Halo formation at early stage of injection in high-intensity hadron rings.

Abstract

Halo formation under a nonequilibrium state for a two-dimensional Gaussian beam in a FODO lattice, which is an array of magnets where F is focusing, D is defocusing, and O is the drift space between magnets, was examined in terms of a transition of time-varying nonlinear resonances. Nonlinear resonant-interactions between individual particles and intrinsic beam-core oscillations result in a beam halo. The location of the halo is analytically tractable using canonical equations derived from an isolated resonance Hamiltonian.