Stabilization of plane polarized Alfven waves by anomalous Doppler resonance

Abstract

This work presents non-linear decay of plane polarized Alfven wave via anomalous Doppler resonance with an electron beam in a magnetized plasma. First order perturbation theory has been employed to derive the expressions for dispersion relation of Alfven waves and their growth rate. Numerical calculations have also been carried out for growth rate and unstable mode frequencies for typical plasma parameters. There exists two modes of wave propagation, one having frequency < ωci corresponds to Alfven wave, and the other has frequency approaching ωce which corresponds to electron cyclotron wave. The waves interact with the electron beam via normal and anomalous Doppler resonance. The normal resonance interaction increases the frequency of plane polarized Alfven wave but shows no growth or decay in amplitude. However, in anomalous resonance interaction the frequency remains unchanged and the wave stabilizes. The variation of frequency and growth rate with magnetic field and number density of plasma electrons is also discussed in the present paper. The phase velocity and the unstable frequency of the wave decrease with an increase in the number density of plasma electrons. The results of our work are applied to explain some of the experimental observations.