Publication

Impact of beam-coupling impedance on the Schottky spectrum of bunched beam

Résumé

The Schottky monitors of the Large Hadron Collider (LHC) can be used for non-invasive beam diagnostics to estimate various bunch characteristics, such as tune, chromaticity, bunch profile or synchrotron frequency distribution. However, collective effects, in particular beam -coupling impedance, can significantly affect Schottky spectra when large bunch charges are involved. In such conditions, the available interpretation methods are difficult to apply directly to the measured spectra, thus preventing the extraction of beam and machine parameters, which is possible for lower bunch charges. To study the impact of impedance on such spectra, we introduce a method for building Schottky spectra from macro -particle simulations performed with the PyHEADTAIL code, applied to LHC beam conditions. In this case, the use of a standard Fast Fourier Transform (FFT) algorithm to recover the spectral content of the beam becomes computationally intractable memory -wise, because of the relatively short bunch length compared to the large revolution period. To circumvent this difficulty, a semi -analytical method was developed to efficiently compute the Fourier transform. The simulated Schottky spectrum is then compared against theoretical formulas and measurements of Schottky signals previously obtained with lead ion beams in the LHC where impedance effects are expected to be limited. Furthermore, this study provides preliminary interpretations of the impact of beam -coupling impedance on proton Schottky spectra by incorporating longitudinal and transverse resonator -like impedance models into the simulations. A theoretical framework is also introduced for the case of the longitudinal impedance, allowing the extension of the existing theoretical formalism.

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Concepts associés (40)
Input impedance
The input impedance of an electrical network is the measure of the opposition to current (impedance), both static (resistance) and dynamic (reactance), into a load network that is external to the electrical source network. The input admittance (the reciprocal of impedance) is a measure of the load network's propensity to draw current. The source network is the portion of the network that transmits power, and the load network is the portion of the network that consumes power.
Transformation de Fourier
thumb|Portrait de Joseph Fourier. En mathématiques, plus précisément en analyse, la transformation de Fourier est une extension, pour les fonctions non périodiques, du développement en série de Fourier des fonctions périodiques. La transformation de Fourier associe à toute fonction intégrable définie sur R et à valeurs réelles ou complexes, une autre fonction sur R appelée transformée de Fourier dont la variable indépendante peut s'interpréter en physique comme la fréquence ou la pulsation.
Grand collisionneur de hadrons
vignette|Tunnel du LHC avec le tube contenant les électroaimants supraconducteurs. Le Grand collisionneur de hadrons (en anglais : Large Hadron Collider — LHC), est un accélérateur de particules mis en fonction en 2008 au CERN et situé dans la région frontalière entre la France et la Suisse entre la périphérie nord-ouest de Genève et le pays de Gex (France). C'est le plus puissant accélérateur de particules construit à ce jour, a fortiori depuis son amélioration achevée en 2015 après deux ans de mise à l'arrêt.
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Digital Signal Processing I
Basic signal processing concepts, Fourier analysis and filters. This module can be used as a starting point or a basic refresher in elementary DSP
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