Multiple harmonics of electron waves studied using weak turbulence theory in a two-dimensional formulation

Abstract

Electrostatic waves with frequencies that are integer multiples of the electron plasma frequency have been observed since the early days of laboratory experiments on beam–plasma interactions, and also in experiments made in the space environment. These waves have also appeared in numerical experiments, and can be explained in the context of weak turbulence theory. This paper presents results obtained by numerical solution of the equations of weak turbulence theory, which show the coupled time evolution of the amplitudes of harmonic waves and of the amplitudes of Langmuir and ion acoustic waves, and the time evolution of the electron distribution function. The results are obtained considering a two-dimensional geometry, considering harmonics up to n ¼ 5, and are consistent with earlier results obtained by one-dimensional analyses.