Green's Function Simulation of Space–Charge Effects in Electron Beams

In this paper, a new numerical model for space-charge forces in electron beams based on a Green's function approach is described. In this model, the beam is simulated by a series of rings with nonzero thickness and length. The space-charge force on a ring is found by summing over all the interactions with all the other rings, where each interaction force is integrated over the entire volume of each source rings. With proper beam initialization of the simulation parameters, the rings can perfectly form the electron beam, leading to a very smooth and accurate calculation of the space-charge fields. The space-charge fields calculated this way can be more accurate than those found with particle-in-cell (PIC) calculations. The fields can also be distributed onto a mesh, as in a PIC calculation, leading to equivalent accuracy with greatly reduced simulation times. The accuracy of this type of model is demonstrated by comparing the harmonic-current evolution from an RF gap for a transversely cold confined beam to analytic theory and we show its utility with a large-signal annular beam klystron simulation using this technique