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arXiv · 2208.11519

Hamiltonian theory of the crossing of the $2 Q_x -2 Q_y=0$ nonlinear coupling resonance

A. Bazzani·F. Capoani·M. Giovannozzi
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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.

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A. Bazzani, F. Capoani, M. Giovannozzi. 2022-08-24. Hamiltonian theory of the crossing of the $2 Q_x -2 Q_y=0$ nonlinear coupling resonance. https://arxiv.org/abs/2208.11519

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