Magnet structure

Abstract

The disclosed magnet array includes a plurality of polyhedral magnets arranged in a Halbach cylindrical configuration, with the centers of each of the plurality of polyhedral magnets positioned substantially in a plane within a magnet rack, the plurality of polyhedral magnets at least partially surrounding a test volume, and includes a first plurality of polyhedral magnets arranged in a Halbach cylindrical configuration and a second plurality of polyhedral magnets arranged in a non-Halbach configuration. In another aspect, the disclosed magnet array includes a first subset and a second subset of polyhedral magnets having different coercive forces. In yet another aspect, the disclosed magnet array includes a central subset of each of the plurality of polyhedral magnets laterally displaced from a nominal position within the magnet rack to cancel the magnetic field gradient of the magnet array.

Description

Technical Field

[0001] Cross - Reference to Related Applications This application claims the benefit of U.S. Provisional Patent Application 62 / 891,336, filed Aug. 24, 2019, the specification of which is hereby incorporated by reference in its entirety.

[0002] The present disclosure relates to magnet structures. More specifically, the present disclosure relates to modified Halbach magnet structures.

Background Art

[0003] In nuclear magnetic resonance (NMR) experiments, a sample for analysis is placed under the influence of a bias static magnetic field that partially aligns the nuclear spin magnetic moments of the sample. The moments precess about the static magnetic field at a frequency called the Larmor frequency, which is proportional to the magnetic field strength. The magnetic moment of the sample can be manipulated by applying a transverse radio - frequency (RF) magnetic field at the Larmor frequency. By observing the response of the sample to the RF magnetic field, insights into the chemical composition of the sample can be obtained. The power of NMR as an analytical method may primarily be a function of how well the properties of the applied magnetic field can be controlled.

[0004] The practice of shimming the magnetic field (making the magnetic field more uniform) has existed since the early days of NMR and originally involved using thin metal pieces physically placed behind the source magnets to adjust the positions of those magnets and improve the magnetic field. More modern shimming techniques use electromagnetic coils. Conventional high-field magnetic resonance spectrometers typically use shimming coils arranged in a substantially cylindrical coil configuration. In contrast, the use of shimming (shim) coils in compact NMR devices has been found to be difficult mainly due to space limitations that may not allow the accommodation of conventional shim coil systems that can have many layers. The space available inside the main magnet of many such devices is often too small to accommodate a typical set of shimming coils where each individual element is designed mainly to address only the geometric aspects or components of the residual inhomogeneity of the main magnetic field.

[0005] Figures 1A, 1B, and 1C compare the main bias magnetic field and sample tube structure of a typical high-field spectrometer design with the design of a compact magnet system based on a cylindrical Halbach array. The arrows labeled B indicate the direction of the main magnetic field. The figures do not show shimming measures. Figure 1A schematically shows the superconducting field magnet coil of a high-field magnet, the inserted cylindrical sample tube, and the magnetic field B generated by the coil. The magnetic field within the sample volume is aligned along the common axis of symmetry of the coil and the tube.

[0006] Figures 1B and 1C show the same sample tube inserted into a cylindrical Halbach magnet array, which generates a magnetic field B perpendicular to the axis of symmetry of the tube. This particular Halbach array consists of eight magnets in a circular (shown in Figure 1B) arrangement around the tube with magnetization vectors of the magnets (shown as arrows) perpendicular to the axis of symmetry of the tube. The magnetization vector quantitatively and directionally represents the polarization of the magnetic dipoles within the material. The magnetic field within the Halbach array is fairly uniform for some applications but can be highly non-uniform in some high-resolution NMR experiments.

[0007] To significantly reduce the inhomogeneity of a magnetic field, it can be useful to independently control the various geometric aspects of the magnetic field inhomogeneity. In many magnetic resonance applications, the main magnetic field is strongly polarized along a specified direction. Within this application, as is generally the case in the art, this direction is understood to be the z-axis of a Cartesian reference coordinate system where the origin is at some fixed point, e.g., near the center of the sample under consideration. The Larmor frequency of a magnetic spin at a point in space is determined by the magnitude of the magnetic field at that point, which, in a moderately homogeneous magnetic field, is very well approximated by the z-component B z of the magnetic field. B can be expanded as a scaled sum of functions z . [Number] where k is a variable (or several variables) used to index the various functions in the set f k , and where x, y, and z are Cartesian or other spatial coordinates defining positions within a volume surrounding at least a portion of the sample. B 0 is the large and spatially homogeneous part of the magnetic field, and the coefficients C k quantify the various components of the magnetic field inhomogeneity. A set of such functions, e.g., x, z, xy, (x 2 -y 2 ), is said to be orthogonal (with respect to a particular function scalar product) if the scalar product between two different functions is zero. The common scalar product between two functions is an integral. [Number] where V indicates the volume associated with the function over which the integral is calculated, where the star indicates the complex conjugate, and where W indicates a weight function defined over the volume, which quantifies how important the volume element at (x, y, z) is in its contribution to the integral. For example, generally, an expansion in spherical harmonic functions is used, where the functions are as follows. [Number] wherein

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[0008] A properly controlled magnetic field is particularly important in nuclear magnetic resonance (NMR) spectroscopy and other magnetic resonance (MR) applications. In many NMR spectroscopy experiments, a strong static magnetic field is applied to the spatial region containing the sample under study, and this magnetic field is desirably as spatially uniform as possible in order to observe important but subtle changes in the magnetic response of the sample. Also, in many NMR applications, it is desirable to have a strong static magnetic field within a practical range.

[0009] To provide a strong static magnetic field to an NMR device, at least three classes of magnets are used, namely, superconducting magnets, resistive magnets, and permanent magnets. Permanent magnets or their arrays (also called assemblies or structures) can be advantageous in applications where low cost, low maintenance, and / or portability are desired.

[0010] In practice, a permanent magnet often involves a pole piece which is a fragment of a permeability material placed near the magnet to contribute to or form a magnetic field. In some applications, it is desirable that the materials used for the pole pieces are magnetically "soft", i.e., they have relatively low coercivity. In some applications, it is also desirable that the pole piece materials are strongly magnetized when placed in a magnetic field, i.e., they have high saturation magnetization.

[0011] One design for generating a substantially strong magnetic field in a small amount is the Halbach cylinder, in which magnetic dipoles in a high coercivity permanent magnet material are arranged around a central cavity. FIG. 2 shows an idealized cross-sectional view of a Halbach cylinder 10, together with a coordinate system 12 used to calculate and select the orientation of the magnetic dipoles shown as arrows 14 within the region surrounding the central volume 16. In the idealized Halbach cylinder, the magnetization direction

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[0012] Figures 3A, 3B, 3C, and 3D show prior art implementations of Halbach cylinder-based magnet structures. Figure 3A (adopted from F. Bertora, A. Trequattrini, M. G. Abele, and H. Rusinek, "Shimming of yokeless permanent magnets designed to generate uniform fields", Journal of Applied Physics 73, 6864, 1993) shows a cylindrical structure 20 of designated magnets surrounding a space 24, whereby the space is efficiently utilized and many diagonal shapes 21, 22, 23 are employed in its design.

[0013] Figure 3B (adopted from E. Danieli, J. Mauler, J. Perlo, B. Blumich, and F. Casanova, "Mobile sensor for high resolution NMR spectroscopy and imaging", Journal of Magnetic Resonance 198, 80, 2009) shows an array 30 surrounding a space 32 using the same hexahedral-shaped permanent magnets 31. However, this implementation has the drawback of low filling density.

[0014] When the space surrounding the central volume is divided into several regions, the individual constituent magnets placed therein may exhibit diagonal shapes as shown in Figure 3A, but are difficult or expensive to manufacture with high tolerance. The magnetization required within the constituent magnets may also be difficult to control with sufficient accuracy to guarantee the quality of the magnetic field within the central volume. Instead, when simpler constituent magnets such as cubes are used as in Figure 3B, these can be manufactured and magnetized easily with high precision, but due to some design geometric constraints, it may result in a low filling density accompanied by a decrease in the magnetic field strength that can be generated.

[0015] FIG. 3C is a cross-sectional view of an embodiment of a Halbach cylinder 40 including an array of closely packed hexagonal prisms 41 surrounding a central space 42, as disclosed in Leskowitz et al.'s U.S. Patent No. 8,712,706, which is incorporated herein by reference in its entirety. FIG. 3D (also disclosed in U.S. Patent No. 8,712,706) shows a general arrangement 50 of individual main magnets 52 within a magnet array around a channel 53 in which a pole piece 54 and a sample 56 are disposed. FIG. 3D also shows the arrangement of a shim panel 58 on the pole piece 54. Arrow 59 indicates the main magnetization direction of each main magnet 52 in the arrangement.

[0016] In the Halbach cylinder model, the ideal is an infinitely long cylinder. In reality, the cylinder has a finite length, which can introduce various technical problems and undesirable features into the primary magnetic field of the array, and designs attempting to overcome these drawbacks can become complex. An alternative approach for generating a homogeneous magnetic field is to use a Halbach sphere, and a practical embodiment thereof has been proposed by H. Leupold in U.S. Patent No. 4,837,542.

[0017] FIG. 4A, adopted from Leskowitz's U.S. Patent No. 9,952,294, which is incorporated herein by reference in its entirety, shows a sphere 60 surrounding a central cavity 62 and having a local magnetic dipole orientation 64.

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[0018] To best approximate a uniform magnetic field in the ideal case, the magnetization direction within the spherical shell surrounding the central cavity

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[0019] It will be observed that the magnetization in the spherical case is different from that in the cylindrical case. In the Halbach sphere model, the position

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[0020] The spherical assembly can be composed of a combination of magnets with complex shapes, as shown in Figure 4B (adopted from Leupold's U.S. Patent No. 4,837,542). In Figure 4B, it can be seen that the sphere 70 includes a plurality of constituent primary magnets 72 having a selected dipole orientation 74 and surrounding a central cavity 76. To achieve the desired structure and magnetic field, a number of different primary magnets with different shapes and magnetic orientations are required. Again, these may be difficult or unrealistic to manufacture with a high tolerance.

[0021] A magnet array and a method for generating a magnetic field are disclosed in Leskowitz's U.S. Patent No. 9,952,294, and a magnet array including a plurality of polyhedral magnets arranged in a lattice structure and at least partially surrounding a test volume is mentioned. This magnet array has a related magnetic field having a specified magnetic field direction

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[0022] In practice, the Halbach sphere structure may generate a larger magnetic field than the magnetic field generated by the Halbach cylinder structure. However, in the structure of the Halbach sphere, access to the central region of the magnet may be restricted compared to the structure of the Halbach cylinder.

[0023] In applications such as magnetic resonance applications, it may be advantageous to use the maximum practical magnetic field. One way to increase the magnetic field present within a Halbach cylinder magnet structure is to insert a pole piece into the bore of the Halbach cylinder magnet structure. U.S. Patent No. 9,341,690 to Leskowitz and McFeetors discloses a shaped pole piece for a cylindrical Halbach magnet structure. Inserting a pole piece into a cylindrical Halbach magnet may increase the magnetic field, but it may also create or exacerbate a harmful magnetic field gradient including a secondary magnetic field gradient. This can be partially alleviated by forming the pole piece with channels on each back surface, i.e., the first surface of the pole piece is on the opposite side of the second surface of the pole piece closest to the center of the Halbach cylinder, which can be configured as the sample position. The problem to be solved is that introducing this back channel into the pole piece can reduce the magnetic field strength within the sample position because the magnetic material is effectively removed when forming the channel.

[0024] Another way to increase the magnetic field present within a Halbach cylinder magnet structure is to increase the number of constituent magnets used to construct the magnet structure. Such constituent magnets can be configured in a concentric ring structure. For example, Fig. 3D shows a single hexagonal ring of six magnets, and Fig. 3C shows a hexagonal ring of six magnets surrounded by a hexagonal ring of twelve magnets. It will be readily understood that each constituent magnet is affected by the magnetic interaction with the total magnetic field generated by all other magnets within the assembly. In particular, the constituent magnets can be arranged at locations where the total magnetic field generated by the other magnets is substantially aligned with the magnetization of the constituent magnet. In that case, the constituent magnet will be under a relatively low coercive stress and will thus be subject to a weak demagnetizing force. Conversely, the constituent magnets can be arranged at locations where the total magnetic field generated by the other magnets is substantially away from or oppositely aligned with the magnetization of the constituent magnet. In that case, the constituent magnet will be under a relatively high coercive stress and will thus be subject to a strong demagnetizing force. Reducing or controlling the demagnetizing force is an important issue in determining the stability and performance of the magnet array in the application. Furthermore, an increase in the coercivity may be associated with an increase in cost.

Prior Art Documents

Patent Documents

[0025]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Patent Document 5

Non-Patent Documents

[0026]

Non-Patent Document 1

[0027] There remains a need for a solution that allows for an increase in magnetic field while maintaining the low cost, convenience, and manufacturability of cylindrical and spherical Halbach magnet structures. [Means for Solving the Problems]

[0028] (Overview) The present disclosure describes a modified Halbach magnet structure. In the present disclosure, the magnet structure may also be referred to as a magnet array or a magnet assembly. The term "modified" Halbach magnet structure means a structure (or arrangement) of individual constituent magnets that includes two or more subsets of magnets, where at least one subset is composed of a Halbach cylindrical magnet structure and at least one other subset has a different (non-Halbach) magnet structure. Further, the modified Halbach magnet structure is understood to increase the strength, uniformity, or both of the magnetic field generated by the magnet structure in some way.

[0029] Embodiments in the present disclosure with a modified Halbach magnet structure include a magnet structure having at least two groups of polyhedral magnets, one group arranged in a Halbach cylindrical structure and one group arranged in a non-Halbach cylindrical structure. Other embodiments of the present disclosure include a magnet structure having at least two groups of polyhedral magnets with different magnetic coercivities. Further embodiments in the present disclosure with a modified Halbach magnet structure include a magnet structure having polyhedral magnets arranged in a Halbach cylindrical structure, where a subset of the polyhedral magnets is laterally displaced from a nominal position to cancel the magnetic field gradient of the magnet structure. Yet another embodiment in the present disclosure with a modified Halbach cylindrical magnet structure includes a magnet structure having composite polyhedral magnets, each of the constituent magnets having its own magnetization vector orientation. These modified Halbach magnet structures can increase the magnetic field generated by the magnet structure and may affect (emphasize or de-emphasize) the magnetic field gradient including the magnetic field gradient generated by introducing one or more pole pieces into the magnet structure. These modified Halbach magnet structures provide solutions that enable an increase in the magnetic field while considering cost, convenience, and manufacturability.

[0030] In one aspect, there is provided a magnet array comprising a first plurality of polyhedral magnets arranged in a Halbach cylindrical structure and a second plurality of polyhedral magnets in a magnet rack, wherein the centers of the individual ones of the first plurality of polyhedral magnets are substantially arranged in a plane within the magnet rack of the magnet array, the first plurality of polyhedral magnets at least partially surround a test volume, and the second plurality of polyhedral magnets are arranged in a non-Halbach structure.

[0031] In one embodiment, the second plurality of polyhedral magnets in the magnet rack include magnets having in-plane magnetization vectors, out-of-plane magnetization vectors, or combinations thereof.

[0032] In one embodiment, the magnet array has a specified magnetic field direction

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[0033] In one embodiment, each of the polyhedral magnets is selected from the group consisting of truncated hexahedrons, rhombic dodecahedrons, Platonic solids, Archimedean solids, Johnson solids, prisms, chamfered polyhedrons, and truncated polyhedrons.

[0034] In one embodiment, the second plurality of polyhedral magnets includes magnets that are obliquely edge magnetized, obliquely vertex magnetized, axially magnetized, or combinations thereof.

[0035] In one embodiment, the first plurality of magnets includes magnets that are diametrically surface magnetized, diametrically edge magnetized, or combinations thereof.

[0036] In one embodiment, the first and second pluralities of polyhedral magnets are hexagonal prismatic magnets.

[0037] In one embodiment, the magnet array includes a plurality of magnet racks arranged in a rack stack. In one embodiment, the magnet array includes four magnet racks. In another embodiment, the magnet array includes five magnet racks.

[0038] In one embodiment, each of the magnet racks includes thirty-six hexagonal prismatic magnets.

[0039] In one embodiment, the thirty-six hexagonal prismatic magnets are arranged in inner, middle, and outer rings of six, twelve, and eighteen hexagonal prismatic magnets respectively, with the inner hexagonal prismatic magnets being closest to the test volume.

[0040] In one embodiment, the magnet rack includes a self-framework and a framework housing.

[0041] In one embodiment, the magnet rack and the first and second pluralities of polyhedral magnets each have a height of 1.5 inches.

[0042] In one embodiment, the cells in the self-framework have a width of 1.25 inches, and the walls of the self-framework have a thickness of 0.030 inches.

[0043] In one embodiment, the first plurality of polyhedral magnets each include an inner ring and a middle ring of six and twelve hexagonal prismatic magnets respectively.

[0044] In one embodiment, the second plurality of polyhedral magnets include positions within the outer ring of eighteen hexagonal prismatic magnets.

[0045] In one embodiment, at least one of the individual magnet racks in the rack stack includes twenty-two diametrically surface-magnetized magnets, eight diagonally vertex-magnetized magnets, four diagonally edge-magnetized magnets, and two axially magnetized magnets.

[0046] In one embodiment, the first magnet rack disposed on the central magnetic reflection surface of the rack stack has a first magnetic structure that is a magnetic reflection of the second magnetic structure of the second magnet rack disposed under the central magnetic reflection surface of the rack stack.

[0047] In one embodiment, the first of the five magnet racks in the rack stack has a magnetic structure that is a magnetic reflection of the fifth of the five magnet racks in the rack stack.

[0048] In one embodiment, each of the first plurality of polyhedral magnets in the first and fifth magnet racks includes eighteen magnets having an in-plane magnetization vector, and each of the second plurality of polyhedral magnets in the first and fifth magnet racks includes eighteen magnets having an out-of-plane magnetization vector.

[0049] In one embodiment, the eighteen in-plane magnetization magnets include fourteen magnets magnetized in the diametrical plane and four magnets magnetized at the edge in the diametrical direction.

[0050] In one embodiment, the eighteen magnets having an out-of-plane magnetization vector are magnetized axially.

[0051] In one embodiment, the second of the five magnet racks in the rack stack has a structure that is a magnetic reflection of the fourth of the five magnet racks in the rack stack.

[0052] In one embodiment, each of the first and second plurality of polyhedral magnets in the second, third, and fourth magnet racks includes magnets having an in-plane magnetization vector.

[0053] In one embodiment, each of the second and fourth magnet racks includes twenty-eight magnets magnetized in the diametrical plane and eight magnets magnetized at the edge in the diametrical direction.

[0054] In one embodiment, the third magnet rack includes twenty diametrically surface magnetized magnets and sixteen diametrically edge magnetized magnets.

[0055] In one embodiment, the magnet array further includes a first subset of polyhedral magnets and a second subset of polyhedral magnets, and the first subset and the second subset of polyhedral magnets have different magnetic coercivities.

[0056] According to another aspect, there is provided a magnet array comprising a first plurality of polyhedral magnets arranged in a Halbach cylinder structure, a second plurality of polyhedral magnets in a magnet rack, and at least one composite magnet, wherein the centers of the individual ones of the first plurality of polyhedral magnets are substantially arranged in a plane within the magnet rack of the magnet array, the first plurality of polyhedral magnets at least partially surround a test volume, and the second plurality of polyhedral magnets are arranged in a non-Halbach structure.

[0057] In one embodiment, the at least one composite magnet includes two or more magnets each having a different magnetization vector, and the two or more magnets are dimensioned and shaped together to be disposed in individual cells of the magnet array.

[0058] In one embodiment, the magnet array further includes at least one composite magnet.

[0059] In one embodiment, the at least one composite magnet is a hexagonal prismatic magnet.

[0060] In one embodiment, the at least one composite magnet includes two magnets each having a different magnetization vector.

[0061] In one embodiment, the at least one composite magnet includes more than two magnets each having a different magnetization vector.

[0062] In one embodiment, the magnetization vector is selected from the group consisting of diametrical plane magnetization, diametrical edge magnetization, oblique edge magnetization, oblique vertex magnetization, and axial magnetization.

[0063] In one embodiment, the two or more magnets are dimensioned and shaped together so as to be disposed in individual cells of a magnet array.

[0064] According to a further aspect, there is provided a magnetic resonance apparatus comprising a magnet array including a first plurality of polyhedral magnets arranged in a Halbach cylinder structure and a second plurality of polyhedral magnets in a magnet rack, wherein centers of individual ones of the first plurality of polyhedral magnets are substantially disposed in a plane within the magnet rack of the magnet array, the first plurality of polyhedral magnets at least partially surround a test volume, and the second plurality of polyhedral magnets are arranged in a non-Halbach structure.

[0065] According to another aspect, there is provided a method of assembling a magnet array comprising providing a first plurality of polyhedral magnets, arranging the first plurality of polyhedral magnets in a Halbach cylinder structure within a magnet rack, wherein centers of individual ones of the first plurality of polyhedral magnets are substantially disposed in a plane within the magnet rack and the first plurality of polyhedral magnets at least partially surround a test volume, providing a second plurality of polyhedral magnets, arranging the second plurality of polyhedral magnets in a non-Halbach structure within the magnet rack, and arranging the magnet rack within a rack stack to assemble the magnet array.

[0066] According to another aspect, there is provided a magnet array comprising a plurality of polyhedral magnets arranged in a magnet structure, the plurality of polyhedral magnets including a first subset of polyhedral magnets and a second subset of polyhedral magnets, the plurality of polyhedral magnets at least partially surrounding a test volume, and the first subset and the second subset of polyhedral magnets having different magnetic coercivities.

[0067] In one embodiment, the individual ones of the first subset of polyhedral magnets have similar magnetic coercivities.

[0068] In one embodiment, the magnet array includes one or more further subsets of polyhedral magnets, each of the subsets of polyhedral magnets has a different coercivity, and the individual ones of the polyhedral magnets within each subset have similar coercivities.

[0069] In one embodiment, when the change in the magnetic coercivity of the individual ones of the polyhedral magnets in a given subset does not exceed 5%, preferably does not exceed 2%, the individual ones of the polyhedral magnets in the given subset are said to have mutually similar magnetic coercivities.

[0070] In one embodiment, two or more polyhedral magnets or subsets of polyhedral magnets are said to have different magnetic coercivities when the difference between the magnetic coercivities exceeds a threshold of 10%, preferably exceeds a threshold of 20%.

[0071] In one embodiment, the first subset of polyhedral magnets has a higher coercivity than the second subset of polyhedral magnets.

[0072] In one embodiment, the first subset of polyhedral magnets having a higher coercivity is arranged closer to the test volume, and the second subset of polyhedral magnets having a lower coercivity is arranged farther away from the test volume.

[0073] In one embodiment, the number of polyhedral magnets in the first and second subsets and their positions within the magnet array of polyhedral magnets are selected according to a simulation.

[0074] In one embodiment, the magnet array includes thirty-six polyhedral magnets respectively arranged in an inner ring, a middle ring, and an outer ring of six, twelve, and eighteen hexagonal prismatic magnets, where four to six of the inner hexagonal prismatic magnets are closest to the test volume and have the highest coercivity.

[0075] In one embodiment, each of the plurality of polyhedral magnets has a unique coercivity H T exceeding a threshold coercivity H c,i and has.

[0076] In one embodiment, the selection of the individual polyhedral magnets that define the first subset and the second subset is based on considerations of symmetry related to the magnet positions within the magnet array.

[0077] In one embodiment, at least some of the polyhedral magnets are arranged in a Halbach structure.

[0078] According to a further aspect, a method for determining a threshold coercivity for one or more magnets in a magnet array including a plurality of polyhedral magnets arranged in a magnet structure, the plurality of polyhedral magnets including a first subset of polyhedral magnets and a second subset of polyhedral magnets, the plurality of polyhedral magnets at least partially surrounding a test volume, and the first subset and the second subset of polyhedral magnets having different magnetic coercivities, comprising: a: Simulating an initial arrangement of the plurality of polyhedral magnets within the magnet array, with each individual polyhedral magnet having a predetermined magnet array position and an initial magnetization vector orientation; b: Selecting a set of points

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[0079] In one embodiment, the method further includes determining one or more symmetry classes of the magnet array before performing step a, and assigning each of the plurality of polyhedral magnets in the magnet array to one of the corresponding symmetry classes; and assigning the value of the threshold coercive force H_T determined in step f to all the magnets in the symmetry class associated with at least one individual polyhedral magnet.

[0080] In one embodiment, each magnet position in a given symmetry class is associated with other magnet positions in the same symmetry class by a symmetry element selected from the group consisting of a reflecting surface, a rotation axis, a rotation-reflection axis, an inversion center, a magnetic reflecting surface, a magnetic rotation axis, a magnetic rotation-reflection axis, and a magnetic inversion center.

[0081] In one embodiment, the method further includes determining a maximum coercive force H max for at least one individual polyhedral magnet; when the threshold coercive force H T calculated in step f exceeds the maximum coercive force H max , selecting an alternative in the direction of the initial magnetization vector for at least one individual polyhedral magnet

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[0082] According to another aspect, there is provided a method for assembling a magnet array, comprising determining a threshold coercive force H T according to claim 44 for each of a plurality of polyhedral magnets at a given magnet array position within the magnet array, and arranging a set of polyhedral magnets within the magnet array, wherein each individual one of the set of polyhedral magnets has a coercive force exceeding the threshold coercive force H T calculated for the given magnet array position for assembling the magnet array.

[0083] According to a further aspect, there is provided a magnetic resonance apparatus comprising a magnet array including a plurality of polyhedral magnets arranged in a magnet structure, the plurality of polyhedral magnets including a first subset of polyhedral magnets and a second subset of polyhedral magnets, the plurality of polyhedral magnets at least partially surrounding a test volume, and the first subset and the second subset of polyhedral magnets having different magnetic coercive forces.

[0084] According to yet another aspect, there is provided a magnet array including a plurality of polyhedral magnets arranged in a Halbach cylinder structure, wherein the centers of the individual ones of the plurality of polyhedral magnets are substantially arranged in a plane within a magnet rack, the plurality of polyhedral magnets at least partially surround a test volume, and a subset of the centers of the individual ones of the plurality of polyhedral magnets is laterally displaced from a nominal position within the magnet rack to cancel a magnetic field gradient of the magnet array.

[0085] In one embodiment, the magnet array includes a pole piece. The pole piece can be adapted to generate a magnetic field gradient.

[0086] In one embodiment, the plurality of polyhedral magnets are hexagonal prismatic magnets.

[0087] In another embodiment, the magnet array includes a plurality of magnet racks arranged in a rack stack. In one embodiment, the magnet array can include four magnet racks. In another embodiment, the magnet array can include five magnet racks.

[0088] In one embodiment, a magnet rack includes thirty-six hexagonal prismatic magnets. The thirty-six hexagonal prismatic magnets can be arranged in inner, middle, and outer rings of six, twelve, and eighteen hexagonal prismatic magnets, respectively, where the inner hexagonal prismatic magnets are closest to the test volume.

[0089] In one embodiment, the centers of two of the six hexagonal prismatic magnets in the inner ring are laterally displaced from a nominal position within a magnet rack that is farther from the test volume, and the centers of four of the six hexagonal prismatic magnets in the inner ring are laterally displaced from a nominal position within a magnet rack that is closer to the test volume.

[0090] In one embodiment, the magnet array may further include a first subset of polyhedral magnets and a second subset of polyhedral magnets, and the first subset and the second subset of polyhedral magnets have different magnetic coercivities.

[0091] In one embodiment, a subset of the centers of the individual polyhedral magnets that are laterally displaced from their nominal positions within the magnet rack are located further away from the test volume.

[0092] In one embodiment, a subset of the centers of the individual polyhedral magnets that are laterally displaced from their nominal positions within the magnet rack are located closer to the test volume.

[0093] In one embodiment, a first portion of a subset of the centers of the individual polyhedral magnets that are laterally displaced from their nominal positions within the magnet rack is located further away from the test volume, and a second portion of the subset of the centers of the individual polyhedral magnets that are laterally displaced from their nominal positions within the magnet rack is located closer to the test volume.

[0094] In another aspect, providing a plurality of polyhedral magnets, providing a self - framework within a magnet rack of the magnet array, and the self - framework is for receiving the polyhedral magnets, arranging the plurality of polyhedral magnets within the self - framework in the magnet rack, and the centers of the individual ones of the plurality of polyhedral magnets are substantially disposed in a plane within the magnet rack, the plurality of polyhedral magnets at least partially surround a test volume, and a subset of the centers of the individual ones of the plurality of polyhedral magnets are laterally displaced from their nominal positions within the magnet rack to cancel the magnetic field gradient of the magnet array, and placing the magnet rack within a rack stack to assemble the magnet array, A method for assembling a magnet array is provided, which comprises the above steps.

[0095] According to a further aspect, there is provided a magnetic resonance apparatus comprising a magnet array including a plurality of polyhedral magnets arranged in a Halbach cylinder structure, wherein the centers of the individual ones of the plurality of polyhedral magnets are substantially arranged in a plane within a magnet rack, the plurality of polyhedral magnets at least partially surround a test volume, and a subset of the centers of the individual ones of the plurality of polyhedral magnets is laterally displaced from a nominal position within the magnet rack to cancel the magnetic field gradient of the magnet array.

[0096] The features and advantages of the subject matter of this specification will become more apparent from the following detailed description of selected embodiments, as illustrated in the accompanying drawings. As will be understood, the disclosed and claimed subject matter can be modified in various respects without departing from the scope of the claims. Accordingly, the drawings and description are to be regarded as illustrative in nature and not as restrictive, and the full scope of the subject matter is set forth in the claims.

Brief Description of the Drawings

[0097] Further features and advantages of the present disclosure will become apparent from the following detailed description in combination with the accompanying drawings.

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[0098] Note that throughout the accompanying drawings, similar features are identified by similar reference numerals.

[0099] (Detailed Description) In one embodiment, a magnet array includes a plurality of polyhedral magnets arranged in a Halbach cylinder structure, wherein the centers of the individual ones of the plurality of polyhedral magnets are substantially arranged in a plane within a magnet rack, the plurality of polyhedral magnets at least partially surround a test volume, and the magnet array includes a first plurality of polyhedral magnets arranged in a Halbach cylinder structure and a second plurality of polyhedral magnets arranged in a non-Halbach structure. In another aspect, a magnet array is disclosed that includes a first subset and a second subset of polyhedral magnets having different coercivities. In yet another aspect, a magnet array is disclosed in which a subset of the centers of the individual ones of the plurality of polyhedral magnets is laterally displaced from a nominal position within a magnet rack to cancel a magnetic field gradient of the magnet array.

[0100] The present invention is not limited in its scope and will be more readily understood by reference to the following examples given for the purpose of illustrating the invention.

[0101] In the present disclosure, the term "Halbach cylinder structure" refers to a structure of individual magnets (often referred to as constituent magnets) arranged around a central volume including an

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[0102] In the present disclosure, the term modified Halbach magnet structure means the structure (or arrangement) of individual constituent magnets that includes at least two subsets of magnets, where at least one subset is composed of a Halbach cylindrical magnet structure and at least one other subset has another (non-Halbach) magnet structure, as discussed in the present disclosure. In some embodiments of the present disclosure, such a modified Halbach magnet structure provides a design condition that can improve the actual implementation of the Halbach cylinder to provide a magnetic field with improved characteristics in use. A subset of magnets may also be referred to as a plurality of magnets or a group of magnets or a part of a magnet.

[0103] In the present disclosure, the term magnet rack means a collection of individual (constitutive) magnets arranged in a holding structure such that their centers lie in a plane. As an example, FIG. 6 shows a plan view of one embodiment of a magnet rack 250 and individual constitutive magnets 210. As shown in FIG. 8A, the magnet rack 250 includes a self-framework 215 and a framework housing 251. In these examples, the individual constitutive magnets are hexagonal prisms, each having a six-fold symmetry axis disposed out of the plane of the page. In some embodiments, the individual constitutive magnets can be arranged such that their centers coincide with points within a lattice. In the present disclosure, the term lattice means a set of points each displaced from the origin by a sum of integer multiples of vectors selected from the [Number] set of vectors.

[0104] In the present disclosure, a magnet rack stack means a collection of magnet racks stacked along an axis perpendicular to the plane containing the centers of the individual constitutive magnets of the magnet racks. As an example, FIG. 7A shows a perspective view of an embodiment of a rack stack 230 comprising four magnet racks 250. In some embodiments, for example, for design or manufacturing purposes, the rack stack can have additional structures attached or mounted thereto, such as an upper structure (not shown in FIG. 7A) or a base structure 260 (as shown in FIGS. 6 and 7A). In some embodiments, the rack stack can include 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, or any number of magnet racks.

[0105] In the present disclosure, the individual ones of the polyhedral magnets within a magnet structure (array) are selected from the group consisting of truncated hexahedrons; rhombic dodecahedrons; Platonic solids; Archimedean solids; Johnson solids; prisms; chamfered polyhedrons; and truncated polyhedrons. A prism is understood to mean a polygon that includes two opposing congruent n-sided polygonal faces with corresponding sides of the polygonal faces joined by n rectangular faces. An example used in the present disclosure is a hexagonal prism where n is 6.

[0106] In the present disclosure, a magnetic field gradient is a characteristic of a magnetic field having a spatial variation in its intensity or direction. In many practical applications, and particularly in magnetic resonance applications, a magnet assembly that generates a strong and spatially uniform magnetic field is desired. In that case, since the magnetic field is well approximated by its projection along an axis, the magnetic field is represented as a scalar value B, which is a component of the magnetic field along that axis.

Number

[0107] In the present disclosure, a second-order magnetic field gradient is a magnetic field gradient in which the component of the magnetic field changes in proportion to the square of a spatial coordinate. For example, a magnetic field having a z-component in the form of

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[0108] In the present disclosure, the term magnetic resonance or MR means the resonant reorientation of the magnetic moment of a sample in one or more magnetic fields, and includes nuclear magnetic resonance (NMR), electron spin resonance (ESR), magnetic resonance imaging (MRI), and ferromagnetic resonance (FMR). Some embodiments can also be applied to ion cyclotron resonance (ICR). In certain applications and embodiments, the disclosed devices and methods are applied to NMR, and in some embodiments, they are applied to an NMR spectrometer or an NMR imager. Materials that exhibit magnetic resonance when exposed to a magnetic field are called magnetic resonance or MR active nuclides or materials.

[0109] In the present disclosure, the terms primary magnetic field, main magnetic field, primary magnetic field and main magnetic field mean the magnetic field generated by a magnet array. In a series of embodiments, a magnetic field strength in the range of 1.0 to 3.0 tesla is achieved. However, in another embodiment, the magnetic field strength may be less than 1.0 tesla or greater than 3.0 tesla. The magnetic field strength varies depending on the number of magnet racks, the strength of individual constituent magnets, the presence or absence and type of pole pieces, the manufacturing materials used, and other variables.

[0110] In embodiments of the present disclosure, the magnet array may be included in a magnetic resonance device or apparatus. For example, FIG. 5 is an exemplary block diagram of a magnetic resonance device 150 according to an embodiment of the present disclosure. The device 150 includes a computer 151 operably connected to a sample rotation control module 152 to control the rotation of an optional sample rotor 154 used to rotate a sample 156 within a sample tube 157 within a sample channel 158 provided in a magnet array 159. The computer 151 may also be operably connected to a pulse magnetic field control and signal detection module 160 used to control a detection coil 162 and receive signals therefrom. The device 150 may also include a magnetic field uniformity control module 164 for controlling the magnetic field within a centrally located test volume 165. A temperature control module 166 may also be provided to control the temperature of the magnet array 159 and the temperature within the channel 158.

[0111] In embodiments of the present disclosure, a method for constructing a magnetic resonance apparatus including a magnet rack, a magnet rack stack, and ultimately a magnet array is disclosed. To describe fabricating a magnetic resonance apparatus based on these magnet arrays, different terms such as assembling, constructing, manufacturing, fabricating, or making can be used. These terms refer to constructing a physical device rather than mimicking the characteristics of the magnet array.

[0112] (Displacement of the magnet) FIG. 6 shows an example of the structure of magnets within a magnet rack 250 shown as a plan view. These magnets can be magnetized according to a Halbach cylinder structure. The magnet array (or known as a magnet assembly) is generally designated as 200. For clarity, the magnet array 200 may include magnets in additional magnet racks not shown in FIG. 6. The individual hexagonal magnets 210 form a hexagonal cylindrical arrangement surrounding a central cavity 220. In FIG. 6, six magnets are shown closest to the central cavity. Additional magnets are arranged further away from the central cavity. The dimensions and composition of the individual hexagonal magnets can vary. For example, some of the magnets 210 in the array may be larger than other magnets 240 in the array. In the example shown in FIG. 6, the smaller magnets 240 can be oriented at different angles relative to the larger magnets 210. The magnets are surrounded by a self - framework within the magnet rack 250 disposed on a base 260. In this example, there are twenty - four larger magnets 210 and twelve smaller magnets 240 within the rack, however, other variations in the number of magnets are possible and magnets of more than two types and / or dimensions can be incorporated into the Halbach - based array. In use, the sample is generally placed at or near the center of the central cavity 220 in a defined sample volume, sample space, or test volume.

[0113] One way to increase the strength of the magnetic field of a magnet array is to use a pole piece that can acquire magnetic polarization when placed in a magnetic field. This polarization can increase the strength of the magnetic field in the spatial region near the pole piece to a value greater than that without the pole piece. In use, it may be desirable to use the pole pieces in pairs rather than individually. FIG. 3D shows a known exemplary structure of a pole piece 54 within a hexagonal cavity defined by a set of six magnets 52, each having the shape of a hexagonal prism.

[0114] FIG. 7A is a perspective view of the magnet assembly of FIG. 6, showing a stack 230 of four cylindrical racks 250 above a base 260, each rack having a magnet arrangement as shown in FIG. 6. Other numbers of racks, such as one, two, three, four, or five racks, can be used, and the magnet arrangement in each rack can be the same as or different from that of the other racks. As an example, FIG. 7B shows a perspective view of a stack 235 of five racks 255. Shown is the upper rack having a magnet structure 201 alternative to those shown in FIGS. 6 and 7A. As shown in FIG. 7B, thirty-six hexagonal prismatic magnets 210 can be arranged in inner, middle, and outer rings of six, twelve, and eighteen hexagonal prismatic magnets respectively, with the inner hexagonal prismatic magnets closest to the central cavity, which can contain the sample test volume in an NMR spectrometer. Just as different numbers of magnet racks can be included in the magnet rack stack, although thirty-six magnets are shown in this example, other numbers, arrangements, and types of magnets can be used in the magnet structures described herein.

[0115] Figure 8A shows a rack 250 that includes a self - framework 215 and a framework housing 251. The self - framework 215 should be regarded as the nominal framework in this disclosure that can be compared with other frameworks. An example of the function of the self - framework is to guide the placement of individual constituent magnets within the magnet rack 250 during the assembly of the rack. Another example of the function of the framework is to separate some or all of the magnets within the rack. In other words, the self - framework defines a number of cells, and each cell is for receiving individual constituent magnets into the magnet rack. In other embodiments, the cells within the self - framework can receive composite magnets as disclosed herein.

[0116] In a non - limiting example, the magnet rack has a height of 1.5 inches, similar to the hexagonal prismatic magnets within the rack (1.5 inches along the six - fold symmetry axis of the hexagonal prism). The width of the cells within the self - framework is 1.25 inches (from the mid - point of one edge across the hexagonal face to the mid - point of the opposite edge), and the thickness of the wall that structures the framework itself is 0.030 inches. In other embodiments, the dimensions of the magnets and the self - framework can be larger or smaller depending on the application and the desired magnetic field strength.

[0117] As shown in Figure 8A, the self - framework 215 defines a plurality of cells, the innermost six of which surround a central cavity and are labeled A for convenience. This framework 215 can receive up to thirty - six magnets arranged around the central cavity 220. The framework 215 includes framework sections 217 that are connected to each other via framework vertices 221. (Note: In the figure, not all framework sections and vertices are explicitly labeled.). A Cartesian coordinate axis system is shown in Figure 8A, with the x - axis directed out of the plane of the page, and this axis system can be understood to pass through Figures 8B - 8G.

[0118] FIG. 8B shows the modified self-framework 316 within the rack 350. This framework 316 can also accept up to thirty-six magnets disposed around the central cavity 320. However, the framework 316 includes fewer framework sections 317 and fewer framework vertices 321 than shown in the framework 215 of FIG. 8A. In particular, there are no several framework sections between the individual magnet cells labeled C and between the magnet cell labeled C and the central cavity of the framework. This removal allows the magnets disposed within the cell labeled C to be brought closer to the central cavity and closer to each other. Further, the framework section between the cell labeled B and the adjacent cell on the side of the cell labeled B opposite the central cavity 320 is also removed. This removal allows the magnets disposed within the cell labeled B to be further separated from the central cavity. In embodiments of the present disclosure, a framework section (e.g., section 318) may have a thinner width than other framework sections (e.g., section 319). In a non-limiting example, when the wall thickness of the nominal framework is 0.030 inches, the displacement range is set to values in the range of approximately ±0.030 inches. In another embodiment, the displacement range will similarly be constrained by the mechanical properties selected for the framework.

[0119] These in-plane (lateral) displacements of the centers of the magnets from the nominal framework shown in FIG. 8A can generate a secondary magnetic field body gradient that is opposite in sign to the secondary magnetic field gradient generated by the insertion of the pole piece into the magnet structure. Thus, the considered placement of the constituent magnets into the framework can be implemented to cancel out the secondary magnetic field gradient generated by the pole piece. FIG. 8C more clearly shows (in the form of arrows) the directions of the displacements just described for the framework 316 in FIG. 8B as compared to the framework 215 in FIG. 8A.

[0120] To affect the magnetic field and magnetic field gradient, alternative modifications can be made to the self - framework. By way of example and not limitation, FIG. 8D shows an alternative embodiment of a modified self - framework 422 within the rack 450. This framework 422 can receive a plurality of magnets disposed around the central cavity 420. The framework 422 is different from the frameworks 316 and 215. The framework 422 includes fewer framework sections 417 and the same number of framework vertices 421 compared to the framework 215. FIG. 8E shows (in the form of arrows) the magnet displacement (change in magnet position) resulting from the framework shown in FIG. 8D compared to the framework shown in FIG. 8A.

[0121] FIG. 8F shows yet another alternative embodiment of the modified self - framework 523. FIG. 8G shows, using arrows, how the positions of a subset of the magnets change from the framework of FIG. 8A to the framework of FIG. 8F.

[0122] The differences between the exemplary frameworks shown in FIGS. 8B, 8D, and 8F compared to the nominal framework shown in FIG. 8A can be regarded as distortions of the nominal framework. The nominal framework shows equal spacing between the magnets, and the distortion can make the spacing between the magnets unequal. Such distortion can amplify or reduce the specific magnetic field gradient imposed by the insertion of the pole piece, thereby potentially reducing the detrimental effects of the gradient in the main magnetic field. This function can potentially broaden the range of pole - piece shapes compatible with various applications. For example, a distorted framework can cancel out the detrimental effects on the magnetic field gradient of a pole piece disposed in the central cavity, resulting in an overall improvement in the uniformity and strength of the magnetic field.

[0123] In one embodiment of the present disclosure, a magnet rack stack can include individual magnet racks that include the same framework or different frameworks. The selection of the framework for an individual magnet rack within the magnet rack stack can be based on factors such as an understanding of the magnetic field gradient of the magnet array (and which magnetic field gradients require suppression), ease of assembly of the magnet array, cost of assembly, or other technical and / or practical factors. FIG. 9 shows an exploded view of one non-limiting example of a magnet rack stack 535 that includes five magnet racks. The upper and lower (first and fifth, counting from the top) magnet racks are shown to include the nominal framework 215 of FIG. 8A, while in this example of the rack stack 535, two magnet racks (second and fourth) include the distorted framework 316 of FIG. 8B, and the central (third) magnet rack of FIG. 9 includes the distorted framework 422 of FIG. 8D. FIG. 9 shows a top-to-bottom symmetry that can be advantageous in some applications, while other applications may require, or may benefit from, an antisymmetric or asymmetric arrangement where the frameworks are different for each rack.

[0124] The disclosed modified Halbach magnet array can be physically assembled (e.g., into a magnet rack, a magnet rack stack, or a magnetic resonance apparatus). In one embodiment of the present disclosure, a method for assembling the magnet array includes providing a physical set of polyhedral magnets and providing a self-framework for receiving the polyhedral magnets within a magnet rack of the magnet array. The method includes placing these polyhedral magnets within the self-framework of the magnet rack. The centers of the polyhedral magnets within the magnet rack can be substantially disposed in a plane within the magnet rack of the magnet array, and the polyhedral magnets can be configured to at least partially surround a test volume that houses a chemical sample for analysis during use. In this method, a subset of the centers of the polyhedral magnets is displaced laterally from the nominal positions of the magnet rack (in accordance with the structure of the self-framework) to cancel out the magnetic field gradient of the magnet array. The method can further include placing the magnet rack within a rack stack to assemble the magnet array.

[0125] The disclosed modified Halbach magnet array, including examples of related magnet racks and magnet rack stacks shown in FIGS. 6-9, can be used, for example, in a magnetic resonance apparatus as shown in FIG. 5. The magnetic resonance apparatus is a magnet array including a plurality of polyhedral magnets arranged in a Halbach cylindrical structure, wherein the centers of the individual ones of the plurality of polyhedral magnets are substantially arranged in a plane within the magnet rack, the plurality of polyhedral magnets at least partially surround a test volume, and also, a subset of the centers of the individual ones of the plurality of polyhedral magnets is laterally displaced from a nominal position within the magnet rack to cancel a magnetic field gradient of the magnet array can be included.

[0126] (Coercive force) Permanent magnet materials can be subject to magnetic stress (demagnetizing force) when the magnets are placed in a strong magnetic field, for example, when they are placed such that their magnetization vectors align opposite to the magnetic field generated by a nearby strong magnet. Magnets under such stress can be partially or completely demagnetized, and this detrimental effect can be exacerbated at high temperatures. The resistance to this effect, for a particular magnetic material, is quantified by its intrinsic magnetic coercive force (also called the intrinsic coercivity) H c,i c. It is often the case that when the term coercive force is used without modification, the term is understood to mean the intrinsic coercive force. The SI unit of coercive force is ampere / meter (A / m), and the cgs unit of coercive force is oersted. Magnets with a high coercive force (high resistance to demagnetization) are generally more costly than magnets with a low coercive force. Thus, to optimize performance and cost when constructing a magnet array for applications including NMR spectroscopy, it is advantageous to know where in the magnet structure high coercivity magnets can be used and where low coercivity magnets can be used. For example, magnets showing a high coercive force may be desirable at locations within the magnet array where the magnetic field is strong and opposes the magnetization of the magnet itself. Such an arrangement of high coercivity magnets may reduce the tendency for the magnets at such locations to be demagnetized or increase the actual temperature range over which a device incorporating the magnet array can be used.

[0127] Commercial manufacturers typically specify magnet materials by grade, and this grade is associated with a coercivity label. For example, grades N42, N42M, N42H, N42SH, N42UH, N42EH, and N42AH are available for purchase. As this list progresses, the coercivity of each grade increases. Between successive grades in the list, the coercivity can vary by more than 20%. Within a grade, the variation in coercivity is typically less than a few percent. In the present disclosure, "same" coercivity magnets are understood to mean magnets of the same commercial grade with a coercivity variation not exceeding 5%, preferably not exceeding 2%. In the present disclosure, "different" coercivity magnets are understood to mean magnets of different grades, where the difference between the coercivities exceeds a threshold of at least 10%, preferably 20%.

[0128] Another important characteristic of magnetic materials and the component magnets made from these materials is the residual magnetization. This quantity is the magnetization present in the magnetic material after being magnetized during manufacture. Often, manufacturers specify, instead of the residual magnetization, for example, the residual magnetic field B r which is a proportional quantity. Residual magnetization is important in the design and use of magnet arrays as it effectively characterizes the "strength" of the component magnets and their ability to generate a magnetic field at locations outside the space occupied by the magnets.

[0129] The "maximum energy product", which is the maximum product achievable of the magnetic flux density and the magnetic field strength, is often associated with the exchange between high residual magnetization and high coercivity in the strongest available magnets. Thus, using knowledge of the overall magnetic field present within a magnet array, particularly within the volume occupied by the individual component magnets, to increase the available overall magnetic field generated within the central test volume of the array or to reduce the overall cost of the device incorporating the magnet array, identifying positions (also referred to as locations or sites within the array) with relatively weak coercive stress for selecting magnets with lower coercivity and lower cost (or correspondingly higher residual magnetization) is one aspect of the present disclosure.

[0130] Disclosed herein is a performance index, a threshold coercive force H T which is for the constituent magnets at a predetermined position within the magnet array. The intrinsic coercive force H c,i of the magnetic material used for the constituent magnets must exceed this threshold coercive force.

[0131] The point inside the magnetic material

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[0132] Björk et al. considered the problem of demagnetization of the magnet array and, as a criterion for estimating when there is a magnet under a magnetizing stress large enough to cause demagnetization [Number] which is given by (see R. Bjork, A. Smith, and C. Bahl, “The efficiency and the demagnetization field of a general Halbach cylinder,” Journal of Magnetism and Magnetic Materials vol. 384, p. 128, 2015, and in particular Equation (8) therein).

[0133] When used in reliable magnet products, this criterion is not stringent enough. The magnet assembly needs to be robust against temperature changes (e.g., during shipping of commercial products) and tolerances in manufacturing specifications related to magnetic materials, constituent magnets, holding structures, etc.

[0134] Taking such factors into account, the manufacturer - specified coercivity [Number] (at the specified standard temperature θ spec , e.g., 20 °C) of each constituent magnet should satisfy the following inequality. [Number] wherein [Number] is the minimum (most negative) value of the dot product [Number] in the magnet, α is a safety factor (e.g., 90% (0.90)), k is the temperature coefficient of coercivity of the magnetic material (e.g., 0.0056 °C -1 ), and ΔT is the difference between the maximum operating temperature and the standard temperature used in the coercivity specification. Also, the following equation defining the threshold coercivity is disclosed herein. [Number]

[0135] To meet the above performance criteria, the manufacturer-specified coercive force for the magnet at a given site must exceed H T for that site.

[0136] In one embodiment of the present disclosure, the coercive force selection method includes the following steps. 1: Arrange the constituent magnets at the specified positions according to the proposed modified Halbach magnet structure, orient their magnetization vectors, and set up a static magnetic simulation. 2: For each position of each constituent magnet 2.1: Select a set of points within the magnet volume associated with the position of the magnet. 2.2: Run the static magnetic simulation to obtain the magnetic field strength

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[0137] Commercially available simulation software can be adapted to perform Step 1. Non-limiting examples of such software include products of COMSOL and products of Ansys, Inc.

[0138] In a second embodiment, prior to the steps of the nominal embodiment, there is a step (Step 0) of assigning each constituent magnet position to a position of a symmetry class, where each position is related to other members of its assigned symmetry class by symmetry elements of the entire assembly such as a reflection plane, a rotation axis, a rotation-reflection axis, or an inversion center, or a magnetic reflection plane, a magnetic rotation axis, a magnetic rotation-reflection axis, or a magnetic inversion center. Next, Step 2 of the nominal method is performed at the positions of each symmetry class.

[0139] As in the theory of symmetry of magnetic materials (see, for example, M. Hamermesh's Group Theory and its Application to Physical Problems, Dover, New York, 1989), in this disclosure, the term magnetic symmetry element including a magnetic reflection plane, a magnetic rotation axis, a magnetic rotation-reflection axis or a magnetic inversion center is understood to mean the corresponding symmetry element followed by a reversal of the current and a reversal of the corresponding magnetization direction.

[0140] In a further embodiment, Step 2.6 of the second embodiment is replaced with a conditional step (2.6-A) as follows. (2.6-A) If the threshold coercive force exceeds the desired maximum coercive force H max then an alternative direction for magnetization at the positions of the above symmetry class [Number] Select and repeat step 2. Otherwise, for each of the magnets at the positions of the symmetric classes, select an available (physical) configured magnet having a coercivity greater than H T In one embodiment of the present disclosure, the magnet array may include two subsets of polyhedral magnets, where one subset has polyhedral magnets with a relatively high coercivity compared to a second subset of magnets having a relatively low coercivity. The first subset of polyhedral magnets having a higher coercivity can be placed closer to the test volume within the array, and the second subset of polyhedral magnets having a lower coercivity can be placed farther from the test volume.

[0141] The number of polyhedral magnets in the first subset having a higher coercivity, the coercivity value, and the location within the magnet array where the first subset is placed can be selected according to a simulation such as a static magnetic simulation. Similarly, the number of polyhedral magnets in the second set having a lower coercivity, the coercivity value, and the location within the magnet array where the second subset is placed can also be specified by the simulation. The locations within the array selected for the magnets with high coercivity can be determined to coincide with those locations in the simulation that exhibit a stronger demagnetizing force, and the locations within the array selected for the magnets with reduced coercivity can be determined to coincide with those locations in the simulation that exhibit a weaker demagnetizing force. Further examples regarding coercivity are described in the next section.

[0142] (Magnetization vector)

[0143] (Magnetization vector) In the present disclosure, a magnet having a magnetization vector in a plane defining a magnet rack (e.g., the yz plane shown in FIG. 8A) is said to be magnetized in the diametrical direction. A magnet having a magnetization vector perpendicular to the plane of the magnet rack is said to be magnetized in the axial direction. A magnet having a magnetization vector that is not in the plane but is not perpendicular to the plane is said to be magnetized obliquely. An axially magnetized magnet or an obliquely magnetized magnet is said to have out-of-plane magnetization.

[0144] Figure 10 shows an example of a magnet in the shape of a hexagonal prism. In Figure 10, magnet A is a magnet magnetized in the diametrical direction, where its magnetization vector (indicated by the arrow) is perpendicular to the rectangular side surface of the magnet and perpendicular to the six-fold symmetry axis of the hexagonal face of the magnet. Magnet B is edge-magnetized in the diametrical direction, where its magnetization vector is perpendicular to the six-fold rotational symmetry axis of the hexagonal face of the magnet and extends from the long edge in contact with the rectangular face of the magnet, across the body of the magnet, to the opposite edge. It will also be readily understood that this vector is parallel to the specific opposing rectangular face of magnet B. Figure 10 also shows magnet E magnetized in the axial direction, i.e., magnetized along a vector that coincides with the six-fold symmetry axis of the magnet.

[0145] Magnets C and D are examples of magnets magnetized obliquely. More precisely, magnet C is obliquely edge-magnetized, where its magnetization vector extends from the midpoint of one edge in contact with the hexagonal face of the magnet to the midpoint of the opposite edge in contact with the opposite hexagonal face of the magnet and across the center of the magnet. It will be recognized from Figure 10 that the magnetization vector of magnet C is perpendicular to the edge and that the magnetization vector forms an acute angle with the six-fold symmetry axis of magnet C. Magnet D is obliquely vertex-magnetized and has a magnetization vector extending from one vertex, passing through the center of the magnet, to the opposite vertex. The magnetization vector of magnet D also forms an acute angle with the six-fold symmetry axis of magnet D.

[0146] In a Halbach cylinder magnet structure such as those shown in Figure 1B, Figures 3A - D, and Figure 5, all magnets are magnetized in the diametrical direction. That is, the magnetization vector has only components in the radial and azimuthal directions and thus lies in the plane of the corresponding magnet rack or other holding structure.

[0147] In the present disclosure, a modified Halbach magnet structure is described that includes a first subset of magnets in a Halbach cylinder structure and a second subset of magnets that may include axially or obliquely magnetized magnets or diametrically magnetized magnets that deviate from the magnetization defined by a strict Halbach cylinder structure. Including the second subset of magnets together with the first subset of magnets can advantageously increase the magnetic field strength within a sample test volume that is at least partially surrounded by the magnet structure.

[0148] By way of example and not limitation, FIG. 11 shows a rack 650 in a perspective view including two subsets of hexagonal prismatic magnets according to one embodiment of the present disclosure. A first subset of magnets indicated by black arrows and labeled 631 are magnetized in the diametrical direction and form a Halbach cylinder structure around a central volume 620. The magnets of the second of the two subsets are not magnetized in the diametrical direction, but rather, in this example, are axially magnetized (641 and 645), obliquely edge magnetized (670), and obliquely vertex magnetized (661) as shown scattered within the rack 650. Each magnet is held in a fixed position within the magnet rack 650 by a self-framework 615.

[0149] Generally, a magnet structure according to one embodiment of the present disclosure includes a plurality of subsets of magnets. The first subset includes magnets magnetized and oriented in the diametrical direction according to a Halbach cylinder structure. The second subset (and further third or fourth or subsequent subsets) of magnets includes magnets that are not magnetized according to a Halbach cylinder structure. These second and further subsets include magnets that can be magnetized in the axial, oblique, or diametrical direction.

[0150] In some embodiments, the displacement within the subset

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[0151] Figures 12A - E collectively show examples of magnet rack stacks and related magnet racks according to embodiments of the present disclosure. FIG. 12A shows a magnet rack stack 700 of five cylindrical racks in an exploded view. The racks are stacked such that their centers are aligned along a central axis 710. The rack stack includes a first (upper) rack 750, two intermediate racks 730 (second and fourth from the top of the rack stack), a third (central) rack 720, and a fifth (lower) rack 740. Each rack is shown in a plan view in one of FIGS. 12B - E. In this example, the second and fourth racks have magnets of the same type and arrangement, and thus FIG. 12C shows the common structure of the two racks in a plan view. The upper and lower racks (750 and 740 respectively) are different, but FIGS. 12D (lower) and 12E (upper) show that these two racks are mirror images of each other, and the mirror plane is at the center of rack 720 in FIG. 12A and perpendicular to axis 710. Axis 710 coincides with the x - axis shown in each of the coordinate frames 723, 733, 743, and 753 shown in FIGS. 12B - E respectively.

[0152] Figure 12B is a plan view of the central rack 720 of FIG. 12A, which as a whole has a plane of symmetry that coincides with the plane of the page of FIG. 12B. Since the second and fourth (intermediate) racks have magnets of the same type and arrangement, and the upper and lower racks are mirror images of each other, the rack stack as a whole (FIG. 12A) shows a plane of mirror symmetry that is perpendicular to the axis 710 and coincides with the center of the rack 720.

[0153] In FIG. 12B, the third (central) rack 720 is shown in plan view, with hexagonal prismatic magnets arranged within the framework housing 721, and the magnetization vectors for each magnet within the rack are indicated by arrows 722. Some magnets, such as 724, belong to a subset of magnets that are magnetized precisely along vectors defined by a Halbach cylinder structure. Some magnets, such as 725, belong to a subset of magnets that are magnetized along vectors closest to the Halbach cylinder structure, given the constraint that magnetization is selected from a finite set of possibilities shown for the hexagonal prism of FIG. 10. The six centrally located magnets 726 are shown in a Halbach cylinder structure, and these magnets belong to a subset of magnets that have a high coercivity compared to other magnets within the magnet assembly. A further subset of magnets, such as 727, exhibit magnetization vectors that do not strictly conform to the Halbach cylinder structure, but rather are reoriented to lower the threshold coercivity at these positions within the magnet rack. At these locations, at the expense of a reduction in the magnetic field within the central bore (central volume) 760 as a result of the deviation of the magnets 727 from the exact Halbach cylinder magnetization orientation, a reduction in the threshold coercivity H T (and magnet cost) is allowed. As a whole, the third (central) magnet rack 720 includes an arrangement of twenty radially surface-magnetized magnets and sixteen radially edge-magnetized magnets, all of which are in-plane magnetized.

[0154] FIG. 12C shows a single intermediate (second and fourth) rack 730 in a plan view. Similar to the central rack 720, in the intermediate rack 730, hexagonal prismatic magnets are disposed within the framework housing 731, and the magnetization vectors are indicated by arrows 732 for each magnet within the rack. A subset of magnets, such as 734, is magnetized precisely along the vectors defined by the Halbach cylinder structure. Some magnets, such as 735, belong to a subset of magnets magnetized along the vector closest to the Halbach cylinder structure when there is a constraint that the magnetization is selected from a finite set of possibilities shown for the hexagonal prisms of FIG. 10. The six centrally disposed magnets 736 exhibit a Halbach cylinder structure, and these magnets belong to a subset of magnets having a high coercivity compared to the other magnets within the magnet assembly. In contrast to FIG. 12B, the magnets 737 within the magnet rack 730 show magnetization vectors that are reoriented such that their corresponding counterparts 727 within the central rack 720 reduce their threshold coercivity H T whereas in FIG. 12C they are not reoriented. In the intermediate rack, the threshold coercivity requirement is not as stringent as in the central rack. Overall, the second and fourth (intermediate) magnet racks 730 include an arrangement of twenty-eight diametrically surface-magnetized magnets and eight diametrically edge-magnetized magnets, all of which are in-plane magnetized.

[0155] Figure 12D shows the lower (fifth) rack 740 in a plan view. Similar to the central magnet rack 720 and the intermediate rack 730, the hexagonal prismatic magnets are arranged in the rack 740 within the framework housing 741, and the magnetization vectors are indicated by arrows 742 for each magnet within the rack. A subset of the magnets, e.g., 744, is magnetized precisely along the vectors defined by the Halbach cylinder structure. Some magnets, e.g., 745, belong to a subset of magnets that are magnetized along the vector closest to the Halbach cylinder structure when there is a constraint that the magnetization is selected from a finite set of possibilities shown for the hexagonal prisms of FIG. 10. Two of the six centrally located magnets 746 belong to a subset of magnets having a high coercivity compared to the other magnets within the magnet assembly. These magnets 746, along with the other types of magnets 747 and 748, exhibit magnetization vectors that deviate substantially from the corresponding ones of the central and intermediate racks 720 and 730, respectively. These magnets 746, 747, and 748 belong to a subset of magnets whose magnetization vectors are substantially determined according to the spherical Halbach structure and equation. Also in this case, in this context, "substantially" means that the magnetization vectors are selected from the finite set of possibilities shown in FIG. 10. Some of the magnets in this subset, e.g., 747 and 748, exhibit out-of-plane magnetization. In particular, these magnets are magnetized axially. In FIG. 12D, this is shown for magnet 748 by a circle enclosing a cross (to indicate magnetization into the plane of the page) and for magnet 747 by a circle enclosing a dot (to indicate magnetization out of the plane of the page).

[0156] FIG. 12E shows the upper (first) rack 750 in a plan view. The magnet rack 750 is a mirror image of the magnet rack 740, and the mirror plane is the plane of the page, i.e., the yz plane defined by the coordinate axes 743 and 753. Overall, the first and fifth (upper 750 and lower 740, respectively) magnet racks each include an arrangement of fourteen diametrically surface-magnetized magnets, four diametrically edge-magnetized magnets, and eighteen axially magnetized magnets. In other words, each of the first and fifth racks has eighteen magnets with in-plane magnetization vectors and eighteen magnets with out-of-plane magnetization vectors.

[0157] According to another embodiment of the present disclosure, a further example of a magnet rack stack is provided in the exploded view of FIG. 13. In FIG. 13, a rack stack 800 having five identical racks 730 is shown. The racks are arranged such that their centers are along the axis 810. Returning to FIG. 12C, all of the constituent magnets within the magnet rack 730 are magnetized in a substantially Halbach cylinder structure. The magnets are divided (subdivided or grouped) into two subsets depending on whether their coercive forces are relatively increased (high) or relatively not increased (low).

[0158] In the foregoing exemplary embodiments, the sites within the magnet rack are occupied by polyhedral magnets, particularly hexagonal prismatic magnets. In other embodiments, the selected sites can be occupied by a plurality of magnets, where the plurality of magnets are substantially shaped together to conform to the shape of the site as a whole. Each magnet within the plurality of magnets can be selected from a finite set of possibilities, such as the set shown in FIG. 10 for a hexagonal prismatic shape. FIG. 14 shows an exemplary embodiment in which a hexagonal prismatic site 900 as a whole is occupied by a plurality including two smaller hexagonal prismatic magnets 910 and 920. Magnets 910 and 920 each have two different magnetization vectors 915 and 925, where magnet 910 is magnetized axially while magnet 920 is obliquely edge magnetized. In the present disclosure, the terms composite magnet and composite polyhedral magnet are understood to mean a plurality of magnets within a cell or lattice site within a magnet assembly where each of the plurality of magnets has its own magnetization vector. The plurality of magnets are shaped together to conform to a single cell or lattice site. Using a composite magnet at a given site can increase the available range of effective average magnetization vectors within the cell or lattice site and the corresponding contribution to the magnetic field within the test volume of the magnet assembly. FIG. 14 shows a plurality including two magnets, and other composite magnets can include more than two magnets.

[0159] The disclosed modified Halbach magnet array can be physically assembled (e.g., into a magnet rack, a magnet rack stack, or a magnetic resonance apparatus). In one embodiment of the present disclosure, a method for assembling a magnet array includes providing a first physical set of polyhedral magnets and arranging these polyhedral magnets in a Halbach cylindrical magnet structure within a magnet rack. The centers of the first physical set of polyhedral magnets within the magnet rack can be substantially arranged in a plane within the magnet array such that the polyhedral magnets at least partially surround a test volume that houses a chemical sample for analysis during use. The method further includes providing a second physical set of polyhedral magnets within the magnet rack and arranging the second set of polyhedral magnets within the magnet rack in a non-Halbach structure. The method may further include arranging the magnet rack within a rack stack to assemble the magnet array.

[0160] The disclosed modified Halbach magnet array, including examples of related magnet racks and magnet rack stacks shown in FIGS. 11-14, can be used in a magnetic resonance apparatus, for example, as shown in FIG. 5.

[0161] A magnetic resonance apparatus comprises a magnet array including a first plurality of polyhedral magnets arranged in a Halbach cylindrical structure and a second plurality of polyhedral magnets within a magnet rack, wherein the centers of the individual ones of the first plurality of polyhedral magnets are substantially arranged in a plane within the magnet rack of the magnet array, the first plurality of polyhedral magnets at least partially surround a test volume, and the second plurality of polyhedral magnets are arranged in a non-Halbach structure.

[0162] A magnetic resonance apparatus comprises a magnet array including a plurality of polyhedral magnets arranged in a magnet structure, the plurality of polyhedral magnets including a first subset of polyhedral magnets and a second subset of polyhedral magnets, the plurality of polyhedral magnets at least partially surround a test volume, and the first subset and the second subset of polyhedral magnets have different magnetic coercivities.

[0163] Preferred embodiments have been described above and are shown in the accompanying drawings, but it will be apparent to those skilled in the art that modifications can be made without departing from the present disclosure. Such modifications are considered to be variations that may be included within the scope of the present disclosure.

Claims

1. A magnet array including a first plurality of polyhedral magnets arranged in a Halbach cylinder structure and a second plurality of polyhedral magnets in a magnet rack, wherein centers of individual magnets of the first plurality of polyhedral magnets are arranged to coincide with points in a lattice within substantially a plane in the magnet rack of the magnet array, the lattice being 【Number 1】 a set of points each displaced from the origin by a sum of integer multiples of vectors selected from a basis function system, the first plurality of polyhedral magnets at least partially surrounding a test volume, the second plurality of polyhedral magnets being arranged in a non-Halbach cylinder structure, the magnet rack including the first plurality of polyhedral magnets and the second plurality of polyhedral magnets, the magnet array including the magnet rack arranged in a rack stack.

2. The magnet array according to claim 1, wherein the second plurality of polyhedral magnets in the magnet rack include magnets having in-plane magnetization vectors, out-of-plane magnetization vectors, or combinations thereof.

3. The magnetization direction of at least one of the second plurality of polyhedral magnets located at a displacement vector 【Number 2】 from the origin within the test volume 【Mathematics 3】 is given by the formula: 【Number 4】 (wherein 【Number 5】 is 【Number 6】 a unit vector along.) and has an associated magnetic field having a specified magnetic field direction 【Number 7】 The magnet array according to claim 1.

4. The magnet array according to claim 1, wherein individual magnets of the polyhedral magnets are selected from the group consisting of truncated hexahedrons, rhombic dodecahedrons, Platonic solids, Archimedean solids, Johnson solids, prisms, chamfered polyhedrons, and truncated polyhedrons.

5. The magnet array according to claim 2, wherein the second plurality of polyhedral magnets include magnets that are obliquely edge-magnetized, obliquely vertex-magnetized, axially magnetized, or combinations thereof.

6. The magnet array according to claim 1, wherein the first plurality of polyhedral magnets include magnets that are diametrically face-magnetized, diametrically edge-magnetized, or combinations thereof.

7. The magnet array according to claim 1, wherein the first and second pluralities of polyhedral magnets are hexagonal prismatic magnets.

8. The magnet array according to any one of claims 1 to 7, including four magnet racks.

9. The magnet array according to any one of claims 1 to 8, including five magnet racks.

10. The magnet array according to any one of claims 1 to 9, wherein each of the magnet racks includes 36 hexagonal prismatic magnets.

11. The magnet array according to claim 10, wherein the 36 hexagonal prismatic magnets are respectively arranged in inner, middle, and outer rings of 6, 12, and 18 hexagonal prismatic magnets, and the inner hexagonal prismatic magnets are closest to the test volume.

12. The magnet array according to claim 1, wherein the polyhedral magnets are densely packed in the magnet rack.

13. The magnet array according to claim 1, wherein the magnet rack includes a self-framework and a framework housing.

14. The magnet array according to claim 13, wherein the magnet rack and the first and second plural polyhedral magnets each have a height of 3.81 cm.

15. The magnet array according to claim 13, wherein the cells in the self-framework have a width of 3.175 cm and the walls of the self-framework have a thickness of 0.0762 cm.

16. The magnet array according to claim 11, wherein at least one of the first plural polyhedral magnets in each of the individual magnet racks in the rack stack includes positions within the inner ring and the middle ring of 6 and 12 hexagonal prismatic magnets respectively.

17. The magnet array according to claim 11, wherein at least one of the second plural polyhedral magnets in each of the individual magnet racks in the rack stack includes a position within the outer ring of 18 hexagonal prismatic magnets.

18. The magnet array according to claim 11, wherein at least one of the individual magnet racks in the rack stack includes 22 diametrically surface-magnetized magnets, 8 obliquely vertex-magnetized magnets, 4 obliquely edge-magnetized magnets, and 2 axially magnetized magnets.

19. The magnet array according to claim 1, wherein the first magnet rack arranged on the central magnetic reflection surface of the rack stack has a first magnetic structure that is a magnetic reflection of the second magnetic structure of the second magnet rack arranged below the central magnetic reflection surface of the rack stack.

20. The magnet array according to claim 9, wherein the first of the five magnet racks in the rack stack has a magnetic structure that is a magnetic reflection of the fifth of the five magnet racks in the rack stack.

21. Each of the first plurality of polyhedral magnets in the first and fifth magnet racks includes 18 magnets having an in-plane magnetization vector, and each of the second plurality of polyhedral magnets in the first and fifth magnet racks includes 18 magnets having an out-of-plane magnetization vector. The magnet array according to claim 20.

22. The magnet array according to claim 21, wherein the 18 in-plane magnetized magnets include 14 diametrically in-plane magnetized magnets and 4 diametrically edge magnetized magnets.

23. The magnet array according to claim 21, wherein the 18 magnets having an out-of-plane magnetization vector are magnetized in the axial direction.

24. The magnet array according to claim 9, wherein the second magnet rack among the first to fifth five magnet racks in the rack stack has a structure that is a magnetic reflection of the fourth magnet rack among the five magnet racks in the rack stack.

25. The magnet array according to claim 24, wherein each of the first and second plurality of polyhedral magnets in the second magnet rack, the third magnet rack, and the fourth magnet rack includes a magnet having an in-plane magnetization vector.

26. The magnet array according to claim 25, wherein each of the second and fourth magnet racks includes 28 diametrically in-plane magnetized magnets and 8 diametrically edge magnetized magnets.

27. The magnet array according to claim 25, wherein the third magnet rack includes 20 diametrically in-plane magnetized magnets and 16 diametrically edge magnetized magnets.

28. The magnet array according to claim 1, further comprising a first subset of polyhedral magnets and a second subset of polyhedral magnets, wherein the first subset of polyhedral magnets and the second subset of polyhedral magnets have different magnetic coercivities.

29. A magnet array including a first plurality of polyhedral magnets arranged in a Halbach cylinder structure, a second plurality of polyhedral magnets in a magnet rack, and at least one composite magnet, wherein the centers of the individual magnets of the first plurality of polyhedral magnets are arranged to coincide with points in a lattice substantially in a plane within the magnet rack of the magnet array, the lattice is a set of points 【Number 8】 each of which is displaced from the origin by the sum of integer multiples of vectors selected from the basis function system and the first plurality of polyhedral magnets at least partially surround a test volume. The second plurality of polyhedral magnets are arranged in a non-Halbach structure, The magnet rack includes the first plurality of polyhedral magnets and the second plurality of polyhedral magnets, A magnet array including the magnet rack disposed within a rack stack.

30. The magnet array according to claim 29, wherein the at least one composite magnet is a hexagonal prismatic magnet.

31. The magnet array according to claim 29, wherein the at least one composite magnet includes two magnets each having a different magnetization vector.

32. The magnet array according to claim 29, wherein the at least one composite magnet includes more than two magnets each having a different magnetization vector.

33. The magnet array according to claim 31 or 32, wherein the magnetization vector is selected from the group consisting of diametrical plane magnetization, diametrical edge magnetization, oblique edge magnetization, oblique vertex magnetization, and axial magnetization.

34. The magnet array according to claim 31 or 32, wherein the two or more magnets are dimensioned and shaped together so as to be disposed within an individual cell of the magnet array.

35. The magnet array according to claim 29, wherein the polyhedral magnets are densely packed within the magnet rack.

36. A magnetic resonance apparatus including a magnet array including a first plurality of polyhedral magnets arranged in a Halbach cylindrical structure and a second plurality of polyhedral magnets within a magnet rack, The centers of the individual magnets of the first plurality of polyhedral magnets are arranged to coincide with points within a lattice within a substantially plane within the magnet rack of the magnet array, The lattice is a set of points 【Number 9】 Each of which is displaced from the origin by a sum of integer multiples of vectors selected from a basis function system, The first plurality of polyhedral magnets at least partially surround a test volume, The second plurality of polyhedral magnets are arranged in a non-Halbach structure, The magnet rack includes the first plurality of polyhedral magnets and the second plurality of polyhedral magnets, The magnetic resonance apparatus, wherein the magnet array includes the magnet rack disposed within a rack stack.

37. The magnetic resonance apparatus according to claim 36, wherein the polyhedral magnets are densely packed within the magnet rack.

38. A method for assembling a magnet array, comprising: Providing a first plurality of polyhedral magnets, A step of arranging the first plurality of polyhedral magnets in a Halbach cylinder structure in a magnet rack, wherein the centers of the individual magnets of the first plurality of polyhedral magnets are arranged to coincide with points in a lattice within a substantially plane in the magnet rack, wherein the lattice is a set of points each displaced from the origin by a sum of integer multiples of vectors selected from a basis function system 【Number 10】 and a step of at least partially surrounding a test volume with the first plurality of polyhedral magnets, a step of providing a second plurality of polyhedral magnets, a step of arranging the second plurality of polyhedral magnets in a non-Halbach structure in the magnet rack, a step of assembling a magnet array by arranging the magnet rack in a rack stack, wherein the magnet rack includes the first plurality of polyhedral magnets and the second plurality of polyhedral magnets, and the step of including the magnet rack arranged in the rack stack in the magnet array. A method.

39. A method for assembling a magnet array according to claim 38, wherein the polyhedral magnets are densely packed in the magnet rack.

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