High gain free electron laser amplifiers starting from coherent and incoherent spontaneous emission

Self-amplification of coherent spontaneous emission and shot noise in high gain single pass free electron lasers is investigated using a multifrequency model. This approach includes intrinsically the coherent spontaneous emission generated by the components of the Fourier transform of electron current that are close to the resonant frequency. The shot noise is modeled by adding random fluctuations to the initial electron phases. The complete model of equations is derived and analytical and numerical results are presented. The main features of the emitted radiation starting from coherent spontaneous emission and shot noise are discussed.