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Intrabunch motion
Physical Review Accelerators and Beams ( IF 1.5 ) Pub Date : 2021-01-22 , DOI: 10.1103/physrevaccelbeams.24.014401
E. Métral

Impedance-driven (but not only) coherent beam instabilities are usually studied analytically with the linearized Vlasov equation, ending up with an eigenvalue system to solve. The eigenvalues describe the beam oscillation mode-frequency shifts, leading in particular to intensity thresholds defined by the longitudinal mode coupling instability in the longitudinal plane and by the transverse mode coupling instability in the transverse plane in the absence of chromaticity. This can be directly compared to measurements in particular for the lowest modes and in the absence of tune spread. In the presence of nonlinearities or when higher-order modes are involved, this becomes quite difficult, if not impossible, and the coupling between the modes cannot be directly measured (or simulated) anymore. Another important observable is the intrabunch motion, which can be also accessed analytically thanks to the eigenvectors. To the author’s knowledge, until now, the intrabunch signal has only been explained theoretically for independent longitudinal or transverse beam oscillation modes, i.e., when the bunch intensity is sufficiently low compared to the mode coupling threshold. It was never explained theoretically in detail when two (or more) modes are involved. For instance, no answers were already given to these questions: is (are) there some fixed point(s) when the transverse mode coupling instability starts? If yes, where is it (are they)? And what happens in the presence of mode decoupling? Any number of modes can be treated with the general approach discussed in this paper, which is based on the galactic Vlasov solver (which was previously successfully benchmarked against the pyheadtail macroparticle tracking code as concerns the beam oscillation mode-frequency shifts). However, to be able to clearly see what happens when the bunch intensity is increased, the simple case of two modes is discussed in detail. The purpose of this paper is to describe the different regimes, below, at, above the transverse mode coupling instability and also after the mode decoupling (as it happens sometimes), using a simple analytical model (where two modes are considered together), which helps to really understand what happens at each step. Better characterizing an instability is the first step before trying to find appropriate mitigation measures and push the performance of a particle accelerator. The evolution of the intrabunch motion with intensity is a fundamental observable with high-intensity high-brightness beams.

中文翻译:

束内运动

通常使用线性化的Vlasov方程对阻抗驱动的(但不仅是)相干光束不稳定性进行分析研究,最后以特征值系统进行求解。特征值描述了光束振荡模式的频移,尤其导致了强度阈值,该强度阈值由纵向平面中的纵向模式耦合不稳定性和在不存在色度的情况下横向平面中的横向模式耦合不稳定性定义。可以将其直接与测量进行比较,尤其是在最低模式下且没有音调扩展的情况下。在存在非线性或涉及高阶模态的情况下,这变得十分困难,甚至不是不可能,并且模态之间的耦合不再能够直接测量(或模拟)。另一个重要的观察结果是束内运动,由于特征向量,也可以通过分析方式访问。据作者所知,到目前为止,束内信号仅在理论上针对独立的纵向或横向束振荡模式进行了解释,即,当束强度与模式耦合阈值相比足够低时。当涉及到两种(或更多)模式时,从理论上就没有详细解释过。例如,对于这些问题尚未给出答案:当横向模式耦合不稳定性开始时,是否存在某个固定点?如果是,那么在哪里(他们在哪里)?在模式解耦的情况下会发生什么?可以使用本文讨论的通用方法来处理任何模式,该方法基于 在理论上,束内信号仅针对独立的纵向或横向束振荡模式进行了解释,即,当束强度与模式耦合阈值相比足够低时。当涉及到两种(或更多)模式时,从理论上就没有详细解释过。例如,对于这些问题尚未给出答案:当横向模式耦合不稳定性开始时,是否存在某个固定点?如果是,那么在哪里(他们在哪里)?在模式解耦的情况下会发生什么?可以使用本文讨论的通用方法来处理任何模式,该方法基于 在理论上,束内信号仅针对独立的纵向或横向束振荡模式进行了解释,即,当束强度与模式耦合阈值相比足够低时。当涉及到两种(或更多)模式时,从理论上就没有详细解释过。例如,对于这些问题尚未给出答案:当横向模式耦合不稳定性开始时,是否存在某个固定点?如果是,那么在哪里(他们在哪里)?在模式解耦的情况下会发生什么?可以使用本文讨论的通用方法来处理任何模式,该方法基于 当束强度与模式耦合阈值相比足够低时。当涉及到两种(或更多)模式时,从理论上就没有详细解释过。例如,尚未对这些问题给出答案:当横向模式耦合不稳定性开始时,是否存在某个固定点?如果是,那么在哪里(他们在哪里)?在模式解耦的情况下会发生什么?可以使用本文讨论的通用方法来处理任何模式,该方法基于 当束强度与模式耦合阈值相比足够低时。当涉及到两种(或更多)模式时,从理论上就没有详细解释过。例如,对于这些问题尚未给出答案:当横向模式耦合不稳定性开始时,是否存在某个固定点?如果是,那么在哪里(他们在哪里)?在模式解耦的情况下会发生什么?可以使用本文讨论的通用方法来处理任何模式,该方法基于 在哪里(他们在)?在模式解耦的情况下会发生什么?可以使用本文讨论的通用方法来处理任何模式,该方法基于 在哪里(他们在)?在模式解耦的情况下会发生什么?可以使用本文讨论的通用方法来处理任何模式,该方法基于银河Vlasov解算器(先前已成功针对p y标进行了基准测试粒子跟踪码有关的光束振荡模式-频移)。但是,为了能够清楚地看到束强度增加时会发生什么,将详细讨论两种模式的简单情况。本文的目的是使用简单的分析模型(将两种模式同时考虑)来描述横向模式耦合不稳定性的以下,不同,不同的状态,以及在模式解耦之后(有时发生)。有助于真正了解每个步骤会发生什么。在试图找到适当的缓解措施并提高粒子加速器性能之前,第一步是更好地表征不稳定性。束内运动随强度的变化是高强度高亮度光束的基本观察结果。
更新日期:2021-01-22
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