Impedance definition and calculation for various traveling-wave gyrotron circuits and modes

A Pierce-type approach to the analysis of a traveling-wave gyrotron is discussed which utilizes an impedance formulation much like that used for O-type traveling-wave tubes. The theory is based on a determinental equation that is determined from a relativistic, cyclotron-rotating electronic equation and a waveguide circuit equation. Expressions for the interaction impedance is presented, an averaging procedure is described, and the small signal gain is calculated for the configuration of the NRL and Varian traveling-wave gyrotrons. These theoretical curves are compared with the experimental data and the theoretical results of others.