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.

Hamiltonian theory of the crossing of the 2Qx−2Qy=0 nonlinear coupling resonance / A. Bazzani; F. Capoani; M. Giovannozzi. - In: PHYSICAL REVIEW. ACCELERATORS AND BEAMS. - ISSN 2469-9888. - STAMPA. - 25:10(2022), pp. 104001.1-104001.21. [10.1103/PhysRevAccelBeams.25.104001]

Hamiltonian theory of the crossing of the 2Qx−2Qy=0 nonlinear coupling resonance

A. Bazzani
Supervision
;
F. Capoani
Investigation
;
2022

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.
2022
Hamiltonian theory of the crossing of the 2Qx−2Qy=0 nonlinear coupling resonance / A. Bazzani; F. Capoani; M. Giovannozzi. - In: PHYSICAL REVIEW. ACCELERATORS AND BEAMS. - ISSN 2469-9888. - STAMPA. - 25:10(2022), pp. 104001.1-104001.21. [10.1103/PhysRevAccelBeams.25.104001]
A. Bazzani; F. Capoani; M. Giovannozzi
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/908681
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