RF field profiles in weakly irregular open resonators

Open resonators are considered with longitudinal profiles described by continuous and sufficiently smooth functions in order to reduce reflections and mode conversion in the cavity. For these types of resonators, it is shown that the single mode approximation is adequate. Using a Langer transformation, the approximate solution for problems with two turning points is given in terms of a uniform expansion valid for all axial positions; for the fundamental mode, the RF field longitudinal distribution is essentially of the form exp [—w2(z)/2], where W(z) is determined by the resonator profile. A comparative study, of the resonant and selective properties, for different resonator types is made, and the influence of the cavity profile upon the electric field longitudinal distribution is analysed. As an example of practical interest, the design of a resonant cavity for a 35 GHz gyrotron operating in the TE021 mode is presented.