热平衡光束中混沌轨道的存在性及其动力学意义
Chaotic Orbits in Thermal-Equilibrium Beams: Existence and Dynamical Implications
摘要：
混沌轨道的相位混合使这些轨道在其可达相空间中呈指数分布。这种现象，通常称为"混沌混合“，与规则轨道的相位混合形成鲜明对比，后者在时间上按幂律进行。它在操作上是不可逆的;因此，其相关的e折叠时间尺度为设想用于发射度补偿的任何过程设定了条件。一个关键的问题是光束是否可以支持混沌轨道，如果可以，在什么条件下？我们数值研究了在线性外聚焦力作用下，含空间电荷的三维热平衡光束的参数空间，以确定相关势是否支持混沌轨道。我们发现，一个大的参数空间的子集不支持混沌，反过来，混沌混合。列举了细节和影响。
英文摘要：
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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