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

Modern electron storage rings produce bright X-rays via spontaneous synchrotron emission, which is useful for a variety of scientific applications. The X-ray free-electron laser oscillator (XFELO) has the potential to amplify this output, both in terms of peak power and photon coherence. However, even current 4th generation storage rings (4GSRs) lack the requisite electron beam brightness to drive the XFELO due to its electron energy spread. The transverse gradient undulator (TGU) can overcome this issue, thus providing a practical means to couple the 4GSR to the XFELO. In this study, we first examine the theoretical basis of the TGU interaction by deriving the 3D TGU gain formula in the low gain approximation. Then, we perform an optimization study of the gain formula in order to determine optimal beam and machine parameters. Finally, we construct a hypothetical storage ring TGU-XFELO based on near-optimal parameters and report on its projected performance using multi-stage numerical simulation. We also discuss potential implementation challenges associated with the ring-FEL coupling.