Solar Type III Bursts and the Generation of Backward Langmuir Wave

It is generally believed that the conversion of Langmuir wave (LW) to electromagnetic wave is the generating mechanism of solar type III bursts. The Langmuir wave can be easily excited by the instability of the electron-beam current, and the interaction of the forward and backward Langmuir waves is considered to be the cause for the second harmonic of a type III burst, but, so far, the dispersion equation and generating mechanism of the backward Langmuir wave have not yet been thoroughly studied. For the equation of two-stream instability with temperature included, an analytical solution is derived. It is found that the dispersion relation of the forward LW strongly depends on the beam-current speed, while that of the backward LW depends only on the thermal velocity, when the other parameters are fixed. These analytical results are partially confirmed by particle-in-cell (PIC) simulations. With the PIC simulation, the generating mechanism of the backward LW is studied, and it is revealed that the backward LW can not be excited directly by the electron-beam current, and that its energy is obtained basically from the scattering of the forward LW. However, the electron-beam current does cause a direct amplification of the second harmonic of the forward LW.