2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/86508A general equation for the centroid motion of free, continuous, intense beams propagating off-axis in solenoidal periodic focusing fields is derived. The centroid equation is found to be independent of the specific beam distribution and may exhibit unstable solutions. A new Vlasov equilibrium for off-axis beam propagation is also obtained. Properties of the equilibrium and the relevance of centroid motion to beam confinement are discussed.12th International Congress on Plasma Physics, 25-29 October 2004, Nice (France)Plasma Physicstext