Nonlinear Plasma Waves

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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.