Weak Langmuir Turbulence

Abstract

Langmuir wave turbulence generated by a beam-plasma interaction has been studied since the early days of plasma physics research. In particular, mechanisms which lead to the quasi power-law spectrum for Langmuir waves and the superthermal electron tail population have been sought. Meanwhile, the generation of harmonic Langmuir waves has been known for some time, 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 can indeed exhibit quasi power-law feature, implying a multi-scale structure in both frequency and wave number space spanning several orders of magnitude. Moreover, the new hyper-diffusion process is shown to be responsible for the generation of superthermal electron population. These findings indicate that the harmonic excitation process and nonlinear hyper-diffusion may be important in understanding the high-frequency turbulent processes in plasmas.