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arXiv · 1105.0196

Nonlinear dispersion of stationary waves in collisionless plasmas

I. Y. Dodin·N. J. Fisch
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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 $Δω$ is found analytically as a function of the wave amplitude $a$. Smooth distributions yield $Δω\sim a^{1/2}$, 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.

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I. Y. Dodin, N. J. Fisch. 2011-05-01. Nonlinear dispersion of stationary waves in collisionless plasmas. https://doi.org/10.1103/physrevlett.107.035005

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