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Formulation of the spherical harmonic coefficients of the entire magnetic field components generated by magnetic moment and current for shimming

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Title: Formulation of the spherical harmonic coefficients of the entire magnetic field components generated by magnetic moment and current for shimming
Authors: Noguchi, So Browse this author →KAKEN DB
Keywords: Magnetic fields
Ferromagnetic
materials
Magnetic moments
Magnets
Ferromagnetism
Issue Date: 28-Apr-2014
Publisher: American Institute of Physics
Journal Title: Journal of Applied Physics
Volume: 115
Issue: 16
Start Page: 163908
Publisher DOI: 10.1063/1.4872244
Abstract: For MRI and NMR magnet design, a highly homogeneous and high magnetic field has to be achieved by active and/or passive shimming. The active and passive shimming commonly homogenize the magnetic field around the magnet center by cancellation of the higher terms of a spherical harmonic series than the 0th term. So far, the spherical harmonic expression in the cylindrical coordinate system is well known for a circular coil, a solenoid coil, and magnetization of ferromagnetic material with/without its volume. In a shimming design, only the z-component of an inhomogeneous magnetic field is compensated because it is dominant to the performance of MRI/NMR. However, various kinds of MRI and NMR systems have recently been developed, and these magnets sometimes have an axially asymmetric configuration or generate a tilted magnetic field. Therefore, the entire x-, y-, and z-components have to be homogenized for such magnets. I derive the spherical harmonic expression of the entire components of magnetic field generated by a circular coil, a dipole coil, and a straight line current. In addition, since the entire magnetization components of the ferromagnetic material having the volume contribute the entire components of the magnetic field around the magnet center, I also derive the equations of the spherical harmonic coefficients of the magnetic field generated by ferromagnetic material. Since these equations need a numerical integration, such as the Gauss quadrature integration, the computation accuracy of the spherical harmonic coefficients is investigated against the number of the evaluation points. We can calculate the highly accurate spherical harmonic coefficients with the small number of the evaluation points. (C) 2014 AIP Publishing LLC.
Rights: Copyright 2014 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in J. Appl. Phys. 115, 163908(2014) and may be found at http://scitation.aip.org/content/aip/journal/jap/115/16/10.1063/1.4872244
Type: article
URI: http://hdl.handle.net/2115/56746
Appears in Collections:情報科学院・情報科学研究院 (Graduate School of Information Science and Technology / Faculty of Information Science and Technology) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)

Submitter: 野口 聡

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