Effect of a weak longitudinal electric field on whistler waves

Abstract

The effect of a longitudinal electric field on whistler waves is studied based on kinetic theory. A local Maxwellian distribution is taken as stationary distribution function of electrons which departs from thermodynamic equilibrium due to the applied electric field. The dielectric tensor is derived by integrating along orbit of the particle in the unperturbed field. Dispersion relation and growth rate are analysed from Hermitian and anti-Hermitian parts of this tensor respectively. It is found that the waves are growing when the angle between the wave vector and the electric field is in range of Θ < 2Θc, otherwise the whistler waves are damping. The growth rate increases with wave frequency and decreases with the angle between the wave vector and the applied field. In the case of ωe ≫ Ω the maximum of growth rate, which is at θ=0, is proportional to the plasma density and anti-proportional to the magnetic field. Some computed results for parameters at top of theF layer are given.