Evolution Of The Transverse Modes In A FEL, And Application To The Orsay Experiment

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Abstract
We derive the most general equations of motion for the electrons and the electromagnetic field in a free electron laser including the effects of diffraction and pulse propagation. The field evolution is expressed in terms of the amplitudes and phases of a complete set of transverse modes. The analytic solution is given in the small signal regime, where the theory is shown to be in excellent agreement with a recent experiment at Orsay.

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