A SOLITARY WAVE THEORY FOR SPIKING PULSES EMITTED BY A RAMAN FREE-ELECTRON LASER

We have extended a solitary wave theory for high power spike pulses em itted from a FEL by including the space charge wave and treating the r adiation field in two dimensions so as to allow for the waveguide. In this manner we derive the ''collective variables'' equations which des cribe the physics of the Columbia Raman FEL. The refractive index of t he electron beam and the saturation intensity of the radiation field a re obtained from a WKB theory. It is shown that the nonlinear behavior of the radiation field can be modeled by the Ginzburg-Landau (GL) equ ation using coefficients which are obtained from the collective variab les analysis. The GL equation has solitary wave solutions that have a spiking character, lasting a few hundred ps. We program the GL equatio n to study the spike evolution from different initial conditions: an i solated spike resembles a solitary wave solution of the GL equation an d is compared with experiment. We have examined how spikes grow from ' 'noisy'' initial conditions in the signal field as well as fluctuation s in the beam current.