Second harmonic electromagnetic emission via beam-driven Langmuir waves

Abstract

The linked nonlinear processes of electrostatic Langmuir decay and electromagnetic emission at the second harmonic plasma frequency are studied for situations in which Langmuir waves are driven by an electron beam. An approximate method for studying wave decay and emission in three spatial dimensions is developed, based on the Langmuir and ion-acoustic wave dynamics in one spatial dimension. The numerical solutions of quasilinear equations to study electromagnetic emission starting from the electron dynamics are carried out. The numerical results are explored for illustrative parameters. The evolution of the transverse waves shows the combined effects of local emission and propagation away from the source. At a given location, the emission rate shows a series of peaks associated with coalescences of Langmuir waves driven by the beam and those produced by successive decays. The emission rate for a given coalescence decreases with time, following an initial increase. The effects of transverse wave propagation are illustrated by the presence of transverse waves both in regions upstream of the beam injection site due to backward propagation, and in regions downstream (e.g., where Langmuir waves are at thermal levels prior to the arrival of the beam) owing to forward propagation. Variation of the background electron to ion temperature ratio, beam injection parameters, and angular widths of the Langmuir spectra are found to affect the emission rate and the transverse wave levels. Furthermore, detailed studies show that the wave numbers of the maximum emission rates are in semiquantitative agreement with a previous theoretical prediction for simple model Langmuir spectra.