We report on the effects of transverse spatial misalignment on the performance and stability of x-ray free electron laser oscillators (XFELOs). For this study, we adopt the FEL driven paraxial resonator model in which the transverse profile of the radiation field is represented by Gauss-Hermite mode expansion. Then, we apply Gaussian optics for transporting the radiation field along with the misalignment in the optical cavity. We divide the misalignment into relevant categories of static and periodic types to understand their effects on FEL gain, lasing, and saturation. After that, we associate the first order moments of the radiation field to that of driven simple harmonic oscillator models to identify regions of instability. Throughout this report, we validate our models and analyses via theoretical calculations, analytical approximations, and simulations.
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