Nuclear magnetic resonance (NMR) technology has been widely used in many fields, such as material science1, 2, structural biology3, medicine4, 5 and so on. Magnetic resonance equipment also has the problems of low magnetic field intensity, poor uniformity and low utilization rate of magnetic materials. In order to increase the intensity of the magnetic field required by the NMR equipment, more magnetic materials have to be used in the equipment. This will enlarge the volume and increase the weight of the equipment, which is contradictory to the concept of portable. Since the emergence of new materials such as NdFeB and SmCo6, it is possible for NMR equipment to be portable.
There are four main structures of portable NMR equipment: single-sided7, 8, C-type9, H-type10 and Halbach array11, 12, in which the Harbach array is use widely due to the characteristics of miniaturization13, 14. The magnetization directions in the magnetic blocks are different, which makes the magnetic field lines converge on one side and weaken on the other side15, 16. The magnetic field intensity can be greater than the remanence of permanent magnetic materials and also there is no iron yoke in the structure17, 18.
Moresi and Magin designed a portable Halbach magnet structure. The magnetic field uniformity is improved by using two high permeability iron plates, but the weight of the whole structure is greatly increased by using iron plates19. In 2004, Raich and Blümler proposed a new structure called NMR Mandhala (Magnet Arrangements for Novel Discrete Halbach Layout) by combining theoretical derivation and simulation optimization. The rectangular, circular and polygonal magnets was also suitable to the structure. The proposed NMR Mandhala structure was with mass of 11.4 kg, homogeneity of 700 ppm and center frequency of 12.8 MHz20, which produces good uniform using magnetic blocks of the same shape and remanence21. However, the volume of the device still greatly limited its application in portable NMR instruments. In 2007, Blümich proposed a method to improve magnetic field homogeneity. They moved the four magnets on the Halbach magnetic ring to 5 mm along its magnetization direction, which increased the uniformity by 10 times. The magnetic field intensity was 0.22T and the homogeneity was 0.05T/m22. However, this method also reduces the magnetic field intensity. A few years later, B. Blümich et al. placed 8 shimming units to compensate for the end effect23. Cooley and Stockmann et al. placed 40 shimming units at both ends of the Halbach structure to optimize the spatial resolution of MRI scanners24. In 2011, Windt et al. demonstrated the idea that the Halbach magnetic ring can be opened and closed with the minimum force at a certain angle. The weight of this structure was 3.1 kg, and the magnetic field intensity was 0.57 T. The spherical region with a diameter of 5 mm, in which the uniformity is better than 200 ppm. However, the working area of this structure is too small, which is only suitable for measuring objects such as plants25. Later, Menzel and Chen et al. developed a formula, which is used to calculate the magnetic field intensity of equidistant stack ring26, 27.
In order to design a portable Halbach permanent magnet with good uniformity and effective compensation for end effect. We present an optimization method which can axial adjust the height of the magnet to compensate for the end effect.
The main contribution in this paper are as follows: 1) Only a small amount of magnetic material needs to be added to the original structure to effectively compensate for the end effect and improve uniformity. 2) Quality factor (Q) is introduced to represent magnetic field performance. In ensuring the magnetic field density and uniformity at the same time, through Q as far as possible to play the performance of magnetic materials and reduce volume. 3) The structure is small in size and compact, which is very suitable for portable NMR systems.
The remainder of this paper is organized as follows: First, we explain the principle of Halbach in Section “Halbach array principle”. Then, we propose the parameters of the original structure in section “Design”. Finally, in section “Simulation method”, an novel optimization method with axial adjustment the height of the magnetic block is proposed, which is compared with another optimization method.