Frequency shift of a plasma mode of arbitrary amplitude

Abstract

A computer simulation of a plasma in which an electron plasma mode was excited was performed. The asymptotic frequency of the mode was determined in correspondence with a wide range of amplitudes. Results at the larger amplitudes, where existing analytical theories are invalid, show an increasingly larger shift in the frequency of the mode, with respect to the linear frequency. At the smaller amplitudes, the simulation points are in good agreement with the analytical results reported by the same authors. To complement the latter results, the nonlinear dispersion equation was solved numerically in time. At times longer than one trapped electron period [${\text{T\hspace{0.17em}=\hspace{0.17em}2π\hspace{0.17em}(m\hspace{0.17em}/\hspace{0.17em}eAk\hspace{0.17em})}}^{\text{1\hspace{0.17em}/2}}$ , where $A$ and $k$ indicate the amplitude and the wavenumber of the mode, respectively], the frequency shift is found to oscillate as predicted by Morales and O'Neil; at shorter times, however, the existence of a new, pronounced minimum for the magnitude of the frequency shift is reported.