| Article | |
| Report number | arXiv:2208.11519 |
| Title | Hamiltonian theory of the crossing of the $2 Q_x -2 Q_y=0$ nonlinear coupling resonance |
| Related title | Hamiltonian theory of the crossing of the 2Qx-2Qy=0 nonlinear coupling resonance |
| Author(s) | Bazzani, A. (U. Bologna, DIFA ; INFN, Bologna) ; Capoani, F. (U. Bologna, DIFA ; INFN, Bologna ; CERN) ; Giovannozzi, M. (CERN) |
| Publication | 2022-10-03 |
| Imprint | 2022-08-24 |
| Number of pages | 21 |
| In: | Phys. Rev. Accel. Beams 25 (2022) 104001 |
| DOI | 10.1103/PhysRevAccelBeams.25.104001 (publication) |
| Subject category | physics.acc-ph ; math.DS ; Accelerators and Storage Rings ; Mathematical Physics and Mathematics |
| Abstract | In a recent paper, the adiabatic theory of Hamiltonian systems was successfully applied to study the crossing of the linear coupling resonance, $Q_x-Q_y=0$. A detailed explanation of the well-known phenomena that occur during the resonance-crossing process, such as emittance exchange and its dependence on the adiabaticity of the process was obtained. In this paper, we consider the crossing of the resonance of nonlinear coupling $2 Q_x -2 Q_y = 0$ using the same theoretical framework. We perform the analysis using a Hamiltonian model in which the nonlinear coupling resonance is excited and the corresponding dynamics is studied in detail, in particular looking at the phase-space topology and its evolution, in view of characterizing the emittance exchange phenomena. The theoretical results are then tested using a symplectic map. Thanks to this approach, scaling laws of general interest for applications are derived. |
| Copyright/License | preprint: (License: arXiv nonexclusive-distrib 1.0) publication: © 2022-2024 authors (License: CC BY 4.0) |
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Record created 2022-11-02, last modified 2023-08-09
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