Normal form approaches and resonance analysis of LHC models

Papaphilippou, Y.; Schmidt, F.

doi:10.1063/1.58427

Cited by 5 publications

(7 citation statements)

References 3 publications

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“…The tune spread produced by the kinematic nonlinearity-obtained by using either UAL / TEAPOT [34] or MARYLIE [35] and by analytical evaluation [36] based on perturbation theory -originates from the large g functions in the straight sections of the SNS ring. It is proportional to the 4th power of the particle transverse momenta (i.e., an octupolelike effect) and becomes noticeable in the SNS, which has a large-emittance beam.…”

Section: B Expected Tune Spreadsmentioning

confidence: 99%

Low-loss design for the high-intensity accumulator ring of the Spallation Neutron Source

Wei

Abell

Beebe‐Wang

et al. 2000

Phys. Rev. ST Accel. Beams

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This paper summarizes the low-loss design for the Spallation Neutron Source accumulator ring ["Spallation Neutron Source Design Manual" (unpublished)]. A hybrid lattice consisting of FODO arcs and doublet straights provides optimum matching and flexibility for injection and collimation. For this lattice, optimization focuses on six design goals: a space-charge tune shift low enough ( below 0.15) to avoid strong resonances, adequate transverse and momentum acceptance for efficient beam collimation, injection optimized for desired target beam shape and minimal halo development, compensation of magnet field errors, control of impedance and instability, and prevention against accidental system malfunction. With an expected collimation efficiency of more than 90%, the uncontrolled fractional beam loss is expected to be at the 10 24 level.

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Section: B Expected Tune Spreadsmentioning

confidence: 99%

Low-loss design for the high-intensity accumulator ring of the Spallation Neutron Source

Wei

Abell

Beebe‐Wang

et al. 2000

Phys. Rev. ST Accel. Beams

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“…An example of this normal form analysis for the LHC is shown in Fig. 1, where a numerical tool was built in order to evaluate and represent graphically resonance strengths up to any order 61 . In this plot, the 7th order resonance strengths are depicted, issued by a normal form analysis of a numerically constructed 11th order map, for a given amplitude, close to the minimum chaotic boundary of this LHC model.…”

Section: B Accelerator Maps and Normal Formsmentioning

confidence: 99%

Detecting chaos in particle accelerators through the frequency map analysis method

Papaphilippou¹

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.

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“…Another indicator of long-term stability is based on frequency analysis [13,14,[50][51][52]. Let ν x (1 : N) and ν y (1 : N) be the frequencies computed over the first N turns in the phase planes (x, p x ) and (y, p y ) respectively, then the tune difference is…”

Section: Tune Variationmentioning

confidence: 99%

Dynamic Aperture for Single-Particle Motion: Overview of Theoretical Background, Numerical Predictions and Experimental Results

Giovannozzi¹

2003

AIP Conference Proceedings

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Higher energies and higher intensities are the necessary conditions for the success of future accelerators. Higher energies need stronger external electromagnetic fields to guide, focus, and accelerate charged particles, while higher intensities result in source of intense selffields. In both cases, particle motion deviates considerably from a plain linear evolution as described by the classical Hill equation of transverse betatron motion. Particle stability becomes an issue: this problem can be properly tackled using tools from the nonlinear theory of dynamical systems. The concept of dynamic aperture for single-particle motion will be presented underlying links with the fundamental theorems of classical mechanics, such as KAM and Nekhoroshev theorems. Modern numerical techniques to compute the dynamic aperture will be discussed with special emphasis on accuracy analysis. Finally, measurements of particle stability in existing circular accelerators will be reviewed.

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Normal form approaches and resonance analysis of LHC models

Cited by 5 publications

References 3 publications

Low-loss design for the high-intensity accumulator ring of the Spallation Neutron Source

Low-loss design for the high-intensity accumulator ring of the Spallation Neutron Source

Detecting chaos in particle accelerators through the frequency map analysis method

Dynamic Aperture for Single-Particle Motion: Overview of Theoretical Background, Numerical Predictions and Experimental Results

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