Comments on the linear theory of the gyrotron

The authors present alternative methods for the calculation of the starting current in a gyrotron, and an analysis of the excitation of parasitic modes in gyrotrons operating in a given mode. Numerical examples are presented which check the validity of some of the assumptions made, and the extension of the formalism to the investigation of the stability of an operating mode when parasitic modes can be excited (mode competition) is also discussed. Results from the problem formulation, which is based on the cold-cathode model of Borie and Jodicke (1987), are compared with both linear and fully nonlinear models. These results illustrate the importance of using a correct model for the field profile and the influence of numerical uncertainties on the results obtained using a linear theory for mode competition. It is noted that the results obtained using the nonlinear theory of mode competition are usually numerically more stable and easier to interpret