Network-theoretical model of the gyrotron oscillator part I: Empty cavity oscillation modes

A network-theoretical model of the gyrotron has been elaborated which is both conspicious and rigorous. The problem of self-consistently representing the field in the presence of the electron beam is attacked by expansion into the empty structure oscillation modes. In this first part, a method is presented to determine the empty gyrotron cavity oscillation modes, i.e. theQ factors, resonance frequencies, and field distributions in axisymmetric, but otherwise quite general cavities. It is based on the field representation in terms of local normal waveguide modes. Matrix equations in these modes for different type of cavity sections (building blocks) are formulated. Along with the open resonator boundary conditions, these equations form a nonstandard eigenvalue problem; the eigenvalues are the complex eigenfrequencies, the eigenvectors correspond to the field distributions. By way of example, the method is applied to a simple and a complex cavity.