• Open Access

Hamiltonian theory of the crossing of the 2Qx2Qy=0 nonlinear coupling resonance

A. Bazzani, F. Capoani, and M. Giovannozzi
Phys. Rev. Accel. Beams 25, 104001 – Published 24 October 2022

Abstract

In a recent paper, the adiabatic theory of Hamiltonian systems was successfully applied to study the crossing of the linear coupling resonance, QxQy=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 2Qx2Qy=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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  • Received 13 August 2022
  • Accepted 7 October 2022

DOI:https://doi.org/10.1103/PhysRevAccelBeams.25.104001

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Accelerators & Beams

Authors & Affiliations

A. Bazzani1,2, F. Capoani1,2,3, and M. Giovannozzi3,*

  • 1Dipartimento di Fisica e Astronomia, Università di Bologna, via Irnerio 46, 40126 Bologna, Italy
  • 2INFN sezione di Bologna, Italy
  • 3Beams Department, CERN, Esplanade des Particules 1, 1211 Geneva 23, Switzerland

  • *Corresponding author. massimo.giovannozzi@cern.ch

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Issue

Vol. 25, Iss. 10 — October 2022

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