Theory of inductively detuned traveling wave structures

As high power rf extraction cavities, traveling wave structures (TWS) have demonstrated significant advantages due to their inherent low field gradients. For applications involving long, multi-cavity devices such as a relativistic klystrons two-beam accelerator (RK-TBA), the extraction cavities must be inductively detuned to maintain longitudinal beam stability. In this paper, the theory of inductively detuned traveling wave cavities is developed within the framework of a coupled-cavity circuit description of TWS. We determine the output cell parameters (eigenfrequency ω0 and quality factor Q) required for proper matching to avoid unwanted reflections. We then derive the power balance equation which quantifies the generation and the transmission of electromagnetic energy in each cell of the TWS. An analytic formula for predicting the power output from a TWS is obtained. Finally, using the analytic results derived we check the applicability of the computer code RKS for inductively detuned TWSs.