纵向相空间中α桶的分岔分析
Alpha Buckets in Longitudinal Phase Space: a Bifurcation Analysis
摘要：
在HZB的BESSY II和PTB的计量光源（MLS）设施中，我们有能力将动量压缩因子$α$调整到第二非线性阶。非线性相关性$α(δ)$给纵向相空间带来了质的变化，并引入了新的固定点$α(δ)=0$，其产生所谓的$α$桶。本文从分岔理论的角度对这一现象进行了分析。通过这种方法，我们能够直接依赖于可调参数来表征固定点的性质及其位置。此外，我们能够对可调参数设置严格的条件，以创建或销毁$α$-bucket。
英文摘要：
At HZB's BESSY II and PTB's Metrology Light Source (MLS) facilities we have the ability to tune the momentum compaction factor $α$ up to second non-linear order. The non-linear dependence $α(δ)$ brings qualitative changes to the longitudinal phase space and introduces new fix points $α(δ)=0$ which produce the so-called $α$-buckets. We present with this paper an analysis of this phenomena from the standpoint of bifurcation theory. With this approach we were able to characterize the nature of the fix points and their position in direct dependence on the tunable parameters. Furthermore, we are able to place stringent conditions onto the tunable parameters to either create or destroy $α$-buckets.
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