Abstract
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 intrabunch 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.
Highlights
The Large Hadron Collider (LHC) transverse Schottky system, whose main objective is to provide the beam operators with noninvasive bunch-by-bunch tune and chromaticity measurements, was commissioned in 2011 [1]
Due to its simpler physical interpretation, we have focused on the spectral region in the immediate vicinity of the 427725th revolution harmonic, where transverse particle motion plays no role
The presented theory is supported by examples of LHC measurements and the obtained bunch profiles are compared with the wall current monitor (WCM) [6]
Summary
The Large Hadron Collider (LHC) transverse Schottky system, whose main objective is to provide the beam operators with noninvasive bunch-by-bunch tune and chromaticity measurements, was commissioned in 2011 [1]. Studies are underway in order to better understand the obtained spectra. A new application for the system has emerged, as a bunched-beam longitudinal profile monitor. We derive a relationship between the Schottky spectrum and the longitudinal bunch profile, under the. A similar result, which uses the distribution function of the radio frequency (rf) bucket instead of the bunch profile, was presented in [4]. The presented theory is supported by examples of LHC measurements and the obtained bunch profiles are compared with the wall current monitor (WCM) [6]
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