Dynamic aperture extrapolation in the presence of tune modulation

Giovannozzi, M.; Scandale, W.; Todesco, E.

doi:10.1103/physreve.57.3432

Cited by 37 publications

(75 citation statements)

References 15 publications

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“…However, for most practical purposes it is found [39,40] that an approximate boundary exists between stable and unstable motion, and the particle amplitude at which this boundary occurs is termed the dynamic aperture by analogy with the real physical machine aperture.…”

Section: Dynamic Aperture Algorithms For Ffagsmentioning

confidence: 99%

The PyZgoubi framework and the simulation of dynamic aperture in fixed-field alternating-gradient accelerators

Tygier¹,

Appleby²,

Garland³

et al. 2015

Nuclear Instruments and Methods in Physics Research Section A:

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a b s t r a c tWe present PyZgoubi, a framework that has been developed based on the tracking engine Zgoubi to model, optimise and visualise the dynamics in particle accelerators, especially fixed-field alternatinggradient (FFAG) accelerators. We show that PyZgoubi abstracts Zgoubi by wrapping it in an easy-to-use Python framework in order to allow simple construction, parameterisation, visualisation and optimisation of FFAG accelerator lattices. Its object oriented design gives it the flexibility and extensibility required for current novel FFAG design. We apply PyZgoubi to two example FFAGs; this includes determining the dynamic aperture of the PAMELA medical FFAG in the presence of magnet misalignments, and illustrating how PyZgoubi may be used to optimise FFAGs. We also discuss a robust definition of dynamic aperture in an FFAG and show its implementation in PyZgoubi.

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Section: Dynamic Aperture Algorithms For Ffagsmentioning

confidence: 99%

The PyZgoubi framework and the simulation of dynamic aperture in fixed-field alternating-gradient accelerators

Tygier¹,

Appleby²,

Garland³

et al. 2015

Nuclear Instruments and Methods in Physics Research Section A:

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“…Based on the outcome of detailed numerical simulations for several accelerator models, in [18] a description of the time evolution of the dynamic aperture was proposed in the form of…”

Section: Original Model and Its Improvementmentioning

confidence: 99%

“…In Ref. [18] it was mentioned that in some conditions the fit parameters might become negative. This implies that, strictly speaking, for those cases the scaling law cannot be justified in terms of Nekhoroshev theorem, which is not satisfactory as we would like to propose a general scaling law for dynamic aperture supported by fundamental theorems of dynamical systems theory.…”

Section: Original Model and Its Improvementmentioning

confidence: 99%

“…Such a system can be made more complicated by introducing a time modulation of the linear frequencies. The reason to consider the modulated version of the 4D Hénon map in this context is twofold: on one hand the tune modulation takes into account the coupling with the longitudinal dynamics, on the other hand in [18] it was observed for the first time that for large values of the modulation amplitude , the proposed model for the DA scaling was providing negative values of the fit parameters.…”

Section: Generalitiesmentioning

confidence: 99%

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Advances on the modeling of the time evolution of dynamic aperture of hadron circular accelerators

Bazzani

Giovannozzi

Maclean

et al. 2019

Phys. Rev. Accel. Beams

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Determining a model for the time scaling of the dynamic aperture of a circular accelerator is a topic of strong interest and intense research efforts in accelerator physics. The motivation arises in the possibility of finding a method to reliably extrapolate the results of numerical simulations well beyond what is currently possible in terms of CPU time. In earlier work, a proposal for a model based on Nekhoroshev theorem and Kolmogorov-Arnold-Moser theory was made. This model has been studied in detail and proved successful in describing the evolution of the dynamic aperture in numerical simulations, however a number of shortcomings had been identified and new models are proposed in this paper, which solve the observed issues. The new models have been benchmarked against numerical simulations for a simple system, the 4D Hénon map, as well as a realistic, nonlinear representation of the beam dynamics in the LHC at 6.5 TeV providing in both cases excellent results.

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“…These studies are aided by methods for early determination of chaos. Such methods include evalu-ation of Lyapunov exponents [7], numerical calculation of resonance amplitudes [8], and use of normal form computations [9].…”

Section: Center For Integrated Plasma Studies and Department Of Physimentioning

confidence: 99%

Increasing the Dynamic Aperture of Accelerator Lattices

Wan

Cary

1998

Phys. Rev. Lett.

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A method for reducing chaotic dynamics in four-dimensional symplectic maps is presented. The method is to reduce certain chaos measures related to the invariants of the tangent map of fixed points. This method is applied to circular accelerators, where chaotic dynamics determines the dynamic aperture, the region of long-time stable orbits. A factor of 3 -4 increase in the phase-space volume of confined trajectories is obtained. [S0031-9007(98)07495-X] 41.85.Ja, 47.20.Ky We present a systematic method for reducing chaos in Hamiltonian systems of 2 1 2 degrees of freedom. Our method is to vary the system parameters so that the invariants of the tangent map at fixed points take on the values they would have at integrability. Our method, applied to accelerators, increased the phase-space volume of stable trajectories by nearly a factor of 4. As these methods are applicable to general 2.5 degrees-of-freedom Hamiltonian systems, they may improve a wide variety of similar systems, such as free-electron lasers and magnetic fusion devices, where chaos limits performance.An accelerator lattice is an example of a Hamiltonian system that is inherently nonlinear [1] and higher dimensional. Courant and Snyder [2] showed that for the linear motion in a lattice of magnetic quadrupoles of alternating polarity there can be confining invariants. For stability with error fields or natural nonlinearities, the tunes (the ratio of the transverse oscillation frequency to the frequency of circulation around the ring) must be far from low-order rationals [3]. For a range of energies to be confined, the chromaticity, or variation of tune with energy, must be reduced so that the tune remains far from low-order rationals over a range of energies. This is accomplished with sextupoles, nonlinear elements. Hence, though alternating gradient focusing is based on a linear concept, for its practical implementation the motion is nonlinear.Unfortunately, nonlinearity can cause the motion to be chaotic, so that particles wander through phase space until they hit the physical aperture, becoming lost. Since the relative strength of nonlinearities decreases as one moves towards the central design orbit, there is a nearby region, the dynamic aperture, of phase space filled with stable, well confined trajectories. Proton storage rings [4] must have sufficient dynamic aperture to operate. Larger dynamic aperture facilitates capture into an electron storage ring [5]. Hence, increasing dynamic aperture is important for both proton and electron rings.Tracking studies are used to assess and improve accelerators. Trajectories are followed for long times (e.g., 10 6 turns) in a computational model to determine the dynamic aperture [6]. These studies are aided by methods for early determination of chaos. Such methods include evalu-ation of Lyapunov exponents [7], numerical calculation of resonance amplitudes [8], and use of normal form computations [9].In this Letter we outline a systematic method for chaos reduction and, hence, dynamic aperture increase. Our...

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Dynamic aperture extrapolation in the presence of tune modulation

Cited by 37 publications

References 15 publications

The PyZgoubi framework and the simulation of dynamic aperture in fixed-field alternating-gradient accelerators

The PyZgoubi framework and the simulation of dynamic aperture in fixed-field alternating-gradient accelerators

Advances on the modeling of the time evolution of dynamic aperture of hadron circular accelerators

Increasing the Dynamic Aperture of Accelerator Lattices

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