Applied Mathematics and Physics
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Applied Mathematics and Physics. 2016, 4(1), 1-8
DOI: 10.12691/amp-4-1-1
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On Instability of Dynamic Equilibrium States of Vlasov-Poisson Plasma

Yuriy G. Gubarev1, 2,

1Laboratory for Fluid and Gas Vortical Motions, Lavrentyev Institute for Hydrodynamics, Novosibirsk, Russian Federation

2Department for Differential Equations, Novosibirsk State University, Novosibirsk, Russian Federation

Pub. Date: July 19, 2016

Cite this paper:
Yuriy G. Gubarev. On Instability of Dynamic Equilibrium States of Vlasov-Poisson Plasma. Applied Mathematics and Physics. 2016; 4(1):1-8. doi: 10.12691/amp-4-1-1


The problem on linear stability of one–dimensional (1D) states of dynamic equilibrium boundless electrically neutral collisionless plasma in electrostatic approximation (the Vlasov–Poisson plasma) is studied. It is proved by the direct Lyapunov method that these equilibrium states are absolutely unstable with respect to small 1D perturbations in the case when the Vlasov–Poisson plasma contains electrons with stationary distribution function, which is constant over the physical space and variable in velocities, and one variety of ions whose distribution function is constant over the phase space as a whole. In addition, sufficient conditions for linear practical instability are obtained, the a priori exponential lower estimate is constructed, and initial data for perturbations, growing in time, are described. Finally, the illustrative analytical example of considered 1D states of dynamic equilibrium and superimposed small 1D perturbations, which grow on time in accordance with the obtained estimate, is constructed.

the Vlasov-Poisson Plasma Dynamic Equilibrium States the Direct Lyapunov Method Instability

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