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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.

Class of Generalized Kapchinskij-Vladimirskij Solutions and Associated Envelope Equations for High-Intensity Charged-Particle Beams