JACoW is a publisher in Geneva, Switzerland that publishes the proceedings of accelerator conferences held around the world by an international collaboration of editors.
TY - CONF AU - Karpov, I. AU - Argyropoulos, T. AU - Nese, S. AU - Shaposhnikova, E.N. ED - Gianfelice, Eliana ED - Nagaitsev, Sergei ED - Kim, Dong Eon ED - Marx, Michaela ED - Schaa, Volker R. W. TI - New Analytical Criteria for Loss of Landau Damping in Longitudinal Plane J2 - Proc. of HB2021, Batavia, IL, USA, 04-08 October 2021 CY - Batavia, IL, USA T2 - ICFA ABDW on High-Intensity and High-Brightness Hadron Beams T3 - 64 LA - english AB - 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. PB - JACoW Publishing CP - Geneva, Switzerland SP - 100 EP - 105 KW - impedance KW - synchrotron KW - damping KW - space-charge KW - dipole DA - 2022/04 PY - 2022 SN - 2673-5571 SN - 978-3-95450-225-7 DO - doi:10.18429/JACoW-HB2021-MOP16 UR - https://jacow.org/hb2021/papers/mop16.pdf ER -