Chaotic dynamics and halo formation in charged-particle beams

An old problem, but a new area of fundamental research, is characterizing orbital dynamics and its consequences in time-dependent potentials. Regarding nonequilibrium space-charge potentials, one clear consequence is halo formation. We show that orbital chaos normally plays a central role in halo formation. In turn, the ability to quantify chaos is centrally important. We show examples of the generation and consequences of chaos in nonequilibrium beams, and we apply a newly developed tool for pinpointing orbital chaos in time-dependent potentials.