Four-element linear resonators with grazing incidence mirrors for high-power FEL´s

A laser resonator for use in high-power free-electron lasers is analyzed:specifically, a symmetric, four-element, linear resonator with two grazing incidence mirrors. Analytic expressions are given for resonator stability, mode radii, and mirror-tilt sensitivity. These expressions clearly illustrate the design choices involved and the advantage gained by the use of grazing incidence mirrors.