Halo formation and chaos in root-mean-square matched beams propagatingthrough a periodic solenoidal focusing channel

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Abstract
The dynamics of continuous space-charge-dominated beams propagating through a periodic solenoidal focusing channel is studied using a test-particle model. It is shown that nonlinearities in the self-fields induce chaotic particle motion and beam halo formation for beams that are root-mean-square matched into the focusing channel but have nonuniform density profiles transverse to the direction of beam propagation. In particular, two parabolic density profiles are considered. For beams with hollow density profiles, it is found that excessive space charge at the edge of the beam induces two pairs of stable and unstable period-one orbits in the vicinity of the beam core envelope, and that the chaotic layer associated with the unstable period-one orbits allows particles to escape from the core to form a halo. On the other hand, for beams with hump density profiles (i.e., with high densities on the beam axis and low densities at the beam edge), it is found that excessive space charge on the beam axis induces an unstable fixed point on the axis and two stable period-one orbits off the axis inside the beam, and that the chaotic layer associated with the unstable fixed point is responsible for halo formation. In both cases, the halo is found to be bounded by a Kolmogorov-Arnold-Moser surface. The ratio of halo to beam core envelope is determined numerically.