Oscillator Simulation

Free-electron laser oscillators have demonstrated high average power operation at infrared wavelengths using energy recovery linacs and using racetrack microtrons at terahertz wavelengths. The interaction in an oscillator is governed by a balance between amplification of the optical field in the gain medium and losses due to out-coupling, mirror heating and distortion, resistive wall effects, etc. A steady-state is achieved when the nonlinear, saturated gain, G, is balanced by the total losses, L. If the power at the wiggler entrance after the nth pass is denoted by Pn, then the power after the (n + 1)th pass is given by Pn + 1 = (1 – L)(1 + G)Pn. Once the oscillator reaches equilibrium, Pn + 1 = Pn; hence, G = L/(1 – L). In a free-electron laser, the gain tends to increase with the length of the wiggler. The low gain regime refers to configurations where the wiggler is not long enough to reach the exponential gain regime. Typically, in the low gain regime, G ∝ Nw3 [Eq. 1.9 ], where Nw is the number of periods in the wiggler. However, the saturation efficiency is estimated as η ≈ (2.4Nw)−1 [Eq. 1.14 ]. Hence, the performance of a low gain free-electron laser oscillator must strike a balance between maximizing both the gain and the efficiency. Often, this is determined by the properties of the mirrors. For example, if we neglect other losses, then if the mirror out-coupling is 20%, then the saturated gain must be 25%. This low gain regime implies that most of the power is recirculating through the resonator; hence, this type of oscillator has low gain but high Q. The alternative is a high-gain/low-Q oscillator design that makes use of a long wiggler to achieve the high gain. For example, if the losses are as high as 95%, then the required gain would be 1900%, and this would necessitate a long wiggler with a correspondingly long cavity length. Of course, the saturation efficiency for such a configuration is η ≈ ρ, which is lower than that typically achieved in low-gain/high-Q oscillators; however, this may be the only choice for an oscillator at wavelengths where there are no high reflectivity mirrors. This is important, in particular, at x-ray wavelengths. This configuration is often referred to as a regenerative amplifier, or RAFEL. Both low-gain/high-Q and high-gain/low-Q configurations will be discussed in this chapter. The general simulation procedure discussed in this chapter makes use of a free-electron laser simulation formulation (code) as discussed in Chap. 6 to simulate the gain medium after which the output optical field is used by an optics propagation code to transport the field through the resonator and back to the wiggler entrance for another pass through the wiggler. The detailed properties of the optical resonator must be included in the transport of the optical field. These include the detailed geometrical configuration of the resonator including, but not limited to, concentric and ring resonators. Examples of a low-gain/high-Q oscillator using a concentric resonator and a high-gain/low-Q oscillator using a ring resonator are described in this chapter. Transmissive, hole, or edge out-coupling of the optical field may be described. In addition, mirror distortion by heating or the formation of color centers due to harmonic generation can also be included.