Multi-dimensional Vlasov simulations on trapping-induced sidebands of Langmuir waves

Abstract

The temporal evolution of Langmuir waves is presented with two-dimensional electrostatic Vlasov simulations. In a muti-wavelength system, trapped electrons can generate sidebands including longitudinal, transverse, and oblique sidebands. We demonstrated that oblique sidebands are important decay channels of Langmuir waves, and the growth rate of oblique sidebands is smaller than that of longitudinal sidebands but higher than that of transverse sidebands. When the amplitudes of sidebands are comparable with that of a Langmuir wave, vortex merging occurs following the broadening of longitudinal and transverse wavenumbers, and finally the system is developed into a turbulent state. In addition, the growth of sidebands can be depicted by the nonlinear Schrödinger model [Dewar–Rose–Yin (DRY) model] with non-Maxwellian Landau damping. The theoretical results show the significance of nonlinear frequency shift in the evolution of Langmuir waves. The growth rates of sidebands in the DRY model are in qualitative agreement with Vlasov simulations.