Analytical method for determining at equilibrium the envelope and emittance of initially mismatched beams

This work presents a fully analytic way of determining relevant equilibrium quantities of a high-intensity charged particle beam submitted to magnetic focusing while inside a linear channel. Through the current approach, some intermediate steps of our original hybrid model which had to be solved numerically can now be eliminated, leading to the obtainment of a fully analytic expression. This expression relates the initial beam parameters with those at equilibrium, allowing beam macroscopic quantities such as envelope and emittance to be naturally and analytically determined. For validation, full self-consistent N -particle beam numerical simulations have been carried out and the results compared with the predictions supplied by the full analytical model. The agreement is shown to be good with the simulations and also with the original hybrid numerical-analytical version of the model.