Analytic theory of a tapered gyrotron resonator

An analytic theory has been derived for determining the eigenfrequencies, RF-field distribution and Q of the TE_mpq modes of a gyrotron resonator consisting of a circular cylinder joined to a slowly tapered section. Explicit results are obtained for a linear taper. The cavity modes are found to have an RF-field distribution which is useful for prebunching the electron beam and enhancing efficiency. For high Q cavities, the cavity Q depends on axial mode number q as q^–2, which is important for mode discrimination. Proper selection of taper length is found to reduce the Q of high q modes, also aiding in mode discrimination. The present approach may be applied to other forms of weakly irregular cavities, such as cavities with nonlinear tapers.Work supported by U.S.D.O.E. Contract DE-AC02-78ET-51013Supported by U.S. Department of Energy