The homogeneity of cylindrical Halbach arrays for low-field MRI is compromised by the finite length and discretisation into individual magnets. In this work we design and construct a large-bore Halbach array intended for imaging hydrocephalus in young children. The magnet is constructed using 23 double-layer Halbach rings with layer radii optimised for homogeneity. Simulated magnetic field strength and homogeneity over a 20cm spherical volume are 50.64mT and 433ppm, respectively. The homogeneity of the realised Halbach array is slightly degraded compared to simulations, but is sufficiently high to allow the use of conventional spatial encoding methods on such a system.
The use of permanent magnets for generating the B0 field in low-cost, low-field MRI is attractive due to the very low stray field and the lack of power requirements. Cylindrical Halbach arrays are a common implementation for both NMR and MRI systems, but the theoretical high field homogeneity is severely compromised by the practical requirement of finite length1, as well as magnetic field perturbations due to the discretised elements of the Halbach array and variations in the magnetisation direction and magnitude of the individual magnets2. Previous work has shown that significant improvements in the magnetic field homogeneity are possible by optimising the positioning of the individual magnets of the Halbach array3. Most magnets produced so far have relatively small diameters, which prevent, for example, imaging of young children with hydrocephalus, which is the end goal of our research.
In this work we design and construct a new large-diameter Halbach array configuration that uses stacked rings of small magnets consisting of two concentric Halbach layers. The radii of the layers in each ring are varied to optimise the homogeneity of the Halbach array. We propose the use of smaller magnets for several reasons: (i) more rings can be stacked in a given length of magnet enabling finer optimisation, (ii) a larger total number of magnets is used which helps average out the variations in the flux of individual magnets, and (iii) the smaller forces associated with smaller magnets increases safety during filling and reduces physical demands on the magnet housing.
The Halbach array consists of 23 rings spaced 22mm apart, each ring contains two layers of 12mm cubic N48 magnets positioned in a k=1 Halbach configuration. Ring sizes of 148 mm radius (50 magnets) to 221mm radius (75 magnets) were simulated in CST Microwave Studio (Darmstadt, Germany). The field variation over a 25cm diameter spherical region was minimised by varying the ring radii in each layer using a genetic algorithm in python. Mirror symmetry of the ring sizes was enforced in order to maximise homogeneity. The outer layer of each ring has a 20/21mm larger radius than the inner layer to facilitate manufacturing. Each ring was assembled individually using a 12mm thick ring of PMMA to holdthe magnets and 3mm rings of PMMA were used as lids. The spacing between rings was fixed using M5 threaded rods.
B0 field measurements were acquired using the frequency of the proton peak of a small sample. Data were acquired using a solenoid RF coil (diameter: 15mm, length: 25mm, f0: 2.151MHz, bandwidth: 41kHz) controlled by a Kea2 Spectrometer (Magritek, Germany) with a 0.1ml sunflower oil phantom placed in the coil centre. Spectra were acquired using block pulse excitation (pulse length: 50µs, acquisition delay: 200µs, dwell time: 100µs, points: 1024, repetition time: 300ms, averages: 25).
1. Turek K, Liszkowski P. Magnetic field homogeneity perturbations in finite Halbach dipole magnets. J. Magn. Reson. 2014;238:52–62
2. Soltner H, Blümler P. Dipolar Halbach magnet stacks made from identically shaped permanent magnets for magnetic resonance. Concepts Magn. Reson. Part A 2010;36A:211–222
3. Cooley CZ, Haskell MW, Cauley SF, et al. Design of Sparse Halbach Magnet Arrays for Portable MRI Using a Genetic Algorithm. IEEE Trans. Magn. 2018;54:1–12