Third-order aberrations of a magnetic quadrupole lens

Lee-Whiting, G.E.

doi:10.1016/0029-554x(70)90465-9

Cited by 32 publications

(11 citation statements)

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“…Since the early analytical studies of Lee-Whiting [15] and Forest [2,3], significant progress has been achieved for the construction of accurate maps which represent the motion of particles through the magnet fringe field, using either direct numerical evaluation with exact integration of the magnetic field [16,17] or parameter fit of an adequate function [18,19,20] (e.g. the Enge function [21]).…”

Section: Discussionmentioning

confidence: 99%

Deflections in magnet fringe fields

2003

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A transverse multipole expansion is derived, including the longitudinal components necessarily present in regions of varying magnetic field profile. It can be used for exact numerical orbit following through the fringe field regions of magnets whose end designs introduce no extraneous components, i.e. fields not required to be present by Maxwell's equations. Analytic evaluations of the deflections are obtained in various approximations. Mainly emphasized is a "straight-line approximation", in which particle orbits are treated as straight lines through the fringe field regions.This approximation leads to a readily-evaluated figure of merit, the ratio of r.m.s. end deflection to nominal body deflection, that can be used to determine whether or not a fringe field can be neglected. Deflections in "critical" cases (e.g. near intersection regions) are analysed in the same approximation. * Present address: European Synchrotron Radiation Facility,

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Section: Discussionmentioning

confidence: 99%

Deflections in magnet fringe fields

2003

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“…In others, the first-order effect is characterized by a kick [1], or as a sudden change in position and momentum at the so-called effective field boundary [4]. Here, using the 30 GeV Neutrino Factory lattice, we compute with COSY INFINITY the linear tunes and chromaticities as a function of the magnet apertures.…”

Section: Aperture Dependent Effects On Linear Tunes and Chromatimentioning

confidence: 99%

“…However, strictly speaking, it is an unphysical model, as the electromagnetic fields of the model do not satisfy Maxwell's equations. The simplest method to take fringe fields into account is to approximate their effect with a kick characterized by the integrated field value [1]. While this model may alleviate some problems, it is not a cure, and more sophisticated models are needed for accurate simulations.…”

Section: Introductionmentioning

confidence: 99%

Fringe field effects in small rings of large acceptance

Berz

Erdélyi

Makino

2000

Phys. Rev. ST Accel. Beams

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Recently there has been renewed interest in the influence of fringe fields on particle dynamics, due to studies that revealed their importance in some cases, as, for example, the proposed Neutrino Factory and muon colliders. In this paper, we present a systematic study of generic fringe field effects. Using as an example a lattice of the proposed Neutrino Factory, we show that fringe fields influence the dynamics of particles at all orders, starting with the linear motion. It is found that the widely used sharp cutoff approximation leads to divergences regardless of the specific fall-off shape of the fields. The results suggest that a careful consideration of fringe field effects in the design stage of small machines for large emittances is always recommended.

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“…(See Smith [2], Lee-Whiting [3], Matsuda & Wollnik [4], Nakabushi & Matsuo [5].) Often, these coefficients are expressed in the on-axis r-derivatives of the field of such devices.…”

Section: Analytical Resultsmentioning

confidence: 99%

“…From Maxwell's equations for the static electromagnetic field, we find that, for a magnetic fieldB in a region without free charges or currents, there exists a scalar potential u, and a vector potentialÃ, satisfying: grad u =B = curlÃ; (1) ࣽu = 0 ; (2) curl curlÃ =0: (3) The vector potentialÃ will be chosen such that divÃ = 0 . In this case, we have ࣽÃ =0.…”

Section: Introductionmentioning

confidence: 99%

Computing transfer functions of multipole devices directly from magnetic field data, including fringe field effects and higher order aberrations

Trines

Botman²,

Eijndhoven³

et al.

Proceedings of the 1999 Particle Accelerator Conference (Cat. No.99CH36366)

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The scalar and vector potentials of a magnetic multipole device are described in terms of magnetic field measurements gathered on either a cylindrical surface or a median plane [1]. Fringe field effects and multipole contributions of arbitrary order, as well as the discrete nature of the field measurements, are taken into account. This description has been used to calculate the transfer function of the device, directly in terms of the field measurements. The method as described in this paper can be applied to single beam guiding elements as well as to clusters of elements, and can be extended to calculate the transfer function for a complete beam line setup or a storage ring. The accuracy of the results is only limited by the accuracy of the field measurements.

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Third-order aberrations of a magnetic quadrupole lens

Cited by 32 publications

References 1 publication

Deflections in magnet fringe fields

Deflections in magnet fringe fields

Fringe field effects in small rings of large acceptance

Computing transfer functions of multipole devices directly from magnetic field data, including fringe field effects and higher order aberrations

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