Impedance minimization of the CERN Super Proton Synchrotron cavities using the generalized coupled S -parameter method

In the context of the Large Hadron Collider (LHC) injector upgrade, components with high contribution to the beam coupling impedance of the injector chain have to be identified and optimized to ensure the delivery of high-intensity proton beams to the LHC. The Super Proton Synchrotron (SPS) is the last accelerator in the LHC injector chain. In the existing design, the longitudinal beam coupling impedance of the SPS cavities limits the increase of the beam intensity in the SPS ring. Since the 200 MHz traveling wave cavities are one of the main contributors to the overall beam coupling budget of the SPS machine, different types of higher-order mode (HOM) couplers are used in the long 33-cell and 44-cell cavities for the damping of various HOMs. The location of the HOM couplers in the cavity, as well as their shape, affects the damping of HOMs. Finding a suitable arrangement of the HOM couplers requires solving a discrete optimization problem. The repetitive calculation of the beam coupling impedance by the conventional time -domain wakefield solvers in the optimization is hindered by the large size of the SPS cavities. The generalized coupled S-parameter method is a domain decomposition method for the calculation of the S parameters and beam coupling impedance of large structures. In this paper, this method is employed to calculate the beam coupling impedance of the SPS cavities. Then, an optimization method is proposed to find an optimal arrangement of the HOM couplers in the cavities. The article presents the geometrical details of the SPS cavities, a short description of the generalized coupled S-parameter method, and a discrete optimization method applied to the SPS cavities.