The design of a light and compact magnet for MRI

MRI是最好的非侵入性诊断成像方式，可提供全身的高质量图像。然而，它的高成本和幽闭恐怖的磁体几何形状阻止了更快的增长和更广泛的应用。因此，我们建议通过基于所谓的Halbach结构设计一种适用于MRI的新磁体来解决这些弱点。海尔贝克磁体具有圆柱形形状并且包括放置在圆柱体表面上的小磁性件。虽然Halbach设计已经被知晓超过30年，但是由磁体产生的磁场的完整分析理论仅针对非常高的长度/直径比而被开发，此时场的数学描述可以被减少到二维（2D）。最近（2014年）已经提出了具有小长度/直径比（<1）的有限长度磁体（“长”磁体）的3D数学模型，但是尚未构建基于该理论的磁体。求解半解析场方程的计算机程序，使用有限元或边界法来计算场，已经开发出来，但并非没有缺点。此外，磁体重量或其尺寸迄今尚未优化。此外，没有完美的制造过程，但没有一个理论模型包括制造误差，例如圆柱体表面上磁性件的不一致分割或它们的不完美位置。已知的是，例如，2D分割导致创建分段数量的倍数的阶的谐波。为了解决这一问题，本文用球谐函数法分析了球体上的磁场。根据该分析，计算了小型补偿磁铁的放置位置，以消除球谐函数并提高磁铁均匀性。还可以通过校正段的位置来改善场均匀性。然而，这些方法都不是完美的。在我们的方法中，我们建议开发一种在圆柱体而不是传统上使用的球体表面上填隙的方法。我们预计这种方法将为“短”Halbach磁体提供有效的匀场。*总之，我们建议开发一种适用于标准和“无梯度”MRI的轻质永磁体的新设计，由申请人共同开发。由于“无梯度”MRI不需要磁场梯度和相关放大器，因此可以为许多新的成像应用生产廉价，轻便和安静的MRI系统。

MRI is the best non-invasive diagnostic imaging modality providing high quality images of the entire body. However, its high costs and claustrophobic magnet geometry prevent a faster growth and broader applications. Therefore we propose to address these weaknesses by designing a new magnet suitable for MRI based on the so-called Halbach structure.****Halbach magnets have a cylindrical shape and comprise small magnetic pieces placed on a surface of a cylinder. Although the Halbach design has been known for over 30 years, a full analytical theory of the magnetic field produced by the magnet has been developed only for a very high length/diameter ratio, when the mathematical description of the field can be reduced to two dimensions (2D). A 3D mathematical model of the finite-length magnet ("long" magnet) with small length/diameter ratio (<1) has been proposed very recently (2014) but a magnet based on this theory has not yet been constructed. Computer programs solving semi-analytical field equations, using the finite elements or the boundary methods to calculate the field have been developed yet not without drawbacks. Furthermore magnet weight or its size have not been optimized so far. In addition, there is no perfect manufacturing process, yet none of the theoretical models include manufacturing errors, such as inconsistent segmentation of the magnetic pieces over the cylinder's surface or their imperfect position.****It is known that, for example, 2D segmentation causes creation of harmonics of the order of a multiple of the number of the segments. To deal with this common problem, the magnetic field over a sphere is analyzed using spherical harmonics. From this analysis, the placement of small compensating magnets is calculated to cancel the spherical harmonics and to improve magnet homogeneity. The field homogeneity may be also improved by correcting positions of the segments. However none of these methods is perfect. In our approach we propose to develop a method of shimming on a surface of a cylinder instead of a sphere, as traditionally used. We expect this approach will provide efficient shimming for "short" Halbach magnets.****In summary, we propose to develop a new design of a light, permanent magnet suitable for standard and "gradient free" MRI, co-developed by the applicant. As "gradient free" MRI does not require gradients of the magnetic field and associated amplifiers, it is feasible to produce inexpensive, light and silent MRI system for many new imaging applications.******