The calculation model of space-charge field based on the Galerkin series

Abstract

In this paper, we present a model of calculating the electron beam space-charge field using the partial Galerkin moments method. The space-charge field can be expanded as a series of different modes and thus using the Galerkin series. So, the space-charge field can be obtained finally through the solving the Galerkin coefficient equations set. A 2.5-dimensinal computer program of the beam-wave interaction in a klystron is compiled based on this model. Using the results from the program, the characteristic of the beam space-charge field is analyzed and the effects of the parameter in the simulation on the calculation result of the space-charge field are studied. This model uses the particle in cell method and it can be used in the 2- or 3-dimensional calculation model of the beam-wave interaction in a klystron.