Wave-particle interactions in electrostatic waves in an inhomogeneous medium

Abstract

The system studied is that of a narrow-band electrostatic wave packet in a collision-free plasma. Inhomogeneous effects are represented by a wave-number, which varies linearly with distance. The system is excited by a weak resonant beam, and, to first order in a smallness parameter associated with the weakness of the beam, the resonant-particle distribution function and charge densities are calculated. It is found that second-order resonant particles become stably trapped in the wave, and, after a few trapping periods, make a dominant contribution to the resonant particle charge density. The growth rate due to the resonant beam was found to increase linearly with trapping time, and typically a pulse which traps particles for n trapping periods exhibits a growth rate ˜ n times the linear Landau value. Furthermore, a reactive component of charge density was found that was able to cause a steady change in wave frequency and wave-number. These features of large growth rates and changing frequency should appear in parallel problems involving other wave types. An obvious application is that of VLF emissions in the whistler mode.