A novel approach to designing cylindrical-surface shim coils for a superconducting magnet of magnetic resonance imaging

doi:10.1088/1674-1056/19/1/018701

Abstract For a superconducting magnet of magnetic resonance imaging (MRI), the novel approach presented in this paper allows the design of cylindrical gradient and shim coils of finite length. The method is based on identification of the weighting of harmonic components in the current distribution that will generate a magnetic field whose z-component follows a chosen spherical harmonic function. Mathematical expressions which relate the harmonic terms in the cylindrical current distribution to spherical harmonic terms in the field expansion are established. Thus a simple matrix inversion approach can be used to design a shim coil of any order pure harmonic. The expressions providing a spherical harmonic decomposition of the field components produced by a particular cylindrical current distribution are novel. A stream function was applied to obtain the discrete wire distribution on the cylindrical-surface. This method does not require the setting of the target-field points. The discussion referring to matrix equations in terms of condition numbers proves that this novel approach has no ill-conditioned problems. The results also indicate that it can be used to design cylindrical-surface shim coils of finite length that will generate a field variation which follows a particular spherical harmonic over a reasonably large-sized volume.

Keywords: active shimming superconducting MRI magnet target-field approach harmonic coils

Received: 14 May 2009
Revised: 08 June 2009
Accepted manuscript online:

PACS:	84.71.Ba	(Superconducting magnets; magnetic levitation devices)
	02.10.Yn	(Matrix theory)
	83.85.Fg	(NMR/magnetic resonance imaging)

Fund: Project supported by the National Natural Science Foundation of China (Grant No. 60871001).

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Liu Wen-Tao(刘文韬), Zu Dong-Lin(俎栋林), and Tang Xin(唐昕) A novel approach to designing cylindrical-surface shim coils for a superconducting magnet of magnetic resonance imaging 2010 Chin. Phys. B 19 018701

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A novel approach to designing cylindrical-surface shim coils for a superconducting magnet of magnetic resonance imaging

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