Calculation of beam loading using the induced-current method in passive cavities

A method for calculating the loaded Q and beam detuning of a passive (gain or idler) cavity in an electron device is presented. It is based on the determination of induced current by a technique often referred to as Ramo´s theorem. The induced current is used in conjunction with a lumped equivalent circuit representing the cavity. This leads to a solution for the self-consistent cavity fields. Although the induced-current expression is usually developed from low-frequency models, it is shown that Ramo´s theorem is valid for high-frequency, steady-state analysis when the unloaded passive cavity Q is high. The method is used to calculate the loaded Q of the passive cavity of a new type of gyro-resonant electron device, the magnicon