Pulse slippage in high-gain, optically guided free-electron lasers

Using the solution of the fully three-dimensional dispersion relation for the fastest-growing mode an expression for slippage in an optically guided free-electron laser (FEL) amplifier is derived. The FEL operates in the exponential regime and the optical beam is guided by the electron beam. The slippage distance is less than that in the low-gain regime. The reduced slippage arises from the dispersion characteristics of the optical beam and is a manifestation of (i) gain effects and (ii) finite-spot-size effects.