Modulation instability and strong Langmuir turbulence of supersonic plasma waves-computer simulations

A one-dimensional computer simulation of the free-evolving turbulence of Langmuir waves with an initial Gaussian spectral distribution and random phases of Fourier harmonics is reported. The discrete Fourier transformation was applied to the Zakharov set of equations. The resulting equations for the time evolution of up to 512 Fourier harmonics of electric field and ion density perturbations were solved by the Runge-Kutta method. The time dependence of energy density of plasmons and excited ion sound waves, as well as the spatial profiles of plasmon energy and ion density and electric field and density spectra in each time step were calculated. In all the runs performed, modulation processes were dominant. About 60 percent of plasmons become trapped in density wells while simultaneously ion sound waves were excited. Nonlinear formations such as quasi-solitons and cavitons are well seen in the plots of temporal evolution of the density and plasmon energy perturbations. (J.U.)