Resistive wall wake for nonultrarelativistic beam in ring model

The nonultrarelativistic wake function theory is not only applicable to proton or heavy ion accelerators, but with the emergence of new accelerator physics, it has been found to be equally applicable to electron accelerators such as the steady-state microbunching (SSMB) storage rings. However, existing results are still far from practical applications. In this paper, building on previous work, we further generalize the previous point source model into a more universal ring model. When considering the nonultrarelativistic limit, we discover a completely new lowest-order transverse wakefield and estimate its intensity to be comparable to the dipole field under certain circumstances. Moreover, by separating the space charge component, we propose a numerical algorithm that can compute the resistive wall field more efficiently. Finally, we calculate the parasitic loss and kick angle using SSMB parameters as simple applications.