. Stepin
Keldysh Institute of Applied Mathematics
Email: eugene.v.stepin@gmail.com
Moscow, Russia
References
- Шафранов В. Д. // ЖЭТФ. 1957. Т. 33. № 3. С. 710–722.
- Grad H., Rubin H. // Proc. 2nd UN Int. Conf. on the Peaceful Uses of Atomic Energy. Geneva. 1958. V. 319. P. 190–197.
- Брушлинский К. В., Стёпин Е. В. // Дифф. уравнения. 2022. Т. 58. № 8. С. 1112–1120.
- Брушлинский К. В., Крюченков В. В., Стёпин Е. В. // Труды МИАН. 2023. Т. 322, С. 58–70.
- Морозов А. И., Франк А. Г. // Физ. Плазмы. 1994. Т. 20. № 11. С. 982–989.
- Веденов А. А., Велихов Е. П., Сагдеев Р. З. // УФН. 1961. Т. 73. Вып. 4. С. 701–766.
- Кадомцев Б. Б. // Вопросы теории плазмы / ред. М. А. Леонтович. М.: 1963. Вып. 2. С. 132–176.
- Bateman G. MHD instabilities. Cambridge: MIT Press. 1978.
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