Mode competition and suppression in free electron laser oscillators

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Abstract
The stability of single‐mode operation of free electron laser (FEL) oscillators is investigated. Two models of an untapered FEL oscillator are considered. The first model is called the klystron model. In the klystron model the FEL interaction occurs at two points: a prebunching point and an energy extraction point. In this model the nonlinear electron dynamics are solvable exactly, leading to a complex delay equation for the wave fields. The stability of single‐mode operation can then be determined easily as a function of a single‐pass gain, energy mismatch–frequency, and the difference between the group velocity of the radiation and the beam velocity. The second, more realistic model has a distributed interaction region of finite length: Stability of single‐mode operation in this device must be determined numerically. The results of the models in the low gain regime are compared and the parameter regimes where stable single‐mode operation is possible are determined. It is found that the time to reach a single‐mode state can be extremely long.

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