An analytical model to determine equilibrium quantities of azimuthally symmetric and mismatched charged particle beams under linear focusing

An analytical model has helped in obtaining equilibrium quantities of interest from high-intensity charged particle beams such as the emittance, beam envelope and the number of beam halo particles. The results are particularized to the case of initially homogeneous beams, with azimuthal symmetry, and are focused by a constant magnetic field while confined in a linear channel.