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A new rigid-rotor Vlasov equilibrium is obtained for an intense, axisymmetric chargedparticle beam with uniform density in the radial direction propagating through a periodic solenoidal focusing field. The beam envelope equation is derived, and examples of periodically focused rigid-rotor Vlasov equilibria are presented. Statistical properties and possible applications of the present beam equilibrium are also discussed.doi:10.1103/physrevlett.79.225 fatcat:nalek522vrh7jfxjmzyaw3f27q