Non-linear analysis of the free electron lasers utilizing a linear wiggler field

A one dimensional steady state (FEL) amplifier, utilizing a linearly polarized magnetic wiggler field, is analyzed in the linear and non-linear operating regimes. Our formulation of the FEL problem includes all the efficiency enhancements schemes, electron beam thermal effects and collective effects, i.e., space charge waves. The axial electron velocity, due to a linearly polarized wiggler field, has a spatially oscillatory component. It is shown that this axial velocity jiggle does not result in phase incoherence between the electrons and the ponderomotive wave. The axial velocity jiggle is explicitly incorporated into our analytical model. The inclusion of the electron jiggle velocity is shown to have a quantitative effect on the non-linear wave particle dynamics. The electron trapping potential associated with the ponderomotive wave is also derived. Finally, a number of numerical examples pertinent to the design of a 10 micron FEL amplifier are presented.