Abstract
The micro-temporal and spectral structure of free electron lasers have been analysed in the low gain, low field and small slippage regime. Analytical expressions of the longitudinal eigen-mode (supermodes) are derived for various configurations including the undulator, the optical klystron and intra-cavity dispersive elements. Longitudinal and spectral narrowing of the laser pulse is predicted down to a limit set by the Fourier transform. On storage rings it is found that the early saturation prevents the laser from reaching this limit, which is in good agreement with results from the Orsay experiment. The insertion of an etalon in the cavity should make possible a relative linewidth of the order of 10 −6.
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