Abstract
Phase mixing of chaotic orbits exponentially distributes these orbits through their accessible phase space. This phenomenon, commonly called ``chaotic mixing'', stands in marked contrast to phase mixing of regular orbits which proceeds as a power law in time. It is operationally irreversible; hence, its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. A key question is whether beams can support chaotic orbits, and if so, under what conditions? We numerically investigate the parameter space of three-dimensional thermal-equilibrium beams with space charge, confined by linear external focusing forces, to determine whether the associated potentials support chaotic orbits. We find that a large subset of the parameter space does support chaos and, in turn, chaotic mixing. Details and implications are enumerated.
Highlights
Rapid, inherently irreversible dynamics is a practical concern in producing high-brightness charged-particle beams
A beam bunch with space charge equates to an N-body system with typically 3N degrees of freedom
One might conjecture that this force, when nonlinear, may support chaotic orbits
Summary
Inherently irreversible dynamics is a practical concern in producing high-brightness charged-particle beams. Time scales of irreversible processes place constraints on methods for compensating against degradation of beam quality caused by, for example, space charge. Simulations of the experiment reveal a substantial fraction of globally chaotic orbits [2], and phase mixing of these orbits thereby presents itself as a contributing evolutionary mechanism This example pertains to a strongly time-dependent nonequilibrium system, yet one might conjecture that nonlinear space-charge forces in a static system could support chaotic orbits as well.
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