An analytical study on the diffraction quality factor of open cavities

Abstract

Open cavities are often employed as interaction structures in a new generation of coherent millimeter, sub-millimeter, and terahertz (THz) radiation sources called the gyrotron. One of the open ends of the cavity is intended for rapid extraction of the radiation generated by a powerful electron beam. Up to the sub-THz regime, the diffraction loss from this open end dominates over the Ohmic losses on the walls, which results in a much lower diffraction quality factor (Qd) than the Ohmic quality factor (Qohm). Early analytical studies have led to various expressions for Qd and shed much light on its properties. In this study, we begin with a review of these studies, and then proceed with the derivation of an analytical expression for Qd accurate to high order. Its validity is verified with numerical solutions for a step-tunable cavity commonly employed for the development of sub-THz and THz gyrotrons. On the basis of the results, a simplified equation is obtained which explicitly expresses the scaling laws of Qd with respect to mode indices and cavity dimensions.