Emission of Electrostatic Whistler Waves Associated With Weak Electron-Beam Excited Langmuir Waves: The 2-D Particle-in-Cell Simulations

In this paper, we perform two-dimensional (2-D) electrostatic particle-in-cell simulations to investigate the emission of electrostatic whistler waves (EWWs) associated with the weak electron-beam excited Langmuir waves. Both the linear theory and simulations have shown that quasi-parallel Langmuir waves can be generated during the linear stage of the beam-plasma interaction process. The 2-D particle-in-cell simulations further demonstrated that when the background magnetic field is strong (Omega(e)/omega(pe) > 1, where Omega(e) and omega(pe) are electron gyrofrequency and electron plasma frequency, respectively), EWWs will be generated in weak electron-beam excited Langmuir waves during the nonlinear stage of wave growth, leading to the increment of perpendicular electric field. When the background magnetic field is weak (Omega(e)/omega(pe) < 1), EWWs cannot be generated during the nonlinear stage and the perpendicular electric field has no obvious nonlinear increment. In addition, the influences of the electron beam density and the electron beam velocity on the generation of EWWs are also analyzed in this paper. The simulation results may also account for observations in the Earth's Auroral region.