Nonlinear development and Fourier analysis of the whistler mode instability

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Abstract
The results of the nonlinear computer investigationof the whistler mode instability with the aid of particle-in-cell simulation methods are presented. The electron plasma considered is hot (kT‖ = 20 keV), anisothermal (T⊥/T‖ ≃ 2) and embedded in a static magnetic field such that β‖ = 0.8. A detailed Fourier analysis of the electromagnetic activity developed under the above stated conditions is carried out: the waves are shown to be electron-like and excellent agreement with the linear stability analysis for the first stages of evolution is found. The feed-back effect of the waves on the particles is shown to result in a continuous decrease of the thermal anisotropy ratio T⊥/T‖ corresponding changes in the Fourier spectra of the electromagnetic activity are observed; additional changes in the wave spectrum are introduced by the interaction between various instability modes. At the end of the run (ωpt ⋍600), the state of the system resembles a quasi-stable equilibrium, in which the electromagnetic energy achieves its maximum value: in this state, unlike the equilibrium one usually considered in the linear stability analysis, a thermally anisotropic plasma with T⊥/T‖⋍1·35 appears to be quasi-stable against the whistler mode instability. This last result is relevant for the geostationary magnetospheric conditions (in the equatorial region) where quasi-stationary states with T⊥/T‖ about 1·3 are observed.