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Three-dimensional simulation codes genesis and opc are used to investigate the dependence of the resonator stability of free-electron laser (FEL) oscillators on the stability parameter, laser wavelength, outcoupling hole size and mirror tilt. We find that to have stable lasing over a wide range of wavelengths, the FEL cavity configuration should be carefully chosen. Broadly, the concentric configuration gives near-Gaussian modes and the best performance. At intermediate configurations the dominant mode often switches to a higher-order mode, which kills lasing. For the same reason, the outcoupled power can also be less. We have constructed a simple analytic model to study resonator stability which gives results that are in excellent agreement with the simulations. This suggests that modes in FEL oscillators are determined more by the cavity configuration and radiation propagation than by the details of the FEL interaction. We find (as in experiments at the CLIO FEL) that tilting the mirror can, for some configurations, lead to more outcoupled power than a perfectly aligned mirror because the mode is now a more compact higher-order mode, which may have implications for the mode quality for user experiments. Finally, we show that the higher-order mode obtained is usually a single Gauss-Laguerre mode, and therefore it should be possible to filter out the mode using suitable intracavity elements, leading to better FEL performance

Resonator stability and higher-order modes in free-electron laser oscillators