Abstract
We have extended a solitary wave theory for high power spike pulses emitted from a FEL by including the space charge wave and treating the radiation field in two dimensions so as to allow for the waveguide. In this manner we derive the “collective variables” equations which describe the physics of the Columbia Raman FEL. The refractive index of the electron beam and the saturation intensity of the radiation field are obtained from a WKB theory. It is shown that the nonlinear behavior of the radiation field can be modeled by the Ginzburg-Landau (GL) equation using coefficients which are obtained from the collective variables analysis. The GL equation has solitary wave solutions that have a spiking character, lasting a few hundred ps. We program the GL equation to study the spike evolution from different initial conditions: an isolated spike resembles a solitary wave solution of the GL equation and is compared with experiment. We have examined how spikes grow from “noisy” initial conditions in the signal field as well as fluctuations in the beam current.
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