Contribution of the third order Landau mode on wave pattern of free-streaming electron

Abstract

A calculation of the contribution of the third order Landau mode to the wave pattern of the free-streaming electron was carried out at the frequencies less than the electron Langmuir frequency by means of the saddle point method. It was found that the excitation coefficient of the free-streaming electron was much larger than that of the third order Landau mode at the position of the grid for the excitation, and that the spatial damping rate of the former was larger than that of the latter. From the above results the wave pattern represent the contribution of the free-streaming electron when x/ lambda D or approximately=35).