Backward Langmuir Wave Analysis and Comparesion with PIC Simulation

Langmuirwaves converted into electromagnetic radiation is an important mechanism of solar type Ⅲ bursts.Langmuir waves can be easily excited by electron beam instability.Generally,the second harmonic waves are produced through coalescence of the forward and backward propagating Langmuir waves.In this paper,the equations of two stream instability are resolved with the thermal velocity,and it is found that the dispersion relation of the forward propagating Langmuir wave depends on the drift speed,and the backward propagating Langmuir wave depends on the thermal velocity.Same conclusions have been confirmed by PIC simulations.