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Stability diagrams for Landau damping
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...
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Lenguaje: | eng |
Publicado: |
2020
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Materias: | |
Acceso en línea: | https://dx.doi.org/10.23732/CYRCP-2020-009.40 http://cds.cern.ch/record/2752327 |
Sumario: | 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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