Frequency shifting in free-electron lasers

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Abstract
Frequency shifting in free-electron laser (FEL) oscillators and amplifiers is investigated theoretically and numerically. The analysis includes frequency shifts from the resonant FEL interaction and the nonresonant beam dielectric. Expressions for the frequency shift in a microwave amplifier with time-dependent beam energy and current are derived and found to be in good agreement with experiments. The theory shows that temporal changes in the detuning are the dominant factor in determining the frequency shift. Electron energy fluctuations produce frequency shifts in the Compton regime, while both current and energy variations are significant in the Raman regime. The effect is particularly important for high-power microwave drivers proposed for high gradient accelerators, where the phase of the radio-frequency radiation is subject to significant constraints. FEL oscillator response to variations in beam energy is examined. It is shown that in a low-gain oscillator which experiences a sudden jump in beam energy the FEL creates spikes at the head and tail of the beam which are at the shifted frequency. The shifting is generated by time dependence in dielectric function which arises from slippage and finite lengths of the electron or optical pulse. The propagation diffusion equation is shown to describe the propagation of the spikes into the main body of the pulse.