纵向平面朗道阻尼损失的阈值

I. Karpov, T. Argyropoulos, E. Shaposhnikova
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引用次数: 7

摘要

朗道阻尼机制在大型强子对撞机、高亮度大型强子对撞机、其他现有的以及以前和将来的(如FCC)圆形强子加速器中提供单束稳定性起着至关重要的作用。本文利用列别捷夫矩阵方程(Lebedev matrix equation, 1968)和van Kampen模态的概念(1983),对纵向平面上朗道阻尼损失的阈值进行了解析推导。我们发现,对于二项族中常用的粒子分布函数,LLD阈值在过渡能量以上的恒定电感阻抗Im$Z/k$存在时消失。因此,详细研究了宽带阻抗的截止频率或谐振频率对波束动力学的影响。这些发现被Lebedev方程的直接数值解以及Oide-Yokoya方法(1990)所证实。此外,对于梁的工作很重要的特性,如残余振荡的振幅和踢井(或注入误差)后的阻尼时间,都被认为高于和低于阈值。分析了阈值与粒子在纵向相空间分布的关系,包括Im$Z/k = const$的非零阈值的一些特殊情况。所有主要结果都得到了宏观粒子模拟的证实,并与大型强子对撞机中可用的光束测量结果一致。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Thresholds for loss of Landau damping in longitudinal plane
Landau damping mechanism plays a crucial role in providing single-bunch stability in LHC, High-Luminosity LHC, other existing as well as previous and future (like FCC) circular hadron accelerators. In this paper, the thresholds for the loss of Landau damping (LLD) in the longitudinal plane are derived analytically using the Lebedev matrix equation (1968) and the concept of the emerged van Kampen modes (1983). We have found that for the commonly-used particle distribution functions from a binomial family, the LLD threshold vanishes in the presence of the constant inductive impedance Im$Z/k$ above transition energy. Thus, the effect of the cutoff frequency or the resonant frequency of a broad-band impedance on beam dynamics is studied in detail. The findings are confirmed by direct numerical solutions of the Lebedev equation as well as using the Oide-Yokoya method (1990). Moreover, the characteristics, which are important for beam operation, as the amplitude of residual oscillations and the damping time after a kick (or injection errors) are considered both above and below the threshold. Dependence of the threshold on particle distribution in the longitudinal phase space is also analyzed, including some special cases with a non-zero threshold for Im$Z/k = const$. All main results are confirmed by macro-particle simulations and consistent with available beam measurements in the LHC.
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