Evolution of Beam Distribution in Crossing a Walkinshaw Resonance

Lee, S. Y.; Ng, K.Y.; Liu, H.; Chao, Hung-Chun

doi:10.1103/physrevlett.110.094801

Cited by 14 publications

(15 citation statements)

References 8 publications

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“…The separatrix that passes through the unstable fixed points on the border of the allowed circle is called coupling arc (as in Ref. [20]), and is found by solving the equation…”

Section: Phase-space Topology Of the Hamiltonian Modelmentioning

confidence: 99%

“…The source of inspiration is the analysis of the impact of crossing the Walkinshaw, i.e. ω x − 2ω y = 0, resonance [20,21], and for the 2ω x − ω y resonance [22]. However, the focus of the analysis performed in Ref.…”

Section: Introductionmentioning

confidence: 99%

“…However, the focus of the analysis performed in Ref. [20] was to estimate the undesired emittance growth due to the resonance crossing, whereas our aim is to intentionally manipulate the transverse emittances for specific applications.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Manipulation of transverse emittances in circular accelerators by crossing non-linear 2D resonances

Bazzani¹,

Capoani²,

Giovannozzi³

2022

Preprint

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Controlling non-linear effects in the transverse dynamics of charged particle beams in circular accelerators opens new possibilities for controlling some of the beam properties. Beam splitting by crossing a stable 1D non-linear resonance is part of the routine operation of the CERN Proton Synchrotron. The beam undergoes trapping and transport inside stable islands created in the horizontal plane to allow multi-turn extraction towards the Super Proton Synchrotron, where the beam is used for fixed-target experiments. This process acts only on the horizontal beam emittance, inducing a reduction of its initial value. In this paper, we present a generalisation of this approach, in which both transverse planes are affected by the proposed technique. We will discuss in detail how to manipulate the transverse emittances by means of a controlled crossing of a 2D non-linear resonance. The novel technique will be presented by discussing the theoretical analysis of a Hamiltonian model, as well as simulating the performance of the proposed manipulation using a more realistic non-linear symplectic map.

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“…The separatrix that passes through the unstable fixed points on the border of the allowed circle is called coupling arc (as in Ref. [20]), and is found by solving the equation…”

Section: Phase-space Topology Of the Hamiltonian Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Manipulation of transverse emittances in circular accelerators by crossing non-linear 2D resonances

Bazzani¹,

Capoani²,

Giovannozzi³

2022

Preprint

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show abstract

“…It is well known [31] that the most important nonlinear effects in the next order are the amplitude-dependent tune shifts,…”

Section: Tune Shiftsmentioning

confidence: 99%

Single-particle dynamics in theoretical minimum emittance cell

Cai

2018

Phys. Rev. Accel. Beams

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We have developed a parametrization of the linear optics in a theoretical minimum emittance cell with three quadrupoles. It consists of five independent parameters: two phase advances, a dimensionless horizontal beta function at the center of the dipole, and a bending angle ϕ and a length L of the dipole. For the zero chromaticity cell, we again find that the dynamic aperture in the normalized phase space is scaled according to,Ā ∝ ϕ ffiffiffi ffi L p. Moreover, we study nonlinear dynamics near the third-order coupled resonances in the framework of the resonance normal form. In particular, we derive the effective Hamiltonians using the Lie algebra method and show that the periodic orbits in tracking can be interpreted as solutions of the Hamilton's equations. Surprisingly, we discover that the scheme is not only applicable to the single resonance but also to the double resonances.

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“…Additionally, in 1970 Pellegrini and Sessler developed a formalism for calculating the displacement and width of a bunch of particles passing through an integer resonance by additional focusing (and the corresponding tune shift) produced by the ions trapped in the storage ring [13]. The authors calculated betatron amplitude growth rates [14,15] and presented the emittance growth factor [16][17][18] for particles traversing different resonances. Lysenko [15] analyzed betatron amplitude growth in the cases when the particle tune is fixed, moves along a single resonance line or crosses an isolated resonance.…”

Section: Introductionmentioning

confidence: 99%

Lossless crossing of a resonance stopband during tune modulation by synchrotron oscillations

et al. 2017

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Modern high performance circular accelerators require sophisticated corrections of nonlinear lattices. The beam betatron tune footprint may cross many resonances, reducing dynamic aperture and causing particle loss. However, if particles cross a resonance reasonably fast, the beam deterioration may be minimized. This paper describes the experiments with the beam passing through a half-integer resonance stopband via tune modulation by exciting synchrotron oscillations. This is the first time that beam dynamics have been kept under precise control while the beam crosses a half-integer resonance. Our results convincingly demonstrate that particles can cross the half-integer resonance without being lost if the passage is reasonably fast and the resonance stopband is sufficiently narrow.

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Evolution of Beam Distribution in Crossing a Walkinshaw Resonance

Cited by 14 publications

References 8 publications

Manipulation of transverse emittances in circular accelerators by crossing non-linear 2D resonances

Manipulation of transverse emittances in circular accelerators by crossing non-linear 2D resonances

Single-particle dynamics in theoretical minimum emittance cell

Lossless crossing of a resonance stopband during tune modulation by synchrotron oscillations

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