Halo formation and chaos in space-charge-dominated beams

Abstract

The mechanisms of halo formation and chaotic particle motion are explored for space‐charge‐dominated beams propagating through a linear, periodic focusing channel provided by an applied periodic solenoidal magnetic field. For root‐mean‐squared (rms) matched beams with nonuniform density profiles, it is shown in a test‐particle model that nonlinearities in the self field forces not only can result in chaotic particle motion but also can cause a halo to develop. The size of the halo is found to be bounded by a Kolmogorov‐Arnold‐Moser (KAM) surface. For rms mismatched beams, it is confirmed in the computer simulations that, for beams mismatched into the periodic focusing channel, the beam envelope exhibits nonlinear resonances and chaotic behavior, as predicted by the previous analysis of the beam envelope equation. As a result of emittance growth, transient effects are observed in the rms beam dynamics, and halos can develop. The halo characteristics for a periodic focusing channel are found to be qualitatively the same as those for a uniform focusing channel. A threshold condition is obtained numerically for halo formation for mismatched beams in the uniform focusing approximation. These results indicate that both precise rms beam matching and precise density profile control are required to prevent space‐charge‐dominated beams from developing halos.