A UNIFIED ANALYSIS OF SPONTANEOUS AND SUPERRADIANT EMISSIONS IN FREE-ELECTRON LASERS

A generalized formulation of spontaneous emission and super-radiance e ffects in a free-electron laser is presented. We consider a stream of electrons of arbitrary temporal duration propagating through the undul ator. The sum of the undulator synchrotron radiation emitted by indivi dual wiggling electrons entering the wiggler at random, results in shu t-noise in the radiation field. Using the waveguide excitation equatio ns formulated in the frequency domain, an analytical expression for th e power spectral density of the electromagnetic radiation is derived. It is shown that for a finite pulse electron beam current, the spectru m of the excited radiation is composed of two terms which are the spon taneous and super-radiant emissions. For an infinitely long e-beam pul se (continuous beam), the shot-noise produces only incoherent spontane ous emission. The power of this radiation is proportional to the DC cu rrent I-o of the electron beam. For shorter e-beam pulses, a partially coherent super-radiant emission is also produced with an average powe r which is proportional to I-o(2). The coherence of this super-radiant emission is enhanced as the pulse duration is reduced. A single formu lation describes the coherent features of the super-radiance and the s tatistical features of the spontaneous emission.