The Large Hadron Collider (LHC) Schottky monitors have been designed to measure various parameters of relevance to beam quality, namely tune, momentum spread and chromaticity. In this work, we present how this instrument can be used to estimate longitudinal bunch characteristics, such as longitudinal bunch profile or synchrotron frequency distribution. Under the assumption of bunched beams with no intra-bunch coherent motion, we start by deriving the relation between the distribution of synchrotron amplitudes within the bunch population and the longitudinal bunch profile from probabilistic principles. Subsequently, we fit the cumulative power density of acquired Schottky spectra with the underlying distribution of synchrotron amplitudes. Finally, the result of this fit is used to reconstruct the bunch profile using the derived model. The results obtained with this method are verified by comparison with longitudinal profile measurements from the LHC Wall Current Monitors.

中文翻译：

---

使用基于肖特基的诊断估计大型强子对撞机的纵向束特征

大型强子对撞机（LHC）肖特基监视器设计用于测量与光束质量相关的各种参数，即调谐，动量扩散和色度。在这项工作中，我们介绍了如何使用该仪器估算纵向束特征，例如纵向束轮廓或同步加速器频率分布。在没有束内相干运动的束束的假设下，我们首先从概率原理推导束群内同步加速器振幅的分布与纵向束轮廓之间的关系。随后，我们用同步加速器振幅的基本分布拟合获得的肖特基光谱的累积功率密度。最后，该拟合的结果用于使用派生模型重建束轮廓。