Simulation of transverse modes with their intrinsic Landau damping for bunched beams in the presence of space charge

Transverse dipole modes in bunches with space charge are simulated using the synergia accelerator modeling package and analyzed with dynamic mode decomposition. The properties of the first three space charge modes, including their shape, damping rates, and tune shifts are described over the entire range of space charge strength. The intrinsic Landau damping predicted and estimated in 2009 by one of the authors is confirmed with a reasonable scaling factor of $\ensuremath{\simeq}2.4$. For the KV distribution, very good agreement with PATRIC simulations performed by Kornilov and Boine-Frankenheim is obtained.