Stream function approach for determining optimal surface currents

Peeren, Geran

doi:10.1016/s0021-9991(03)00320-6

Cited by 136 publications

(150 citation statements)

References 11 publications

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“…Peeren [22], [23], Tomasi [24]. For the manufacture of the coils, copper strips are placed on this pattern.…”

Section: The Maxwell Pairmentioning

confidence: 99%

“…In this approach the desired field is specified and the corresponding current distribution on the cylindrical surface is computed. Approaches using stream functions to determine optimal surface structures are reported among others by Peeren [22], [23], and Tomasi [24]. In [22], [23], the optimal structure is related to a minimization of the magnetic energy.…”

Section: Introductionmentioning

confidence: 99%

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Eddy currents in a gradient coil, modeled as circular loops of strips

2007

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The z-coil of an MRI-scanner is modeled as a set of circular loops of strips, or rings, placed on one cylinder. The current in this set of thin conducting rings is driven by an external source current. The source, and all excited fields, are time harmonic. The frequency is low enough to allow for a quasi-static approximation. The rings have a thin rectangular cross-section; the thickness is so small that the current can be assumed uniformly distributed in the thickness direction. Due to induction, eddy currents occur, resulting in a so-called edge-effect. Higher frequencies cause stronger edge-effects. As a consequence, the resistance of the system increases and the self-inductance decreases. From the Maxwell equations, an integral equation for the current distribution in the rings is derived. The Galerkin method is applied, using Legendre polynomials as global basis functions, to solve this integral equation. This method shows a fast convergence, so only a very restricted number of basis functions is needed. The general method is worked out for N (N ≥ 1) rings, and explicit results are presented for N = 1, N = 2 and N = 24.

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“…Peeren [22], [23], Tomasi [24]. For the manufacture of the coils, copper strips are placed on this pattern.…”

Section: The Maxwell Pairmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Eddy currents in a gradient coil, modeled as circular loops of strips

2007

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“…To perform this we use the stream function approach from Ref. 11. It is based on the fact that for a static current density function J(x, y, z) the divergence vanishes…”

Section: Coils -Discretization Of the Current Density Distributionmentioning

confidence: 99%

Active compensation of magnetic field distortions based on vector spherical harmonics field description

et al. 2017

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An analytic solution to the magnetostatic inverse problem in the framework of vector spherical harmonic basis functions is presented. This formalism is used for the design of a spherical magnetic field compensation system and its performance is compared with an already existing rectangular coil system. The proposed set of spherical coils with 15 degrees of freedom achieves a shielding factor of 1000 or better in a large part of the volume enclosed by the coils for a dipolar type external perturbation.

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“…These numerical methods produce continuous current density profiles that can be used to obtain a coil-winding pattern with the aid of a stream function. The winding patterns are realized by equally contouring the current density stream function [37,38].…”

Section: Gradient Coil Design Methodsmentioning

confidence: 99%

Gradient coil design and acoustic noise control in magnetic resonance imaging systems

Wang¹

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In magnetic resonance imaging (MRI), three-dimensional linearly varied magnetic field gradients are required in the imaging volume, for the encoding of the spatial information of the imaged object.The gradient magnetic field is generated by gradient coils, whose performance directly affects the final MR image quality. Modern MRI applications demand gradient coils to be designed with higher performance such as a faster slew rate for rapid imaging, and fewer system interactions to ensure distortion-free images.During MR imaging, the gradient coil current switches quickly and the alternating current under a strong magnetic field generates a large Lorentz force, thus increasing the vibrations and noise in the gradient assembly, and the vibrations can also transmit to other components in the system. Moreover, the gradient magnetic field induces eddy currents on the surrounding conductive materials, resulting in further mechanical vibration. The sound pressure level (SPL) of an MRI scanner very commonly exceeds 100 dB, which may be discomforting to patients. Therefore, an effective acoustic noise control is necessary for the MRI operation.This thesis attempts to design a novel gradient coil system in an MRI scanner with a particular focus on the investigation of an acoustic noise control scheme. A brief summary of the thesis work is as follows.(1) Gradient coil design A conventional cylindrical MRI scanner has a long patient bore, which may make some patients uneasy due to claustrophobia. In order to alleviate this, an asymmetric gradient coil was proposed to accommodate an asymmetric MRI magnet. The coil was designed with a number of features, for example, to enable the installation of the shim tray, the coil was configured with one end connected and the other end separated. The electromagnetic and acoustic performances were also improved compared with a conventional non-connected coil system.The stream function approach is commonly used in gradient coil design, but an issue with this design is a connection problem between coil loops. To eliminate the field errors due to the coil connections, this thesis proposed a novel spiral coil design scheme, including both transverse coils and a longitudinal coil. The proposed coil design method was not only able to improve the magnetic II performance of the coil, but also could integrate the cooling system into the coil design using hollow wires in the discrete wire space.Wire spacing is a major engineering problem in gradient coil design. Conventional gradient coils are designed with three primary layers and three shielding layers, and in general, primary transverse coils are located in two layers separated by a very dense wire structure. In this thesis, a novel gradient coil design strategy using a layer-sharing scheme was proposed. This design scheme mutually combined the x and y gradient coil layers, effectively utilizing the unoccupied or sparse coil-layer space. The new method was modelled in the case of an asymmetric head coil design, and enhanced coil performan...

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Stream function approach for determining optimal surface currents

Cited by 136 publications

References 11 publications

Eddy currents in a gradient coil, modeled as circular loops of strips

Eddy currents in a gradient coil, modeled as circular loops of strips

Active compensation of magnetic field distortions based on vector spherical harmonics field description

Gradient coil design and acoustic noise control in magnetic resonance imaging systems

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