Generation of low frequency plasma waves after the wave-breaking

Spatio-temporal evolution of a non-relativistic electrostatic waves in a cold plasma has been studied in the wave-breaking regime using a 1D particle-in-cell simulation. It is found that, the plasma gets heated after the wave-breaking, but a fraction of initial energy always remains with the remnant wave in the form of BGK mode in the warm plasma. An interesting finding of this work is that the frequency of the resultant BGK wave, is found be below electron-plasma frequency, which decreases further with increasing initial amplitude. Moreover, the acceleration mechanism after the wave-breaking is also found to be different from the previous work. In order to explain the results observed in the numerical experiments, a simplified theoretical model is constructed, which exhibits a good agreement with the simulation. These investigations may have relevance for wake-field acceleration experiments.