Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics

Dragt, Alex J.; Neri, Filippo; Rangarajan, Govindan; Douglas, D.; Healy, Liam; Ryne, Robert D.

doi:10.1146/annurev.ns.38.120188.002323

Cited by 100 publications

(44 citation statements)

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“…One possible resolution scheme is to seek explicitly time-dependent canonical transformations in terms applied to different topics in the literature [250][251][252][253]. In particular, it has been extensively used to solve beam dynamics in particle accelerators [254,255]. However, the arguments in these exponentials correspond to a unique power of the expansion parameter.…”

Section: Classical Physicsmentioning

confidence: 99%

On the Fer expansion: Applications in solid-state nuclear magnetic resonance and physics

Mananga

2016

Physics Reports

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Section: Classical Physicsmentioning

confidence: 99%

On the Fer expansion: Applications in solid-state nuclear magnetic resonance and physics

Mananga

2016

Physics Reports

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“…We will collectively describe q 1 and p 1 by a single 2-vector z = (q 1 , p 1 ). The time evolution of this Hamiltonian system over time t can be represented by a symplectic map M [19] as follows We obtain a symplectic integration algorithm as follows. As described in I, we find another map J specified by the following product of P + 1 jolt maps…”

Section: Jolt Factorization In a Two-dimensional Phase Spacementioning

confidence: 99%

Jolt factorization of pendulum map

Rangarajan¹

1998

J. Phys. A: Math. Gen.

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“…It is worth emphasising that the problem of determining the DA, whether analytically or numerically, has fostered knowledge-transfer from other scientific fields, such as non-linear dynamical systems (see, e.g., the introduction and application of normal forms [13][14][15][16][17][18] in the eighties). It has also demanded an increased effort in the field of massive numerical simulations to gain insight to the DA characteristics, and direct measurements in existing machines (see, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Dynamic aperture computation for the as-built CERN Large Hadron Collider and impact of main dipoles sorting

Fartoukh

Giovannozzi

2012

Nuclear Instruments and Methods in Physics Research Section A:

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During the design phase of the CERN Large Hadron Collider the dynamic aperture, i.e., the amplitude of the domain in phase space where the particle motion is stable, was used as one of the most important figures-of-merit to specify the field quality of the various types of superconducting magnets and to quantify the machine performance. The programme of magnetic measurements performed during the production and acceptance testing of the magnets generated a large amount of information, which was used to obtain a best estimate of the dynamic aperture of the actual machine. In this paper the results of massive numerical simulations based on the measured field quality of several optical configurations and beam energies, are presented and discussed. The effect of the sorting of the main dipoles on the final value of the dynamic aperture has also been studied and the results are reviewed in detail. AbstractDuring the design phase of the CERN Large Hadron Collider the dynamic aperture, i.e., the amplitude of the domain in phase space where the particle motion is stable, was used as one of the most important figures-of-merit to specify the field quality of the various types of superconducting magnets and to quantify the machine performance. The programme of magnetic measurements performed during the production and acceptance testing of the magnets generated a large amount of information, which was used to obtain a best estimate of the dynamic aperture of the actual machine. In this paper the results of massive numerical simulations based on the measured field quality of several optical configurations and beam energies, are presented and discussed. The effect of the sorting of the main dipoles on the final value of the dynamic aperture has also been studied and the results are reviewed in detail.

show abstract

Lie Algebraic Treatment of Linear and Nonlinear Beam Dynamics

Cited by 100 publications

References 0 publications

On the Fer expansion: Applications in solid-state nuclear magnetic resonance and physics

On the Fer expansion: Applications in solid-state nuclear magnetic resonance and physics

Jolt factorization of pendulum map

Dynamic aperture computation for the as-built CERN Large Hadron Collider and impact of main dipoles sorting

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