主页 > Stability diagrams for Landau damping |
Published Articles | |
Title | Stability diagrams for Landau damping |
Author(s) | Berg, J Scott (Brookhaven Natl. Lab.) |
Publication | 2020 |
Number of pages | 5 |
In: | ICFA mini-Workshop on Mitigation of Coherent Beam Instabilities in Particle Accelerators (MCBI 2019), Zermatt, Switzerland, 23 - 27 Sep 2019, pp.40-44 (CERN-2020-009) |
DOI | 10.23732/CYRCP-2020-009.40 |
Subject category | Accelerators and Storage Rings |
Abstract | Stability diagrams allow one to determine whether a system is stable due to the presence of incoherent tune spread in a beam, a phenomenon known as Landau damping. This paper presents an overview of the mathematical foundations that underpin stability diagrams. I first describe stability diagrams as a mapping between two complex planes: the space of eigenvalues of the underlying Vlasov equation, and a space that can most easily be described as the product of beam current and an effective impedance. I go on to describe the circumstances when the Vlasov description of impedance-driven instabilities can or can not be formulated to construct a stability diagram. Finally I outline how this is applied to impedance-driven collective effects in particle accelerators. |
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