Conventional free electron laser (FEL) oscillators minimize the optical mode volume around the electron beam in the undulator by making the resonator Rayleigh length about one third of the undulator length. This maximizes gain and beam-mode coupling. In compact configurations of high-power infrared FELs or moderate power UV FELs, the resulting optical intensity can damage the resonator mirrors. To increase the spot size and thereby reduce the optical intensity at the mirrors below the damage threshold, a shorter Rayleigh length can be used, but the FEL interaction is significantly altered. A new FEL interaction is described and analyzed with a Rayleigh length that is only one tenth the undulator length, or less. The effect of mirror vibration and positioning are more critical in the short Rayleigh length design, but we find that they are still within normal design tolerances.

For compact short-Rayleigh length FELs, the area of the optical beam can be thousands of times greater at the mirrors than at the beam waist. A fixed numerical grid of sufficient resolution to represent the narrow mode at the waist and the broad mode at the mirrors would be prohibitively large. To accommodate this extreme change of scale with no loss of information, we employ a coordinate system that expands with the diffracting optical mode. The simulation using the new expanding coordinates has been validated by comparison to analytical cold-cavity theory, and is now used to simulate short-Rayleigh length FELs.

A short-Rayleigh length FEL will operate primarily in the fundamental mode with a Gaussian profile that is narrow at the waist and broad at the mirrors. The gain medium will distort the optical mode profile and produce higher-order modes that will expand more rapidly than the fundamental. Wavefront propagation simulations are used to study the higher-order modes, as the cavity length, Rayleigh length, electron beam current and radius, undulator taper, and the focus positions of the optical mode and electron beam are varied.

Twenty-seven years after the first operation of the short wavelength free electron laser (FEL) at Stanford University, there continue to be many important experiments, proposed experiments, and user facilities around the world. Properties of FELs operating in the infrared, visible, UV, and x-ray wavelength regimes are listed and discussed.

Motivated by the prospect of constructing an FEL with short Rayleigh length in a high-vibration shipboard environment, we have studied the effect of mirror vibration and distortion on the behavior of the fundamental optical mode of a cold-cavity resonator. A tilt or transverse shift of a mirror causes the optical mode to rock sinusoidally about the original resonator axis. A longitudinal mirror shift or a change in the mirror’s radius of curvature causes the beam diameter at a mirror to dilate and contract with successive impacts. Results from both ray-tracing techniques and wavefront propagation simulations are in excellent agreement.