Landau-Ginzburg equation for the cyclotron resonance maser

A set of collective variable equations are derived that accurately describe the electron and field dynamics in a low-efficiency cyclotron resonance maser amplifier up to the saturation of the field amplitude. Using this collective variable description, it is shown that the evolution of the slowly varying electromagnetic field can be described qualitatively by a Landau-Ginzburg equation with complex coefficients. This is a model that also describes the field evolution in an atomic laser. The electromagnetic field evolution can now be described by an analytical solution far into the nonlinear regime, where numerical integration of the evolution equations was previously necessary.