Nonlinear Plasma Waves

Abstract

A numerical solution of the equations for unstable electrostatic plasma waves propagating in a uniform infinite plasma with a weak beam is performed. Space dependent variables are Fourier transformed and the computations are done first with only one and then with two harmonics included. In both cases the first harmonic electric field reaches a maximum amplitude and thereafter oscillates periodically, the period being different in the two cases. Thus, the time evolution of the field depends strongly on the presence of the second harmonic. The second harmonic electric field itself has negligible amplitude compared with the fundamental but the corresponding perturbed distribution functions are comparable in the vicinity of the wave resonance. In the frame of the background plasma the frequency of the first harmonic electric field is close to the plasma frequency ωp but the nonlinearly generated second harmonic frequency is 2ωp. Because of this it is found that the wave-wave interaction terms are important and resonant processes occur. The neglect of such terms in quasilinear theory is questioned.

Raman backscattering saturation due to coupling betweenωpand 2ωpmodes in plasma

“…An early experiment provided evidence of plasma wave harmonic modes [30]. Moreover, a numerical study of nonlinear plasma waves has shown that second harmonic plasma waves strongly influence the time evolution of the fundamental through a resonant wavewave interaction [31].…”

Wave-particle interactions in electrostatic waves in an inhomogeneous medium

“…A good deal of research has been done on resonant wave-particle interactions in the case of electrostatic waves in a homogeneous plasma (Dungey 1961;Sagdeev & Galeev 1966;Klozenberg 1970;Armstrong & Montgomery 1969). The particular case of the weak-beam excitation of a narrow-band electrostatic pulse in a collision-free plasma has been studied in detail (Nunn 1970 a).…”

Observation of steepening in electron plasma waves driven by stimulated Raman backscattering

“…2 The presence of the second harmonic also strongly affects the time evolution of the fundamental in numerical investigations of a beam-plasma system. 3 Steepening may also reduce Raman backscatter (SRS), an instability that is of current interest in laser fusion 4 because it may hinder the absorption of laser energy by the plasma. An electrostatic plasma oscillation is excited in SRS by the ponderomotive force due to the beating between an incident electromagnetic wave and a light wave that is reflected in the backward direction from plasma noise.…”