WO2023049989A1

WO2023049989A1 - Magnet configurations

Info

Publication number: WO2023049989A1
Application number: PCT/CA2022/000052
Authority: WO
Inventors: Neal GALLAGHER; Garett Leskowitz
Original assignee: Nanalysis Corp.
Priority date: 2021-09-28
Filing date: 2022-09-28
Publication date: 2023-04-06

Abstract

Disclosed is a magnet rack comprising a central cavity and a rack framework surrounding the central cavity, the rack framework defining a plurality of lattice sites for receiving a plurality of magnets wherein centers of the magnets occupying said lattice sites are arranged in a hexagonal Bravais lattice configuration; wherein the lattice sites in the rack framework define a plurality of concentric rings around the central cavity; and wherein the shape of the central cavity is defined by the lattice sites of at least the innermost ring and the second innermost ring.

Description

MAGNET CONFIGURATIONS

BACKGROUND

(a) Field

[0001] The subject matter disclosed generally relates to magnet configurations. More particularly, it relates to modified Halbach magnet configurations.

(b) Related Prior Art

[0002] In a nuclear magnetic resonance (NMR) experiment, a sample for analysis is placed under the influence of a biasing static magnetic field, which partially aligns the sample’s nuclear-spin magnetic moments. The moments precess in the static field at a frequency, called the Larmor frequency, which is proportional to the field strength. The magnetic moments of the sample can be manipulated by applying a transverse radio frequency (RF) magnetic field at the Larmor frequency. By observing the reaction of the sample to the RF field, insight into the chemical composition of the sample can be gained. The power of NMR as an analytical method may be largely a function of how well the characteristics of the applied magnetic fields can be controlled.

[0003] The practice of shimming magnetic fields (rendering the fields more uniform) has existed since the earliest days of NMR and originally used thin pieces of metal physically placed behind source magnets to adjust the positions of those magnets to refine the magnetic field. More modern shimming techniques use electro-magnetic coils. Conventional high-field magnetic resonance spectrometers commonly use shimming coils disposed on substantially cylindrical coil forms. In contrast, the use of shimming (shim) coils in compact NMR devices has proved difficult primarily due to space restrictions that may not accommodate traditional shim coil systems, which can have many layers. The space available inside a main magnet in many such devices may be too small to accommodate a typical set of shimming coils whose individual elements are each designed predominantly to address one and only one geometrical aspect or geometrical component of the residual inhomogeneity of the main magnetic field.

[0004] FIGS. 1A, 1B, and 1C compare the main biasing field and sample tube configurations of typical high-field spectrometer designs with a design for compact magnet systems that is based on a cylindrical Halbach array. The arrows labelled B indicate the main magnetic field direction. No shimming measures are shown in the figures. FIG. 1A schematically shows the superconducting field coils of the high-field magnet, an inserted cylindrical sample tube, and the field, B, produced by the coils. The magnetic field within the sample volume is aligned along the common symmetry axis of the coils and the tube.

[0005] FIGS. 1 B and 1C show the same sample tube inserted into a cylindrical Halbach magnet array, which produces a field, B, perpendicular to the symmetry axis of the tube. This particular Halbach array is composed of eight magnets in a circular (as shown in FIG. 1B) arrangement placed around the tube, with the magnetization vectors of the magnets (shown as arrows) perpendicular to the tube's symmetry axis. The magnetization vector is a quantitative and directional representation of the polarization of magnetic dipoles in a material. The field inside the Halbach array is quite uniform for some applications but can be too inhomogeneous for some high-resolution NMR experiments.

[0006] In order to substantially reduce the inhomogeneity of a magnetic field, it may be helpful to have independent control over different geometrical aspects of the field inhomogeneity. In many magnetic resonance applications, the main magnetic field is strongly polarized along a specified direction. Within this application, as is common practice in the art, this direction is understood to be the z-axis in a Cartesian reference frame in which the origin is at some fixed point, for example near the center of a sample under study. The Larmor frequency of magnetic spins located at a point in space is determined by the magnitude of the field at that point, which in reasonably homogeneous fields is very well approximated by the z-component of the field, B_z. One can expand B_z as a scaled sum of functions,

B_z (x, y, z) = B₀ + Σ_K c_kƒ_k (x, y, z) , where k is a variable (or a number of variables) used to index the various functions, f_k, in the set, and where x, y, and z are Cartesian or other spatial coordinates defining positions within a volume enclosing at least part of the sample. B₀ is the large and spatially uniform part of the field, and the coefficients, c_k, quantify different components of the field inhomogeneity. Such sets of functions, for example x, z, xy, (x² — y²) are said to be orthogonal (with respect to a specified scalar product of functions) if the scalar product between two functions that are not the same is zero. A common scalar product between two functions is the integral,

where V denotes a volume relevant to the functions over which the integral is calculated, where the star denotes complex conjugation, and where W denotes a weighting function defined on the volume, which quantifies how important the volume element at (x, y, z) is in its contribution to the integral.

[0007] Well-controlled magnetic fields are 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 in a region of space that contains a sample under study, and it is desirable that this field be as spatially uniform as possible in order to observe important but subtle variations in the magnetic response of the sample. It is also desirable in many NMR applications to have a static magnetic field that is as strong as is practical.

[0008] At least three classes of magnets have been used to provide strong, static magnetic fields in NMR devices: superconducting electromagnets, resistive electromagnets, and permanent magnets. Permanent magnets or arrays (also called assemblies or configurations) thereof can be advantageous in applications where low cost, low maintenance and/or portability are desirable. A particularly useful design for compact applications is a permanent magnet assembly based on Halbach cylinders, which comprise component magnets oriented and arranged around a central bore (sometimes referred to as a central volume, central space, central channel or central cavity) in the magnet array.

[0009] In practice, permanent magnets are often accompanied by pole pieces, which are pieces of magnetically permeable material placed in the vicinity of magnets in order to contribute to or shape a magnetic field. In some applications, it is desirable that materials used for pole pieces be magnetically “soft," that is, that they have a relatively low coercivity. It is also desirable in some applications that pole piece materials be strongly magnetized when placed in a magnetic field, that is, that they have a high saturation magnetization. In the present disclosure, we will refer to such materials as “magnetically permeable,” a designation that is standard and well understood in the art.

[0010] One design for producing a substantially strong magnetic field in a small volume is the Halbach cylinder, wherein magnetic dipoles within high- coercivity permanent magnet materials are arranged around a central cavity. FIG. 2 shows a cross-sectional view of an idealization of a Halbach cylinder 10, along with a coordinate system 12 that is used to compute and select the orientations of magnetic dipoles, shown as arrows 14, within a region surrounding a central volume 16. In the idealized Halbach cylinder, magnetization direction m is positiondependent according to the equation,

in cylindrical polar coordinates p, cp, x, with integer parameter k = 1 for the most prevalent case, which produces a substantially uniform field in the central volume 16. Other choices of k provide different, non-uniform field configurations. In practical implementations, discrete component magnets are used as an approximation to the continuously varying magnetization suggested by FIG. 2.

[0011] FIGS. 3A, 3B, 3C and 3D show example prior art implementations of Halbach-cylinder-based magnet configurations. FIG. 3A (adapted 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 configuration of magnets designated 20 surrounding space 24, that makes efficient use of space and employs many oblique shapes 21 , 22, 23 in its design.

[0012] FIG. 3B (adapted 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 that uses permanent magnets of the same cubic shape 31 to enclose space 32. However, this implementation suffers from low packing density.

[0013] When the space surrounding a central volume is broken up into regions, the individual component magnets placed therein may exhibit oblique shapes, such as those shown in FIG. 3A, that are difficult or expensive to fabricate with high tolerance. The magnetizations required within the component magnets may also be difficult to control with precision sufficient to ensure the quality of the magnetic field within the central volume. If, instead, simpler component magnets such as cubes are used, as in FIG. 3B, these can be fabricated and magnetized with high precision straightforwardly, but the geometrical constraints for some designs can result in a low packing density, with an attendant reduction in the field strength that can be produced.

[0014] FIG, 3C is a cross section of an embodiment of a Halbach cylinder 40 comprising an array of closely packed hexagonal prisms 41 surrounding central space 42, disclosed in US patent no. 8,712,706 to Leskowitz, et al., incorporated herein by reference in its entirety. FIG. 3D (also disclosed in US patent no. 8,712,706), shows the general arrangement 50 of individual mam magnets 52 in a magnet array around a central cavity 53 in which pole pieces 54 and a sample 56 are positioned. FIG. 3D also illustrates the positioning of shim panels 58 on the pole pieces 54. Arrows 59 show the predominant magnetization directions of each main magnet 52 in the arrangement.

[0015] In a Halbach cylinder model, the ideal is an infinitely long cylinder. In practice, the cylinder is of finite length, which can lead to various technical problems and undesirable features in the primary magnetic field of the array, and designs attempting to overcome these disadvantages can be complex. An alternative approach for producing homogeneous fields uses a Halbach sphere, practical embodiments of which have been suggested by H. Leupold in US patent no. 4,837,542.

[0016] FIG. 4A, adapted from US patent no. 9,952,294 to Leskowitz, incorporated herein by reference in its entirety, shows a sphere 60 enclosing a central cavity 62 and having local magnetic dipole orientations 64. Once a desired magnetic field axis, v, is selected, the required magnetization directions for the component magnets in the assembly can be calculated by establishing a spherical polar coordinate system 66 with colatitude angle 0=0 along the magnetic field direction v, then calculating the magnetization direction m for the given magnet's center coordinates according to formulas disclosed in US patent no. 9,952,294 to Leskowitz.

[0017] In order to best approximate a uniform field in the idealized case, magnetization direction m within the spherical shell surrounding the central cavity is position-dependent according to the equation,

in spherical polar coordinates r, θ, Φ, again with parameter k=1 for the uniform-field case. [0018] It will be observed that magnetization in the spherical case differs from the magnetization in the cylindrical case. In the Halbach sphere model, the magnetization of the dipole at a position

lies in the meridional plane spanned by

and

, but in the Halbach cylinder model, the magnetization lies in a plane spanned by

the unit vector directed away from the cylindrical symmetry axis, and the azimuthal unit vector. In the idealized

Halbach cylinder case, the magnetization direction has no

component (along the cylindrical symmetry axis) and is independent of the x coordinate of the dipole's position. A variety of numerical representations of such position-dependent magnetizations are possible and will be readily identified and understood.

[0019] Spherical assemblies can be composed of combinations of magnets having complex shapes, as illustrated in FIG. 4B (adapted from US patent no. 4,837,542 to Leopold). In FIG. 4B it will be seen that the sphere 70 comprises multiple component primary magnets 72 having chosen dipole orientations 74 and surrounding central cavity 76. In order to achieve the desired configuration and field, a large number of different primary magnets having different shapes and magnetic orientations is required. Again, these can be challenging or impractical to fabricate with high tolerance.

[0020] Magnet arrays and methods for generating magnetic fields are disclosed in US patent no. 9,952,294 to Leskowitz, including a magnet array comprising a plurality of polyhedral magnets arranged in a lattice configuration and at least partly enclosing a testing volume, the magnet array having an associated magnetic field with a designated field direction wherein the magnetization

direction

of an individual polyhedral magnet located at a displacement vector

from an origin point in the testing volume is determined by the formula:

[0021] As illustrated in FIG. 4G (adapted from US patent no. 9,954,294 to Leskowitz), magnet array 100 is based on a simple cubic lattice and polyhedral magnets 101 are truncated cubes. Further, some of the polyhedral magnets 101 comprised in the lattice configuration making up the magnet array 100 are larger first magnets 103 and others are smaller second magnets 106. The smaller second magnets 106 form composite magnets 104 at particular sites in the array. As will be seen in FIG. 4C, the use of such smaller second magnets 106 is exploited to provide a sample channel 107, in this case oriented along a body diagonal of the array.

[0022] In practice, a Halbach sphere configuration can produce a magnetic field that is larger than that produced by a Halbach cylinder configuration. However, Halbach sphere configurations can suffer from limited access to the central region of the magnet compared to Halbach cylinder configurations.

[0023] In applications such as magnetic resonance applications, it may be advantageous to use the largest magnetic fields that are practical. One way to increase the field present inside a Halbach cylinder magnet configuration is to insert pole pieces into the bore of the Halbach cylinder magnet configuration. US patent no. 9,341 ,690 to Leskowitz and McFeetors discloses shaped pole pieces in a cylindrical Halbach magnet configuration.

[0024] Another way to increase the field present inside a Halbach cylinder magnet configuration is to increase the number of component magnets that are used to constitute the magnet configuration. Such component magnets may be configured in concentric ring structures. For example, FIG. 3D exhibits a single hexagonal ring of six magnets, and FIG. 3C exhibits a hexagonal ring of six magnets surrounded by a hexagonal ring of twelve magnets. It will be readily appreciated that each component magnet is subject to magnetic interaction with the total magnetic field generated by all the other magnets in an assembly. In particular, a component magnet may be located at a site where the total magnetic field generated by the other magnets is substantially aligned with the magnetization of said component magnet. In that case, said component magnet would be under relatively low coercive stress and would therefore be subject to a weak demagnetizing force. Conversely, a component magnet may be located at a site where the total magnetic field generated by the other magnets is substantially aligned away from or opposing the magnetization of said component magnet. In that case, said component magnet would be under relatively high coercive stress and would therefore be subject to a strong demagnetizing force. Mitigating or controlling demagnetizing forces is a critical issue in determining the stability and performance of magnet arrays in applications. Moreover, elevated coercivity can be associated with increased cost.

[0025] Another important consideration in applications, especially in high- resolution magnetic resonance, is the temporal stability of the magnetic field, that is, it is desirable to limit the fluctuations of magnetic field strength over time. These temporal fluctuations are strongly influenced when changes of temperature (thermal changes) are present. It is well known that the magnetization of permanent magnet materials is subject to variation with temperature. Indeed, a common specification of commercial grades of permanent magnet materials, including rare-earth permanent magnet materials, is their temperature coefficient (the fractional variation in magnetization strength), which can be on the order of 0.1 % per degree Celsius. Such variation in strength can proportionately affect the magnetic field produced by the permanent magnets. Those applications which rely on a temporally stable magnetic field can be deleteriously affected by magnets that are strongly thermally coupled to variations in temperature of a sample or other components in a magnet array’s central cavity.

[0026] There is therefore a need for magnet array designs which balance the need for high field with the desired increased internal space that can facilitate improved thermal isolation between a magnet array and an enclosed sample. Further, there remains a need for a solution that allows for increased magnetic fields while maintaining the low-cost, convenience, and manufacturability of cylindrical, spherical and modified Halbach magnet configurations. SUMMARY

[0027] According to one aspect of the invention, there is provided a magnet rack comprising a central cavity and a rack framework surrounding the central cavity, the rack framework defining a plurality of lattice sites for receiving a plurality of magnets wherein centers of the magnets occupying said lattice sites are arranged in a hexagonal Bravais lattice configuration; wherein the lattice sites in the rack framework define a plurality of concentric rings around the central cavity; and wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring.

[0028] In an embodiment, a location of the innermost ring defines the shape of a single lattice site.

[0029] In another embodiment, the central cavity comprises a sample volume, the central cavity also being adapted to receive at least one of: one or more pole pieces and one or more hexagonal prismatic magnets.

[0030] In another embodiment, the central cavity comprises a sample volume, the central cavity also being adapted to receive at least one of: one or more pole pieces and one or more component magnets.

[0031] In a further embodiment, the hexagonal prismatic magnets in the central cavity are diametrically edge-magnetized and do not conform to a Halbach cylinder configuration.

[0032] In one embodiment, the sample volume is located in the innermost ring, and the pole pieces and/or hexagonal prismatic magnets are provided in lattice sites of the second innermost ring.

[0033] In another embodiment, faces of the pole pieces that are adjacent to the sample volume define a cutout/cutaway region/gap to allow for shaping a magnetic field generated by the magnet rack and/or dissipating a heat introduced by a sample in the sample volume. [0034] In another embodiment, the rack framework comprises a first subset of hexagonal prismatic magnets, each occupying a lattice site in said rack framework, wherein the magnetization vectors of said magnets are arranged in a cylindrical Halbach configuration having a designated predominant field direction.

[0035] In another embodiment, the rack framework comprises a second subset of hexagonal prismatic magnets, each occupying a lattice site in said rack framework, wherein the magnetization vectors of said magnets in the second subset are arranged in a non-Halbach configuration, said magnetization vectors being oriented to reduce coercive stress on at least one magnet in the first or second subset of hexagonal prismatic magnets.

[0036] According to another aspect of the invention, there is provided a magnet array comprising a plurality of magnet racks, each comprising a central cavity and a rack framework surrounding the central cavity, the rack framework defining a plurality of lattice sites for receiving a plurality of magnets wherein centers of the magnets occupying said lattice sites are arranged in a hexagonal Bravais lattice configuration; wherein the lattice sites in the rack framework define a plurality of concentric rings around the central cavity; and wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring.

[0037] According to another aspect of the invention, there is provided a magnetic resonance device comprising the magnet rack as described above.

[0038] According to another aspect of the invention, there is provided a method of shimming a magnetic field generated by a modified Halbach magnet array, the method comprising: a) providing one or more pole pieces; and b) arranging the one or more pole pieces within a central cavity defined by a plurality of polyhedral magnets in the magnet array for shimming the magnetic field generated by the modified Halbach magnet array, wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring.

[0039] In one embodiment, the faces of the pole pieces that are adjacent to the central cavity define a cutout/cutaway region/gap to allow for shaping a magnetic field generated by the magnet rack and/or dissipating a heat introduced by a sample in the central cavity.

[0040] In another embodiment, the pole pieces have a truncated shape that provides space in the central cavity for improved magnetic field homogeneity and temporal stability.

[0041] According to another aspect of the invention, there is provided a A method of assembling a magnet array, comprising: a) providing a plurality of polyhedral magnets; b) providing one or more steel pole pieces; c) providing a cell framework in a magnet rack of the magnet array, the cell framework for receiving the polyhedral magnets and the steel pole pieces; d) arranging the plurality of polyhedral magnets in the cell framework in the magnet rack, the centers of individual ones of the plurality of polyhedral magnets being arranged substantially in a plane in the magnet rack, the plurality of the polyhedral magnets defining a central cavity in the magnet rack, wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring; e) arranging the one or more steel pole pieces in the cell framework in the magnet rack; and f) arranging the magnet rack in a rack stack to assemble the magnet array.

[0042] In one embodiment, the faces of the pole pieces that are adjacent to the central cavity define a cutout/cutaway region/gap to allow for shaping a magnetic field generated by the magnet rack and/or dissipating a heat introduced by a sample in the central cavity.

[0043] In another embodiment, the pole pieces have a truncated shape that provides space in the central cavity for improved magnetic field homogeneity and temporal stability.

[0044] Features and advantages of the subject matter hereof will become more apparent in light of the following detailed description of selected embodiments, as illustrated in the accompanying figures. As will be realized, the subject matter disclosed and claimed is capable of modifications in various respects, all without departing from the scope of the claims. Accordingly, the drawings and the 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

[0045] Further features and advantages of the present disclosure will become apparent from the following detailed description, taken in combination with the appended drawings, in which:

[0046] FIG. 1A is a schematic side view showing a sample tube in a prior art arrangement of superconducting coils for producing a strong magnetic field aligned along a sample tube's symmetry axis;

[0047] FIG. 1 B is a schematic top view showing a sample tube in a prior art cylindrical Halbach magnet array viewed along the symmetry axis of the tube;

[0048] FIG. 1C is a schematic perspective view showing a sample tube in a prior art cylindrical Halbach magnet array viewed along an axis perpendicular to the symmetry axis of the tube;

[0049] FIG. 2 is a cross-sectional view of a prior art idealized Halbach cylinder; [0050] FIGS. 3A-3C are cross-sectional views of implementations of prior art Halbach-cylinder-based magnet assemblies;

[0051] FIG. 3D shows a prior art arrangement of pole pieces and shim panels inside a central cavity within a Halbach cylinder magnet array;

[0052] FIG. 4A depicts a prior art idealized magnetization scheme for a Halbach sphere;

[0053] FIG. 4B shows a practical prior art embodiment of a Halbach sphere;

[0054] FIG. 4C is a corner view of a prior art embodiment of a magnet assembly based on a lattice configuration of polyhedral magnets;

[0055] FIG. 5 shows a top view of an embodiment of a magnet array;

[0056] FIG. 6 shows a perspective view of an embodiment of a magnet rack stack comprising five magnet racks;

[0057] FIG. 7 shows different types of hexagonal prismatic magnets having different magnetization vectors;

[0058] FIG. 8 shows a block diagram of a magnetic resonance device including a magnet array, in accordance with an embodiment of the disclosure;

[0059] FIG. 9 shows a top view of another embodiment of a magnet array;

[0060] Fig. 10A shows an exploded view of an embodiment of multiple magnet racks in a rack stack;

[0061] FIG. 10B shows the top view of the embodiment of FIG. 5 with radial ring coordinate labels added;

[0062] FIG. 10C shows the top view of the embodiment of FIG. 5 and FIG. 10B with azimuthal coordinate labels added;

[0063] FIG.11 A shows a top view of yet a further embodiment of a magnet array; [0064] FIG. 11 B shows a top view of part of the embodiment of FIG. 11A; and

[0065] FIG. 11C shows a side view of part of magnet racks +1 , 0 and -1 of the embodiment of FIG. 11 A and 11 B.

[0066] It will be noted that throughout the appended drawings, like features are identified by like reference numerals.

DETAILED DESCRIPTION

[0067] In the present disclosure, the term Halbach cylinder configuration means a configuration of individual magnets (often called component magnets) disposed around a central volume containing an axis x, in which the magnetization of each magnet is substantially oriented according to the equation

where ρ, φ, x, are the cylindrical polar coordinates of the center of said individual component magnet relative to an origin location and a preferred axis with Φ = 0, and where k is an integer parameter. A magnetization is “substantially oriented” along a direction if it is exactly oriented along that direction or if it is chosen from a finite set of possibilities (such as from the set of directions defined by vectors connecting the vertices or the midpoints of edges or faces of a fixed polyhedron) as the closest approximation thereto. The most prevalent case is k = 1 , which produces a substantially uniform magnetic field, directed along the preferred Φ = 0 axis, within a portion of the central volume of the configuration. For instance, FIG. 2 shows magnetization vectors 14 selected according to the k = 1 case within a region 11 surrounding a central volume 16.

[0068] In the present disclosure, the term modified Halbach magnet configuration (sometimes referred to as a magnet assembly or magnet array) means a configuration (or arrangement) of individual component magnets that comprises two or more subsets of magnets, at least one subset being configured in a Halbach cylinder magnet configuration and at least one other subset having another (non-Halbach) magnet configuration as discussed in this disclosure. In embodiments of the present disclosure, such modified Halbach magnet configurations provide a design context within which practical implementations of Halbach cylinders can be improved to provide magnetic fields having improved characteristics in applications. A subset of magnets may also be referred to as a plurality of magnets or a group of magnets. Examples of modified Halbach magnet configurations are described in PCT Application PCT/CA2020/051158 to Gallagher & Leskowitz, incorporated herein by reference in its entirety.

[0069] In the present disclosure, the term magnet rack means a collection of individual (component) magnets arranged in a holding structure so that their centers lie in a plane. By way of example, FIG. 5 depicts a portion of a magnet array (alternatively known as a magnet assembly or magnet configuration) which is generally designated 500. FIG. 5 shows a top view of one embodiment of a magnet rack 505 and individual component magnets 510. For clarity, the magnet array to which portion 500 belongs may include magnets in additional magnet racks not shown in FIG. 5.

[0070] In FIG. 5, the individual component magnets 510 are hexagonal prisms, each of which has a six-fold symmetry axis that is aligned out of the plane of the page. The individual hexagonal magnets 510 form a hexagonal-cylindrical arrangement surrounding a central cavity 520. In embodiments, the individual component magnets may be placed so their centers coincide with points in a lattice. In the present disclosure, the term lattice refers to a set of points, each of which is displaced from an origin by a sum of integer multiples of vectors chosen from a basis set

[0071] In the present disclosure, magnet rack stack means a collection of magnet racks that are stacked along an axis that is perpendicular to the said plane(s) containing the centers of the individual component magnets of the magnet racks. By way of example, FIG. 6 depicts a magnet array which is generally designated 600. FIG. 6 shows a perspective view of an embodiment of a rack stack 635, including five cylindrical magnet racks 605. An arrangement of component magnets 610 is visible in the top rack of the magnet rack stack surrounding a central cavity 620. In embodiments, a rack stack may contain 1 , 2, 3, 4, 5, 6, 7, 8, 9, 10, or any number of magnet racks.

[0072] In embodiments of the present disclosure, the magnet arrangement in each rack may be the same or different from the other racks and may include the magnet arrangement of FIG. 5 and FIG. 6. As shown in these FIGS., thirty-six hexagonal prismatic magnets may be arranged in inner, middle, and outer rings of six, twelve and eighteen hexagonal prismatic magnets, respectively, and with the inner hexagonal prismatic magnets being closest to the central cavity, which in an NMR spectrometer may include a sample testing volume. Just as different numbers of magnet racks may be included in a magnet rack stack, although thirty- six magnets are illustrated in this example, other numbers, arrangements, and types of magnets and pole pieces may be used in a magnet configuration as described herein.

[0073] In the present disclosure, individual ones of the polyhedral magnets in a magnet configuration (also called an array, assembly, or arrangement) are selected from the group consisting of: a truncated cube; a rhombic dodecahedron; a Platonic solid; an Archimedean solid; a Johnson solid; a prism; a chamfered polyhedron; and a truncated polyhedron. A prism is understood to mean a polyhedron comprising two opposing congruent n-sided polygonal faces with corresponding sides of the polygonal faces joined by n rectangular faces. An example used in this disclosure is a hexagonal prism, wherein n equals 6. Examples of hexagonal prismatic component magnets, with a range of magnetization vectors, are exhibited in FIG. 7. In the present disclosure, magnets A and B are said to be diametrically magnetized, with magnetization vectors perpendicular to the sixfold symmetry axis of the bodies’ overall hexagonal prismatic shape. Magnets C and D are said to be obliquely magnetized, and magnet E is said to be axially magnetized.

[0074] In the present disclosure, a magnet having a magnetization vector lying in the plane (in-plane) defining a magnet rack (for example, in the yz plane shown in FIG. 5) is said to be diametrically magnetized. A magnet having a magnetization vector perpendicular to the plane of the magnet rack is said to be axially magnetized. A magnet having a magnetization vector that does not lie in the plane, but is not perpendicular to the plane, is said to be obliquely magnetized. A magnet that is either axially magnetized or obliquely magnetized is said to possess out-of-plane magnetization.

[0075] FIG. 7 shows examples of magnets that are in the shape of hexagonal prisms. In FIG. 7, magnet A is a diametrically face-magnetized magnet, wherein the magnetization vector (indicated by an arrow) is normal to a rectangular side face of the magnet and perpendicular to the six-fold symmetry axis of the hexagonal face of the magnet. Magnet B is diametrically edge-magnetized, wherein the magnetization vector is perpendicular to the six-fold rotational symmetry axis of the hexagonal face of the magnet and extends from a long edge bounding a rectangular face of the magnet to the opposite edge across the body of the magnet. It will be readily appreciated that this vector is also parallel to certain opposing rectangular faces of the magnet B. FIG. 7 also shows a magnet E, which is axially magnetized, that is, magnetized along a vector that is coincident with the six-fold symmetry axis of the magnet.

[0076] Magnets C and D are examples of obliquely magnetized magnets. More precisely, magnet C is obliquely edge magnetized, wherein the magnetization vector extends from the midpoint of one edge bounding a hexagonal face of the magnet to the midpoint of the opposite edge bounding the opposite hexagonal face of the magnet and across the center of the magnet. It will be appreciated from FIG. 7 that the magnetization vector of magnet C is perpendicular to said edges and that the magnetization vector forms an acute angle with the six- fold symmetry axis of magnet C. Magnet D is obliquely vertex magnetized, having a magnetization vector that extends from one vertex, 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.

[0077] In the present disclosure, a magnetic field gradient is a characteristic of a magnetic field which has a spatial variation in its strength or direction. In many practical applications, and in particular in magnetic resonance applications, a magnet assembly that creates a strong, spatially homogeneous field is desired. In that case, a magnetic field is well approximated by its projection along an

axis, so that the magnetic field is expressed as a scalar value B_z, the component of the field along that axis.

[0078] In the present disclosure, a quadratic field gradient is a magnetic field gradient in which a component of the field varies in proportion to a second power of some spatial coordinate. For example, a magnetic field having a z component that is substantially of the form

possesses a quadratic field gradient due to its spatial dependence on the second power of the coordinates x and y. Note that, in the present disclosure, "bilinear” gradients such as those exhibited by a field of the form

are formally quadratic according to this definition since the function

when expressed in the linearly related coordinates

[0079] In the present disclosure the term magnetic resonance or MR means resonant reorientation of magnetic moments of a sample in a magnetic field or fields, and includes nuclear magnetic resonance (NMR), electron spin resonance (ESR), magnetic resonance imaging (MRI) and ferromagnetic resonance (FMR). As the present disclosure pertains to methods and apparatuses for rendering general static magnetic fields more uniform, in embodiments the disclosure is also applicable in ion cyclotron resonance (ICR) or in trapped-ion or particle-beam technology generally. For simplicity of explanation, the term magnetic resonance or MR as used herein will be understood to include all these alternative applications. In particular applications and embodiments, the apparatuses and methods disclosed are applied to NMR and in embodiments they are applied to NMR spectrometers or to NMR imagers. Materials that display magnetic resonance when exposed to a magnetic field are referred to as magnetically resonant or MR active nuclides or materials.

[0080] In the present disclosure the terms primary field, main field, primary magnetic field and main magnetic field mean the magnetic field generated by a magnet array. In one series of embodiments a field strength in the range of 1.0 to 3.0 Tesla is achieved. However, in alternative embodiments, the field strength may be below 1.0 Tesla or above 3.0 Tesla. The field strength will depend on the number of magnet racks, the strength of the individual component magnets, the presence or absence and types of pole pieces, construction materials used, and other variables.

[0081] In embodiments of this disclosure, the magnet array may be comprised in a magnetic resonance apparatus (device). For example, FIG. 8 is an exemplary block diagram of a magnetic resonance device 850 in accordance with an embodiment of the disclosure. The device 850 comprises a computer 851 operably connected to a sample rotation control module 852 for controlling rotation of an optional sample rotator 854 used for rotating a sample 856 in a sample tube 857 within a channel 858 provided in a magnet array 859. The computer 851 may also be operably connected to a pulsed magnetic field control and signal detection module 860 used for controlling a detection coil 862 and receiving a signal therefrom. The device 850 may also include a field homogeneity control module 864 for controlling the magnetic field in a centrally located testing volume 865. A temperature control module 866 may also be provided for controlling the temperature inside the channel 858.

[0082] Returning to the magnet rack 505 of FIG. 5, the magnets 510 are illustrated as magnetized according to a Halbach cylinder configuration. The magnet rack 505 further comprises a cell framework 515 and a framework housing 525. The cell framework 515 is to be considered a nominal framework in this disclosure against which other frameworks can be compared. The cell framework may be made of a suitable weakly magnetic or nonmagnetic material, for example a metal such as aluminum or titanium, a high-performance plastic such as Delrin or ABS, or a ceramic or glassy material, or any combination thereof.

[0083] An example of a function of the cell framework is to guide the placement of individual component magnets in the magnet rack during assembly of the rack. Another example of a function of the framework is to provide separation between some or all magnets in the rack. In other words, the cell framework defines a number of cells, each cell for receiving one or more individual component magnets into the magnet rack.

[0084] In embodiments, the geometric center of each cell in a framework is a point that substantially coincides with a point in a lattice. In the example of FIG. 5 the lattice is a two-dimensional hexagonal lattice. It will be understood that when racks are stacked as shown in FIG. 6, the resulting lattice is a three-dimensional hexagonal Bravais lattice.

[0085] As illustrated in FIG. 5, the cell framework 515 defines multiple cells, the innermost six of which, surrounding the central cavity 520, are labeled A for convenience. Additional magnets are positioned farther away from the central cavity. Although not illustrated in FIG. 5, the size, composition, and magnetization direction of the individual hexagonal magnets may vary, e.g., some magnets in the array may be larger than other magnets in the array. In this example, the cell framework 515 can accept up to thirty-six magnets positioned around the central cavity 520. However, in other embodiments, variations in magnet numbers are possible and one, two, or more than two types and/or sizes of magnets may be incorporated into the Halbach-based array.

[0086] In use, a sample, such as a chemical sample, will generally be positioned in a defined sample volume, sample space, or testing volume at or close to the center of the central cavity 520. The cell framework 515 further includes framework sections 517 which are connected to one another through framework vertices 521. (Not all framework sections and vertices are explicitly labeled in the figure.) A Cartesian coordinate axis system is shown in both FIG. 5 and FIG. 9 (described below), with the x-axis being directed out of the plane of the page.

[0087] One way to increase the strength of a magnetic field in a magnet array is to use pole pieces, which can acquire a magnetic polarization when placed in a magnetic field. This polarization can increase the strength of the magnetic field in the region of space near the pole piece to a value that is larger than it would be in the absence of the pole piece. Sometimes in applications it is desirable to use pole pieces in pairs rather than individually. As described above, FIG. 3D shows a known example configuration of pole pieces 54 within a hexagonal cavity defined by a set of six magnets 52, each of which is in the shape of a hexagonal prism.

[0088] In this disclosure, a preferred way to increase the strength of the magnetic field in a magnet array is to use pole pieces in other positions in the magnet array that are close to the sample volume and chosen to enhance the strength of the field. We emphasize here that the sample volume is generally inside the central cavity, that is, the central cavity is a larger region than the sample volume and may contain other features, devices, or materials in addition to the sample volume. A sample volume is a region of space within the central cavity that can receive a sample (e.g., such as a chemical sample) under study. A goal of this disclosure is to provide apparatuses and methodologies for increasing the magnetic field strength for applications in a manner that permits relaxation of certain constraints limiting the use of magnet arrays based on Halbach cylinders. One of those limiting constraints is a small size of the central cavity. In this disclosure, a judicious choice of the shape and positioning of pole pieces may allow for increasing the size of the central cavity to create more space for thermal (temperature) regulation and shimming technology to improve the temperature stability of the magnet configuration, the homogeneity of the magnetic field, and the overall performance of the magnet array.

[0089] Illustrative of another embodiment of the present disclosure, FIG. 9 depicts a magnet array which is generally designated 900. FIG. 9 shows a top view of a magnet rack 905 and individual component magnets 910. FIG. 9 differs from FIG. 5 in that the central cavity 920 is larger in FIG. 9 than the central cavity 520 shown in FIG. 5. The central cavity 920 in FIG. 9 includes the space where a first ring of six hexagonal prismatic magnets (labeled A) would have been positioned around the smaller central cavity 520 as shown in FIG. 5. The outer rings 922 are still present in the magnet array 900, with the component magnets held in place by cell framework 915 and framework housing 925. To describe the central cavity with reference to the rest of the magnet rack, central cavity 920 is considered to be positioned within a rack framework 980. The rack framework 980 includes the cell framework 915 and any magnets positioned (or receivable) therein.

[0090] The larger cavity 920, like the smaller cavity 520, is convenient for use with a lattice-based implementation of a Halbach cylinder, and, in particular, with use of a repeated unit - the diametrically magnetized hexagonal prism - which can be fabricated in bulk quantities for reduced cost, convenience in assembly, and tight manufacturing tolerance. However, the larger central cavity 920 has advantages over a smaller cavity. These advantages include more space to incorporate improved thermal isolation measures relative to prior art designs, and more space with which to position larger pole piece assemblies. These advantages are purchased at the cost of somewhat lower field produced by a magnet array that is on average further away from an enclosed sample volume; however, this balance between field strength and other performance characteristics can be beneficial in some applications (e.g., compact NMR).

[0091] In the non-limiting embodiment of a rack stack illustrated in FIG. 6, the magnet racks are 1 .5” in height, as are the hexagonal prismatic magnets within the racks (1 .5" along the six-fold symmetry axis of the hexagonal prism). The cells in the cell framework are 1.25” across (from the midpoint of one edge to the midpoint of the opposing edge across a hexagonal face), and the walls making up the framework itself are 0.030” thick. In alternative embodiments, the magnet dimensions and cell framework dimensions may be larger or smaller depending on the application and the desired magnetic field strength.

[0092] FIG. 10A shows a magnet rack stack 1000 of five cylindrical racks in perspective view. The racks are stacked so that their centers align along a central axis 1010. The rack stack comprises a first (top) rack 1030, two intermediate racks 1040 (second and fourth in order from the top), a third (central or center) rack 1060, and a fifth (bottom) rack 1070.

[0093] Such a plurality of stacked racks, with one of said racks designated as the center rack, may be configured to receive magnets such that the center of each magnet is positioned in a hexagonal Bravais lattice configuration around a central cavity that extends longitudinally from the top rack to the bottom rack through the center of each rack. Each of the lattice configuration sites may be specified by three integers: a rack coordinate, a radial ring coordinate, and an azimuthal coordinate.

[0094] Rack coordinates are indicated by the numbers +2, +1 , 0, -1 or -2 in FIG. 10A. In embodiments where additional magnet racks are included such that the total number of racks equals an odd number, the rack coordinates may continue to increase (i.e., +3, +4... for racks at the top of the magnet rack stack) and decrease (i.e., -3, -4... for racks at the bottom of the magnet rack stack). If the total number of magnet racks in a rack stack equals an even number, then the “0” rack coordinate may be excluded. For instance, a magnet rack with four racks would have rack coordinates +3/2 +1/2, -1/2 and -3/2. A magnet rack with six racks would have rack coordinates +5/2, +3/2, +1/2, -1/2, -3/2 and -5/2, and so on.

[0095] A radial ring coordinate may be chosen such that a lattice site designated as the center of the magnet array in a given magnet rack is assigned a radial ring coordinate of zero, said radial ring coordinate further selected such that each hexagonal ring of lattice sites in the magnet rack is assigned a coordinate incremented by one relative to its inner neighbor.

[0096] Radial ring coordinates are indicated by the numbers 0, 1 , 2 or 3 in FIG. 10B, which shows a top view of the central rack 1060 of FIG. 10A. A preferred sample volume will be situated at or near the central location at radial ring coordinate 0 and rack coordinate 0 and may extend for a distance that is small compared to a rack or ring coordinate spacing or equal to or larger than a rack or ring coordinate spacing as needed for an application. If fewer or more rings of magnets are present in a magnet rack, then the rings would be numbered accordingly in the same manner as shown in FIG. 10B.

[0097] Azimuthal coordinates are indicated by the numbers 0, 1 , 2, ... as shown in FIG. 10C. It will be appreciated that, as the numbers of magnets contained in radial rings 1 , 2, 3, ..., n are equal to 6, 12, 18, ..., 6n, an appropriate azimuthal integer coordinate will take on the values from 0 to 6n - 1 in a ring with radial ring coordinate equal to n. For example, in radial ring 1 , azimuthal coordinates run as shown from 0 to 5, and in radial ring 2, azimuthal coordinates run as shown from 0 to 11. A particularly convenient choice for the component magnet labeled with azimuthal coordinate 0, for example magnet 1080, is the component magnet displaced from the central axis along the primary field direction of the Halbach cylinder as a whole, that is along the z axis in FIG. 10C.

[0098] The cell framework of each rack in FIG. 10A has a central cell at radial ring coordinate 0, and for each such cell the azimuthal coordinate is not and need not be defined. The north and south magnetic pole directions coincide with framework cells with azimuthal coordinates 0 and n/2 in radial ring n. For example, as shown in FIG. 10C, the cells labelled “0” and “3” in ring 1 correspond to the “north" and “south” directions of the Halbach magnet as a whole. Resultant from the preceding description of rack and cell nomenclature, each magnet or framework cell is assigned a unique trio of rack, radial-ring, and azimuthal coordinates. For example, in FIG. 10C, magnet 1080 has rack, ring, and azimuthal coordinates (0, 1 , 0), and magnet 1090 has coordinates (0, 1 , 3).

[0099] Returning to FIG. 9, the rack coordinates, radial ring coordinates, and azimuthal coordinates continue to apply; however, the central cavity 920 is understood to encompass not only a central, unoccupied hexagonal prismatic bore within a magnet rack (radial ring coordinate position “0”), but in addition is understood to encompass the space denoted by the ring assigned radial ring coordinate positions “1" in FIG. 10B. Stated in another way, the lattice sites in the rack framework define a plurality of concentric rings around the central cavity, and the shape of the central cavity may be defined by the lattice sites of at least an innermost ring and a second innermost ring. For instance, in FIG. 9, the shape of the central cavity 920 includes the location of an innermost ring defining the shape of a single lattice site (per rack) at radial ring coordinate position “0” and a second innermost ring defining the shape of an outer wall of the central cavity at radial ring coordinate positions “1”.

[00100] By opening up the central cavity from the size shown in FIG. 5 to the larger size shown in FIG. 9, opportunities are created for increasing the magnetic field produced by a magnet array, managing the temperature of the air and contents within the central cavity, and improving the homogeneity of the magnetic field. All of these opportunities lead to improved performance of a magnetic resonance device incorporating the magnet array. In particular, an increase in magnetic field relative to prior art Halbach cylinders can be achieved by inserting a pole piece, such as one shaped (by example and without limitation) as a hexagonal prism, of a suitable soft (permeable) magnetic material at azimuthal positions 0 and 3 in radial ring 1 (see FIG 10C). This is possible because suitable soft magnetic materials, such as some grades of steel, and alloys such as Hiperco, bear saturation magnetizations that are substantially higher than remanent magnetizations of available hard magnetic materials, such as neodymium-iron- bo ron.

[00101] The space provided by a larger central cavity, such as central cavity 920 shown in FIG. 9, can be occupied by materials that support the opportunities for increased field strength, improved homogeneity, and improved thermal isolation. In one embodiment of the present disclosure, a magnet rack may have a configuration of magnets and pole pieces as shown in FIG. 11 A.

[00102] FIG. 11A shows a central rack 1160 in top view. Polyhedral hexagonal prismatic component magnets are positioned within a framework housing 1125 and cell framework 1115, with magnetization vectors indicated by arrows 1122. According to this disclosure, some of the magnets, e.g., 1124, belong to a subset of magnets that are strictly magnetized along a vector prescribed by a Halbach cylinder configuration. Some of the magnets, e.g., 1145, belong to a subset of magnets that are magnetized along a vector that is a closest approximation to a Halbach cylinder configuration given a constraint that the magnetization be chosen from the finite set of possibilities shown for a hexagonal prism in FIG. 7.

[00103] Four magnets 1126, each with a radial ring coordinate of 1 and therefore within the enlarged central cavity 1120 of the present disclosure, are diametrically edge-magnetized and do not conform to a Halbach cylinder configuration. A last subset of magnets, e.g., 1127 exhibit magnetization vectors that do not strictly conform to a Halbach cylinder configuration, but, rather, are reoriented in order to reduce coercive stress on the component magnets at those locations at the cost of a modest decrease in field strength in the sample volume. This type of magnet (1127) and positioning is also discussed in PCT Application PCT/CA2020/051158 to Gallagher & Leskowitz.

[00104] It should be noted that not every magnet (1124, 1145, 1126, 1127, etc.) that is described with respect to a given figure is explicitly indicated in the figure. For example, of four magnets 1126 in FIG. 11 A, just two of four are indicated by the reference number 1126.

[00105] Also illustrated in FIG. 11A are two hashed areas 1175 which represent positions where pole piece material is used in the magnet rack. For example, steel or hiperco alloy may be used in these locations 1175. It should be noted that although there are two pole pieces 1175 where magnetically permeable material is placed in FIG. 11 A, just one is explicitly indicated. As well, FIG. 11 A illustrates that an interior space 1121 within central cavity 1120 has been expanded compared to the central cavity 520 shown in FIG. 5, for example, because each steel pole piece is not a ‘perfect’ hexagonal prism; rather the face of each steel pole piece 1175 that is proximal to the interior space 1121 within the central cavity 1120 is truncated to make more room in the central cavity 1120.

[00106] Further, portions of the cell framework (see FIG. 5) that might otherwise be proximal to the central cavity 1120 have been removed (in other words, are not present in this embodiment in FIG. 11 A). The cell framework 1115 closest to the central cavity 1120 is shown with a thicker line; for the purposes of this figure, the thicker line is for emphasis and does not necessarily represent a physically thicker cell framework.

[00107] Removing, for example, approximately 0.150” of material off the face of each steel pole piece proximal to the interior space 1121 may reduce the effect of some (in particular, quadratic) magnetic field gradients that may otherwise be produced. The exact size and surface shape of the steel pole pieces can be optimized using field measurements or magnetostatic simulations. A further advantage of removing both the magnetic material and the (for example, aluminum) corresponding cell framework is a reduced effective thermal conductivity in that region.

[00108] Steel pole pieces serve the function of pole pieces; in other words, the steel pole pieces are composed of soft (permeable) ferromagnetic material which helps to focus or shape the magnetic field. In magnet configurations as disclosed herein, there are selected sites in which it is feasible to utilize steel or other pole piece materials to produce beneficial effects. Suitable materials are steel, soft iron, hiperco alloys, or pieces made of these materials in bulk and coated with other metals, such as gold or nickel, or with epoxy or other suitable polymer materials to improve resistance to corrosion.

[00109] Steps to assemble a magnet array comprising the pole pieces described above include, but are not limited to: a) providing a plurality of polyhedral magnets (e.g., hexagonal prisms); b) providing one or more truncated pole (e.g., steel) pieces; c) providing a cell framework in a magnet rack of the magnet array, the cell framework for receiving the polyhedral magnets and the truncated pole pieces; d) arranging the plurality of polyhedral magnets in the cell framework in the magnet rack, the centers of individual ones of the plurality of polyhedral magnets being arranged substantially in a plane in the magnet rack, the plurality of the polyhedral magnets defining a central cavity in the magnet rack, wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring; e) arranging the one or more truncated pole pieces in the cell framework in the magnet rack; wherein the one or more truncated pole pieces are located within the central cavity; and f) arranging the magnet rack in a rack stack to assemble the magnet array. [00110] This arrangement of polyhedral component magnets and truncated pole pieces to create a central cavity that is larger relative to using only polyhedral magnets supports improved magnetic field homogeneity and temporal stability and, in turn, improved performance of the magnet rack/array in magnetic resonance applications.

[00111] A method of shimming a magnetic field generated by a modified Halbach magnet array is also disclosed herein. The method includes but is not limited to the following steps: a) providing one or more truncated pole pieces; and b) arranging the one or more truncated pole pieces within a central cavity defined by a plurality of polyhedral magnets in the magnet array, wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring, for shimming the magnetic field generated by the magnet array; and wherein the truncated shape of the pole pieces provides space in the central cavity for improved magnetic field homogeneity and temporal stability.

[00112] In an embodiment, in a magnet rack stack of five magnet racks, steel pole pieces may be used in six positions: two opposing positions having a radial ring coordinate of “1" in each of racks -1 , 0, and +1 (as shown for rack “0” in FIG. 11 A) and having azimuthal coordinates 0 and 3. These positions are compatible with the Halbach magnet configuration as a whole because the predominant magnetic field present within these lattice sites is along the direction which magnetizes the permeable magnetic material favorably for enhancing the magnetic field produced by the other component magnets. Therefore, inserting steel pole pieces in these six positions increases the strength of the magnetic field. A further benefit is that the use of these pole pieces allows for a larger central space. Because the steel pole pieces generally have a low temperature coefficient (typically -20 ppm per degree Celsius) compared to that of NdFeB rare-earth permanent magnets (-1100 ppm per degree Celsius), using the steel pole pieces may allow for improved thermal control when the magnet rack stack is used as part of an analytical device such as an NMR spectrometer for chemical analysis. In other words, such a configuration of magnets and pole pieces may have improved stability when exposed to temperature changes (for example, temperature changes in the central space) and may provide a homogeneous region around a sample positioned in the central space for analysis by magnetic resonance techniques, especially when used in combination with electronic shimming measures inserted into the central cavity.

[00113] In embodiments, the steel pole pieces may not be the same size in racks -1 , 0 and +1. FIG. 11 B shows a portion (just radial rings 0 and 1) of the top view of rack 0 of FIG. 11A. FIG. 11C shows a side view of the interior space 1121 of FIG. 11 A spanning three racks -1 , 0 and +1 in a rack stack. As in FIG. 11A, FIG. 11 B shows four diametrically edge-magnetized component magnets 1126 and two pole pieces 1175. For clarity, the component magnets 1126 are not shown in the side view of FIG. 11 C.

[00114] The portion of the pole pieces 1175 that are in rack 0 are smaller in the dimension shown by an amount roughly equal to about 0.150” (12%) of the total thickness 1.250” of the cell site in the framework in this example, but the reduction in size can range from about 0% to about 50% or more in applications. Also shown in the side view of FIG. 11C is a cutaway region 1184 extending into rack -1 and, by symmetry, rack +1 , and an angled portion 1186 at the end of the cutaway region. In embodiments, the cutaway region 1184 may extend for variable length within the outer racks -1 and +1 and in other embodiments may extend between 0% and 100% of the length of the pole piece element within racks -1 and +1. The angled portion can exhibit variable angles in embodiments.

[00115] As a whole, the cutaway and angled features provide for the magnet array a larger central space within which thermal control measures such as insulation, heating elements, Dewar walls, circulated heat-transfer fluids, or the like can be inserted as needed for more precise temperature control of the component magnets or thermal isolation of the component magnets from a sample that may be at a temperature that is different from that of the component magnets.

[00116] In many magnetic resonance applications, spatial uniformity (homogeneity) and temporal stability are critical to the quality of the data that are gathered using a device such as the magnetic resonance apparatus of FIG. 8. This permits the central cavity to comprise open spaces that can contain measures (such as thermal insulation, thermal sensors and/or heating elements) for more precise thermal control. In combination with the reduced temperature coefficients of typical soft ferromagnetic materials (relative to “hard," high-coercivity materials like rare-earth magnets) this arrangement permits improved temporal stability of the magnetic field, both in normal operation of the magnetic resonance device and, equally important, during shimming and calibration operations.

[00117] Given that effective sample analysis by magnetic resonance requires temperature stability and magnetic field homogeneity, alternatives for creating more space by enlarging the central cavity may involve the use of smaller and triangular-shaped or diamond-shaped component magnets and/or steel pole pieces in the volume of the magnet rack shown as the central cavity 920 in FIG. 9. The magnetic field within the sample volume is particularly responsive to changes within the central cavity, including insertion of magnetic bodies such as pole pieces or permanent magnets, due to the proximity within the central cavity to any samples that are inserted for sample analysis.

[00118] The present application discloses a magnet array comprising a plurality of magnet racks, one of said magnet racks designated as the center rack. The magnet array comprises component magnets, the centers of each of which are located at points in a hexagonal Bravais lattice configuration around a central cavity. Each of the lattice configuration sites may be specified by three integers: a rack coordinate, a radial ring coordinate, and an azimuthal coordinate. The radial ring coordinate may be chosen so that a site designated as the center of the magnet array is assigned a radial ring coordinate of zero, said radial ring coordinate specified such that each hexagonal ring of sites in the magnet rack is assigned a radial ring coordinate incremented by one relative to its inner neighbor.

[00119] The magnet array comprises a plurality of hexagonal prismatic magnets, each occupying a lattice site such that the magnetization vectors of said hexagonal prismatic magnets are arranged in a cylindrical Halbach configuration having a designated predominant magnet field direction.

[00120] Said central cavity comprises lattice sites assigned radial ring coordinates zero and one in at least one magnet rack of a rack stack of the magnet array.

[00121] Within the magnet array, the rack coordinate may be selected so that sites in each rack are assigned a rack coordinate incremented by one relative to the corresponding site in a neighboring rack, and further specified so that a rack coordinate of zero is assigned to magnets in said center rack.

[00122] The magnet array may further comprise a second plurality of magnets located in designated sites within designated magnet racks, the second plurality of magnets each having a magnetization vector such that the second plurality of magnets is arranged in a non-Halbach configuration. The magnetization vectors of said second plurality of magnets may be aligned along a vector normal to said magnet racks or aligned obliquely as depicted in FIG. 7.

[00123] The magnet array may further comprise magnets located substantially at lattice sites in the central cavity with a radial ring coordinate equal to one. Said magnets may have an in-plane magnetization vector (in the plane of a rack) that is perpendicular to said designated field direction. Said magnets within the central cavity defined by radial ring 1 are not limited to hexagonal prismatic or triangular or diamond shapes and may have another shape. [00124] The magnet array may further comprise a plurality of pole pieces, each of said pole pieces substantially occupying a lattice site within the central cavity. Said pole pieces may be composed of a soft magnetic material.

[00125] In a Halbach cylinder magnet configuration, such as the ones depicted in FIGS. 1B, 1 C, 2, 3A, B, C, and D, all magnets are diametrically magnetized. That is, the magnetization vectors have only radial and azimuthal components and therefore lie in the plane of a corresponding magnet rack or other holding structure.

[00126] In the present disclosure, modified Halbach magnet configurations are described which comprise a first subset of magnets in a Halbach cylinder configuration and a second subset of magnets that may include axially or obliquely magnetized magnets or diametrically magnetized magnets that otherwise deviate from the magnetization prescribed by a strict Halbach cylinder configuration. Including the second subset of magnets with the first subset of magnets may advantageously increase the magnetic field strength within a sample testing volume at least partially enclosed by the magnet configuration.

[00127] While preferred embodiments have been described above and illustrated in the accompanying drawings, it will be evident to those skilled in the art that modifications may be made without departing from this disclosure. Such modifications are considered as possible variants comprised in the scope of the disclosure.

Claims

CLAIMS;

1. A magnet rack comprising a central cavity and a rack framework surrounding the central cavity, the rack framework defining a plurality of lattice sites for receiving a plurality of magnets wherein centers of the magnets occupying said lattice sites are arranged in a hexagonal Bravais lattice configuration; wherein the lattice sites in the rack framework define a plurality of concentric rings around the central cavity; and wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring.

2. The magnet rack of claim 1 , wherein a location of the innermost ring defines the shape of a single lattice site.

3. The magnet rack of claim 1 , wherein the central cavity comprises a sample volume, the central cavity also being adapted to receive at least one of: one or more pole pieces and one or more hexagonal prismatic magnets.

4. The magnet rack of claim 1 , wherein the central cavity comprises a sample volume, the central cavity also being adapted to receive at least one of: one or more pole pieces and one or more component magnets.

5. The magnet rack of claim 3, wherein the hexagonal prismatic magnets in the central cavity are diametrically edge-magnetized and do not conform to a Halbach cylinder configuration.

6. The magnet rack of claim 3, wherein the sample volume is located in the innermost ring, and the pole pieces and/or hexagonal prismatic magnets are provided in lattice sites of the second innermost ring.

7. The magnet rack of claim 6, wherein faces of the pole pieces that are adjacent to the sample volume define a cutout/cutaway region/gap to allow for shaping a magnetic field generated by the magnet rack and/or dissipating a heat introduced by a sample in the sample volume.

8. The magnet rack of claim 1 , wherein the rack framework comprises a first subset of hexagonal prismatic magnets, each occupying a lattice site in said rack framework, wherein the magnetization vectors of said magnets are arranged in a cylindrical Halbach configuration having a designated predominant field direction.

9. The magnet rack of claim 8, further comprising a second subset of hexagonal prismatic magnets, each occupying a lattice site in said rack framework, wherein the magnetization vectors of said magnets in the second subset are arranged in a non-Halbach configuration, said magnetization vectors being oriented to reduce coercive stress on at least one magnet in the first or second subset of hexagonal prismatic magnets.

10. A magnet array comprising a plurality of magnet racks according to claim 1 .

11. A magnetic resonance device comprising the magnet rack of claim 1 .

12. A magnetic resonance device comprising the magnet array of claim 10.

13. A method of shimming a magnetic field generated by a modified Halbach magnet array, the method comprising: c) providing one or more pole pieces; and d) arranging the one or more pole pieces within a central cavity defined by a plurality of polyhedral magnets in the magnet array for shimming the magnetic field generated by the modified Halbach magnet array, wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring.

14. The method of claim 13, wherein faces of the pole pieces that are adjacent to the central cavity define a cutout/cutaway region/gap to allow for shaping a magnetic field generated by the magnet rack and/or dissipating a heat introduced by a sample in the central cavity.

15. The method of claim 13, wherein the pole pieces have a truncated shape that provides space in the central cavity for improved magnetic field homogeneity and temporal stability.

16. A method of assembling a magnet array, comprising: a) providing a plurality of polyhedral magnets; b) providing one or more steel pole pieces; c) providing a cell framework in a magnet rack of the magnet array, the cell framework for receiving the polyhedral magnets and the steel pole pieces; d) arranging the plurality of polyhedral magnets in the cell framework in the magnet rack, the centers of individual ones of the plurality of polyhedral magnets being arranged substantially in a plane in the magnet rack, the plurality of the polyhedral magnets defining a central cavity in the magnet rack, wherein the shape of the central cavity is defined by the lattice sites of at least an innermost ring and a second innermost ring; e) arranging the one or more steel pole pieces in the cell framework in the magnet rack; and f) arranging the magnet rack in a rack stack to assemble the magnet array.

17. The method of claim 16, wherein faces of the steel pole pieces that are adjacent to the central cavity define a cutout/cutaway region/gap to allow for shaping a magnetic field generated by the magnet rack and/or dissipating a heat introduced by a sample in the central cavity.

18. The method of claim 16, wherein the pole pieces have a truncated shape that provides space in the central cavity for improved magnetic field homogeneity and temporal stability.