AC-Space-Charge Effects on Gap Coupling Coefficient of a Klystron Cavity

A novel model was developed to evaluate gap coupling coefficient considering ac-space-charge effects due to the bunching in the interaction gap. The formulation was derived based on Webster´s debunching theory and the electron-stream oscillation equation with arbitrary gap field distribution on the gridless gap. The coupling coefficient with ac-space-charge effects was investigated through both analysis and particle-in-cell simulation. The calculation results are in reasonable agreement with the simulation results. With the ac-space-charge effects, the coupling coefficient is lower than that calculated by ballistic theory. It is found that the plasma gap transit angle is a key factor in the effects of ac space charge on the coupling coefficient. Large beam current or gap length and, hence, mean large plasma transit angle indicate strong ac-space-charge effects on the coupling coefficient.