Kinetic equation for nonlinear wave-particle interaction: solution properties and asymptotic dynamics

We consider a kinetic equation describing evolution of the particle distribution function in a system with nonlinear wave-particle interactions (trappings into resonance and nonlinear scatterings). We study properties of its solutions and show that the only stationary solution is a constant, and tha...

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Bibliographic Details
Main Authors: A.V. Artemyev, Anatoly Neishtadt, Alexei Vasiliev
Format: Article
Language:English
Subjects:
Distribution function
Kinetic equation
Mathematical Sciences not elsewhere classified
Other mathematical sciences not elsewhere classified
Resonances
Wave-particle nonlinear interaction
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Summary:We consider a kinetic equation describing evolution of the particle distribution function in a system with nonlinear wave-particle interactions (trappings into resonance and nonlinear scatterings). We study properties of its solutions and show that the only stationary solution is a constant, and that all solutions with smooth initial conditions tend to a constant as time grows. The resulting flattening of the distribution function in the domain of nonlinear interactions is similar to one described by the quasi-linear plasma theory, but the distribution evolves much faster. The results are confirmed numerically for a model problem.