Quantum wave kinetics of high-gain free-electron lasers

A wave kinetic equation equivalent to the Schrodinger-like equation for the electrons is derived from relativistic theory in the eikonal approximation. This equation is used to study the interaction of the relativistic electron beam in a wiggler field in the quantum regime, i.e., when the normalized quantum free-electron laser parameter ρ¯⩽1. A general quantum dispersion relation and an expression for free-electron laser instabilities are derived. Conditions for kinetic instability, which takes into account the Landau damping effect, are established.