Energy Transfer Mechanisms and Equipartitioning in non-Equilibrium   Space- Charge-Dominated Beams
  A process of energy transfer is demonstrated in non-equilibrium charged particle beams with anisotropy and space charge. Equipartitioning of energy between available degrees of freedom occurs in just a few betatron wavelengths, without halo formation. Collective space charge modes similar to those observed in recent experiments provide the underlying coupling mechanism. Since laboratory beams are commonly far from equilibrium, the traditional K-V stability analysis does not necessarily apply, implying that selection of an operating point based on theory does not necessarily avoid equipartitioning. Furthermore, the rate of equipartitioning is shown to depend on a single free parameter related space charge content of the final (equipartitioned) beam, and does not depend on how the kinetic energy is initially distributed between the two planes. 
R. A. Kishek, P. G. O'Shea, and M. Reiser