Author: Zannini, C.
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MOP10 Closed Form Formulas of the Indirect Space Charge Wake Function for Axisymmetric Structures 65
 
  • N. Mounet, E. Dadiani, E. Métral, C. Zannini
    CERN, Geneva, Switzerland
  • A. Rahemtulla
    EPFL, Lausanne, Switzerland
 
  Indirect space charge contributes significantly to the impedance of non ultrarelativistic machines such as the LEIR, PSB and PS, at CERN. While general expressions exist in frequency domain for the beam coupling impedance, the time domain wake function is typically obtained numerically, thanks to an inverse Fourier transform. An analytical expression for the indirect space charge wake function, including the time dependence as a function of particle velocity, is nevertheless highly desirable to improve the accuracy of time domain beam dynamics simulations of coherent instabilities. In this work, a general formula for the indirect space charge wake function is derived from the residue theorem. Moreover, simple approximated expressions reproducing the time and velocity dependence are also provided, which can even be corrected to recover an exact formula, thanks to a numerical factor computed once for all. The expressions obtained are successfully benchmarked with a purely numerical approach based on the Fourier transform.  
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DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-HB2021-MOP10  
About • Received ※ 30 September 2021 — Revised ※ 28 October 2021 — Accepted ※ 22 November 2021 — Issue date ※ 30 January 2022
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MOP12 Understanding of the CERN-SPS Horizontal Instability with Multiple Bunches 77
 
  • C. Zannini, H. Bartosik, M. Carlà, K.S.B. Li, E. Métral, G. Rumolo, B. Salvant
    CERN, Geneva, Switzerland
  • L.R. Carver
    ESRF, Grenoble, France
  • M. Schenk
    EPFL, Lausanne, Switzerland
 
  At the end of 2018, an instability with multiple bunches has been consistently observed during high intensity studies at the CERN-SPS. This instability could be a significant limitation to achieve the bunch intensity expected after the LHC Injector Upgrade (LIU). Therefore, a deep understanding of the phenomena is essential to identify the best mitigation strategy. Extensive simulation studies have been performed to explore the consistency of the current SPS model, give a possible interpretation of the instability mechanism and outline some possible cures.  
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DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-HB2021-MOP12  
About • Received ※ 07 October 2021 — Revised ※ 20 October 2021 — Accepted ※ 28 December 2021 — Issue date ※ 11 April 2022
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