Superradiance in a short pulse fel oscillator and its relevance to the x-ray fel

Superradiance (SR) in the short pulse free-electron laser (FEL oscillator is the optimal way of extracting optical radiation from an electron beam. SR is characterized by a peak intracavity optical power, , scaling as the square of the electron charge, Q, (Q2), an optical pulse duration, z, scaling inversely with the square root of the charge, (2Q−1/2) and an efficiency, , scaling with the inverse of optical pulse length (1/zQ1/2). The latter scaling also implies that the relative spectral brightness, /(/), is constant and close to /2. Similar scaling of the peak power, temporal width, energy and efficiency with the cavity quality factor also exist. The efficiency in SR emission is enhanced above the usual natural efficiency, =1/2Nu, for the weakly saturated CW FEL, where Nu is the number of undulator periods. We show that SR in the oscillator has analogous properties to that in a high gain amplifier and discuss the relevance of these analogies to the X-ray FEL starting from self-amplified spontaneous emission (SASE).