微波谐振腔中电子与微波作用的非稳态过程研究

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

在微波腔中微波场影响电子的运动,同时电子束作为电流源也产生辐射,影响微波场,这种相互作用包含线性和非线性过程。根据Maxwell理论,微波腔中的实际微波场可以按微波腔的模式展开,而且不同模式与电子束之间的相互作用不同。将电子束作为激励源,根据Maxwell方程和电子受到的洛伦兹力,建立不同模式在电子束作用下的激励方程和电子束电子在不同模式作用下的运动方程(即微波谐振腔中电子束与微波场相互作用的自洽方程组),并由此进一步分析一维情况下单间隙微波腔中微波建场、辐射场呈指数增长和饱和等非稳态作用过程,该过程涉及到电子束与微波作用的线性和非线性过程。

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 determined by cavity structure and electron velocity when the beam current is high enough.