Analytical expressions for magnetic fields and field gradients of current‐carrying triangles. Issue Volume 44:Issue1(2014) (February 2014)

• Record Type: Journal Article
• Authors: Forthmann, Peter; Amthor, Thomas
• Is Part Of: Concepts in magnetic resonance. Volume 44:Issue1(2014)
• Page Start: 18
• Page End: 25
• Publication Date: 2014-02
• Subjects: magnetic field -- field gradient -- stream function; Magnetic resonance -- Periodicals; Nuclear magnetic resonance -- Periodicals; Biomedical engineering -- Periodicals; Magnetic Resonance Spectroscopy -- Periodicals; 538.36
• DOI: 10.1002/cmr.b.21255
• Languages: English
• ISSNs: 1552-5031

Abstract

ABSTRACT: We present an analytical method for calculating magnetic field gradients generated by arbitrary triangulated surfaces. Our work builds upon the results published by Pissanetzky and Xiang, who presented formulas for calculating the magnetic field of current‐carrying faceted surfaces. We show that the analytical gradient expressions can be computed considerably faster than finite field value differences. We also find that the aforementioned published expressions for the magnetic field can be simplified and optimized substantially. Closer inspection of the algorithms, for both field and gradient, reveals a number pathological parameter constellations, which require special treatment. We present a detailed discussion on this. Our results can be directly applied in the optimization of complex magnetic field coils, such as magnetic resonance gradient coils. © 2014 Wiley Periodicals, Inc. Concepts Magn Reson Part B (Magn Reson Engineering) 44B: 18–25, 2014