New modes of propagation of high-intensity charged particle beams

A class of new modes of propagation of high-intensity charged particle beams in a general focusing lattice is discovered. It generalizes the classical Kapchinskij-Vladimirskij solutions of the Vlasov-Maxwell equations and the associated envelope equations. For a given lattice, the classical KV solution is speci?ed by two free parameters, whiles the generalized distribution functions and the envelope equations are speci?ed by ten free parameters. The class of solutions discovered captures a wider range of dynamical behavior of high-intensity charged particle beams, and can be used as a new theoretical tool to study the collective dynamics of high-intensity beams.