Quantum plasma fluid model for high-gain free-electron lasers

Starting from the eikonal approximation (geometrical optics), a set of nonlinear quantum plasma fluid equations to describe the quantum free-electron laser (FEL) is presented. Subsequently, by using these fluid equations for a relativistic electron beam, interacting with stimulated radiation and an optical wiggler field, a general dispersion relation for quantum FEL instability is derived taking into account the beam space-charge mode modulated by the ponderomotive potential well. It is shown that the saturation time for the quantum FEL instability can be estimated from the solutions of three-wave coupled equations which describe the FEL dynamics in the fluid model.