Maxwell's Equations and Boundary Value Problems in Magnetostatics

Russenschuck, Stephan

doi:10.1002/9783527635467.ch4

Cited by 2 publications

(2 citation statements)

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“…Let us briefly introduce the concepts of differential geometry required for accelerator magnet design; for details and derivations see [17,Chapter 19], [12], and the appendix of [16]. The conductor geometry is defined by the baseline r(t) : R → R 3 , to which the triad of vectors (T (t), N (t), B(t)) is attached.…”

Section: Differential Geometry For Coil Designmentioning

confidence: 99%

Coil Design for Strongly Curved Magnets Based on the Differential Geometry of the Frenet Frame

Liebsch,

Russenschuck

2024

IEEE Trans. Appl. Supercond.

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Recent accelerator projects for radiation-therapy centers demand strongly curved magnets in transfer lines and gantries. Several advances have been achieved in designing and manufacturing strongly curved, cosine-theta, and canted-cosinetheta type magnets. This paper presents a new computer-aided design (CAD) engine for generating coil geometries for various types of mandrel surfaces (elliptical, curved, conical) and interfacing with field simulation software as well as CAD tools. The CAD engine is based on the differential geometry of the Frenet frame and allows the analytical computation of the curvature parameters, such as curvature, twist, and torsion. Applying the theory of developable surfaces it is possible to generate conductor geometries with zero Gaussian curvature, which are particularly interesting for strain-sensitive supercondors such as high-temperature superconductor tapes.

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Section: Differential Geometry For Coil Designmentioning

confidence: 99%

Coil Design for Strongly Curved Magnets Based on the Differential Geometry of the Frenet Frame

Liebsch,

Russenschuck

2024

IEEE Trans. Appl. Supercond.

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“…Moving a single wire loop surface A with the velocity v in a static magnetic field B, induces the voltage [12] U ind (t) =…”

Section: Rotating Coil Measurementsmentioning

confidence: 99%

Local field reconstruction from rotating coil measurements in particle accelerator magnets

Ion,

Liebsch,

Simona

et al. 2021

Preprint

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In this paper a general approach to reconstruct three dimensional field solutions in particle accelerator magnets from distributed magnetic measurements is presented. To exploit the locality of the measurement operation a special discretization of the Laplace equation is used. Extracting the coefficients of the field representations yields an inverse problem which is solved by Bayesian inversion. This allows not only to pave the way for uncertainty quantification, but also to derive a suitable regularization. The approach is applied to rotating coil measurements and can be extended to any other measurement procedure.

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Maxwell's Equations and Boundary Value Problems in Magnetostatics

Cited by 2 publications

References 12 publications

Coil Design for Strongly Curved Magnets Based on the Differential Geometry of the Frenet Frame

Coil Design for Strongly Curved Magnets Based on the Differential Geometry of the Frenet Frame

Local field reconstruction from rotating coil measurements in particle accelerator magnets

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