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Low-Cost, Pseudo-Halbach Dipole Magnets for NMR

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Low-Cost, Pseudo-Halbach Dipole Magnets for NMR Low-cost, pseudo-Halbach dipole magnets for NMR Michael C. D. Taylera,b,∗, Dimitrios Sakellariouc aMagnetic Resonance Research Center, Department of Chemical Engineering and Biotechnology, University of Cambridge, Cambridge, UK. bDepartment of Physics, University of California, Berkeley, CA 94720, USA. cNIMBE, CEA-CNRS, Universit´eParis-Saclay, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France. Abstract We present designs for compact, inexpensive and strong dipole permanent magnets aimed primarily at magnetic resonance applications where prepolarization and detection occur at different locations. Low-homogeneity magnets with a 7.5 mm bore size and field up to nearly 2 T are constructed using low-cost starting materials, standard workshop tools and only few hours of labor – an achievable project for a student or postdoc with spare time. As an application example we show how our magnet was used to polarize the nuclear spins in approximately 1 mL of pure [13C]- methanol prior to detection of its high-resolution NMR spectrum at zero field (measurement field below 10−10 T), 1 where signals appear at multiples of the carbon-hydrogen spin-spin coupling frequency JCH = 140:7(1) Hz. Keywords: Nuclear magnetic resonance (NMR), Permanent magnets, Low-field NMR, Zero-field NMR 1. Introduction with very good resistance to demagnetization.[3] Very soon after NdFeB was introduced in the early 1980s, Nuclear magnetic resonance (NMR) spectra are of- Klaus Halbach was one of the first to capitalize on these ten desired at the highest available strength of magnetic properties, proposing an ingenious way to design and field, B, since detection sensitivity is proportional to build magnets producing multipolar fields.[4] The cylin- 7=4 B and the resolution of chemical shifts (subject to drical structure and later the spherical structure[5] al- field homogeneity) scales linearly with B. The highest lowed dipolar magnetic fields exceeding 2 T to be pro- static fields available today are up to 23 T using per- duced. Since then, several research groups and compa- sistent superconducting magnets, which when coupled nies have refined Halbach’s structures and together with with optimized signal detection achieve sensitivities in shim coils magnets up to around 1.5 T can be obtained −12 the low picomole (10 moles) range. with homogeneity to better than 0.05 ppm, allowing for The design and construction of a single NMR mag- the resolution of chemical shifts and nuclear spin-spin net to meet the demands of high field strength, part-per- couplings in the measured NMR spectra.[6, 7, 8, 9, 10, billion homogeneity, high stability and minimal stray 11, 12, 13, 14] The sensitivity at 1.5 T is around 10−7 field, however, is an expensive undertaking and at the 1H moles, sufficing for most analyses of solution-state strongest fields the final product is neither compact or samples in the synthetic chemistry laboratory and at a mobile.[1, 2] For a significant reduction in the power re- price point that can enter the teaching laboratory. quired for NMR and an improved mobility of the instru- mentation, the use of rare-earth permanent magnet as- In the present work we discuss the design, assem- semblies (up to 1.5 tesla) has become popular. Sintered bly and application of permanent magnet arrays where neodymium-iron-boron (NdFeB) magnets have revolu- field strength and ease of construction are prioritized tionized a number of technologies, including electric over magnetic field homogeneity. These are aimed motors and recently the design of NMR magnets, due at magnetic resonance applications that do not require to their high values of remanence and coercivity that sub-ppm field uniformity, for example nuclear pre- allow for very strong and compact magnet structures polarization of samples prior to remote detection of the signal in earth’s field[15] or ultra-low field.[16, 17, 27] In some cases the magnetic field homogeneity may ∗Corresponding author Email addresses: [email protected] (Michael C. D. Tayler), be acceptable for in situ high-resolution NMR spec- [email protected] (Dimitrios Sakellariou) troscopy of small-volume samples, which are less sus- Preprint submitted to J. Magn. Reson. March 1, 2017 ceptible to field inhomogeneity,[18, 19] or in con- junction with RF pulse sequences that correct for the inhomogeneity.[20] 2. Design of pseudo-Halbach arrays The original theoretical design of Halbach for mul- tipolar permanent magnets assumed an infinitely long cylindrical structure having a continuous distribution Figure 1: Cross sections of the Pseudo-Halbach permanent magnet of orientation-dependent, fixed-magnitude magnetiza- assemblies involving 2, 4, 8 and 24 NdFeB magnet blocks. Arrows tions. Practical implementations, however, must have represent the axis of magnetization in the material. The first three finite length and allow for a segmented assembly. Most structures use a single type of material, while the last one uses two high performance assemblies use wedge-shaped magnet types to reduce demagnetization effects. blocks, which require special magnet grinding and are best produced and assembled by experts. A few pseudo- No. of blocks 2 4 8 24 Halbach dipole magnets for NMR have been built using Magnetization: clusters of identical permanent magnets that can be pur- Rigid 0.651 1.031 1.482 2.000 chased, such as cylinders,[6] cubes[12] and other reg- Non-rigid 0.629 1.007 1.445 1.950 ular prisms.[21, 22, 23] This last approach gave rise to Experimental - - 1.380 1.93 the “Mandhalas” family of magnets. However, in most cases these assemblies are designed for optimal mag- Table 1: Calculated and measured central magnetic fields (in tesla) for the arrays shown in Figure 1 calculated using N52 and N48SH netic field homogeneity at the expense of magnetiza- materials data at room temperature. The central gap measures 0.5 tion density, and sometimes to constrain the magneti- inches (12.7 mm) by 0.3 inches (7:6 mm). zation density to give a “convenient” value of nuclear Larmor frequency or for some other reason, e.g. to fa- cilitate sample access.[14, 24] Our effort here was to dicates the resilience of the material to demagnetiza- design an ultra-compact dipole magnet inspired by the tion in the presence of an external magnetic field at a original Halbach design, which can be produced using given temperature. Temperature and mechanical stress many identical permanent magnet pieces, similar to the are important factors as these govern the dynamics of Mandhalas concept, and has an even higher magnetiza- magnetic domain shape and orientation.[26] Even slight tion density. increases in temperature may lead to a higher plastic- The initial design was based on the availability of par- ity and values of coercivity subject to demagnetization. allelepipedic NdFeB magnet blocks with dimensions of One has to be careful when designing a very strong per- 2:00 × 0:500 × 0:500 inches3 each magnetized through manent magnet to compute the values of the magnetic the 0.5 inch thickness (CMS Magnetics: N52 grade, re- field everywhere in space and in particular inside the manent field Br = 1.44 T, Ni-Cu-Ni plating, dimensions magnetic material – during assembly as well as for the accurate to +0:002 inch, $4:50 per block, $ = USD, final structure[29] – in order to avoid moving the work- 1 inch = 25.4 mm exactly). In anticipation of hold- ing point of the material beyond the demagnetization ing the NMR sample inside the magnet array within a “shoulder”. Going past this point leads to an irreversible standard 5 mm outer-diameter glass NMR tube, a rect- loss of magnetization, which in turn will reduce the pro- angular cross section of 0.5 inch by 0.3 inch (7.5 mm) duced magnetic field and induce substantial field inho- was reserved for non-magnetic material. Exact numer- mogeneities. For this reason, the magnet should also not ical calculations were then performed using analytical be exposed to temperatures outside its intended operat- formulae from the literature[11] to determine the max- ing range. imum field strength obtainable in assemblies of two, To obtain a practical design where field is maxi- four, eight and twenty four of the block units surround- mized but the effects of demagnetization are reduced, ing the void (or “bore”), assuming perfectly rigid and we searched for the optimal arrangement for two grades uniform magnetizations over the block volumes. of magnet material when using more than 8 magnet Demagnetization within permanent magnet arrays blocks. For the second material, N48SH grade was cho- can become an important factor when high magnetic sen (Br = 1.37 T, $10 per block), since the remanence fields are involved. Magnetic materials are also char- value is only around 5 percent less than N52 but the co- acterized by a coercivity field (Hc) value,[25] which in- ercivity is approximately 2 times greater. The magnet 2 orientations producing the strongest total field within blocks to give the desired central void. In the next stage, the array structure are illustrated in Figure 1. The field the magnet blocks inserted are those which partially at- values at the geometric centers of each array are sum- tract to those already in place and are easily inserted by marized in Table 1. The calculated value of field in hand. Figure 2(b) shows how these blocks are kept in all four magnet arrays given on the first line ignores their correct position by filling also the remainder of the demagnetization effects and is calculated using a rigid- array with non-magnetic “dummy” blocks made from magnetization model: magnetization is uniform over the aluminum. The dummy blocks are approximately 0.002 material volume, and constant through it, equal to the inches oversize in width and depth to assist the next value of the remanence Br.
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