Phase Mixing of Chaotic Orbits as an Irreversible “relaxation” Mechanism*

Orbits that are chaotic will tend to phase-mix exponentially through their accessible phase space. This phenomenon, commonly called “chaotic mixing”, stands in marked contrast to phase mixing of regular orbits. It is inherently irreversible, and thus its associated e-folding time scale sets a condition on any process envisioned for emittance compensation. Accordingly, two questions arise. First, under what conditions does chaotic mixing manifest itself in beams? Second, when it is active, over what time scale does it operate? The work described here is part of an ongoing effort to answer these questions.