Formation of quasi-power law weak Langmuir turbulence spectrum by harmonic generation

Langmuir wave turbulence generated by a beamplasma interaction has been studied since the early days of plasma physics research. Despite a long history of investigation on this subject, among the outstanding issues is the generation of harmonic Langmuir waves observed in both laboratory and computer-simulated experiments. However, the phenomenon has not been adequately explained in terms of theory, nor has it been fully characterized by means of numerical simulations. In this paper, a theory of harmonic Langmuir wave generation is put forth and tested against the Vlasov simulation results. It is found that the harmonic Langmuir mode spectra exhibit quasi power-law feature implying a multi-scale structure in both frequency and wave number space spanning several orders of magnitude.