The linear and self-consistent nonlinear theory of the electron cyclotron maser instability

The discussion covers the linear and nonlinear theory of the electron cyclotron maser (ECM) instability. A time-dependent frequency shift and a time-dependent field amplitude are included in the analysis, which is self-consistent with particle and wave dynamics treated as a unit. The linear dispersion relation, equations for the nonlinear growth rate and frequency shift of the excited wave, and the two nonlinear saturation processes of the ECM instability are discussed. Validity of the approximations and numerical results for a broad range of beam parameters are discussed. Recovery of the linear dispersion relation from the nonlinear formalism is discussed in an appendix. The ECM instability may be an efficient mechanism for generation of high-power radiation at mm and sub-mm wavelengths. Saturation efficients at the fundamental waveguide mode and cyclotron mode are obtained.