Numerical simulation of the weak turbulence excited by a beam of electrons in the interplanetary plasma

The electron distribution functions measured at 1 AU in an electron stream passing the ISEE-3 spacecraft (Lin et al., 1981) are used as input data to a programme which simulates in a one-dimensional model the interaction between fast electrons and plasma waves (quasi-linear relaxation) together with the plasma wave scattering off the background ions. While the computed spectral energy density of the plasma waves excited in resonance with the streaming of electrons is below Zakharov's threshold of strong turbulence, it is sufficiently high to undergo a fast induced scattering off the background ions. The resulting spectrum is concentrated around the wave vector k = 0. Some simple analytic considerations show that this stage leads necessarily to the crossing of Zakharov's threshold and therefore this indirect excitation of strong turbulence seems to play an essential role in understanding the Langmuir turbulence generated by the motion of fast electron beams in the interplanetary plasma.