Harmonic Langmuir Wave Turbulence Generated by Beam-Plasma Instability: Theory and Simulation

The beam-plasma interaction is one of the most fundamental and important problems in plasma physics for both scientific and commercial applications. The weak beam-plasma (or bump-on-tail) instability and the ensuing generation of Langmuir turbulence is fundamental to many radio emission phenomena in interplanetary space, including solar and interplanetary type II and III bursts as well as radiation from the Earth's foreshock. It has also played a crucial role as a testbed for various nonlinear plasma theories, including quasilinear, weak, and strong turbulence theories. In particular, Langmuir wave turbulence generated by a beam-plasma interaction has been studied since the early days of plasma physics research. Mechanisms which lead to the quasi power-law spectrum for Langmuir waves have been sought. Meanwhile, 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 harmonic Langmuir mode spectra can indeed exhibit quasi power-law feature, implying multi-scale structure in both frequency and wave number space spanning several orders of magnitude. This indicates that the harmonic excitation process may be intimately related to the generation of high-frequency turbulence in plasmas.