On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas
https://doi.org/10.26907/2541-7746.2024.1.36-51
Abstract
The one-dimensional problem of the linear stability of dynamic states of local thermodynamic equilibria with respect to small perturbations was studied for the case when the Vlasov–Poisson electron gas contains electrons with a stationary distribution function that is constant in physical space and variable in a continuum of velocities. The absolute instability of all considered one-dimensional dynamic states of any local thermodynamic equilibrium was proved using the direct Lyapunov method. The scope of applicability of the Newcomb–Gardner–Rosenbluth sufficient condition for linear stability was outlined. An a priori exponential estimation was obtained for the rise of small one-dimensional perturbations from below. Analytic counterexamples to the spectral Newсomb–Gardner theorem and the Penrose criterion were constructed. Earnshaw’s theorem was extended from classical mechanics to
statistical one.
About the Authors
Yu. G. Gubarev
Lavrentyev Institute of Hydrodynamics, Siberian Branch,
Russian Academy of Sciences
Russian Federation
Russian Federation
630090; Novosibirsk
M. S. Kotelnikova
Lavrentyev Institute of Hydrodynamics, Siberian Branch,
Russian Academy of Sciences
Russian Federation
Russian Federation
630090; Novosibirsk
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Review
For citations:
Gubarev Yu.G., Kotelnikova M.S. On the stability of a particular class of one-dimensional states of dynamic equilibrium of the Vlasov–Poisson electron gas. Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki. 2024;166(1):36-51. (In Russ.) https://doi.org/10.26907/2541-7746.2024.1.36-51
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