Class of generalized Kapchinskij-Vladimirskij solutions and associated envelope equations for high-intensity charged-particle beams

A class of generalized Kapchinskij-Vladimirskij solutions of the Vlasov-Maxwell equations and the associated envelope equations for high-intensity beams in an uncoupled lattice is derived. It includes the classical Kapchinskij-Vladimirskij solution as a special case. For a given lattice, the distribution functions and the envelope equations are specified by ten free parameters. The class of solutions derived captures a wider range of dynamical envelope behavior for high-intensity beams, and thus provides a new theoretical tool to investigate the dynamics of high-intensity beams.