Microtemporal and spectral structure of storage ring free-electron lasers

The microtemporal and spectral structure of free-electron lasers has been analyzed in the low gain, low field, and small slippage regime. Analytical expressions of the longitudinal eigenmode (super-modes) is derived for various configurations including the undulator, the optical klystron, and an intracavity dispersive element. Longitudinal and spectral narrowing of the laser pulse is predicted down to a limit set by the Fourier transform. On stage ring, it is found that early saturation prevents the laser from reaching this limit, in good agreement with results from the Orsay experiment. The insertion of a Fabry-Perot etalon in the cavity should make possible a relative line-width on the order of 0.00001.