Stability of off-axis motion for intense particle beams in periodically   focusing channels
  A 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. 
Jorge S. Moraes (IFUFRGS), Renato Pakter (IFUFRGS), Felipe B. Rizzato   (IFUFRGS)