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Modern electron storage rings produce bright X-rays via spontaneoussynchrotron emission, which is useful for a variety of scientific applications.The X-ray free-electron laser oscillator (XFELO) has the potential to amplifythis output, both in terms of peak power and photon coherence. However, evencurrent 4th generation storage rings (4GSRs) lack the requisite electron beambrightness to drive the XFELO due to its electron energy spread. The transversegradient undulator (TGU) can overcome this issue, thus providing a practicalmeans to couple the 4GSR to the XFELO. In this study, we first examine thetheoretical basis of the TGU interaction by deriving the 3D TGU gain formula inthe low gain approximation. Then, we perform an optimization study of the gainformula in order to determine optimal beam and machine parameters. Finally, weconstruct a hypothetical storage ring TGU-XFELO based on near-optimalparameters and report on its projected performance using multi-stage numericalsimulation. We also discuss potential implementation challenges associated withthe ring-FEL coupling.

Transverse Gradient Undulator in a Storage Ring X-ray Free Electron Laser Oscillator