Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications

Details Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications

2003-05-31

arxiv.org/abs/physics/0306006v1

Phys.Rev.ST Accel.Beams 6 (2003) 034203

Physics

Accelerator Physics

39 pages, including 14 figures

Scientific paper

10.1103/PhysRevSTAB.6.034203

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.

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