THEORY AND SIMULATION OF CUSPTRON MICROWAVE OSCILLATORS.

A nonlinear theory for describing the temporal evolution of the electron cyclotron maser instability excited by a concentric E-layer in a slotted cylindrical waveguide has been formulated. The purpose is to study the nonlinear wave dynamics, which enables the operating characteristics of the device to be optimized. The nonlinear evolution is studied by averaging the orbit equations of a single electron over the fast time scale and then using a systematic procedure to perform the average over the initial random phases of electrons on the orbit equations. A set of coupled equations for averaged phase function and beam energy is obtained that define the collective response of electrons to the wave fields. The energy conservation equation is then used to determine the response of the wave fields to the induced current associated with the electron bunching. This self-consistent approach leads to a single nonlinear differential integral equation for the wave amplitude. The approach reduces considerably the numerical effort needed through particle simulation approach. A particle simulation code is also developed and used to assess the accuracy of the results obtained by the phase average approach.