A resistive transverse damper is often needed in particle accelerators operating with many bunches and it is usually very efficient as it can considerably reduce the necessary amount of nonlinearities needed to reach beam stability through Landau damping. In the CERN LHC for instance, the required current in the Landau octupoles is predicted to be reduced by an order of magnitude for zero chromaticity (for the beam and machine parameters used during the last year of Run 2, in 2018, this corresponded to $\sim 2000\mathrm{A}$ without damper and $\sim 200\mathrm{A}$ with damper, knowing that the maximum current available in the Landau octupoles is $\sim 550\mathrm{A}$). However, a resistive transverse damper also destabilizes the single-bunch motion below the transverse mode coupling instability intensity threshold (for zero chromaticity), introducing a new kind of instability, which has been called ITSR instability (for imaginary tune split and repulsion). Until now, only one type of impedance-driven transverse coherent instability has been explained for a single bunch in a circular particle accelerator, at zero chromaticity and without a multiturn wake: the transverse mode coupling instability. A transverse mode coupling instability can also be observed in the presence of Landau damping, beam-beam, electron cloud or space charge. However, the ITSR instability exhibits a different mechanism, which is not due to mode coupling. The purpose of this article is to explain in detail both this new instability mechanism and its mitigation using a simplified analytical model, which has been carefully benchmarked, using the pyheadtail macroparticle tracking code, by Oeftiger (one of the code’s developers).

中文翻译：

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电阻性横向阻尼器存在时的虚假分流与排斥单束不稳定性机制及其缓解

在许多束中运行的粒子加速器中通常需要一个电阻横向阻尼器，并且它通常非常有效，因为它可以大大减少通过Landau阻尼达到光束稳定性所需的非线性程度。例如，在CERN大型强子对撞机中，预计零色度时Landau八极所需的电流将减少一个数量级（对于运行2的最后一年2018年使用的光束和机器参数，这相当于$〜2000\mathrm{一种。}$ 没有阻尼器和 $〜200\mathrm{一种。}$ 带有阻尼器，知道在朗道八极管中可用的最大电流为 $〜550\mathrm{一种。}$）。但是，电阻性横向阻尼器还会使横向横向耦合不稳定性强度阈值（对于零色度）以下的单脉冲运动不稳定，从而引入了一种新的不稳定性，称为ITSR不稳定性（对于虚构的音调分裂和斥力）。到目前为止，对于圆形粒子加速器中单束，色度为零且无多圈唤醒的情况，仅解释了一种阻抗驱动的横向相干不稳定性：横向模式耦合不稳定性。在存在Landau阻尼，电子束，电子云或空间电荷的情况下，还可以观察到横向模式耦合的不稳定性。但是，ITSR不稳定性表现出不同的机制，这不是由于模式耦合引起的。p ÿ headtail大粒子跟踪代码，由Oeftiger（的代码的开发者之一）。