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.

Field Formation in the Interaction Space of Gyrotrons

“…The careful analysis of the diffractive Q factor carried out in [18] resulted in deriving an analytical formula for Q D given by Eq. (42) there.…”

“…(42) of [18] as the ratio of the diffractive Q defined in the presence of reflections to the minimum diffractive Q given above by (10):…”

“…In this section, it is shown that the standard formula for the minimum diffractive Q widely used by many authors for evaluating the gyrotron operation gives a wrong scaling of the diffractive Q with the cavity length to the wavelength ratio: Q D ∝(L/λ) 2 . A more accurate is the scaling Q D ∝(L/λ) 3 that follows from the formulas derived in [9] and [18]. It is also shown that the analytical formulas derived in [18] for the diffractive Q, which contain four parameters, can be reduced to the formulas containing one parameter only.…”

“…A more accurate is the scaling Q D ∝(L/λ) 3 that follows from the formulas derived in [9] and [18]. It is also shown that the analytical formulas derived in [18] for the diffractive Q, which contain four parameters, can be reduced to the formulas containing one parameter only. In Sect.…”

“…In Sect. 3, we analyze the diffractive quality factor Q D in a relatively general way following the treatment done in [9], [18][19][20]. In this section, it is shown that the standard formula for the minimum diffractive Q widely used by many authors for evaluating the gyrotron operation gives a wrong scaling of the diffractive Q with the cavity length to the wavelength ratio: Q D ∝(L/λ) 2 .…”