Prescription for a Gain-Enhanced Free Electron Laser with an Electromagnetic Pump Field

The equations of motion for a free electron laser with an electromagnetic pump field are presented. A scalar potential representing an external static axial electric field for gain enhancement has been included in the model. Equations governing gain and phase shift for each of the electromagnetic fields are given. The equation for the separatrix has been derived using the resonant particle concept and found to contain new terms. These expressions have been incorporated into a computer code which has been used to simulate several amplifier designs. The results of these designs and, in particular, the z-dependence of the accelerating voltage are discussed.