Nonlinear dispersion of stationary waves in collisionless plasmas

Abstract

A nonlinear dispersion of a general stationary wave in collisionless plasma is obtained in a non-differential form from a single-particle oscillation-center Hamiltonian. For electrostatic oscillations in nonmagnetized plasma, considered as a paradigmatic example, the linear dielectric function is generalized, and the trapped particle contribution to the wave frequency shift $\Delta \omega$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $\Delta \omega \sim a^{1/2}$, as usual. However, beam-like distributions of trapped electrons result in different power laws, or even a logarithmic nonlinearity, which are derived as asymptotic limits of the same dispersion relation.

References in corpus (4)

• Weakly collisional Landau damping and three-dimensional Bernstein-Greene-Kruskal modes: New results on old problems
• Positive and negative effective mass of classical particles in oscillatory and static fields
• Self-consistent Langmuir waves in resonantly driven thermal plasmas
• Dressed-particle approach in the nonrelativistic classical limit

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