Theoretical study on the transient process in a microwave gun with a thermionic cathode

In this paper we treat the Schottky effect with a polynomial approximately, and obtain the stored energy differential equation of the transient process. On the basis of the result, the equations both the electron energy gain and the best coupling coefficient can be obtained. The rate of change of the energy spread versus time at the gun exit and the function of the building-up field during the transient process can also be given. Finally, several pictures of a transient process in the microwave gun with a thermionic cathode are also shown. The theory makes an important guide for the coupling design of a microwave gun with a thermionic cathode.