Enhanced phase stability for a Raman free-electron laser amplifier in the exponential growth regime

The wave propagation number for the growing wave of a free-electron laser in the exponential growth regime is a complicated function of electron beam current and voltage. As a result if the electron beam voltage drifts the imaginary part of the propagation number in general will change too, leading to a change in the radio-frequency phase of the output power. For typical gains, the two largest contributions to the shift in the imaginary component of the propagation constant are due to the change in the beam’s reduced plasma wave number and the change in the detuning from resonance. This paper demonstrates that these changes can be made to cancel each other with the correct selection of plasma reduction factor and initial detuning from resonance if the interaction strength is weakly dependent on beam velocity, leading to a device that is first-order phase and gain stable under voltage fluctuations. The analysis is performed for the axial free-electron laser interaction and the results also apply for transverse-coupling free-electron lasers.