Chaos, a source of charge redistribution and halo formation in space-charge dominated beams

A significant breakthrough in the understanding of the space-charge dominated beam dynamics has been achieved with the introduction of the particle-core model at the previous PAC (O´Connell, Wangler, Mills and Crandall, May 1993). Using this model, we have shown the chaotic behaviour of the particles for mismatched beams in continuous focusing channels (August 1993 and August 1991) and for matched beams in FODO channels (December 1993 and June 1994). In these studies, it has been settled that the recent theories developed for the analysis of nonlinear dynamic systems (“chaotic dynamics”) are very useful to understand charge redistribution and halo formation phenomena. They are now used to describe the behaviour of mismatched beams in FODO channels. It is shown that a mismatch adds perturbing forces which can deeply modify the dynamics. The particle diffusion far from the beam core is studied