Study of Linear Stability for Cylindrically Symmetrical States of Dynamic Equilibrium of Two-Component Vlasov–Poisson Plasma Full article
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12th International Conference on Mathematical Modeling in Physical Sciences 28-31 Aug 2023 , Belgrade |
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| Journal |
Springer Proceedings in Mathematics and Statistics
ISSN: 2194-1009 |
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| Output data | Year: 2024, Volume: 446, Pages: 471-480 Pages count : 10 DOI: 10.1007/978-3-031-52965-8_37 | ||||
| Tags | Vlasov-Poisson plasma, cylindrically symmetrical dynamic equilibria, absolute linear instability | ||||
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Abstract:
We consider the linear stability problem for dynamic equilibria of two-component Vlasov–Poisson plasma in cylindrically symmetrical statement. The hydrodynamic substitution of independent variables is performed in order to transform the Vlasov–Poisson equations to an infinite system of gas-dynamic equations. It is important that exact stationary solutions to gas-dynamic equations are equivalent to exact stationary solutions to the Vlasov–Poisson equations. The sufficient condition of linear stability for exact stationary solutions to the Vlasov–Poisson equations is studied. Previously, this condition was not reversed either for small or, especially, for finite perturbations. To fulfill such reversion in the linear approximation, these gas-dynamic equations are linearized near their exact stationary solutions. The a priori exponential estimate from below is constructed for a subclass of small cylindrically symmetrical perturbations of exact stationary solutions to gas-dynamic equations, which grow over time and are described by the field of Lagrangian displacements. The countable set of sufficient conditions for linear practical instability is obtained. Thus, the Newcomb-Gardner-Rosenbluth sufficient condition for linear stability of exact stationary solutions to the Vlasov–Poisson equations is reversed. Moreover, a formal nature of this condition is revealed with respect to the considered small perturbations. As a result, by the direct Lyapunov method, an absolute instability for exact stationary solutions to the mathematical model of two-component Vlasov–Poisson plasma in relation to small cylindrically symmetrical perturbations is proved.
Cite:
Gubarev Y.G.
, Luo J.
Study of Linear Stability for Cylindrically Symmetrical States of Dynamic Equilibrium of Two-Component Vlasov–Poisson Plasma
Springer Proceedings in Mathematics and Statistics. 2024. V.446. P.471-480. DOI: 10.1007/978-3-031-52965-8_37 Scopus РИНЦ OpenAlex
Study of Linear Stability for Cylindrically Symmetrical States of Dynamic Equilibrium of Two-Component Vlasov–Poisson Plasma
Springer Proceedings in Mathematics and Statistics. 2024. V.446. P.471-480. DOI: 10.1007/978-3-031-52965-8_37 Scopus РИНЦ OpenAlex
Dates:
| Published online: | May 24, 2024 |
Identifiers:
| Scopus: | 2-s2.0-85195273602 |
| Elibrary: | 69070103 |
| OpenAlex: | W4398251080 |
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