Mathematical model of a cavity gyrotron on the basis of hypersingular integral equations

Hypersingular integral equation (HSIE) for a coaxial gyrotron full wave analysis is derived in case of TM waves. Considered electrodynamic problem is a problem to find nontrivial solutions for homogenous Maxwell equations. It reduced to a problem of the first kind for a two-dimensional Helmholtz equation for electric Borgnis function in cross-section of a cavity gyrotron. Derived HSIE can be solved numerically using a method of discrete singularities and special quadrature formulas of the interpolative type.