Analytic Model for Halo Formation in High Current Ion Linacs

We construct an azimuthally symmetric 2D model for halo formation in high current ion linacs. The driving term, a "breathing" oscillation caused by a transverse mismatch along the linac, leads to growth of ion amplitudes in the core through the parametric resonance. As the ion amplitude grows, its wave number increases, enhancing the resonance. This leads to the formation of a halo surrounding the core. We explore the dependence of this mechanism on the tune depression and the size of the mismatch. The model agrees well with simulations at Los Alamos, but does not yet include the effects of chaos observed in the simulations as the tune depression becomes severe.