NONLINEAR TRAVELLING-WAVE EQUILIBRIA FOR FREE ELECTRON LASER APPLICATIONS

The class of large-amplitude travelling wave solutions to the nonlinear Vlasov-Maxwell equations are investigated in which the wave pattern is station-ary in a frame of reference moving with the pondermotive phase velocity v = p w/(k + k0). Here, X0 = 27r/k 0 is the wavelength of the transverse helical wig-gler field, and (wk) are the frequency and wavenumber of the saturated radia-tion field which is assumed to be monochromatic and circularly polarized. The conservation of (average) density, momentum and energy are imposed as addition-al exact constraint equations that connect the final (saturated) and initial states of the combined electron beam-radiation field-wiggler field system. These constraint equations reduce the generality of the nonlinear equilibrium BGK solutions, and allow estimates to be made of the saturated field amplitude in terms of initial properties of the beam-wiggler system. As a simple example that is analytically tractable, we consider the case where the initial distrib