Investigation of unstable progress of microwave induced by electron beam in RF cavity

In RF cavity, the motion of electrons is affected by microwave. And at the same time, the electron can generate radiation and has influence on microwave in the cavity. According to Maxwell theory, the RF field in the RF cavity can be expressed by modes of the cavity, and actions are different between microwave of different modes and electron beam. In this paper, the self-consistent equations about such actions are established according to Maxwell theory and Lorentz force on electrons. Based on these equations, the single-gap RF cavity is one-dimensionally studied (including how microwave increases and saturates in the cavity), the curves of microwave field versus time are given for different beam currents. The study shows that nonlinear action is very important and microwave field is only