The method of singular integral equations in the eigenvalue analysis of a coaxial gyrotron with a corrugated insert

A number of works dealing with analysis of a coaxial gyrotron with a corrugated insert has appeared lately. The simplified surface impedance model is used there. According to this model the field is considered homogeneous inside the slots, and eigenvalues are determined from some transcendental equations. As one goes to high frequencies with this approach, one may come to significant errors. This work deals with new approach to full wave analysis of the gyrotrons of this type. It is based on rigorous formulation of the boundary value problem for Maxwell´s equations (without any additional assumptions) taking into account all harmonics of the field. The proposed method is valid in any range of frequencies for arbitrary sizes of corrugation.