Computation of the Biot–Savart line integral with higher-order convergence using straight segments

McGreivy, N.; Zhu, C.; Gunderson, L. M.; Hudson, S. R.

doi:10.1063/5.0058014

Computation of the Biot–Savart line integral with higher-order convergence using straight segments

Journal Article · Mon Aug 16 00:00:00 EDT 2021 · Physics of Plasmas

DOI:https://doi.org/10.1063/5.0058014· OSTI ID:1817216

^[1]; Zhu, C. ^[2]; Gunderson, L. M. ^[3]; Hudson, S. R. ^[2]

Princeton Univ., NJ (United States); Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Princeton Plasma Physics Lab. (PPPL), Princeton, NJ (United States)
Univ. College London (United Kingdom)

One common approach to computing the magnetic field produced by a filamentary current-carrying coil is to approximate the coil as a series of straight segments. The Biot–Savart field from each straight segment is analytically known. However, if the endpoints of the straight segments are chosen to lie on the coil, then the accuracy of the Biot–Savart computation is generally only the second order in the number of endpoints. In this work, we propose a simple modification: shift each end point of the coil in the outward normal direction by an amount proportional to the local curvature. With this modification, the Biot–Savart accuracy increases to the fourth order and the numerical error is dramatically reduced for a given number of discretization points.

Research Organization:: Princeton Plasma Physics Laboratory (PPPL), Princeton, NJ (United States)

Sponsoring Organization:: USDOE

Grant/Contract Number:: AC02-09CH11466

OSTI ID:: 1817216

Journal Information:: Physics of Plasmas, Journal Name: Physics of Plasmas Journal Issue: 8 Vol. 28; ISSN 1070-664X

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

References (11)

An improvement in the calculation of the magnetic field for an arbitrary geometry coil with rectangular cross section I. Babic, Slobodan; Akyel, Cevdet International Journal of Numerical Modelling: Electronic Networks, Devices and Fields, Vol. 18, Issue 6 https://doi.org/10.1002/jnm.594	journal	January 2005
A new version of the Fast Multipole Method for the Laplace equation in three dimensions Greengard, Leslie; Rokhlin, Vladimir Acta Numerica, Vol. 6 https://doi.org/10.1017/S0962492900002725	journal	January 1997
Confirmation of the topology of the Wendelstein 7-X magnetic field to better than 1:100,000 Pedersen, T. Sunn; Otte, M.; Lazerson, S. Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms13493	journal	November 2016
Compact expressions for the Biot–Savart fields of a filamentary segment Hanson, James D.; Hirshman, Steven P. Physics of Plasmas, Vol. 9, Issue 10 https://doi.org/10.1063/1.1507589	journal	October 2002
New method to design stellarator coils without the winding surface Zhu, Caoxiang; Hudson, Stuart R.; Song, Yuntao Nuclear Fusion, Vol. 58, Issue 1 https://doi.org/10.1088/1741-4326/aa8e0a	journal	November 2017
Vector potential and magnetic field of current-carrying circular finite arc segment in analytical form. V. Polygon cross section Urankar, L. IEEE Transactions on Magnetics, Vol. 26, Issue 3 https://doi.org/10.1109/20.53995	journal	May 1990
Vector potential and magnetic field of current-carrying finite arc segment in analytical form, Part I: Filament approximation Urankar, L. IEEE Transactions on Magnetics, Vol. 16, Issue 5 https://doi.org/10.1109/TMAG.1980.1060864	journal	September 1980
Vector potential and magnetic field of current-carying finite arc segment in analytical form, part II: Thin sheet approximation Urankar, L. IEEE Transactions on Magnetics, Vol. 18, Issue 3 https://doi.org/10.1109/TMAG.1982.1061927	journal	May 1982
Vector potential and magnetic field of current-carrying finite arc segment in analytical form, Part III: Exact computation for rectangular cross section Urankar, L. IEEE Transactions on Magnetics, Vol. 18, Issue 6 https://doi.org/10.1109/TMAG.1982.1062166	journal	November 1982
Vector potential and magnetic field of current-carrying finite arc segment in analytical form, part IV: General three-dimensional current density Urankar, L. IEEE Transactions on Magnetics, Vol. 20, Issue 6 https://doi.org/10.1109/TMAG.1984.1063579	journal	November 1984
Vector Potential and Magnetic Field of Current-carrying Finite Elliptic Arc Segment in Analytical Form Urankar, L. Zeitschrift für Naturforschung A, Vol. 40, Issue 11 https://doi.org/10.1515/zna-1985-1101	journal	November 1985

Similar Records

Biot--Savart formula for an equilibrium plasma

Journal Article · Wed Sep 01 00:00:00 EDT 1982 · Sov. Phys. - Dokl. (Engl. Transl.); (United States) · OSTI ID:5904465

Performance of low-rank QR approximation of the finite element Biot-Savart law

Conference · Wed Jan 11 23:00:00 EST 2006 · OSTI ID:885135

Modeling the APLE injector solenoid magnetic field with the Biot-Savart Law

Conference · Tue Dec 31 23:00:00 EST 1991 · OSTI ID:6855659

Related Subjects

70 PLASMA PHYSICS AND FUSION TECHNOLOGY
electromagnetism
integral calculus
numerical methods
power series
stellarators
tokamaks
vector calculus

Computation of the Biot–Savart line integral with higher-order convergence using straight segments

Citation Formats

References (11)

Similar Records

Related Subjects