An equivalent network analysis of waveguide broad-wall coupled RF gun structures

An equivalent network for a waveguide broad-wall coupled 1 (1/2)-cell RF gun cavity is derived and solved using a combination of different techniques. The 1 (1/2)-cell cavity consists of two cylindrical cells coupled via an iris with an exit hole in the second cell. Using the small aperture approximation, the coupling between the rectangular waveguide and the two cylindrical cells (without the iris, the exit hole, and ohmic losses) is rigorously represented by an equivalent network. The circuit elements of this network (as a function of geometry and frequency) are found from first principles. The iris, the exit hole, and ohmic losses are then modeled as reactive and resistive elements, respectively; their values are extracted using a numerical field solver. The frequency domain behaviour of the whole waveguide broad-wall coupled cavity system is completely characterized by this model. The resultant equivalent network is well approximated by two driven coupled oscillators. From this model, we show that the desired pi-mode can be selectively excited by properly tuning the gun. Predictions based on this theory agree well with experimental results.