An analytical study on the diffraction quality factor of open cavities
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 (Q{sub d}) than the Ohmic quality factor (Q{sub ohm}). Early analytical studies have led to various expressions for Q{sub d} 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 Q{sub d} 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 Q{sub d} with respect to mode indices and cavity dimensions.