A nonlinear free-electron laser model of whistler-mode chorus amplification in the magnetosphere

We extend the free-electron laser (FEL) model of whistler chorus amplification in the magnetosphere to the nonlinear regime. Under typical conditions the model predicts a seed wave will initially grow exponentially, in agreement with the linear model. However, whereas the linear model predicts exponential growth for all times, the nonlinear model predicts mode saturation followed by quasiperiodic amplitude pulses. It has been shown that a nonlinear free-electron laser (NLFEL) can be modeled by the Ginzburg-Landau equation (GLE) whose coefficients can be derived via a WKB approximation of the NLFEL equations. We explore the consequences of the GLE for whistler-mode chorus, including the potential formation of solitary wave solutions, which are known solutions of the GLE (these solutions are not solitons because the GLE fails the Painleve test). In the spatially homogeneous limit, the GLE reduces to the Stuart-Landau equation (SLE). We find that the SLE reproduces the exponential growth phase and the saturation amplitude predicted by the NLFEL equations, furthering the connection between the NLFEL equations and the GLE. We will compare analytical and numerical solutions with in situ satellite observations.