Long and short light pulses propagation in a long free electron laser: Effects and possible applications in high-field physics

We have studied propagation of Gaussian electromagnetic pulses through a long undulator free electron laser (FEL). Our analysis takes into account both the active and dispersive properties of the laser active medium. We have introduced the definitions of the FEL operating bandwidth and characteristic time. With the last definition a natural time scale has been established, and this allowed us to differentiate the input signals as long and short pulses. We have established that the results of the conventional theories, based on the model of a monochromatic wave, are applicable for pulses of finite but long duration. The propagation of pulses of finite lengths has been examined analytically in the (a) small spectral gain and (b) high spectral gain regimes. We have discovered a stabilization effect in the case (a). Namely, short pulses, which have random initial lengths at the laser entrance, will have the same duration at laser exit. On the other hand, the propagation of short pulses results in a nearly harmonic modulation of their envelopes. In the case (b) we have calculated the light phase and group velocities and ascertained that the laser active medium is like a plasma medium in the amplification regime; whereas it is simultaneously similar to plasma and resonant atom medium in the absorption regime. In the amplification regime, the pulse propagation is accompanied by a smooth increasing of its duration. On the contrary, the FEL can operate as a slight compressor or explosive stretcher in the absorption regime. Besides, the amplification and absorption regimes provide a linear chirping of light pulses and controlling the pulse peak amplitude. Thus the long FELs might be in principle employed to control the amplitude, phase, duration and profile of superintense short pulses, which damage ordinary atom media.