THEORY AND SIMULATION OF TRANSVERSE SUPERMODE EVOLUTION IN A FREE-ELECTRON LASER-OSCILLATOR

We derive the conditions for establishment of a transverse supermode i n a free-electron laser (FEL) oscillator, and demonstrate the evolutio n of a supermode by means of a three-dimensional nonlinear code. Both the analytical formulation and the numerical code are based on coupled -mode theory. The oscillator supermode is a combination of transverse modes that keeps its field profile at any point along the oscillator i ntact after each round trip, and therefore it is the steady-state resu lt of the oscillation buildup process. In the FEL, as in any laser, th e oscillator supermode is identical with the amplifier supermode only if the feedback process is entirely nondispersive. If this is not the case, the steady-state supermode field profile varies alone the oscill ator axis. The simulations demonstrate that the transverse supermode e volution process is primarily a linear regime process and can be proce eded or even completed before saturation.