APS : Adiabaticity of emittance exchange due to crossing of the coupling resonance

Bazzani, A.; Capoani, F.; Giovannozzi, M.; Neishtadt, A.I.

doi:10.1103/PhysRevAccelBeams.24.094002

Article
Report number	arXiv:2105.04219
Title	Adiabaticity of emittance exchange due to crossing of the coupling resonance
Related title	On the adiabaticity of emittance exchange due to crossing of the coupling resonance
Author(s)	Bazzani, A. (Bologna U., Dept. Astron.) ; Capoani, F. (Bologna U., Dept. Astron. ; CERN) ; Giovannozzi, M. (CERN) ; Neishtadt, A.I. (Loughborough U. ; IMCS, Moscow)
Publication	2021-09-01
Imprint	2021-05-10
Number of pages	21
In:	Phys. Rev. Accel. Beams 24 (2021) 094002
DOI	10.1103/PhysRevAccelBeams.24.094002 (publication)
Subject category	physics.acc-ph ; Accelerators and Storage Rings
Abstract	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 for Hamiltonian mechanics, which explains in detail various features of the emittance exchange process.
Copyright/License	preprint: (License: CC BY 4.0) publication: © 2021-2025 authors (License: CC BY 4.0)

$Phase-space portraits of the Hamiltonian~\eqref{eq:ham_fundamental} for $q=1$ and $\delta=1$ (top), $\delta=0$ (center), and $\delta=-1$ (bottom) in three different representations: action-angle co-ordinates $(\phi,\, J)$ on the left column, Cartesian co-ordinates $(X=\sqrt{2J}\sin\phi,\,Y=\sqrt{2J}\cos\phi)$ in the central column, and on a spherical surface (as described in Section~\ref{sec:sphere}) on the right column, where the coordinate $\phi$ is the polar angle while the azimuthal angle is given by $\theta = \asin(2J-1)$. The red line represents the critical curve (the so-called {\sl coupling arc} in Refs.~\cite{Lee:2651939,PhysRevLett.110.094801}). The plots on the left column are the equirectangular projections of the spherical surface, the poles being represented by the $J=0$ and $J=1$ lines while the plots on the central column are the azimuthal representations centered around the south pole. Note that the artificially-large value of $q$, together with large values of $\delta$ and of $J$, is used to make more visible the key features of the phase-space portrait.$ $Phase-space portraits of the Hamiltonian~\eqref{eq:ham_fundamental} for $q=1$ and $\delta=1$ (top), $\delta=0$ (center), and $\delta=-1$ (bottom) in three different representations: action-angle co-ordinates $(\phi,\, J)$ on the left column, Cartesian co-ordinates $(X=\sqrt{2J}\sin\phi,\,Y=\sqrt{2J}\cos\phi)$ in the central column, and on a spherical surface (as described in Section~\ref{sec:sphere}) on the right column, where the coordinate $\phi$ is the polar angle while the azimuthal angle is given by $\theta = \asin(2J-1)$. The red line represents the critical curve (the so-called {\sl coupling arc} in Refs.~\cite{Lee:2651939,PhysRevLett.110.094801}). The plots on the left column are the equirectangular projections of the spherical surface, the poles being represented by the $J=0$ and $J=1$ lines while the plots on the central column are the azimuthal representations centered around the south pole. Note that the artificially-large value of $q$, together with large values of $\delta$ and of $J$, is used to make more visible the key features of the phase-space portrait.$ $Phase-space portraits of the Hamiltonian~\eqref{eq:ham_fundamental} for $q=1$ and $\delta=1$ (top), $\delta=0$ (center), and $\delta=-1$ (bottom) in three different representations: action-angle co-ordinates $(\phi,\, J)$ on the left column, Cartesian co-ordinates $(X=\sqrt{2J}\sin\phi,\,Y=\sqrt{2J}\cos\phi)$ in the central column, and on a spherical surface (as described in Section~\ref{sec:sphere}) on the right column, where the coordinate $\phi$ is the polar angle while the azimuthal angle is given by $\theta = \asin(2J-1)$. The red line represents the critical curve (the so-called {\sl coupling arc} in Refs.~\cite{Lee:2651939,PhysRevLett.110.094801}). The plots on the left column are the equirectangular projections of the spherical surface, the poles being represented by the $J=0$ and $J=1$ lines while the plots on the central column are the azimuthal representations centered around the south pole. Note that the artificially-large value of $q$, together with large values of $\delta$ and of $J$, is used to make more visible the key features of the phase-space portrait.$ Show more plots

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记录创建於2021-05-12，最後更新在2021-10-02

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