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Phase mixing of chaotic orbits exponentially distributes these orbits throughtheir accessible phase space. This phenomenon, commonly called ``chaoticmixing'', stands in marked contrast to phase mixing of regular orbits whichproceeds as a power law in time. It is operationally irreversible; hence, itsassociated e-folding time scale sets a condition on any process envisioned foremittance compensation. A key question is whether beams can support chaoticorbits, and if so, under what conditions? We numerically investigate theparameter space of three-dimensional thermal-equilibrium beams with spacecharge, confined by linear external focusing forces, to determine whether theassociated potentials support chaotic orbits. We find that a large subset ofthe parameter space does support chaos and, in turn, chaotic mixing. Detailsand implications are enumerated.Comment: 39 pages, including 14 figure

Chaotic orbits in thermal-equilibrium beams: Existence and dynamical implications