Keyword: damping
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MOP15 Threshold for Loss of Longitudinal Landau Damping in Double Harmonic RF Systems impedance, synchrotron, simulation, dipole 95
 
  • L. Intelisano, H. Damerau, I. Karpov
    CERN, Meyrin, Switzerland
 
  Landau damping is a natural stabilization mechanism to mitigate coherent beam instabilities in the longitudinal phase space plane. In a single RF system, binominal particle distributions with a constant inductive impedance above transition (or capacitive below) would lead to a vanishing threshold for the loss of Landau damping, which can be avoided by introducing an upper cut-off frequency to the impedance. This work aims at expanding the recent loss of Landau damping studies to the common case of double harmonic RF systems. Special attention has been paid to the configuration in the SPS with a higher harmonic RF system at four times the fundamental RF frequency, and with both RF systems in counter-phase (bunch shortening mode). Refined analytical estimates for the synchrotron frequency distribution allowed to extend the analytical expression for the loss of Landau damping threshold. The results are compared with semi-analytical calculations using the MELODY code, as well as with macroparticle simulations in BLonD.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-HB2021-MOP15  
About • Received ※ 16 October 2021 — Revised ※ 19 October 2021 — Accepted ※ 05 February 2022 — Issue date ※ 11 April 2022
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MOP16 New Analytical Criteria for Loss of Landau Damping in Longitudinal Plane impedance, synchrotron, space-charge, dipole 100
 
  • I. Karpov, T. Argyropoulos, E.N. Shaposhnikova
    CERN, Meyrin, Switzerland
  • S. Nese
    University of Bergen, Bergen, Norway
 
  Landau damping is a very important stabilization mechanism of beams in circular hadron accelerators. In the longitudinal plane, Landau damping is lost when the coherent mode is outside of the incoherent synchrotron frequency spread. In this paper, the threshold for loss of Landau damping (LLD) for constant inductive impedance ImZ/k is derived using the Lebedev matrix equation (1968). The results are confirmed by direct numerical solutions of the Lebedev equation and using the Oide-Yokoya method (1990). For more realistic impedance models of the ring, new definitions of an effective impedance and the corresponding cutoff frequency are introduced which allow using the same analytic expression for the LLD threshold. We also demonstrate that this threshold is significantly overestimated by the Sacherer formalism based on the previous definition of an effective impedance using the eigenfunctions of the coherent modes.  
DOI • reference for this paper ※ https://doi.org/10.18429/JACoW-HB2021-MOP16  
About • Received ※ 16 October 2021 — Revised ※ 24 October 2021 — Accepted ※ 02 December 2021 — Issue date ※ 11 April 2022
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