Particle-core analysis of beam halo formation in anisotropic beams

We have derived a method to apply the particle-core analysis to coasting beams executing general envelope oscillation which is a superposition of two normal modes. Applying this method to transversely isotropic and anisotropic beams, the effects of simultaneous excitation of two normal modes on halo development mechanism have been explored. We find that, in isotropic cases with the same emittance and external focusing strength in the two transverse directions, single-particle motion exhibits strong chaosity in wide parameter space due to the resonance overlap of two 2:1 particle-core resonances. The strong chaosity is expected to result in an increase of halo intensity enhancing the chance for the particles to gain excess energy through resonant interaction with the core. Of particular importance is the result that the resonance overlap can be avoided by introducing appropriate anisotropy provided that the beam density is lower than a certain threshold. The avoidance of the resonance overlap suppresses chaosity in single-particle motion, which strongly suggests that halo intensity can be reduced in anisotropic situations by choosing appropriate parameters such as beam density and external focusing force strength. This gives us a practical criterion to choose parameters in designing a high-intensity ion synchrotron and storage ring.