Numerical application of the mode matching technique to the longitudinal impedance computation in particle accelerators - N. Biancacci; A. Passarelli (Physical Review Accelerators and Beams)
The accurate knowledge of the beam coupling impedance in particle accelerators is important in order to address potential impedance-driven instabilities and for planning machine upgrades. While simple models exist for various components (e.g., beam pipes, step transitions, and collimators), they are often insufficient to correctly describe the overall machine impedance with the necessary precision. Numerical 3D simulations, such as those performed with CST wakefield and eigenmode solvers, are typically used to improve the impedance model accuracy accounting for the accelerator device’s detailed geometry. Nevertheless, for structures exhibiting low ohmic losses in low energy machines, where the beam velocity is not yet ultrarelativistic, existing 3D codes face computational challenges. Specifically, wakefield simulation times can become excessively long, and the eigenmode resonator model is not physically valid for nonultrarelativistic cases. To overcome these limitations, the mode matching technique, previously applied exclusively to canonical geometries, has been extended to arbitrary 3D particle accelerator structures by numerically computing the eigenmodes within their volume. With appropriate field manipulation at the beam pipe interfaces, the impedance of resonant structures can be accurately calculated without being affected by ohmic losses or particle velocity. Additionally, being combined with CST eigenmode simulations, this method takes advantage of the underlying tetrahedral mesh, providing a more accurate representation of device geometry compared to the hexahedral mesh used in wakefield simulations. In this work, we present the theory, development, and results of this generalized method, with a particular focus on the longitudinal impedance computation for a buncher of the High Brightness Beams Test Facility, where the effects of low wall losses and low beam velocity play a significant role.