Design and Optimization of HOM Damping for the S³FEL 3.9-GHz TESLA Superconducting Cavity

The Shenzhen medium-energy high-repetition-rate X-ray free-electron laser (S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>FEL) will be the first medium-energy X-ray free-electron laser operating at megahertz repetition rates worldwide. The facility is equipped with 24 sets of 1.3-GHz superconducting acceleration modules for energy acceleration by fundamental wave and two sets of 3.9-GHz superconducting acceleration modules to compensate for the nonlinear longitudinal spatial distortion caused by the curvature of the acceleration field. We optimize the radio-frequency design of the S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>FEL 3.9-GHz TESLA superconducting cavity by changing the size of the higher-order-mode (HOM) coupler to decrease <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R/Q</i> and external Q, ensuring continuous-wave operation. Furthermore, we evaluated the dangerous modes of the cavity to fulfill the design requirements for safety and calculated the HOM power loss of the cavity using the Azimuthal beam cavity interaction.