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

• Published in: Chinese physics B Vol. 19; no. 1; pp. 563 - 574
• Main Author: 刘文韬 俎栋林 唐昕
• Format: Journal Article
• Language: English
• Published: IOP Publishing 2010
• Subjects: Current distribution; Decomposition; Harmonics; Inversions; Magnetic fields; Magnetic resonance imaging; Mathematical analysis; Shim coils; Spherical harmonics; Streams; Superconducting magnets; Weighting; Wire; 圆柱面; 核磁共振成像; 电流分布; 磁场变化; 线圈设计; 谐波分解; 超导磁体
• ISSN: 1674-1056; 2058-3834
• DOI: 10.1088/1674-1056/19/1/018701

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 cylin- drical 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.