In circular accelerators, crossing the linear coupling resonance induces the exchange of the transverse emittances, provided the process is adiabatic. This has been considered in some previous works, where the description of the phenomenon has been laid down, and more recently, where a possible explanation of the numerical results has been proposed. In this paper, we introduce a theoretical framework to analyze the crossing process, based on the theory of adiabatic invariance of Hamiltonian mechanics, which explains in detail various features of the emittance exchange process.

• Received 3 May 2021
• Accepted 9 September 2021

DOI:https://doi.org/10.1103/PhysRevAccelBeams.24.094002

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Published by the American Physical Society