Report of the working group on single-particle nonlinear dynamics

Bazzani, Armando; Bongini, Lorenzo; Corbett, Jeff; Dome, G.; Fedorova, Antonina N.; Freguglia, Paolo; Ng, K.; Ohmi, K.; Owen, Hywel; Papaphilippou, Y.; Robin, D.; Safranek, J.; Scandale, W.; Terebilo, A.; Turchetti, G.; Todesco, E.; Warnock, Robert; Zeitlin, Michael G.

doi:10.1063/1.58424

Cited by 2 publications

(5 citation statements)

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“…The linear motion is parametrised by the three Twiss parameters [27] β z (s), α z (s), γ z (s), where z = x, y for horizontal or vertical motion, respectively, and s represents the path length from the reference section of the ring. Under the assumption that the non-linear elements are represented as single kicks [28], the so-called Poincaré map (see Ref. [28] and references therein), can be written in the form of a polynomial map [17]…”

Section: Numerical Model For Generating Multimode Beamsmentioning

confidence: 99%

“…Under the assumption that the non-linear elements are represented as single kicks [28], the so-called Poincaré map (see Ref. [28] and references therein), can be written in the form of a polynomial map [17]…”

Section: Numerical Model For Generating Multimode Beamsmentioning

confidence: 99%

“…with κ, χ real parameters, the latter representing the ratio β y /β x at the location of the sextupoles and octupoles. The map (1) is a Hénon-like [29] map in 4D, and the components of the vector (X, X , Y, Y ) are dimensionless coordinates [28] allowing to set the coefficient of the quadratic term of the map (1)…”

Section: Numerical Model For Generating Multimode Beamsmentioning

confidence: 99%

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Numerical simulations of electron cloud build-up in circular accelerators in the presence of multimode distribution beams

Cui

Gilardoni

Giovannozzi

et al. 2020

EPL

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Electron cloud effects have become one of the main performance limitations for circular particle accelerators operating with positively-charged beams. Among other machines worldwide, the CERN Super Proton Synchrotron (SPS), as well as the Large Hadron Collider (LHC) are affected by these phenomena. Intense efforts have been devoted in recent years to improve the understanding of electron cloud (EC) generation with the aim of finding efficient mitigation measures. In a different domain of accelerator physics, non-linear resonances in the transverse phase space have been proposed as novel means of manipulating charged particle beams. While the original goal was to perform multi-turn extraction from the CERN Proton Synchrotron (PS), several other applications have been proposed. In this paper, the study of EC generation in the presence of charged particle beams with multimode horizontal distribution is presented. Such a peculiar distribution can be generated by different approaches, one of which consists in splitting the initial Gaussian beam distribution by crossing a non-linear resonance. In this paper, the outcome of detailed numerical simulations is presented and discussed.

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Section: Numerical Model For Generating Multimode Beamsmentioning

confidence: 99%

Section: Numerical Model For Generating Multimode Beamsmentioning

confidence: 99%

Section: Numerical Model For Generating Multimode Beamsmentioning

confidence: 99%

See 1 more Smart Citation

Numerical simulations of electron cloud build-up in circular accelerators in the presence of multimode distribution beams

Cui

Gilardoni

Giovannozzi

et al. 2020

EPL

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“…The infinite series (6) is not convergent by construction. Furthermore, the number of terms grows very sharply with the order n = j + k + l + m [1][2][3]. In practice, one takes a truncated expression of the series (6), and in our case, we usually found sufficient to carry out the calculation of the perturbing series up to 12th order which corresponds to an 11th order map.…”

Section: Graphical Representation Of Resonances a Resonance Strengthmentioning

confidence: 99%

“…The necessary insight regarding the system's non-linear dynamics can be given by applying the methods of high order perturbation theory [1][2][3]. These approaches can be conducted by using an explicit form of the system's Poincaré map.…”

Section: Introductionmentioning

confidence: 99%

Normal form approaches and resonance analysis of LHC models

Papaphilippou¹,

Schmidt²

1999

AIP Conference Proceedings

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In order to understand the dynamic aperture limitations in LHC optics versions 4 and 5 at injection energy (450 GeV), a thorough resonance analysis is performed through Lie perturbation methods and Normal Form construction. In this respect, a simple numerical tool has been developed, the Graphical Representation of Resonances (GRR), allowing the evaluation and graphical representation of the resonance strengths and detuning, up to a desired order. The resonance analysis performed by means of GRR enabled us to understand the effect of the large errors in some special quadrupoles of LHC optics version 5. We were also able to identify and minimise the resonance which was correlated with the drop of the dynamic aperture, following the introduction of a large skew octupole bias in the LHC optics version 5, using the "target" error table. As shown by subsequent tracking studies, the proposed correction procedures led to a considerable improvement of the dynamic aperture of the studied LHC models.

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Report of the working group on single-particle nonlinear dynamics

Cited by 2 publications

References 0 publications

Numerical simulations of electron cloud build-up in circular accelerators in the presence of multimode distribution beams

Numerical simulations of electron cloud build-up in circular accelerators in the presence of multimode distribution beams

Normal form approaches and resonance analysis of LHC models

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