Computations of VSWR and mode conversion for complex gyrotron window geometries

A computational method is described for determining VSWR and mode conversion for complex gyrotron window geometries. Assuming symmetric TEOnmodes propagating in a circular cross-section guide containing the window, one can write the total solution to the wave equation as the sum of an incident wave plus a wave scattered from the dielectric window region. The equations can be reformulated in terms of the scattered wave, resulting in a Helmholtz wave equation with an inhomogeneous driving term corresponding to the polarization current of the dielectric. Solutions are obtained using a suitable modification of the wave equation solver OPNCAV; and reflection coefficients, VSWR´s and mode conversion information are then derived from an analysis of the reflected and transmitted powers. VSWR computations for typical single- and double-disk windows agree with conventional impedance calculations to within about one percent. Results for more complicated curved-boundary windows which cannot be treated by the standard methods are discussed.