Singular integral equation approach in the theory of coaxial cavity gyrotrons

In this paper, we describe a full wave analysis of the coaxial gyrotron resonator, based on the singular integral equation (SIE) approach. It incorporates several advantages compared to the surface impedance model as well as to other full wave approaches used for modelling coaxial gyrotron cavities. First, it reduces the initial multidimensional boundary value problem for Maxwell equations to seeking for a function of one variable in an interval of length less than the wavelength of the RF field. Second, it needs no simplifying assumptions. The basic SIE for the unknown function is fully identical to the initial boundary-value problem. It can be solved by direct numerical methods having rigorous mathematical grounding. The numerical solution can be obtained with any desired accuracy, which is restricted only by the accuracy of computer calculations. No Gibbs instability occurs, which usually appears in other rigorous approaches due to the truncation of Fourier or spatial harmonic series.