Hamiltonian analysis of the transition to the high-gain regime in a Compton free-electron-laser amplifier

The dynamics of a Compton free-electron-laser amplifier is described by a Hamiltonian treatment. The structure of the 2N-dimensional phase space, N being the number of electrons, and the stability of the critical points are investigated with the detuning as control parameter. It is shown that the small-gain and high-gain regimes are characterized by different phase-space topologies. In particular, the transition to the high-gain regime is described as a bifurcation in which two well-defined fixed points coalesce. To test the validity of this description, the period of the saturation oscillation of the radiation field amplitude is evaluated by means of the Lie-transform method.